Increase in hepatic and decrease in peripheral insulin clearance characterize abnormal temporal patterns of serum insulin in diabetic subjects

Kaoru Ohashi; Masashi Fujii; Shinsuke Uda; Hiroyuki Kubota; Hisako Komada; Kazuhiko Sakaguchi; Wataru Ogawa; Shinya Kuroda

doi:10.1038/s41540-018-0051-6

Increase in hepatic and decrease in peripheral insulin clearance characterize abnormal temporal patterns of serum insulin in diabetic subjects

Ohashi, Kaoru; Fujii, Masashi; Uda, Shinsuke; Kubota, Hiroyuki; Komada, Hisako; Sakaguchi, Kazuhiko; Ogawa, Wataru; Kuroda, Shinya 2018-03-14 00:00:00 www.nature.com/npjsba ARTICLE OPEN Increase in hepatic and decrease in peripheral insulin clearance characterize abnormal temporal patterns of serum insulin in diabetic subjects 1 1,2 3 3 4 4 4 Kaoru Ohashi , Masashi Fujii , Shinsuke Uda , Hiroyuki Kubota , Hisako Komada , Kazuhiko Sakaguchi , Wataru Ogawa and 1,2,5 Shinya Kuroda Insulin plays a central role in glucose homeostasis, and impairment of insulin action causes glucose intolerance and leads to type 2 diabetes mellitus (T2DM). A decrease in the transient peak and sustained increase of circulating insulin following an infusion of glucose accompany T2DM pathogenesis. However, the mechanism underlying this abnormal temporal pattern of circulating insulin concentration remains unknown. Here we show that changes in opposite direction of hepatic and peripheral insulin clearance characterize this abnormal temporal pattern of circulating insulin concentration observed in T2DM. We developed a mathematical model using a hyperglycemic and hyperinsulinemic-euglycemic clamp in 111 subjects, including healthy normoglycemic and diabetic subjects. The hepatic and peripheral insulin clearance signiﬁcantly increase and decrease, respectively, from healthy to borderline type and T2DM. The increased hepatic insulin clearance reduces the amplitude of circulating insulin concentration, whereas the decreased peripheral insulin clearance changes the temporal patterns of circulating insulin concentration from transient to sustained. These results provide further insight into the pathogenesis of T2DM, and thus may contribute to develop better treatment of this condition. npj Systems Biology and Applications (2018) 4:14 ; doi:10.1038/s41540-018-0051-6 INTRODUCTION circulating insulin concentration transiently increases during the ﬁrst 10 min and then continuously increases during the following Insulin is the major anabolic hormone regulating the glucose 120 min, which are known as the ﬁrst and second phase of insulin homeostasis. The impaired action of insulin is a characteristic of 1 12 secretion, respectively. type 2 diabetes mellitus (T2DM), accompanied by abnormality in 2–4 These temporal patterns of circulating insulin concentration the temporal patterns of circulating insulin concentration. The differ between normal glucose tolerance (NGT), borderline type, circulating insulin concentration changes over the course of 24 h, including a persistently low level during fasting and a surge in and T2DM. Based on an OGTT, a subject with FPG <110 mg/dL response to food ingestion, consisting of basal and additional (6.1 mM) and 2-h PG <140 mg/dL (7.8 mM) is categorized as NGT. 5,6 secretions from the pancreas, respectively. A subject with FPG of 110–125 mg/dL (6.1–6.9 mM) or 2-h PG of Ability of additional insulin secretion is assessed by the oral 140–199 mg/dL (7.8–11.0 mM) is categorized as borderline type, glucose tolerance test (OGTT), in which a subject’s ability to and those with FPG ≥126 mg/dL (7.0 mM) or 2-h PG ≥200 mg/dL tolerate the glucose load (glucose tolerance) is evaluated by (11.1 mM) as T2DM. In general, plasma insulin concentration measuring the circulating glucose concentration after an over- during the late-phase secretion of an OGTT in borderline type night fast (fasting plasma glucose concentration; FPG) and again subjects is higher than in NGT subjects, whereas the concentration 2 h after a 75-g oral glucose load (2-h post-load glucose during the early-phase secretion is similar in NGT and borderline concentration; 2-h PG). During this test, the circulating insulin 9,10 type subjects. Plasma insulin concentration during the ﬁrst- concentration transiently increases and then continuously phase secretion of an IVGTT decreases as glucose intolerance increases or decreases, known as the early and late phases of 9,10 progresses, whereas that during the second-phase secretion is insulin secretion, respectively. The direct contribution of 2–4 relatively maintained. Such changes of the temporal patterns of circulating glucose concentration to circulating insulin concentra- circulating insulin concentration during the progression of glucose tion is assessed by the use of an intravenous glucose tolerance intolerance from NGT to T2DM suggest that these temporal test (IVGTT). This test excludes the effects of intestinal patterns are involved in the maintenance and impairment of absorption of glucose and incretins secretion that trigger insulin glucose homeostasis. Together with the measurement of circulat- secretion, thus permitting quantitative estimates of the ability of circulating glucose to initiate insulin secretion. During this test, the ing glucose concentration, the time course of circulating insulin 1 2 Department of Biological Sciences, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan; Molecular Genetics Research Laboratory, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan; Division of Integrated Omics, Research Center for Transomics Medicine, Medical Institute of Bioregulation, Kyushu University, 3-1-1 Maidashi, Higashi-ku, Fukuoka, Fukuoka 812-8582, Japan; Division of Diabetes and Endocrinology, Department of Internal Medicine, Kobe University Graduate School of Medicine, 7-5-1 Kusunoki-cho, Chuo-ku, Kobe, Hyogo 650-0017, Japan and CREST, Japan Science and Technology Corporation, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan Correspondence: Shinya Kuroda (skuroda@bs.s.u-tokyo.ac.jp) Received: 23 May 2017 Revised: 12 February 2018 Accepted: 12 February 2018 Published in partnership with the Systems Biology Institute Increase in hepatic and decrease in peripheral K Ohashi et al. 26–28 concentration is used to assess the insulin secretion from the concentration by accounting for this mutual dependence. The pancreas and insulin sensitivity. model known as the minimal model is used to estimate insulin However, it is difﬁcult to assess the insulin secretion and sensitivity and insulin secretion abilities for each individual based sensitivity of body tissues directly from the circulating insulin on the time courses of circulating glucose and insulin concentra- concentration because of the negative feedback between tions during IVGTT. Furthermore, from the parameters of the circulating insulin and glucose. A rise in circulating glucose model, Bergman et al. identiﬁed a relationship between the concentration stimulates insulin secretion, and the resultant rise in subject’s glucose intolerance and the product of insulin secretion circulating insulin concentration stimulates glucose uptake, and sensitivity. causing circulating glucose concentration to fall. This feedback We previously developed a mathematical model based on time means there is mutual dependence between glucose and insulin, courses of plasma glucose and serum insulin during consecutive making it difﬁcult to distinguish the effect of insulin secretion and hyperglycemic and hyperinsulinemic-euglycemic clamp condi- sensitivity directly from the circulating insulin concentration. tions, and estimated the parameters of insulin secretion, To directly assess insulin secretion without the effect of the sensitivity, and peripheral insulin clearance for each subject. We feedback from insulin to glucose, DeFronzo et al. developed the found that peripheral insulin clearance signiﬁcantly decreased hyperglycemic clamp technique, in which insulin secretion is from NGT to borderline type to T2DM. However, the hepatic and measured while circulating glucose concentration is at a ﬁxed peripheral insulin clearance could not be distinguished because C- hyperglycemic plateau maintained by exogenous continuous peptide was not incorporated in the model. glucose infusion. The measurements of circulating insulin Hepatic insulin clearance is calculated as the difference concentration during the ﬁrst 10 min and after 10 min are used between pre-hepatic and post-hepatic insulin concentrations to assess the insulin secretion ability and are known as the ﬁrst- assessed by comparing circulating C-peptide and insulin concen- 13,14 and second-phase insulin secretions, respectively. trations, because C-peptide, unlike insulin, is not removed by the Conversely, to directly assess insulin sensitivity without the liver. Since the circulating C-peptide concentration is also effect of the feedback from glucose to insulin, the controlled by its secretion and clearance, a mathematical model hyperinsulinemic-euglycemic clamp was developed. In this for C-peptide kinetics was developed. The models for circulating method, circulating insulin concentration is maintained at a ﬁxed insulin and C-peptide have been used to estimate the secretion hyperinsulinemic plateau and circulating glucose at a ﬁxed normal and kinetics of insulin and C-peptide, as well as hepatic insulin 32–39 plateau by continuous infusion of both insulin and glucose. Tissue clearance. However, peripheral insulin clearance was not insulin sensitivity is deﬁned as the ratio of the glucose infusion assessed in the models, because exogenous insulin infusion, rate to the circulating insulin concentration when they reach which is required for accurate estimation of peripheral insulin 13,14 plateaus. clearance, was not performed. The body controls the circulating insulin concentration by 40 Recently, Polidori et al. reported that both hepatic and balancing insulin secretion and insulin clearance. The major extrahepatic insulin clearance, corresponding to peripheral insulin organs responsible for insulin clearance are the liver, which clearance, can be estimated by modeling analysis using plasma 15,16 removes portal insulin during ﬁrst-pass transit, and insulin- insulin and C-peptide concentrations obtained from the insulin- sensitive tissues such as muscle, which remove insulin from the modiﬁed frequently sampled IVGTT. The parameters of hepatic systemic circulation. The insulin clearance from portal vein in the and peripheral insulin clearance in the model were not highly liver and from peripheral plasma in other organs is called hepatic correlated, suggesting that the two types of insulin clearance are and peripheral insulin clearance, respectively. Although the regulated differently. In addition, hepatic insulin clearance was relationship between changes of insulin clearance and the negatively correlated with insulin secretion, and peripheral insulin progression of glucose intolerance have been reported, the clearance was positively correlated with insulin sensitivity. effects of insulin clearance are controversial. Some studies found However, hepatic and peripheral insulin clearance in T2DM that during the progression of glucose intolerance, insulin 18–21 subjects and the roles of both types of clearance in the changes clearance decreased, whereas hepatic insulin clearance 22 18,23 in temporal pattern of circulating insulin concentration during the increased or decreased. Thus, the hepatic and peripheral progression of glucose intolerance have yet to be examined. insulin clearances were not explicitly distinguished, making it In this study, we developed a mathematical model based on the difﬁcult to interpret the effect of both types. time course of the serum insulin and C-peptide concentrations Hepatic insulin clearance cannot be assessed directly from during consecutive hyperglycemic and hyperinsulinemic- circulating insulin concentration because insulin is extracted from euglycemic clamp conditions, and estimated the hepatic and the liver before secreted insulin is delivered into the systemic peripheral insulin clearance for each subject. The parameters from circulation. However, insulin is secreted at an equimolar ratio with 111 subjects (47 NGT, 17 borderline type, and 47 T2DM) showed a C-peptide, a peptide cleaved from proinsulin to produce insulin, signiﬁcant increase in hepatic insulin clearance and signiﬁcant which is not extracted in the liver. Thus, by measuring circulating decrease in peripheral insulin clearance from NGT to borderline C-peptide concentration simultaneously with circulating insulin type and T2DM, respectively. We also found that hepatic and concentration, the pre-hepatic insulin concentration can be peripheral insulin clearance play distinct roles in the abnormal accurately assessed. The C-peptide index, which is the ratio of temporal patterns of serum insulin concentration from NGT to circulating glucose to C-peptide concentration, is an index of borderline type and T2DM, namely an increase in hepatic insulin insulin secretion with clinical utility. Hepatic insulin clearance is clearance reduces the amplitude of serum insulin concentration, clinically quantiﬁed as the ratio of circulating insulin to C-peptide whereas a decrease in peripheral insulin clearance changes the concentration during the ﬁrst 10 min under the hyperglycemic temporal patterns of serum insulin concentration from transient to clamp condition. sustained. The clinical indices of insulin secretion and clearance are indirect measures because they are obtained from temporal patterns of circulating concentrations, which are simultaneously RESULTS affected by insulin secretion and clearance. Therefore, the clinical Consecutive hyperglycemic and hyperinsulinemic-euglycemic index of insulin secretion implicitly involves the effect of insulin clamp data clearance and vice versa. Mathematical models have been developed for speciﬁcally quantifying insulin secretion, sensitivity, We calculated the averaged time courses of concentrations of and clearance abilities from temporal patterns of circulating plasma glucose, serum insulin, and C-peptide during consecutive npj Systems Biology and Applications (2018) 14 Published in partnership with the Systems Biology Institute 1234567890():,; Increase in hepatic and decrease in peripheral K Ohashi et al. hyperglycemic and hyperinsulinemic-euglycemic clamp condi- Mathematical model for serum insulin and C-peptide tions of NGT (n = 50), borderline type (n = 18), and T2DM (n = 53) concentrations 14,30 (Fig. 1, Supplementary Figure S1). During the hyperglycemic Many mathematical models that reproduce circulating insulin and 29,32–37 clamp, plasma glucose concentrations at the hyperglycemic C-peptide concentrations have been developed. We devel- plateau were similar among the NGT, borderline type, and T2DM oped six mathematical models based on these models, and the best model was selected for reproducing measured serum insulin groups. and C-peptide concentrations during consecutive hyperglycemic Both the ﬁrst (0–15 min) and second phase of insulin secretion 14,30 and hyperinsulinemic-euglycemic clamp (Supplementary Fig- (15–90 min) were clearly observed in the NGT and borderline type ure S2). These models contain serum insulin and C-peptide subjects, whereas the two phases of insulin secretion were concentrations including both insulin and C-peptide secretion and signiﬁcantly reduced in the T2DM subjects. Serum C-peptide their hepatic and peripheral clearance. Plasma glucose perturba- concentration showed a similar increase during the ﬁrst and tion and insulin infusion were used as inputs (Supplementary second phase of insulin secretion in the NGT and borderline type Figure S1). For each of the 121 subjects, parameters of the six subjects, whereas serum C-peptide concentration was signiﬁcantly models were estimated by using measured concentrations of lower in the T2DM subjects during both phases. Although insulin plasma glucose, serum insulin, and C-peptide. The resulting model and C-peptide should be secreted in an equimolar manner, the was selected based on minimizing the Akaike information serum C-peptide concentration was higher than the serum insulin 41 criterion (AIC), taking into account model complexity and concentration because insulin—but not C-peptide—was removed goodness of ﬁt of serum insulin and C-peptide time courses. by the liver and C-peptide clearance in the periphery was slower The model consisting of four variables (Model VI in Supplemen- than insulin clearance. tary Figure S2) was selected as the best model with the minimum During the hyperinsulinemic-euglycemic clamp at 100–220 min, AIC for 76 of 121 subjects (Fig. 2a, Table 1). In this model, the serum insulin concentration was at a steady-state plateau of variables I and CP correspond to serum concentrations of insulin hyperinsulinemia, but serum insulin concentration differed and C-peptide, respectively. The variable X corresponds to stored signiﬁcantly from the NGT to borderline type and T2DM subjects. insulin and C-peptide in β-cells or β-cell masses. Because the The average serum insulin concentration of the NGT subjects was amounts of stored insulin and C-peptide are equal, a single lowest and that of the borderline type subjects was highest. These variable, X, is used for both. The variable Y is the insulin provision rate depending on plasma glucose concentration. The differential differences indicate that the ability to remove infused insulin from equations of the model are as follows: serum is different among the three groups and suggest that the difference lies in the peripheral insulin clearance. The plasma dY αfβðG hÞ YgðG>hÞ ¼ ; Yð0Þ¼ 0 (1) glucose concentration returned to the basal level from hypergly- dt αY ðG hÞ cemia at a different decay rate among the three groups. The average decay rate was lowest in the T2DM subjects and highest Y m X ðÞ G>h dX ¼ Y v ¼ ; Xð0Þ¼ X (2) in the NGT subjects, suggesting that insulin sensitivity, which is CPin b dt YGðÞ h the ability to promote the hypoglycemic effect in response to serum insulin, decreases from NGT to borderline type to T2DM. dI ¼ k v v þ influx ratio CPin Iout The serum C-peptide concentration returned to the fasting level in dt all groups, and differed signiﬁcantly between the NGT and k m X k ðÞ I I þ fðtÞ ðÞ G>h ratio Iout b borderline type subjects. Only insulin was infused during ¼ ; Ið0Þ¼ I k ðÞ I I þ fðtÞ ðÞ G h Iout b the hyperinsulinemic-euglycemic clamp, indicating that serum (3) C-peptide was derived only from endogenous secretion. Fig. 1 Concentrations of plasma glucose, serum insulin, and C-peptide during consecutive hyperglycemic and hyperinsulinemic-euglycemic clamps. The mean ± SD among the subjects for NGT (green, n = 50), borderline type (red, n = 18), and T2DM (blue, n = 53) of experimental (upper 3 panels) and simulation with Model VI (lower 2 panels) time courses are shown. Hyperglycemic clamp (HGC) was performed for 90 min and hyperinsulinemic-euglycemic clamp (HEC) for 120 min with a 10-min interval. The plasma glucose level is the average value calculated every 5 min of the measurements made every 1 min, and the serum insulin and C-peptide levels are measured values at sampling time (Methods). Simulation time courses are plotted every 10 min. Supplementary Figure S1 and Supplementary Table S1 illustrate the signiﬁcant difference of concentrations at each time point among the three groups Published in partnership with the Systems Biology Institute npj Systems Biology and Applications (2018) 14 Increase in hepatic and decrease in peripheral K Ohashi et al. For the 45 of 121 subjects who were not optimal for this model Table 1. Comparison of the models based on the Akaike information (Fig. 2a; Model VI in Supplementary Figure S2), the distributions of criterion (AIC) the residual sum of squares (RSS) between modeled and measured concentrations of insulin and C-peptide in this model Model No. subjects of min NGT Borderline T2DM AIC mean ± were not signiﬁcantly different from the distributions of the RSS of AIC SD the remaining 76 subjects who were optimal with minimum AIC I 25 7 4 14 −21.1 ± 22.9* for this model (Supplementary Figure S3). There also seems to be no bias in the distribution of the NGT, borderline type, and T2DM II 531 1 −19.0 ± 24.2* subjects among the best models (Table 1). Model VI was also III 000 0 −16.2 ± 24.9* selected when AIC of each model was calculated using measured IV 700 7 −17.2 ± 25.3* time courses of all 121 subjects (Supplementary Table S2). V 843 1 −28.4 ± 26.2 However, in the RSS distributions of all 121 subjects in this model, VI 76 36 10 30 −31.4 ± 25.2 RSS values of three subjects were relatively high and detected as Total 121 50 18 53 outliers, and the three subjects were excluded from the analysis in this study (Supplementary Figure S3). In addition, there seems to The number of subjects optimal for each model with minimum AIC is be no bias of temporal patterns of serum insulin and C-peptide shown (see Methods) concentrations among the subjects in each model (Supplementary *AIC different from Model VI (P < 0.01, corrected by the number of t-tests, Figure S4, Supplementary Table S3). Therefore, we selected the multiplied by 5) model (Fig. 2a; Model VI in Supplementary Figure S2) for further study because it was able to reproduce time courses of serum insulin and C-peptide concentrations for the remaining 118 sub- dCP ¼ v v jects. The simulation with Model VI (Fig. 1, Supplementary Figure CPin CPout dt S1) reproduced measured concentrations of insulin and C-peptide, m X k ðÞ CP CP ðÞ G>h CPout b and reﬂected signiﬁcant differences among the NGT, borderline ¼ ; CPð0Þ¼ CP ; k ðÞ CP CP ðÞ G h type, and T2DM subjects. Seven subjects (one NGT, one borderline CPout b type, and ﬁve T2DM subjects) were excluded because their model (4) parameters were detected as outlier based on the adjusted where I and CP correspond to fasting (basal) serum insulin and b b outlyingness (Methods), and we analyzed the model for the C-peptide concentration, respectively, directly given by the remaining 111 subjects (47 NGT, 17 borderline type, and 47 T2DM) measurement, and X is an initial value of X to be estimated. (Supplementary Table S4). Equation 1 describes how insulin provision rate Y increases according to αβ(G − h) when G > h, and decreases with αY. This Changes in opposite direction of hepatic and peripheral insulin means that provision of X, stored amounts of insulin and C- clearance from NGT to borderline type and T2DM peptide, depends on parameters α and β, and stimulated only We statistically compared the model parameters among the NGT, when the plasma glucose concentration exceeds the threshold borderline type, and T2DM groups (Fig. 2b and Methods). Four of value, h, which corresponds to FPG. the nine parameters, k , k , h, and X , were signiﬁcantly Equation 2 describes how X increases according to the provision Iout ratio b different. rate Y and decreases according to the insulin and C-peptide The parameter k is the degradation rate of serum insulin and secretion v . v is X secreted at the rate m when G > h. Since Iout CPin CPin corresponds to peripheral insulin clearance. The value of k in X , which is the initial value of X, relates to the insulin and C- Iout the NGT subjects was higher than that in the borderline type and peptide secretion when G > h for the ﬁrst time during hypergly- T2DM subjects (Fig. 2c), indicating that peripheral clearance cemic clamp, X is responsible for the ﬁrst-phase secretion. decreases in development of glucose intolerance, which is Equation 3 describes how serum insulin concentration I 30,40 consistent with previous studies. increases according to the post-hepatic insulin delivery, k · ratio The parameter k is the ratio of post-hepatic insulin to C- , and decreases according to peripheral insulin clearance v . ratio CPin Iout I also increases according to infused insulin, inﬂux. k · v is peptide, and (1 − k ) corresponds to the insulin extracted by ratio ratio CPin the liver, that is, hepatic insulin clearance. The value of (1 − k ) expanded as k · m · X, which corresponds to insulin delivered ratio ratio into peripheral circulation after passage through the liver when G in the NGT subjects was lower than that in the borderline type and > h. The parameter k is the molar ratio of post-hepatic insulin T2DM subjects (Fig. 2c), indicating the increase of hepatic insulin ratio clearance in the borderline type and T2DM subjects. This is to C-peptide, which represents the fraction of insulin delivered to the peripheral circulation without being extracted by the liver. consistent with an earlier clinical observation. Given that C-peptide is not extracted by the liver, k can The parameter h is the threshold of plasma glucose concentra- ratio represent the remaining fraction of insulin after the extraction by tion for the insulin secretion and corresponds to FPG. This the liver over the total amount of secreted insulin, and ranges parameter in the T2DM subjects was signiﬁcantly higher than that from 0 to 1. Therefore, (1 − k ) represents the fraction of insulin in the NGT subjects (Fig. 2b), consistent with the fact that FPG is ratio 9,10 extracted by the liver and not delivered to the peripheral higher in T2DM. circulation and corresponds to hepatic insulin clearance; inﬂux is The parameter X is the initial value of X, which corresponds to the insulin infusion rate during hyperinsulinemic-euglycemic the stored amounts of insulin and C-peptide or β-cell masses clamp. The infusion rate at time t is represented by the function before the start of the hyperglycemic clamp. This parameter in the f(t) (Methods). v represents serum insulin degradation with the T2DM subjects was signiﬁcantly lower than that in the NGT Iout rate parameter k . Therefore, k represents insulin degradation subjects (Fig. 2b), consistent with observations that β-cell masses Iout Iout 42–44 in the periphery and corresponds to peripheral insulin clearance. and stored insulin decrease in T2DM patients. Equation 4 describes how serum C-peptide concentration CP Using the same clamp data, we previously showed that insulin 14,30 increases according to the C-peptide secretion v and decreases secretion decreases from NGT to borderline type to T2DM. In CPin according to peripheral C-peptide clearance v . v is C- this study, however, the parameters α and β, related to insulin CPout CPin peptide secreted and delivered to peripheral serum without secretion, did not show any signiﬁcant differences among the hepatic clearance. v represents serum C-peptide degradation NGT, borderline type, and T2DM subjects, possibly because CPout with the rate parameter k . previously deﬁned insulin secretion is described by insulin CPout npj Systems Biology and Applications (2018) 14 Published in partnership with the Systems Biology Institute Increase in hepatic and decrease in peripheral K Ohashi et al. Fig. 2 Mathematical model of serum insulin and C-peptide. a The structure of the model (see also Eqs. 1–4 and Model VI in Supplementary Figure S2). I and CP are serum insulin and C-peptide concentration, respectively. X is the amount of stored insulin and C-peptide, and Y is the provision rate controlled by plasma glucose concentration, G. Arrows indicate ﬂuxes with corresponding parameters (red). b The estimated parameters for the NGT (green), borderline type (red), and T2DM (blue) subjects. Each dot corresponds to the indicated parameter for an individual subject. c The parameters of k and (1 − k ), corresponding to peripheral and hepatic insulin clearance, respectively. *P < 0.05, Iout ratio **P < 0.01, NS not signiﬁcant (two-sided Wilcoxon rank sum test with FDR-correction). Post-hoc statistical power analysis is shown in Supplementary Table S5. The bar and error bar show the median and lower and upper quartiles, respectively. Each dot corresponds to the indicated parameter for an individual subject secretion and delivery in this model, which depends on other ﬁnding that peripheral insulin clearance is highly correlated with parameters such as h, m, X , and k , and the parameters ISI and MCR. k is the degradation rate of serum insulin, which Iout b ratio depends on the number of insulin receptors on target tissues, involved in insulin secretion and delivery are too diverse. indicating that serum insulin degradation and insulin sensitivity The parameters k , k , k , h, and X show smaller ratio Iout CPout b are mutually correlated. Therefore, it is reasonable that k is variations than others (Fig. 2b). This is probably because Iout correlated not only with MCR but also with ISI. these parameters are directly related to the measured concentra- The model parameter showing the highest correlation with tions of serum insulin and C-peptide and plasma glucose, and insulin secretion during the ﬁrst phase, AUC (see Methods), therefore can be accurately estimated, whereas other parameters IRI10 which is the index of insulin secretion, was k (r = 0.425, P < ratio are not, resulting in large variation possibly due to inaccurate 0.01). Note that (1 − k ) corresponds to hepatic insulin ratio estimation. clearance. Because the parameter k is the fraction of insulin ratio remaining after the hepatic extraction, its correlation with insulin Relationship between hepatic and peripheral insulin clearance secretion is reasonable. parameters and clinical indices of serum insulin regulation In addition, the model parameter showing the highest We examined the correlation of the estimated model parameters correlation with both FPG and 2-h PG, the main indices of glucose with clinical indices of circulating insulin regulation among tolerance, was h (r = 0.448 and 0.504, respectively, both P < 0.001), 111 subjects (Fig. 3, Supplementary Table S6). The model which is the threshold glucose concentration for insulin secretion. parameter showing the highest correlation with insulin sensitivity This ﬁnding is consistent with h corresponding to FPG. The model index (ISI) and with the metabolic clearance rate (MCR), which is parameter showing the highest correlation with the clamp the index of insulin clearance (see Methods for details), was disposition index, clamp DI, which is calculated as the peripheral insulin clearance, k (r = 0.761 and 0.790, respectively, product of insulin secretion AUC and ISI and is the index of Iout IRI10 both P < 0.001). This correlation is consistent with our previous glucose tolerance, was k · k (r = 0.540, P < 0.001). ratio Iout Published in partnership with the Systems Biology Institute npj Systems Biology and Applications (2018) 14 Increase in hepatic and decrease in peripheral K Ohashi et al. Fig. 3 Model parameters showing the highest correlation with clinical indices. a Scatter plots for the indicated measured clinical indices versus the highest correlated model parameters (Supplementary Table S6). ISI insulin sensitivity index, MCR metabolic clearance rate, AUC IRI10 amount of insulin secretion during the ﬁrst 10 min of hyperglycemic clamp. Each dot indicates the value of an individual subject. The correlation coefﬁcient, r, and the P value for testing the hypothesis of no correlation are shown. The partial correlation coefﬁcients among k , ISI, and MCR are shown in Supplementary Figure S5. b Summary of the model parameters k and k showing the highest correlation Iout Iout ratio with the indicated clinical indices Considering that k is related to post-hepatic insulin delivery, secretion. Note that the decrease in k also increases the ratio Iout and k is related to insulin sensitivity, which depends on the amplitude of I. Iout Because both k and k decreased from NGT to borderline number of insulin receptors on target organs, it is reasonable that ratio Iout type and T2DM (Fig. 2b), we examined the effect of the the product k · k shows the highest correlation with clamp ratio Iout simultaneous changes of k and k on the amplitude and ratio Iout DI, which is also the product of clinically estimated insulin transient/sustained patterns of I. When both k and k ratio Iout secretion and sensitivity. increased with the same ratio, I increased during ﬁrst-phase secretion (0–10 min), whereas I decreased during second-phase Selective regulation of amplitude and temporal patterns of serum secretion (10–30 min) (Fig. 4a, right panel, red line). Thus, insulin concentration by hepatic and peripheral insulin clearance simultaneous increase of k and k results in the increase of ratio Iout Because k and k were the parameters showing the highest Iout ratio peak amplitude of I and in changes in the temporal pattern of I correlation with clinical indices of insulin sensitivity and secretion, from sustained to transient. respectively, both of which are related to the progression of We quantiﬁed the role of k and k in the peak amplitude ratio Iout glucose intolerance and T2DM, we analyzed the roles of k and ratio and temporal patterns of I.Wedeﬁned the index ipeak k in the temporal changes of serum insulin concentration (Fig. (incremental peak) for the peak amplitude of I, and the index Iout 4). We changed the originally estimated values of k or k or iTPI (incremental transient peak index; modiﬁed from Kubota ratio Iout −1 1 46 both by 2 to 2 times and simulated the time course of I, serum et al. ) for the temporal pattern of I (Fig. 4b), as follows: insulin concentration, during hyperglycemic clamp for each ipeak ¼ ItðÞ IðÞ 0 ; ItðÞ>IðÞ t ; (5) local max local max local max next subject (Supplementary Figure S6). Similar temporal changes of I versus changes in the parameters were observed in all 111 sub- Iðt ÞIðt Þ local max local min iTPI ¼ ; jects, so only the simulation result of subject #3 (NGT) is shown ipeak (6) (Fig. 4a). Iðt Þ<Iðt Þ; t >t ; local min local min next local min local max The time course of I with the original parameters in the model where I(t) represents I at time t, t is the time at which I local_max of subject #3 showed the transient increase (Fig. 4a, black line). As stops increasing for the ﬁrst time from 0 min, t is the local_max_next k increased, I increased without changing the transient pattern ratio next sampling time of t , t is the time at which I local_max local_min (Fig. 4a, left panel, red line). Indeed, an increase of k affects the ratio stops decreasing for the ﬁrst time after t , and t local_max local_min_next value of I similarly at any time point, because k controls the ratio is the next sampling time of t . local_min gain of time derivative of I.As k increased, I decreased and the Iout The index ipeak is the difference in I between the local temporal pattern became more transient with an earlier peak time maximum I(t ) and the initial fasting concentration I(0) and local_max (Fig. 4a, middle panel, red line). Conversely, as k decreased, I Iout represents the peak amplitude of I during the ﬁrst-phase increased and the temporal pattern became more sustained with secretion. The index iTPI is the ratio of the difference of I between a delayed peak time (Fig. 4a, middle panel, blue line). This result the local maximum I(t ) and the local minimum I(t ) local_max local_min suggests that k controls the shift in the temporal patterns of I Iout of I against ipeak, which reﬂects the ratio of I during the ﬁrst- and from transient to sustained. These changes in the temporal second-phase secretions. As iTPI approaches 1, the difference in I pattern of I are characterized by a relative decrease in the ﬁrst- between the ﬁrst- and second-phase secretions becomes larger, phase secretion and relative increase in the second-phase meaning that the temporal change of I becomes more transient. npj Systems Biology and Applications (2018) 14 Published in partnership with the Systems Biology Institute Increase in hepatic and decrease in peripheral K Ohashi et al. Fig. 4 The roles of k and k in the amplitude and temporal patterns of serum insulin concentration. a Simulated time course of serum ratio Iout insulin concentration I during hyperglycemic clamp of subject #3 by changing k or k or both by scaling the ﬁtted parameter value with ratio Iout −1.0 −0.5 0.5 1.0 2 ,2 ,1,2 , and 2 (see Methods). Dotted arrows indicate the direction of the change in the temporal pattern as the parameter increases. b The deﬁnition of ipeak (incremental peak) and iTPI (incremental transient peak index), reﬂecting the peak amplitude and the temporal pattern of serum insulin concentration I. c ipeak and iTPI of I of subject #3 by changing k or k or both ratio Iout Conversely, as iTPI approaches 0, the difference in I between the ﬁrst- and second-phase secretions becomes smaller, meaning that the temporal change of I becomes more sustained. We calculated ipeak and iTPI from the simulated time courses of −1 I by changing the original estimates of k or k or both by 2 ratio Iout to 2 times. As k increased, ipeak increased but iTPI did not ratio change (Fig. 4c, left panel), indicating that increasing k ratio increases the peak amplitude of I during the ﬁrst-phase secretion without changing its temporal pattern. As k increased, iTPI Iout increased and ipeak decreased (Fig. 4c, middle panel), indicating that increasing k changes the temporal patterns of I from Iout sustained to transient and decreases the peak amplitude of I during the ﬁrst-phase secretion. When both k and k increased at the same ratio, both ratio Iout ipeak and iTPI increased (Fig. 4c, right panel), indicating that increasing both k and k increases the peak amplitude of I ratio Iout and changes the temporal pattern from sustained to transient. The increase in ipeak means that the effect of k , which increases ratio ipeak, is stronger than that of k , which decreases ipeak. Given Iout that both k and k decrease from NGT to borderline type and ratio Iout T2DM, both ipeak and iTPI decrease (Fig. 5). This ﬁnding is consistent with earlier clinical observations that the peak amplitude of circulating insulin concentration during the ﬁrst- phase secretion decreases and the temporal pattern becomes 2–4 more sustained during the progression of glucose intolerance. Fig. 5 Overview of our study and main results. Mathematical We performed parameter sensitivity analysis on ipeak and iTPI in modeling based on hyperglycemic and hyperinsulinemic- the simulation for each model parameter (Table 2, Methods). We euglycemic clamp (glucose and insulin clamp) data in subjects compared the median of the parameter for all 111 subjects as the showed changes in opposite direction of hepatic and peripheral parameter sensitivity index (Table 2). For ipeak, the k had the ratio insulin clearance from NGT to T2DM. Hepatic insulin clearance (1 signiﬁcantly highest median, and for iTPI, k showed the Iout −k ) increases and peripheral insulin clearance k decreases, ratio Iout signiﬁcantly highest median, indicating that hepatic insulin characterizing the decrease in peak amplitude and the change in the temporal pattern of serum insulin concentration from transient clearance and peripheral insulin clearance are the most critical to sustained, respectively parameters controlling the peak amplitude and temporal patterns of serum insulin concentration, respectively. The measured temporal changes of the serum insulin concen- tration during hyperglycemic clamp (0–90 min) showed no clear suggesting that hepatic and peripheral insulin clearance are not difference between the NGT and borderline type subjects (Fig. 1). the only parameters responsible for the peak amplitude and However, the estimated k and k in the NGT subjects were temporal patterns of serum insulin concentration, respectively. ratio Iout signiﬁcantly higher than those in the borderline type subjects, Other parameters such as insulin secretion, which also affects the Published in partnership with the Systems Biology Institute npj Systems Biology and Applications (2018) 14 Increase in hepatic and decrease in peripheral K Ohashi et al. Table 2. Parameter sensitivity analysis for ipeak and iTPI Rank ipeak iTPI Median P Median P −1 1 k 1.00 k 4.64 × 10 ratio Iout −1 −38 −1 −6 2 m 3.52 × 10 6.26 × 10 β −2.53 × 10 1.30 × 10 −1 −36 −1 −15 3 k −2.74 × 10 1.23 × 10 α −1.42 × 10 5.36 × 10 Iout −4 −34 −1 −7 4 h −3.64 × 10 4.04 × 10 h 1.38 × 10 8.70 × 10 −4 −36 −2 −9 5 β 2.59 × 10 1.23 × 10 m 7.18 × 10 2.56 × 10 −4 −36 −15 −35 6 α 1.61 × 10 1.23 × 10 k 8.28 × 10 2.62 × 10 ratio Medians of the indicated parameters for all 111 subjects were used for parameter sensitivity analysis for ipeak and iTPI (see Methods). The higher the absolute value of the parameter, the higher the sensitivity. P values relative to the median for the top-ranked parameter were determined by two-sided Wilcoxon rank –3 sum test, and the value of <4.17 × 10 (=0.05/12, corrected by the number of tests, divided by 12) is considered statistically signiﬁcant temporal changes of serum insulin concentration, may compen- clearance and the temporal pattern changes from transient to sate for the temporal changes by insulin clearance between the sustained occur because of a decrease in peripheral insulin NGT and borderline type subjects. This also means that changes in clearance (Fig. 5). Importantly, the decrease in peripheral insulin the hepatic and peripheral insulin clearance from NGT to clearance alone can explain only the temporal change of serum borderline type and T2DM cannot be directly assessed from the insulin concentration, not the decrease of peak amplitude. Thus, measured time course of serum insulin concentration, but must be the increase of hepatic insulin clearance and decrease of evaluated with a mathematical model. peripheral insulin clearance simultaneously cause the decrease From Eq. 3, the parameter k directly reﬂects post-hepatic in the peak amplitude of serum insulin concentration during the ratio insulin delivery and is involved in the increase in gain of I. ﬁrst-phase secretion and change in temporal pattern from Therefore, the change of k is directly reﬂected in the peak transient to sustained. Our result demonstrates that, in addition ratio 3,4 amplitude, so the sensitivity to ipeak becomes 1. This means that to the decrease in insulin secretion, the increase in hepatic hepatic insulin clearance is more responsible for the peak clearance also contributes to the decrease in peak amplitude of amplitude of serum insulin concentration than the pre-hepatic serum insulin concentration in the ﬁrst-phase secretion from NGT insulin secretion before extraction by the liver. to borderline type and T2DM. The parameter k corresponds to peripheral insulin clearance In our model, as k , the ratio of post-hepatic insulin compared Iout ratio and is the degradation rate of I, meaning that k is the time to C-peptide, increased, ipeak, the peak amplitude of peripheral Iout constant of serum insulin degradation. k is the parameter insulin concentration, increased (Fig. 4c). According to clinical Iout directly responsible for temporal conversion of input X, delivered measurements, k was also correlated with ipeak calculated ratio insulin after the extraction by the liver, into output, I. Thus, k is directly from the serum insulin concentration measured during Iout the ﬁrst-phase secretion in hyperglycemic clamp (Supplementary the most sensitive parameter for iTPI corresponding to the shift Figure S8a, r = 0.423, P < 0.001), indicating that hepatic insulin between the transient and sustained temporal pattern of serum insulin concentration. clearance is pathologically correlated with the peak amplitude in the ﬁrst-phase secretion from NGT to borderline type and T2DM. On the other hand, in our model, as k , the peripheral insulin Iout DISCUSSION clearance, increased, iTPI, representing the temporal pattern of We developed several alternative mathematical models using peripheral insulin concentration, increased (Fig. 4c). However, in concentrations of plasma glucose, serum insulin, and C-peptide clinical measurements, k was not highly correlated with iTPI Iout during consecutive hyperglycemic and hyperinsulinemic- calculated directly from the serum insulin concentration measured euglycemic clamps, and selected the model showing the best ﬁt during hyperglycemic clamp (Supplementary Figure S8a, r = for most subjects. Although Model VI was selected for 76 of 0.297, P < 0.01). The reason for this lack of correlation between 121 subjects, 45 subjects were not optimal for Model VI. This k and iTPI in clinical measurement remains unclear; however, it Iout suggests that some of the parameters of Model VI were may be because little insulin was secreted during hyperglycemic unnecessary in subjects whose selected model is Model I, II, IV, clamp in some borderline type and T2DM subjects, and iTPI or V by comparing the structure with Model VI. However, no cannot be estimated accurately because of low concentration of parameter of Model VI showed signiﬁcant difference between serum insulin. subjects who selected Model I, II, IV,or V and subjects who Many studies have shown that insulin clearance decreases in 18–21,47,48 selected Model VI (Supplementary Figure S7), suggesting that T2DM patients. However, the change in hepatic insulin there is no biased feature on the structure of the control of clearance in this condition has been controversial, with some circulating insulin concentration in subjects who were not optimal studies ﬁnding an increase in T2DM subjects and others a 18,23 for Model VI, and Model VI can be applied to all subjects. decrease. We previously developed a mathematical model During the progression of glucose intolerance, it has been using data gathered during hyperglycemic and hyperinsulinemic- shown that the peak amplitude of circulating insulin concentra- euglycemic clamps, and peripheral insulin clearance signiﬁcantly tion during the ﬁrst-phase secretion decreases and the temporal decreased from NGT to borderline type to T2DM. However, 2–4 pattern becomes more sustained. In this study, we found that hepatic and peripheral insulin clearances were not estimated both k , corresponding to peripheral insulin clearance, and k separately because we did not use C-peptide data. Recently, Iout ratio decrease from NGT to borderline type and T2DM. Given that (1 − Polidori et al. estimated both hepatic and peripheral insulin k ), corresponding to hepatic insulin clearance, increases as the clearance by modeling analysis using plasma insulin and C- ratio k decreases, our ﬁnding strongly suggests that, from NGT to peptide concentrations obtained from the insulin-modiﬁed ratio borderline type and T2DM, the peak amplitude of serum insulin frequently sampled IVGTT. They found that the peripheral insulin concentration decreases due to the increase in hepatic insulin clearance signiﬁcantly decreased in borderline type subjects npj Systems Biology and Applications (2018) 14 Published in partnership with the Systems Biology Institute Increase in hepatic and decrease in peripheral K Ohashi et al. compared with NGT subjects, whereas hepatic insulin clearance circulating insulin concentration selectively regulate insulin did not signiﬁcantly differ between the borderline type and NGT actions on the target tissues. Given that hepatic and peripheral subjects ; the former ﬁnding is consistent with our result that insulin clearances are responsible for the amplitude and temporal peripheral insulin clearance decreases from NGT to borderline pattern of circulating insulin concentration, these clearances are type and T2DM. We demonstrated that hepatic insulin clearance likely to be involved in selective control of insulin action, glucose signiﬁcantly increases, whereas peripheral insulin clearance homeostasis, and the pathogenesis of T2DM. signiﬁcantly decreases from NGT to borderline type and T2DM. We previously developed a mathematical model for concentra- One difference between the study by Polidori et al. and our study tions of plasma glucose and serum insulin measured during is C-peptide kinetics. They used the reported two-compartment consecutive hyperglycemic and hyperinsulinemic-euglycemic model of C-peptide kinetics for calculating insulin secretion rate clamps and found signiﬁcant decreases in insulin secretion, by deconvolution, while we selected the structure of C-peptide sensitivity, and peripheral insulin clearance from NGT to border- kinetics that ﬁtted for our data, which may improve the accuracy line type to T2DM. The differences between our previous study of the parameter estimation of hepatic insulin clearance, and this study are the model structure and C-peptide data. The estimated by use of serum insulin and C-peptide concentration. previous model consisted of plasma glucose and serum insulin The increase in hepatic insulin clearance may be caused by and required only glucose and insulin infusion as inputs. The impaired suppression of endocytosis of insulin receptors on the model in this study does not have plasma glucose concentration liver, and the decrease in peripheral insulin clearance may be but includes serum insulin and C-peptide concentrations, while caused by a decrease of the number of insulin receptors on target plasma glucose concentration and insulin infusion are used as 45 40 tissues. Polidori et al. also found that hepatic and peripheral inputs (Fig. 2a, Supplementary Figure S2). In the previous study, insulin clearances were not highly correlated. Consistent with their only peripheral insulin clearance, but not hepatic insulin clearance, results, in our analysis, the insulin clearance parameters k and was estimated because C-peptide data were not used. The ratio k were not highly correlated (Supplementary Figure S8b, r = decrease of insulin clearance from NGT to T2DM in the previous Iout 0.296, P < 0.01), suggesting that both insulin clearances are study is consistent with the decrease of peripheral insulin independently regulated. clearance from NGT to T2DM in this study. In the previous study, We are aware that some of the results of this analysis only hold the parameter corresponding to insulin secretion in the NGT and if the parameters are identiﬁable based on our serum insulin and borderline type subjects was signiﬁcantly higher than that in the C-peptide data. We performed 20 trials of parameter estimation T2DM subjects; however, the parameter related to insulin for each subject (Methods), but most subjects (107 subjects) had secretion did not show a signiﬁcant difference between the only one trial which minimized RSS. The values of estimated NGT, borderline type, and T2DM subjects in this study, possibly parameters and RSS varied among the 20 trials of each subject. For because previously deﬁned insulin secretion is described by the remaining four subjects, estimated parameters varied among insulin secretion and delivery in this model, and the parameters trials that returned the same RSS, especially the parameters α and related to insulin secretion and delivery (α, β, h, m, X , and k ) b ratio β differed to a large extent, while the parameters k and k are too diversiﬁed. The parameter corresponding to insulin Iout ratio did not largely differ (Supplementary Figure S9). If the number of sensitivity was not incorporated in this study. estimated trials, parents, and generations of evolutionary pro- Many mathematical models to reproduce circulating C-peptide gramming increases, a trial that gives a different parameter concentration have been developed. A two-compartment model solution with smaller RSS than that reported in this study might be for C-peptide kinetics was originally proposed. A combined obtained. Structural or a priori identiﬁability of parameters based model that included both circulating insulin and C-peptide on the system equations, which tests if model parameters can kinetics described by a single compartment structure was be determined from the available data, was not performed in this introduced to estimate hepatic insulin clearance. The C- study. Large variability in the ﬁtted parameters, like for instance in peptide minimal model describing peripheral insulin and C- α and β, could be due to the identiﬁability of the parameters and peptide appearance and kinetics was also developed to assess 33–37 not due to biological variance, and interpretation of the results has hepatic insulin clearance, and several other model structures 38,39 to take this into account. for circulating C-peptide concentration were reported. One Insulin selectively regulates various functions, such as signaling difference between others’ and our studies is the experimental activities, metabolic control, and gene expression, depending on protocol in which data were applied to parameter estimation. its temporal patterns. For example, we previously reported that IVGTT or hyperglycemic clamp were performed for parameter pulse stimulation of insulin in rat hepatoma Fao cells, resembling estimation in models of circulating C-peptide concentration, the ﬁrst-phase secretion, selectively regulated glycogen synthase whereas we used hyperglycemic and hyperinsulinemic- kinase-3β (GSK3β), which regulates glycogenesis, and S6 kinase, euglycemic clamps, which may improve the accuracy of the which regulates protein synthesis, whereas ramp stimulation of parameter estimation of peripheral insulin clearance, k . Iout insulin, resembling the second-phase secretion, selectively regu- Recently, a model of plasma insulin concentration including lated GSK3β and glucose-6-phosphatase (G6Pase), which regulates hepatic and peripheral insulin clearance and the delivery of insulin gluconeogenesis. We also found that insulin-dependent meta- from the systemic circulation to the liver during the insulin- bolic control and gene expression are selectively regulated by modiﬁed IVGTT was proposed. In that model, the parameter of 50,51 temporal patterns and doses of insulin in FAO cells. Sustained hepatic insulin clearance was negatively correlated with acute stimulation of insulin suppressed the expression of insulin insulin secretion in response to glucose, and the parameter of 52–54 receptors, leading to reduced insulin sensitivity in FAO cells. peripheral insulin clearance was correlated with insulin sensitiv- Likewise, phosphorylation of the insulin receptor substrate (IRS)-1/ ity, consistent with the results in this study (Fig. 3). Since the age 2 in rat liver increased when pulsatile (rather than continuous) of subjects in our study differed between groups with NGT, stimulation of insulin was imposed in the portal circulation. This borderline type, and T2DM (Supplementary Table S4), the may have occurred through the negative feedback within the correlations between the parameters and clinical indices may be insulin signaling pathway, the phosphatidylinositide (PI) 3-kinase/ affected by age. However, the parameters showing the highest 53,56 Alt pathway, targeting IRS-1/2. In addition, IRS-2, rather than correlation with clinical indices of insulin secretion, AUC , IRI10 IRS-1, mainly regulates hepatic gluconeogenesis through its rapid insulin sensitivity, ISI, and insulin clearance, MCR, were not downregulation by insulin, suggesting the selective roles of IRS- changed with conditioning of age (Supplementary Table S7). 1/2 in response to temporal patterns of plasma insulin. These The high correlation between the parameter of hepatic insulin ﬁndings indicate that the amplitude and temporal pattern of clearance, k , and the clinical index of insulin secretion, AUC , ratio IRI10 Published in partnership with the Systems Biology Institute npj Systems Biology and Applications (2018) 14 Increase in hepatic and decrease in peripheral K Ohashi et al. suggests the possibility that hepatic insulin clearance considerably models, I represents serum insulin concentration (pM), and CP and CP represent serum C-peptide concentration (pM) including insulin and C- affects the clinical index of insulin secretion measured by peptide secretion and hepatic and peripheral clearance. We used a peripheral insulin concentration because the clinical index of conversion factor of insulin (6.00 nmol/U) and the molecular weights of insulin secretion, AUC , was measured by the post-hepatic IRI10 glucose (180.16 g/mol) and C-peptide (3020.3 g/mol) to convert the unit of insulin delivery, and therefore reﬂects both insulin secretion and serum insulin, plasma glucose, and serum C-peptide, respectively. We used hepatic insulin clearance. This suggests that insulin secretion plasma glucose concentration G (mM) as input in the models, which was per se in the clinical index of insulin secretion may be determined by stepwise interpolation of the measured plasma glucose overestimated because of the involvement of hepatic insulin data. Note that plasma glucose data were obtained as the 5-min average clearance. Further study is necessary to address this issue. values, and each sampling time was reduced by 2 min in the calculation of In conclusion, using the mathematical model for serum insulin stepwise interpolation. The actual insulin infusion rate (IIR, mU/kg/min) was converted to the and C-peptide concentrations during consecutive hyperglycemic corresponding serum concentrations (cIIR) as follows: and hyperinsulinemic-euglycemic clamps, we determined the quantitative structure of the control of circulating insulin IIR ðmU=kg=minÞ 6:00 10 ðpmol=mUÞ (7) cIIRðÞ pM=min¼ ; concentration. The estimated model parameters revealed the 3 BV 10 increase of hepatic insulin clearance and decrease of peripheral where BV denotes blood volume (75 and 65 mL/kg for men and women, insulin clearance from NGT to borderline type and T2DM, and respectively ). these changes selectively regulate the amplitude and temporal In the models, insulin infusions are represented by inﬂux. This ﬂux patterns of serum insulin concentration, respectively. The changes follows the nonlinear function f that predicts insulin infusion concentra- tions. Given that insulin infusion was performed only during the in opposite direction of both types of clearance shed light on the hyperinsulinemic-euglycemic (from 100 to 220 min) clamp, the function f pathological mechanism underlying the abnormal temporal was given by the following equations: patterns of circulating insulin concentration from NGT to border- line type and T2DM. 0 ðt 100Þ fðtÞ¼ ; (8) ii expðii ðt 100ÞÞ þ ii ðt>100Þ 1 2 3 where the parameters ii (j = 1, 2, 3) are estimated to reproduce cIIR for MATERIALS AND METHODS j each subject with a nonlinear least squares technique. Parameters for all Subjects and measurements subjects are shown in Supplementary Table S9. The plasma and serum measurement data originated from our previous 14,30 research. This metabolic analysis was approved by the ethics Parameter estimation committee of Kobe University Hospital and was registerd with the University hospital Medical Information Network (UMIN000002359), and The model parameters for each subject were estimated to reproduce the written informed consent was obtained from all subjects. In brief, 50 NGT, experimentally measured time course by a meta-evolutionary program- 18 borderline type, and 53 T2DM subjects underwent the consecutive ming method to approach the neighborhood of the local minimum, clamp analyses. From 0 to 90 min, a hyperglycemic clamp was applied by followed by application of the nonlinear least squares technique to reach 2 61 intravenous infusion of a bolus of glucose (9622 mg/m ) within 15 min the local minimum. Each parameter was estimated in the range from −6 4 followed by that of a variable amount of glucose to maintain the plasma 10 to 10 . For these methods, the model parameters were estimated to glucose level at 200 mg/dL. Ten minutes after the end of the minimize the objective function value, which is deﬁned as the RSS between the actual time course obtained by clamp analyses and the hyperglycemic clamp, a 120-min hyperinsulinemic-euglycemic clamp was model trajectories. RSS is given by: initiated by intravenous infusion of human regular insulin (Humulin R, Eli Lilly Japan K.K.) at a rate of 40 mU/m /min and with a target plasma 2 2 X X IðtÞ I ðtÞ CPðtÞ CP ðtÞ sim sim glucose level of 90 mg/dL. For the NGT and borderline type subjects whose RSS ¼ þ ; (9) I CP plasma glucose levels were <90 mg/dL, the plasma glucose concentration mean mean points points was clamped at the fasting level. We measured the plasma glucose level where every 1 min during the clamp analyses and obtained the 5-min average P P values. We also measured insulin and C-peptide level in serum samples IðtÞ points collected at 5, 10, 15, 60, 75, 90, 100, 190, and 220 min after the onset of subjects I ¼ ; (10) mean the tests. First-phase insulin secretion during the hyperglycemic clamp was points subjects deﬁned as the incremental area under the immunoreactive insulin (IRI) concentration curve (μU/mL/min) from 0 to 10 min (AUC ). The ISI IRI10 P P derived from the hyperinsulinemic-euglycemic clamp was calculated by CPðtÞ subjects points dividing the mean glucose infusion rate during the ﬁnal 30 min of the CP ¼ : (11) mean points clamp (mg/kg/min) by both the plasma glucose (mg/dL) and serum insulin subjects (μU/mL) levels at the end of the clamp and then multiplying the result by 100. A clamp-based analog of the disposition index, the clamp disposition I(t) and CP(t) are the serum insulin and C-peptide concentration, and index (clamp DI), was calculated as the product of AUC and ISI, as IRI10 I (t) and CP (t) are simulated serum insulin and C-peptide concentra- sim sim 14 13 described previously. The MCR, an index of insulin clearance, was tions at t min, respectively. Serum insulin and C-peptide concentrations calculated by dividing the insulin infusion rate at the steady state were normalized by dividing them by the averages of serum concentra- (1.46 mU/kg/min) by the increase in insulin concentration above the basal tions over all time points of all subjects of insulin (I , 302.7 pM) and C- mean level in the hyperinsulinemic-euglycemic clamp : 1.46 (mU/kg/min) × peptide (CP , 1475 pM), respectively. The numbers of parents and mean body weight (kg) × body surface area (m ) / (end IRI− fasting IRI) (μU/mL), generations in the meta-evolutionary programming were 400 and 4000, 1/2 where body surface area is deﬁned as (body weight (kg)) × (body height respectively. Parameter estimation was tried 20 times by changing the 1/2 (cm)) / 60 (Mosteller formula). Since this study is a retrospective analysis initial parameter values for each subject, and the parameter with the of previously collected data, randomization and blinding of the groups smallest RSS among 20 trials was taken as the estimated solution of each with NGT, borderline type, and T2DM was not performed. The actual data subject. Model parameters for all subjects are shown in Supplementary for all 121 subjects are shown in Supplementary Figure S10 and Table S9. Supplementary Table S8. Model selection Mathematical models The model was chosen among the six models according to the AIC. For a We developed six mathematical models based on the proposed models in given model and a single subject, AIC was calculated as follows: order to choose the best model for reproducing our measurement of 2π RSS serum insulin and C-peptide during consecutive hyperglycemic and AIC ¼ n ln þ n þ 2K ; (12) hyperinsulinemic-euglycemic clamps (Supplementary Figure S2). In these npj Systems Biology and Applications (2018) 14 Published in partnership with the Systems Biology Institute Increase in hepatic and decrease in peripheral K Ohashi et al. where n is the total number of sampling time points of serum insulin and REFERENCES C-peptide, and K is the number of estimated parameters of the model. 1. DeFronzo, R. A., Bonadonna, R. C. & Ferrannini, E. Pathogenesis of NIDDM. A balanced overview. Diabetes Care 15, 318–368 (1992). 2. Cerasi, E. & Luft, R. The plasma insulin response to glucose infusion in healthy Determination of parameter outliers subjects and in diabetes mellitus. Acta Endocrinol. (Copenh) 55, 278–304 (1967). The outliers of RSS and model parameters were detected by the adjusted 3. Del Prato, S. & Tiengo, A. The importance of ﬁrst-phase insulin secretion: impli- 62 3MC outlyingness (AO). The cutoff value of AO was Q + 1.5e · IQR, where cations for the therapy of type 2 diabetes mellitus. Diabetes Metab. Res. Rev. 17, Q , MC, and IQR are the third quartile, medcouple, and interquartile range, 164–174 (2001). respectively. The medcouple is a robust measure of skewness. The 4. Seino, S., Shibasaki, T. & Minami, K. Dynamics of insulin secretion and the clinical number of directions was set at 8000. Subjects found to have outlier implications for obesity and diabetes. J. Clin. Invest. 121, 2118–2125 (2011). parameters (one NGT, one borderline type, and ﬁve T2DM subjects) were 5. Lindsay, J. R. et al. Meal-induced 24-hour proﬁle of circulating glycated insulin in excluded from further study. type 2 diabetic subjects measured by a novel radioimmunoassay.Metabolism 52, 631–635 (2003). 6. Polonsky, K. S., Given, B. D. & Van Cauter, E. Twenty-four-hour proﬁles and pul- Parameter sensitivity analysis satile patterns of insulin secretion in normal and obese subjects. J. Clin. Invest. 81, We deﬁned the individual model parameter sensitivity for each subject as 442–448 (1988). follows: 7. Stumvoll, M. et al. Use of the oral glucose tolerance test to assess insulin release and insulin sensitivity. Diabetes Care 23, 295–301 (2000). ∂ log fðxÞ x ∂fðxÞ 8. Seino, Y. et al. Report of the committee on the classiﬁcation and diagnostic SðfðxÞ; xÞ¼ ¼ ; (13) ∂ log x fðxÞ ∂x criteria of diabetes mellitus. J. Diabetes Investig. 1, 212–228 (2010). 9. Hayashi, T. et al. Patterns of insulin concentration during the OGTT predict the where x is the parameter value and f(x)is ipeak or iTPI. The differentiation is risk of type 2 diabetes in Japanese Americans. Diabetes Care 36, 1229–1235 ∂fðxÞ fðxþΔxÞfðxΔxÞ numerically approximated by central difference , and x ∂x 2Δx (2013). + Δx and x − Δx were set so as to be increased [x (1.1x)] or decreased [x 10. Abdul-Ghani, M. A., Tripathy, D. & DeFronzo, R. A. Contributions of beta-cell (0.9x)] by 10%, respectively. Finally, we deﬁned the parameter sensitivity by dysfunction and insulin resistance to the pathogenesis of impaired glucose tol- the median of the individual parameter sensitivity for all subjects. We erance and impaired fasting glucose. Diabetes Care 29, 1130–1139 (2006). examined the parameter sensitivity for six parameters of the rate constant 11. Perley, M. J. & Kipnis, D. M. Plasma insulin responses to oral and intravenous related to serum insulin concentration, except X and k . The higher the b CPout glucose: studies in normal and diabetic sujbjects. J. Clin. Invest. 46, 1954–1962 absolute value of parameter sensitivity, the larger the effect of the (1967). parameter on ipeak or iTPI. 12. Pfeifer, M. A., Halter, J. B. & Porte, D. Insulin secretion in diabetes mellitus. Am. J. Med. 70, 579–588 (1981). 13. DeFronzo, R. A., Tobin, J. D. & Andres, R. Glucose clamp technique: a method for Statistical analysis quantifying insulin secretion and resistance. Am. J. Physiol. 237, E214–E223 Unless indicated otherwise, data are expressed as the median with ﬁrst and (1979). third quartiles. Medians of parameter values were compared among the 14. Okuno, Y. et al. Postprandial serum C-peptide to plasma glucose concentration NGT, borderline type, and T2DM subjects with the use of the two-sided ratio correlates with oral glucose tolerance test- and glucose clamp-based dis- Wilcoxon rank sum test with Benjamini Hochberg FDR multiple testing position indexes. Metabolism 62, 1470–1476 (2013). correction. An FDR-corrected P value <0.05 was considered statistically 15. Sato, H., Terasaki, T., Mizuguchi, H., Okumura, K. & Tsuji, A. Receptor-recycling signiﬁcant. model of clearance and distribution of insulin in the perfused mouse liver. Dia- betologia 34, 613–621 (1991). 16. Duckworth, W. C., Hamel, F. G. & Peavy, D. E. Hepatic metabolism of insulin. Am. J. Data availability Med. 85,71–76 (1988). The SBToolbox2 (http://www.sbtoolbox2.org/main.php) was used 17. Rabkin, R. & Kitaji, J. Renal metabolism of peptide hormones. Miner. Electrolyte together with MATLAB R2015a (http://mathworks.com/) in the mathema- Metab. 9, 212–226 (1983). tical modeling. The code ﬁles implementing the 6 analyzed models and 18. Marini, M. A. et al. Differences in insulin clearance between metabolically healthy used in the simulation are freely available at http://kurodalab.bs.s.u-tokyo. and unhealthy obese subjects. Acta Diabetol. 51, 257–261 (2014). ac.jp/info/. 19. Lee, C. C. et al. Insulin clearance and the incidence of type 2 diabetes in Hispanics and African Americans: the IRAS Family Study. Diabetes Care 36, 901–907 (2013). 20. Rudovich, N. N., Rochlitz, H. J. & Pfeiffer, A. F. Reduced hepatic insulin extraction ACKNOWLEDGEMENTS in response to gastric inhibitory polypeptide compensates for reduced insulin We thank fellow laboratory members for critical reading of the manuscript and for secretion in normal-weight and normal glucose tolerant ﬁrst-degree relatives of technical assistance with the analysis. The computations for this work were type 2 diabetic patients. Diabetes 53, 2359–2365 (2004). performed in part on the NIG supercomputer system at ROIS National Institute of 21. Jones, C. N. et al. Alterations in the glucose-stimulated insulin secretory dose- Genetics. This work was supported by the Creation of Fundamental Technologies for response curve and in insulin clearance in nondiabetic insulin-resistant indivi- duals. J. Clin. Endocrinol. Metab. 82, 1834–1838 (1997). Understanding and Control of Biosystem Dynamics, CREST (JPMJCR12W3), of the 22. Tamaki, M. et al. The diabetes-susceptible gene SLC30A8/ZnT8 regulates hepatic Japan Science and Technology Agency (JST); Japan Diabetes Foundation; Ono insulin clearance. J. Clin. Invest. 123, 4513–4524 (2013). Medical Research Foundation; and the Japan Society for the Promotion of Science 23. Bonora, E., Zavaroni, I., Coscelli, C. & Butturini, U. Decreased hepatic insulin (JSPS) KAKENHI Grant Number (17H06300). extraction in subjects with mild glucose intolerance. Metabolism 32, 438–446 (1983). 24. Saisho, Y. et al. Postprandial serum C-peptide to plasma glucose ratio as a pre- AUTHOR CONTRIBUTIONS dictor of subsequent insulin treatment in patients with type 2 diabetes. Endocr. J. K.O., M.F., W.O., and S.K. conceived the project; H.Ko., K.S., and W.O. designed and 58, 315–322 (2011). performed the experiments; K.O. and M.F. developed the computational model; K.O., 25. Ahrén, B. & Thorsson, O. Increased insulin sensitivity is associated with reduced M.F., S.U., and H.Ku. analyzed the data; K.O., W.O., and S.K. wrote the manuscript. insulin and glucagon secretion and increased insulin clearance in man. J. Clin. Endocrinol. Metab. 88, 1264–1270 (2003). 26. Breda, E., Cavaghan, M. K., Toffolo, G., Polonsky, K. S. & Cobelli, C. Oral glucose ADDITIONAL INFORMATION tolerance test minimal model indexes of beta-cell function and insulin sensitivity. Supplementary information accompanies the paper on the npj Systems Biology and Diabetes 50, 150–158 (2001). Applications website (https://doi.org/10.1038/s41540-018-0051-6). 27. Picchini, U., De Gaetano, A., Panunzi, S., Ditlevsen, S. & Mingrone, G. A mathe- matical model of the euglycemic hyperinsulinemic clamp. Theor. Biol. Med. Model Competing interests: The authors declare no competing interests. 2, 44 (2005). 28. Cobelli, C. et al. The oral minimal model method. Diabetes 63, 1203–1213 (2014). 29. Bergman, R. N., Phillips, L. S. & Cobelli, C. Physiologic evaluation of factors con- Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims trolling glucose tolerance in man: measurement of insulin sensitivity and beta- in published maps and institutional afﬁliations. Published in partnership with the Systems Biology Institute npj Systems Biology and Applications (2018) 14 Increase in hepatic and decrease in peripheral K Ohashi et al. cell glucose sensitivity from the response to intravenous glucose. J. Clin. Invest. 50. Noguchi, R. et al. The selective control of glycolysis, gluconeogenesis and gly- 68, 1456–1467 (1981). cogenesis by temporal insulin patterns. Mol. Syst. Biol. 9, 664 (2013). 30. Ohashi, K. et al. Glucose homeostatic law: insulin clearance predicts the pro- 51. Sano, T. et al. Selective control of up-regulated and down-regulated genes by gression of glucose intolerance in humans. PLoS ONE 10, e0143880 (2015). temporal patterns and doses of insulin. Sci. Signal 9, ra112 (2016). 31. Eaton, R. P., Allen, R. C., Schade, D. S., Erickson, K. M. & Standefer, J. Prehepatic 52. Goodner, C. J., Sweet, I. R. & Harrison, H. C. Rapid reduction and return of surface insulin production in man: kinetic analysis using peripheral connecting peptide insulin receptors after exposure to brief pulses of insulin in perifused rat hepa- behavior. J. Clin. Endocrinol. Metab. 51, 520–528 (1980). tocytes. Diabetes 37, 1316–1323 (1988). 32. Vølund, A., Polonsky, K. S. & Bergman, R. N. Calculated pattern of intraportal 53. Hirashima, Y. et al. Insulin down-regulates insulin receptor substrate-2 expression insulin appearance without independent assessment of C-peptide kinetics. Dia- through the phosphatidylinositol 3-kinase/Akt pathway. J. Endocrinol. 179, betes 36, 1195–1202 (1987). 253–266 (2003). 33. Cobelli, C. & Pacini, G. Insulin secretion and hepatic extraction in humans by 54. Hori, S. S., Kurland, I. J. & DiStefano, J. J. Role of endosomal trafﬁcking dynamics minimal modeling of C-peptide and insulin kinetics. Diabetes 37, 223–231 (1988). on the regulation of hepatic insulin receptor activity: models for Fao cells. Ann. 34. Grodsky, G. M. A threshold distribution hypothesis for packet storage of insulin Biomed. Eng. 34, 879–892 (2006). and its mathematical modeling. J. Clin. Invest. 51, 2047–2059 (1972). 55. Matveyenko, A. V. et al. Pulsatile portal vein insulin delivery enhances hepatic 35. Ličko, V. & Silvers, A. Open-loop glucose-insulin control with threshold secretory insulin action and signaling. Diabetes 61, 2269–2279 (2012). mechanism: analysis of intravenous glucose tolerance tests in man. Math. Biosci. 56. Sedaghat, A. R., Sherman, A. & Quon, M. J. A mathematical model of metabolic 27, 319–332 (1975). insulin signaling pathways. Am. J. Physiol. Endocrinol. Metab. 283, E1084–E1101 36. Toffolo, G. et al. Quantitative indexes of beta-cell function during graded (2002). up&down glucose infusion from C-peptide minimal models. Am. J. Physiol. 57. Kubota, N. et al. Dynamic functional relay between insulin receptor substrate 1 Endocrinol. Metab. 280,E2–E10 (2001). and 2 in hepatic insulin signaling during fasting and feeding. Cell Metab. 8,49–64 37. Toffolo, G., Campioni, M., Basu, R., Rizza, R. A. & Cobelli, C. A minimal model of (2008). insulin secretion and kinetics to assess hepatic insulin extraction. Am. J. Physiol. 58. Vølund, A. et al. In vitro and in vivo potency of insulin analogues designed for Endocrinol. Metab. 290, E169–E176 (2006). clinical use. Diabet. Med. 8, 839–847 (1991). 38. Chase, J. G. et al. A three-compartment model of the C-peptide-insulin dynamic 59. Choi, E. & Ahn, W. A new mixture ratio of heparin for the cell salvage device. during the DIST test. Math. Biosci. 228, 136–146 (2010). Korean J. Anesthesiol. 60, 226 (2011). 39. Mari, A., Tura, A., Gastaldelli, A. & Ferrannini, E. Assessing insulin secretion by 60. Lagarias, J., Reeds, J., Wright, M. & Wright, P. Convergence properties of the modeling in multiple-meal tests: role of potentiation. Diabetes 51(Suppl. 1), Nelder-Mead simplex method in low dimensions. Siam J. Optim. 9, 112–147 S221–S226 (2002). (1998). 40. Polidori, D. C., Bergman, R. N., Chung, S. T. & Sumner, A. E. Hepatic and extra- 61. Fujita, K. A. et al. Decoupling of receptor and downstream signals in the Akt hepatic insulin clearance are differentially regulated: results from a novel model- pathway by its low-pass ﬁlter characteristics. Sci. Signal 3, ra56 (2010). based analysis of intravenous glucose tolerance data. Diabetes 65, 1556–1564 62. Hubert, M. & der Van der Veeken, S. Outlier detection for skewed data. J. Che- (2016). mom. 22, 235–246 (2008). 41. Akaike, H. In Proc. 2nd International Symposium on Information Theory (eds. Pet- 63. Brys, G., Hubert, M. & Struyf, A. A robust measure of skewness. J. Comput. Graph. rov, B. N. & Csáki, F.) 267–281 (Akademiai Kiado, Budapest, Hungary, 1973). Stat. 13, 996–1017 (2004). 42. Butler, A. E. et al. Beta-cell deﬁcit and increased beta-cell apoptosis in humans 64. Benjamini, Y. & Hochberg, Y. Controlling the false discovery rate: a practical and with type 2 diabetes. Diabetes 52, 102–110 (2003). powerful approach to multiple testing. J. R. Stat. Soc. B 57, 289–300 (1995). 43. Inaishi, J. et al. Effects of obesity and diabetes on α- and β-cell mass in surgically 65. Schmidt, H. & Jirstrand, M. Systems Biology Toolbox for MATLAB: a computational resected human pancreas. J. Clin. Endocrinol. Metab. 101, 2874–2882 (2016). platform for research in systems biology. Bioinformatics 22, 514–515 (2006). 44. Mizukami, H. et al. Involvement of oxidative stress-induced DNA damage, endoplasmic reticulum stress, and autophagy deﬁcits in the decline of β-cell mass in Japanese type 2 diabetic patients. Diabetes Care 37, 1966–1974 Open Access This article is licensed under a Creative Commons (2014). Attribution 4.0 International License, which permits use, sharing, 45. Duckworth, W. C., Bennett, R. G. & Hamel, F. G. Insulin degradation: progress and adaptation, distribution and reproduction in any medium or format, as long as you give potential. Endocr. Rev. 19, 608–624 (1998). appropriate credit to the original author(s) and the source, provide a link to the Creative 46. Kubota, H. et al. Temporal coding of insulin action through multiplexing of the Commons license, and indicate if changes were made. The images or other third party AKT pathway. Mol. Cell 46, 820–832 (2012). material in this article are included in the article’s Creative Commons license, unless 47. Benzi, L. et al. Insulin degradation in vitro and in vivo: a comparative study in indicated otherwise in a credit line to the material. If material is not included in the men. Evidence that immunoprecipitable, partially rebindable degradation pro- article’s Creative Commons license and your intended use is not permitted by statutory ducts are released from cells and circulate in blood. Diabetes 43, 297–304 (1994). regulation or exceeds the permitted use, you will need to obtain permission directly 48. Polonsky, K. S. et al. Quantitative study of insulin secretion and clearance in from the copyright holder. To view a copy of this license, visit http://creativecommons. normal and obese subjects. J. Clin. Invest. 81, 435–441 (1988). org/licenses/by/4.0/. 49. Raue, A., Karlsson, J., Saccomani, M. P., Jirstrand, M. & Timmer, J. Comparison of approaches for parameter identiﬁability analysis of biological systems. Bioinfor- © The Author(s) 2018 matics 30, 1440–1448 (2014). npj Systems Biology and Applications (2018) 14 Published in partnership with the Systems Biology Institute http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png npj Systems Biology and Applications Springer Journals http://www.deepdyve.com/lp/springer-journals/increase-in-hepatic-and-decrease-in-peripheral-insulin-clearance-v0BOiI5NSn

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References (73)

Guy Brys, M. Hubert, Anja Struyf (2004)
A Robust Measure of Skewness
Journal of Computational and Graphical Statistics, 13
J. Chase, Klaus Mayntzhusen, P. Docherty, S. Andreassen, K. McAuley, T. Lotz, C. Hann (2010)
A three-compartment model of the C-peptide-insulin dynamic during the DIST test.
Mathematical biosciences, 228 2
A. Vølund, J. Brange, K. Drejer, I. Jensen, J. Markussen, U. Ribel, A. Sorensen, J. Schlichtkrull (1991)
In Vitro and In Vivo Potency of Insulin Analogues Designed for Clinical Use
Diabetic Medicine, 8
W. Duckworth, F. Hamel, D. Peavy (1988)
Hepatic metabolism of insulin.
The American journal of medicine, 85 5A
R. Rabkin, J. Kitaji (1983)
Renal metabolism of peptide hormones.
Mineral and electrolyte metabolism, 9 4-6
N. Kubota, Tetsuya Kubota, S. Itoh, Hiroki Kumagai, H. Kozono, Iseki Takamoto, T. Mineyama, H. Ogata, K. Tokuyama, M. Ohsugi, Takayoshi Sasako, M. Moroi, K. Sugi, S. Kakuta, Y. Iwakura, T. Noda, Shin Ohnishi, R. Nagai, K. Tobe, Y. Terauchi, K. Ueki, T. Kadowaki (2008)
Dynamic functional relay between insulin receptor substrate 1 and 2 in hepatic insulin signaling during fasting and feeding.
Cell metabolism, 8 1
Y. Hirashima, K. Tsuruzoe, S. Kodama, M. Igata, T. Toyonaga, K. Ueki, C. Kahn, E. Araki (2003)
Insulin down-regulates insulin receptor substrate-2 expression through the phosphatidylinositol 3-kinase/Akt pathway.
The Journal of endocrinology, 179 2
C. Goodner, I. Sweet, H. Harrison (1988)
Rapid Reduction and Return of Surface Insulin Receptors After Exposure to Brief Pulses of Insulin in Perifused Rat Hepatocytes
Diabetes, 37
E. Bonora, I. Zavaroni, C. Coscelli, U. Butturini (1983)
Decreased hepatic insulin extraction in subjects with mild glucose intolerance.
Metabolism: clinical and experimental, 32 5
C. Cobelli, G. Pacini (1988)
Insulin Secretion and Hepatic Extraction in Humans by Minimal Modeling of C-Peptide and Insulin Kinetics
Diabetes, 37
K. Polonsky, B. Given, E. Cauter (1988)
Twenty-four-hour profiles and pulsatile patterns of insulin secretion in normal and obese subjects.
The Journal of clinical investigation, 81 2
Rei Noguchi, Hiroyuki Kubota, K. Yugi, Yu Toyoshima, Yasunori Komori, T. Soga, Shinya Kuroda
Molecular Systems Biology Peer Review Process File the Selective Control of Glycolysis, Gluconeogenesis and Glycogenesis by Temporal Insulin Patterns Transaction Report
S. Seino, T. Shibasaki, K. Minami (2011)
Dynamics of insulin secretion and the clinical implications for obesity and diabetes.
The Journal of clinical investigation, 121 6
CC Lee (2013)
Insulin clearance and the incidence of type 2 diabetes in Hispanics and African Americans: the IRAS Family Study
Diabetes Care, 36
Yoko Okuno, H. Komada, K. Sakaguchi, Tomoaki Nakamura, Naoko Hashimoto, Y. Hirota, W. Ogawa, S. Seino (2013)
Postprandial serum C-peptide to plasma glucose concentration ratio correlates with oral glucose tolerance test- and glucose clamp-based disposition indexes.
Metabolism: clinical and experimental, 62 10
Kazuhiro Fujita, Yu Toyoshima, Shinsuke Uda, Yu-ichi Ozaki, Hiroyuki Kubota, Shinya Kuroda (2010)
Decoupling of Receptor and Downstream Signals in the Akt Pathway by Its Low-Pass Filter Characteristics
Science Signaling, 3
Y. Saisho, Kinsei Kou, Kumiko Tanaka, T. Abe, Hideaki Kurosawa, A. Shimada, S. Meguro, T. Kawai, H. Itoh (2011)
Postprandial serum C-peptide to plasma glucose ratio as a predictor of subsequent insulin treatment in patients with type 2 diabetes.
Endocrine journal, 58 4
B. Ahrén, O. Thorsson (2003)
Increased insulin sensitivity is associated with reduced insulin and glucagon secretion and increased insulin clearance in man.
The Journal of clinical endocrinology and metabolism, 88 3
G. Toffolo, M. Campioni, R. Basu, R. Rizza, C. Cobelli (2006)
A minimal model of insulin secretion and kinetics to assess hepatic insulin extraction.
American journal of physiology. Endocrinology and metabolism, 290 1
Jun Inaishi, Y. Saisho, Seiji Sato, Kinsei Kou, Rie Murakami, Yuusuke Watanabe, M. Kitago, Y. Kitagawa, Taketo Yamada, H. Itoh (2016)
Effects of Obesity and Diabetes on α- and β-Cell Mass in Surgically Resected Human Pancreas
The Journal of Clinical Endocrinology and Metabolism, 101
M. Marini, S. Frontoni, E. Succurro, F. Arturi, T. Fiorentino, A. Sciacqua, F. Perticone, G. Sesti (2014)
Differences in insulin clearance between metabolically healthy and unhealthy obese subjects
Acta Diabetologica, 51
M. Stumvoll, A. Mitrakou, W. Pimenta, T. Jenssen, H. Yki-Järvinen, T. Haeften, W. Renn, J. Gerich (2000)
Use of the oral glucose tolerance test to assess insulin release and insulin sensitivity.
Diabetes care, 23 3
Henning Schmidt (2006)
Systems biology Systems Biology Toolbox for MATLAB : a computational platform for research in systems biology
Hiroyuki Kubota, Rei Noguchi, Yu Toyoshima, Yu-ichi Ozaki, Shinsuke Uda, Kanako Watanabe, W. Ogawa, Shinya Kuroda (2012)
Temporal coding of insulin action through multiplexing of the AKT pathway.
Molecular cell, 46 6
Tomoshige Hayashi, E. Boyko, K. Sato, M. McNeely, D. Leonetti, S. Kahn, W. Fujimoto (2013)
Patterns of Insulin Concentration During the OGTT Predict the Risk of Type 2 Diabetes in Japanese Americans
Diabetes Care, 36
Motoyuki Tamaki, Y. Fujitani, Akemi Hara, Toyoyoshi Uchida, Y. Tamura, Kageumi Takeno, Minako Kawaguchi, Takahiro Watanabe, T. Ogihara, Ayako Fukunaka, Tomoaki Shimizu, T. Mita, A. Kanazawa, M. Imaizumi, T. Abe, H. Kiyonari, Shintaro Hojyo, T. Fukada, T. Kawauchi, S. Nagamatsu, T. Hirano, R. Kawamori, H. Watada (2013)
The diabetes-susceptible gene SLC30A8/ZnT8 regulates hepatic insulin clearance.
The Journal of clinical investigation, 123 10
S. Prato, A. Tiengo (2001)
The importance of first‐phase insulin secretion: implications for the therapy of type 2 diabetes mellitus
Diabetes/Metabolism Research and Reviews, 17
H. Mizukami, Kazunori Takahashi, Wataru Inaba, Kentaro Tsuboi, Sho Osonoi, T. Yoshida, S. Yagihashi (2014)
Involvement of Oxidative Stress–Induced DNA Damage, Endoplasmic Reticulum Stress, and Autophagy Deficits in the Decline of β-Cell Mass in Japanese Type 2 Diabetic Patients
Diabetes Care, 37
C. Lee, S. Haffner, L. Wagenknecht, C. Lorenzo, J. Norris, R. Bergman, D. Stefanovski, A. Anderson, J. Rotter, M. Goodarzi, A. Hanley (2013)
Insulin Clearance and the Incidence of Type 2 Diabetes in Hispanics and African Americans
Diabetes Care, 36
M. Pfeifer, J. Halter, D. Porte (1981)
Insulin secretion in diabetes mellitus.
The American journal of medicine, 70 3
M. Abdul-Ghani, D. Tripathy, R. DeFronzo (2006)
Contributions of beta-cell dysfunction and insulin resistance to the pathogenesis of impaired glucose tolerance and impaired fasting glucose.
Diabetes care, 29 5
Umberto Picchini, A. Gaetano, S. Panunzi, Susanne Ditlevsen, G. Mingrone (2005)
A mathematical model of the euglycemic hyperinsulinemic clamp
Theoretical Biology & Medical Modelling, 2
W. Duckworth, R. Bennett, F. Hamel (1998)
Insulin degradation: progress and potential.
Endocrine reviews, 19 5
R. Bergman, L. Phillips, C. Cobelli (1981)
Physiologic evaluation of factors controlling glucose tolerance in man: measurement of insulin sensitivity and beta-cell glucose sensitivity from the response to intravenous glucose.
The Journal of clinical investigation, 68 6
E. Breda, M. Cavaghan, G. Toffolo, K. Polonsky, C. Cobelli (2001)
Oral glucose tolerance test minimal model indexes of beta-cell function and insulin sensitivity.
Diabetes, 50 1
V. Ličko, A. Silvers (1975)
Open-loop glucose-insulin control with threshold secretory mechanism: Analysis of intravenous glucose tolerance tests in man
Bellman Prize in Mathematical Biosciences, 27
C. Cobelli, C. Man, G. Toffolo, R. Basu, A. Vella, R. Rizza (2014)
The Oral Minimal Model Method
Diabetes, 63
A. Matveyenko, D. Liuwantara, T. Gurlo, David Kirakossian, C. Man, C. Cobelli, M. White, Kyle Copps, E. Volpi, S. Fujita, P. Butler (2012)
Pulsatile Portal Vein Insulin Delivery Enhances Hepatic Insulin Action and Signaling
Diabetes, 61
K. Polonsky, B. Given, Lawrence Hirsch, E. Shapiro, H. Tillil, C. Beebe, J. Galloway, B. Frank, T. Karrison, E. Cauter (1988)
Quantitative study of insulin secretion and clearance in normal and obese subjects.
The Journal of clinical investigation, 81 2
Takanori Sano, Kentaro Kawata, S. Ohno, K. Yugi, H. Kakuda, Hiroyuki Kubota, Shinsuke Uda, Masashi Fujii, Katsuyuki Kunida, Daisuke Hoshino, Atsushi Hatano, Yuki Ito, Miharu Sato, Yutaka Suzuki, Shinya Kuroda (2016)
Selective control of up-regulated and down-regulated genes by temporal patterns and doses of insulin
Science Signaling, 9
R Noguchi (2013)
10.1038/msb.2013.19
Mol. Syst. Biol., 9
H Schmidt, M Jirstrand (2006)
Systems Biology Toolbox for MATLAB: a computational platform for research in systems biology
Bioinformatics, 22
E. Cerasi, R. Luft (1967)
The plasma insulin response to glucose infusion in healthy subjects and in diabetes mellitus.
Acta endocrinologica, 55 2
A. Butler, J. Janson, S. Bonner-Weir, R. Ritzel, R. Rizza, P. Butler (2003)
Beta-cell deficit and increased beta-cell apoptosis in humans with type 2 diabetes.
Diabetes, 52 1
A. Vølund, K. Polonsky, R. Bergman (1987)
Calculated Pattern of Intraportal Insulin Appearance Without Independent Assessment of C-Peptide Kinetics
Diabetes, 36
J. Lagarias, J. Reeds, M. Wright, P. Wright (1998)
Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions
SIAM J. Optim., 9
L. Benzi, P. Cecchetti, Aannamaria Ciccarone, A. Pilo, G. Cianni, R. Navalesi (1994)
Insulin Degradation In Vitro and In Vivo: A Comparative Study in Men: Evidence That Immunoprecipitable, Partially Rebindable Degradation Products Are Released From Cells and Circulate in Blood
Diabetes, 43
A. Butler, J. Janson, S. Bonner-Weir, R. Ritzel, R. Rizza, P. Butler (2003)
β-Cell Deficit and Increased β-Cell Apoptosis in Humans With Type 2 Diabetes
Diabetes, 52
R. DeFronzo, J. Tobin, R. Andres (1979)
Glucose clamp technique: a method for quantifying insulin secretion and resistance.
The American journal of physiology, 237 3
D. Polidori, R. Bergman, S. Chung, A. Sumner (2016)
Hepatic and Extrahepatic Insulin Clearance Are Differentially Regulated: Results From a Novel Model-Based Analysis of Intravenous Glucose Tolerance Data
Diabetes, 65
Kaoru Ohashi, H. Komada, Shinsuke Uda, Hiroyuki Kubota, Toshinao Iwaki, H. Fukuzawa, Yasunori Komori, Masashi Fujii, Yu Toyoshima, K. Sakaguchi, W. Ogawa, Shinya Kuroda (2015)
Glucose Homeostatic Law: Insulin Clearance Predicts the Progression of Glucose Intolerance in Humans
PLoS ONE, 10
A. Mari, A. Tura, A. Gastaldelli, E. Ferrannini (2002)
Assessing insulin secretion by modeling in multiple-meal tests: role of potentiation.
Diabetes, 51 Suppl 1
H. Sato, T. Terasaki, H. Mizuguchi, K. Okumura, A. Tsuji (1991)
Receptor-recycling model of clearance and distribution of insulin in the perfused mouse liver
Diabetologia, 34
M. Perley, D. Kipnis (1967)
Plasma insulin responses to oral and intravenous glucose: studies in normal and diabetic sujbjects.
The Journal of clinical investigation, 46 12
N. Rudovich, H. Rochlitz, A. Pfeiffer (2004)
Reduced hepatic insulin extraction in response to gastric inhibitory polypeptide compensates for reduced insulin secretion in normal-weight and normal glucose tolerant first-degree relatives of type 2 diabetic patients.
Diabetes, 53 9
J. Lindsay, A. McKillop, M. Mooney, P. Flatt, P. Bell, F. O'Harte (2003)
Meal-induced 24-hour profile of circulating glycated insulin in type 2 diabetic subjects measured by a novel radioimmunoassay.
Metabolism: clinical and experimental, 52 5
H Schmidt (2006)
10.1093/bioinformatics/bti799
Bioinformatics, 22
R. DeFronzo, Riccardd Bonadonna, E. Ferrannini (1992)
Pathogenesis of NIDDM: A Balanced Overview
Diabetes Care, 15
G. Toffolo, E. Breda, M. Cavaghan, D. Ehrmann, K. Polonsky, C. Cobelli (2001)
Quantitative indexes of beta-cell function during graded up&down glucose infusion from C-peptide minimal models.
American journal of physiology. Endocrinology and metabolism, 280 1
A. Raue, J. Karlsson, M. Saccomani, M. Jirstrand, J. Timmer (2014)
Comparison of approaches for parameter identifiability analysis of biological systems
Bioinformatics, 30 10
E. Choi, W. Ahn (2011)
A new mixture ratio of heparin for the cell salvage device
Korean Journal of Anesthesiology, 60
A. Sedaghat, A. Sherman, M. Quon (2002)
A mathematical model of metabolic insulin signaling pathways.
American journal of physiology. Endocrinology and metabolism, 283 5
E. Breda, M. Cavaghan, G. Toffolo, K. Polonsky, C. Cobelli (2001)
Oral Glucose Tolerance Test Minimal Model Indexes of β-Cell Function and Insulin Sensitivity
Diabetes, 50
Eaton Rp, R. Allen, D. Schade, K. Erickson, J. Standefer (1980)
Prehepatic insulin production in man: kinetic analysis using peripheral connecting peptide behavior.
The Journal of clinical endocrinology and metabolism, 51 3
M. Abdul-Ghani, D. Tripathy, R. DeFronzo (2006)
Contributions of β-Cell Dysfunction and Insulin Resistance to the Pathogenesis of Impaired Glucose Tolerance and Impaired Fasting Glucose A table elsewhere in this issue shows conventional and Système International (SI) units and conversion factors for many substances.
Diabetes Care, 29
V Ličko, A Silvers (1975)
Open-loop glucose-insulin control with threshold secretory mechanism: analysis of intravenous glucose tolerance tests in man
Math. Biosci., 27
Y. Benjamini, Y. Hochberg (1995)
Controlling the false discovery rate: a practical and powerful approach to multiple testing
Journal of the royal statistical society series b-methodological, 57
R Noguchi (2013)
The selective control of glycolysis, gluconeogenesis and glycogenesis by temporal insulin patterns
Mol. Syst. Biol., 9
M. Hubert, Stephan Veeken (2008)
Outlier detection for skewed data
Journal of Chemometrics, 22
Y. Seino, K. Nanjo, N. Tajima, T. Kadowaki, A. Kashiwagi, E. Araki, C. Ito, N. Inagaki, Y. Iwamoto, M. Kasuga, T. Hanafusa, M. Haneda, K. Ueki (2010)
Report of the Committee on the Classification and Diagnostic Criteria of Diabetes Mellitus
Journal of Diabetes Investigation, 1
Clare Jones, Dee Pei, Patricia Staris, Kenneth Polonsky, Y-D. Chen, G. Reaven (1997)
Alterations in the glucose-stimulated insulin secretory dose-response curve and in insulin clearance in nondiabetic insulin-resistant individuals.
The Journal of clinical endocrinology and metabolism, 82 6
Sharon Hori, I. Kurland, J. DiStefano (2006)
Role of Endosomal Trafficking Dynamics on the Regulation of Hepatic Insulin Receptor Activity: Models for Fao Cells
Annals of Biomedical Engineering, 34
G. Grodsky (1972)
A threshold distribution hypothesis for packet storage of insulin and its mathematical modeling.
The Journal of clinical investigation, 51 8

Publisher: Springer Journals
Copyright: Copyright © 2018 by The Author(s)
Subject: Life Sciences; Life Sciences, general; Systems Biology; Computer Appl. in Life Sciences; Computational Biology/Bioinformatics; Systems Biology; Bioinformatics
eISSN: 2056-7189
DOI: 10.1038/s41540-018-0051-6
Publisher site: See Article on Publisher Site

Abstract

www.nature.com/npjsba ARTICLE OPEN Increase in hepatic and decrease in peripheral insulin clearance characterize abnormal temporal patterns of serum insulin in diabetic subjects 1 1,2 3 3 4 4 4 Kaoru Ohashi , Masashi Fujii , Shinsuke Uda , Hiroyuki Kubota , Hisako Komada , Kazuhiko Sakaguchi , Wataru Ogawa and 1,2,5 Shinya Kuroda Insulin plays a central role in glucose homeostasis, and impairment of insulin action causes glucose intolerance and leads to type 2 diabetes mellitus (T2DM). A decrease in the transient peak and sustained increase of circulating insulin following an infusion of glucose accompany T2DM pathogenesis. However, the mechanism underlying this abnormal temporal pattern of circulating insulin concentration remains unknown. Here we show that changes in opposite direction of hepatic and peripheral insulin clearance characterize this abnormal temporal pattern of circulating insulin concentration observed in T2DM. We developed a mathematical model using a hyperglycemic and hyperinsulinemic-euglycemic clamp in 111 subjects, including healthy normoglycemic and diabetic subjects. The hepatic and peripheral insulin clearance signiﬁcantly increase and decrease, respectively, from healthy to borderline type and T2DM. The increased hepatic insulin clearance reduces the amplitude of circulating insulin concentration, whereas the decreased peripheral insulin clearance changes the temporal patterns of circulating insulin concentration from transient to sustained. These results provide further insight into the pathogenesis of T2DM, and thus may contribute to develop better treatment of this condition. npj Systems Biology and Applications (2018) 4:14 ; doi:10.1038/s41540-018-0051-6 INTRODUCTION circulating insulin concentration transiently increases during the ﬁrst 10 min and then continuously increases during the following Insulin is the major anabolic hormone regulating the glucose 120 min, which are known as the ﬁrst and second phase of insulin homeostasis. The impaired action of insulin is a characteristic of 1 12 secretion, respectively. type 2 diabetes mellitus (T2DM), accompanied by abnormality in 2–4 These temporal patterns of circulating insulin concentration the temporal patterns of circulating insulin concentration. The differ between normal glucose tolerance (NGT), borderline type, circulating insulin concentration changes over the course of 24 h, including a persistently low level during fasting and a surge in and T2DM. Based on an OGTT, a subject with FPG <110 mg/dL response to food ingestion, consisting of basal and additional (6.1 mM) and 2-h PG <140 mg/dL (7.8 mM) is categorized as NGT. 5,6 secretions from the pancreas, respectively. A subject with FPG of 110–125 mg/dL (6.1–6.9 mM) or 2-h PG of Ability of additional insulin secretion is assessed by the oral 140–199 mg/dL (7.8–11.0 mM) is categorized as borderline type, glucose tolerance test (OGTT), in which a subject’s ability to and those with FPG ≥126 mg/dL (7.0 mM) or 2-h PG ≥200 mg/dL tolerate the glucose load (glucose tolerance) is evaluated by (11.1 mM) as T2DM. In general, plasma insulin concentration measuring the circulating glucose concentration after an over- during the late-phase secretion of an OGTT in borderline type night fast (fasting plasma glucose concentration; FPG) and again subjects is higher than in NGT subjects, whereas the concentration 2 h after a 75-g oral glucose load (2-h post-load glucose during the early-phase secretion is similar in NGT and borderline concentration; 2-h PG). During this test, the circulating insulin 9,10 type subjects. Plasma insulin concentration during the ﬁrst- concentration transiently increases and then continuously phase secretion of an IVGTT decreases as glucose intolerance increases or decreases, known as the early and late phases of 9,10 progresses, whereas that during the second-phase secretion is insulin secretion, respectively. The direct contribution of 2–4 relatively maintained. Such changes of the temporal patterns of circulating glucose concentration to circulating insulin concentra- circulating insulin concentration during the progression of glucose tion is assessed by the use of an intravenous glucose tolerance intolerance from NGT to T2DM suggest that these temporal test (IVGTT). This test excludes the effects of intestinal patterns are involved in the maintenance and impairment of absorption of glucose and incretins secretion that trigger insulin glucose homeostasis. Together with the measurement of circulat- secretion, thus permitting quantitative estimates of the ability of circulating glucose to initiate insulin secretion. During this test, the ing glucose concentration, the time course of circulating insulin 1 2 Department of Biological Sciences, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan; Molecular Genetics Research Laboratory, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan; Division of Integrated Omics, Research Center for Transomics Medicine, Medical Institute of Bioregulation, Kyushu University, 3-1-1 Maidashi, Higashi-ku, Fukuoka, Fukuoka 812-8582, Japan; Division of Diabetes and Endocrinology, Department of Internal Medicine, Kobe University Graduate School of Medicine, 7-5-1 Kusunoki-cho, Chuo-ku, Kobe, Hyogo 650-0017, Japan and CREST, Japan Science and Technology Corporation, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan Correspondence: Shinya Kuroda (skuroda@bs.s.u-tokyo.ac.jp) Received: 23 May 2017 Revised: 12 February 2018 Accepted: 12 February 2018 Published in partnership with the Systems Biology Institute Increase in hepatic and decrease in peripheral K Ohashi et al. 26–28 concentration is used to assess the insulin secretion from the concentration by accounting for this mutual dependence. The pancreas and insulin sensitivity. model known as the minimal model is used to estimate insulin However, it is difﬁcult to assess the insulin secretion and sensitivity and insulin secretion abilities for each individual based sensitivity of body tissues directly from the circulating insulin on the time courses of circulating glucose and insulin concentra- concentration because of the negative feedback between tions during IVGTT. Furthermore, from the parameters of the circulating insulin and glucose. A rise in circulating glucose model, Bergman et al. identiﬁed a relationship between the concentration stimulates insulin secretion, and the resultant rise in subject’s glucose intolerance and the product of insulin secretion circulating insulin concentration stimulates glucose uptake, and sensitivity. causing circulating glucose concentration to fall. This feedback We previously developed a mathematical model based on time means there is mutual dependence between glucose and insulin, courses of plasma glucose and serum insulin during consecutive making it difﬁcult to distinguish the effect of insulin secretion and hyperglycemic and hyperinsulinemic-euglycemic clamp condi- sensitivity directly from the circulating insulin concentration. tions, and estimated the parameters of insulin secretion, To directly assess insulin secretion without the effect of the sensitivity, and peripheral insulin clearance for each subject. We feedback from insulin to glucose, DeFronzo et al. developed the found that peripheral insulin clearance signiﬁcantly decreased hyperglycemic clamp technique, in which insulin secretion is from NGT to borderline type to T2DM. However, the hepatic and measured while circulating glucose concentration is at a ﬁxed peripheral insulin clearance could not be distinguished because C- hyperglycemic plateau maintained by exogenous continuous peptide was not incorporated in the model. glucose infusion. The measurements of circulating insulin Hepatic insulin clearance is calculated as the difference concentration during the ﬁrst 10 min and after 10 min are used between pre-hepatic and post-hepatic insulin concentrations to assess the insulin secretion ability and are known as the ﬁrst- assessed by comparing circulating C-peptide and insulin concen- 13,14 and second-phase insulin secretions, respectively. trations, because C-peptide, unlike insulin, is not removed by the Conversely, to directly assess insulin sensitivity without the liver. Since the circulating C-peptide concentration is also effect of the feedback from glucose to insulin, the controlled by its secretion and clearance, a mathematical model hyperinsulinemic-euglycemic clamp was developed. In this for C-peptide kinetics was developed. The models for circulating method, circulating insulin concentration is maintained at a ﬁxed insulin and C-peptide have been used to estimate the secretion hyperinsulinemic plateau and circulating glucose at a ﬁxed normal and kinetics of insulin and C-peptide, as well as hepatic insulin 32–39 plateau by continuous infusion of both insulin and glucose. Tissue clearance. However, peripheral insulin clearance was not insulin sensitivity is deﬁned as the ratio of the glucose infusion assessed in the models, because exogenous insulin infusion, rate to the circulating insulin concentration when they reach which is required for accurate estimation of peripheral insulin 13,14 plateaus. clearance, was not performed. The body controls the circulating insulin concentration by 40 Recently, Polidori et al. reported that both hepatic and balancing insulin secretion and insulin clearance. The major extrahepatic insulin clearance, corresponding to peripheral insulin organs responsible for insulin clearance are the liver, which clearance, can be estimated by modeling analysis using plasma 15,16 removes portal insulin during ﬁrst-pass transit, and insulin- insulin and C-peptide concentrations obtained from the insulin- sensitive tissues such as muscle, which remove insulin from the modiﬁed frequently sampled IVGTT. The parameters of hepatic systemic circulation. The insulin clearance from portal vein in the and peripheral insulin clearance in the model were not highly liver and from peripheral plasma in other organs is called hepatic correlated, suggesting that the two types of insulin clearance are and peripheral insulin clearance, respectively. Although the regulated differently. In addition, hepatic insulin clearance was relationship between changes of insulin clearance and the negatively correlated with insulin secretion, and peripheral insulin progression of glucose intolerance have been reported, the clearance was positively correlated with insulin sensitivity. effects of insulin clearance are controversial. Some studies found However, hepatic and peripheral insulin clearance in T2DM that during the progression of glucose intolerance, insulin 18–21 subjects and the roles of both types of clearance in the changes clearance decreased, whereas hepatic insulin clearance 22 18,23 in temporal pattern of circulating insulin concentration during the increased or decreased. Thus, the hepatic and peripheral progression of glucose intolerance have yet to be examined. insulin clearances were not explicitly distinguished, making it In this study, we developed a mathematical model based on the difﬁcult to interpret the effect of both types. time course of the serum insulin and C-peptide concentrations Hepatic insulin clearance cannot be assessed directly from during consecutive hyperglycemic and hyperinsulinemic- circulating insulin concentration because insulin is extracted from euglycemic clamp conditions, and estimated the hepatic and the liver before secreted insulin is delivered into the systemic peripheral insulin clearance for each subject. The parameters from circulation. However, insulin is secreted at an equimolar ratio with 111 subjects (47 NGT, 17 borderline type, and 47 T2DM) showed a C-peptide, a peptide cleaved from proinsulin to produce insulin, signiﬁcant increase in hepatic insulin clearance and signiﬁcant which is not extracted in the liver. Thus, by measuring circulating decrease in peripheral insulin clearance from NGT to borderline C-peptide concentration simultaneously with circulating insulin type and T2DM, respectively. We also found that hepatic and concentration, the pre-hepatic insulin concentration can be peripheral insulin clearance play distinct roles in the abnormal accurately assessed. The C-peptide index, which is the ratio of temporal patterns of serum insulin concentration from NGT to circulating glucose to C-peptide concentration, is an index of borderline type and T2DM, namely an increase in hepatic insulin insulin secretion with clinical utility. Hepatic insulin clearance is clearance reduces the amplitude of serum insulin concentration, clinically quantiﬁed as the ratio of circulating insulin to C-peptide whereas a decrease in peripheral insulin clearance changes the concentration during the ﬁrst 10 min under the hyperglycemic temporal patterns of serum insulin concentration from transient to clamp condition. sustained. The clinical indices of insulin secretion and clearance are indirect measures because they are obtained from temporal patterns of circulating concentrations, which are simultaneously RESULTS affected by insulin secretion and clearance. Therefore, the clinical Consecutive hyperglycemic and hyperinsulinemic-euglycemic index of insulin secretion implicitly involves the effect of insulin clamp data clearance and vice versa. Mathematical models have been developed for speciﬁcally quantifying insulin secretion, sensitivity, We calculated the averaged time courses of concentrations of and clearance abilities from temporal patterns of circulating plasma glucose, serum insulin, and C-peptide during consecutive npj Systems Biology and Applications (2018) 14 Published in partnership with the Systems Biology Institute 1234567890():,; Increase in hepatic and decrease in peripheral K Ohashi et al. hyperglycemic and hyperinsulinemic-euglycemic clamp condi- Mathematical model for serum insulin and C-peptide tions of NGT (n = 50), borderline type (n = 18), and T2DM (n = 53) concentrations 14,30 (Fig. 1, Supplementary Figure S1). During the hyperglycemic Many mathematical models that reproduce circulating insulin and 29,32–37 clamp, plasma glucose concentrations at the hyperglycemic C-peptide concentrations have been developed. We devel- plateau were similar among the NGT, borderline type, and T2DM oped six mathematical models based on these models, and the best model was selected for reproducing measured serum insulin groups. and C-peptide concentrations during consecutive hyperglycemic Both the ﬁrst (0–15 min) and second phase of insulin secretion 14,30 and hyperinsulinemic-euglycemic clamp (Supplementary Fig- (15–90 min) were clearly observed in the NGT and borderline type ure S2). These models contain serum insulin and C-peptide subjects, whereas the two phases of insulin secretion were concentrations including both insulin and C-peptide secretion and signiﬁcantly reduced in the T2DM subjects. Serum C-peptide their hepatic and peripheral clearance. Plasma glucose perturba- concentration showed a similar increase during the ﬁrst and tion and insulin infusion were used as inputs (Supplementary second phase of insulin secretion in the NGT and borderline type Figure S1). For each of the 121 subjects, parameters of the six subjects, whereas serum C-peptide concentration was signiﬁcantly models were estimated by using measured concentrations of lower in the T2DM subjects during both phases. Although insulin plasma glucose, serum insulin, and C-peptide. The resulting model and C-peptide should be secreted in an equimolar manner, the was selected based on minimizing the Akaike information serum C-peptide concentration was higher than the serum insulin 41 criterion (AIC), taking into account model complexity and concentration because insulin—but not C-peptide—was removed goodness of ﬁt of serum insulin and C-peptide time courses. by the liver and C-peptide clearance in the periphery was slower The model consisting of four variables (Model VI in Supplemen- than insulin clearance. tary Figure S2) was selected as the best model with the minimum During the hyperinsulinemic-euglycemic clamp at 100–220 min, AIC for 76 of 121 subjects (Fig. 2a, Table 1). In this model, the serum insulin concentration was at a steady-state plateau of variables I and CP correspond to serum concentrations of insulin hyperinsulinemia, but serum insulin concentration differed and C-peptide, respectively. The variable X corresponds to stored signiﬁcantly from the NGT to borderline type and T2DM subjects. insulin and C-peptide in β-cells or β-cell masses. Because the The average serum insulin concentration of the NGT subjects was amounts of stored insulin and C-peptide are equal, a single lowest and that of the borderline type subjects was highest. These variable, X, is used for both. The variable Y is the insulin provision rate depending on plasma glucose concentration. The differential differences indicate that the ability to remove infused insulin from equations of the model are as follows: serum is different among the three groups and suggest that the difference lies in the peripheral insulin clearance. The plasma dY αfβðG hÞ YgðG>hÞ ¼ ; Yð0Þ¼ 0 (1) glucose concentration returned to the basal level from hypergly- dt αY ðG hÞ cemia at a different decay rate among the three groups. The average decay rate was lowest in the T2DM subjects and highest Y m X ðÞ G>h dX ¼ Y v ¼ ; Xð0Þ¼ X (2) in the NGT subjects, suggesting that insulin sensitivity, which is CPin b dt YGðÞ h the ability to promote the hypoglycemic effect in response to serum insulin, decreases from NGT to borderline type to T2DM. dI ¼ k v v þ influx ratio CPin Iout The serum C-peptide concentration returned to the fasting level in dt all groups, and differed signiﬁcantly between the NGT and k m X k ðÞ I I þ fðtÞ ðÞ G>h ratio Iout b borderline type subjects. Only insulin was infused during ¼ ; Ið0Þ¼ I k ðÞ I I þ fðtÞ ðÞ G h Iout b the hyperinsulinemic-euglycemic clamp, indicating that serum (3) C-peptide was derived only from endogenous secretion. Fig. 1 Concentrations of plasma glucose, serum insulin, and C-peptide during consecutive hyperglycemic and hyperinsulinemic-euglycemic clamps. The mean ± SD among the subjects for NGT (green, n = 50), borderline type (red, n = 18), and T2DM (blue, n = 53) of experimental (upper 3 panels) and simulation with Model VI (lower 2 panels) time courses are shown. Hyperglycemic clamp (HGC) was performed for 90 min and hyperinsulinemic-euglycemic clamp (HEC) for 120 min with a 10-min interval. The plasma glucose level is the average value calculated every 5 min of the measurements made every 1 min, and the serum insulin and C-peptide levels are measured values at sampling time (Methods). Simulation time courses are plotted every 10 min. Supplementary Figure S1 and Supplementary Table S1 illustrate the signiﬁcant difference of concentrations at each time point among the three groups Published in partnership with the Systems Biology Institute npj Systems Biology and Applications (2018) 14 Increase in hepatic and decrease in peripheral K Ohashi et al. For the 45 of 121 subjects who were not optimal for this model Table 1. Comparison of the models based on the Akaike information (Fig. 2a; Model VI in Supplementary Figure S2), the distributions of criterion (AIC) the residual sum of squares (RSS) between modeled and measured concentrations of insulin and C-peptide in this model Model No. subjects of min NGT Borderline T2DM AIC mean ± were not signiﬁcantly different from the distributions of the RSS of AIC SD the remaining 76 subjects who were optimal with minimum AIC I 25 7 4 14 −21.1 ± 22.9* for this model (Supplementary Figure S3). There also seems to be no bias in the distribution of the NGT, borderline type, and T2DM II 531 1 −19.0 ± 24.2* subjects among the best models (Table 1). Model VI was also III 000 0 −16.2 ± 24.9* selected when AIC of each model was calculated using measured IV 700 7 −17.2 ± 25.3* time courses of all 121 subjects (Supplementary Table S2). V 843 1 −28.4 ± 26.2 However, in the RSS distributions of all 121 subjects in this model, VI 76 36 10 30 −31.4 ± 25.2 RSS values of three subjects were relatively high and detected as Total 121 50 18 53 outliers, and the three subjects were excluded from the analysis in this study (Supplementary Figure S3). In addition, there seems to The number of subjects optimal for each model with minimum AIC is be no bias of temporal patterns of serum insulin and C-peptide shown (see Methods) concentrations among the subjects in each model (Supplementary *AIC different from Model VI (P < 0.01, corrected by the number of t-tests, Figure S4, Supplementary Table S3). Therefore, we selected the multiplied by 5) model (Fig. 2a; Model VI in Supplementary Figure S2) for further study because it was able to reproduce time courses of serum insulin and C-peptide concentrations for the remaining 118 sub- dCP ¼ v v jects. The simulation with Model VI (Fig. 1, Supplementary Figure CPin CPout dt S1) reproduced measured concentrations of insulin and C-peptide, m X k ðÞ CP CP ðÞ G>h CPout b and reﬂected signiﬁcant differences among the NGT, borderline ¼ ; CPð0Þ¼ CP ; k ðÞ CP CP ðÞ G h type, and T2DM subjects. Seven subjects (one NGT, one borderline CPout b type, and ﬁve T2DM subjects) were excluded because their model (4) parameters were detected as outlier based on the adjusted where I and CP correspond to fasting (basal) serum insulin and b b outlyingness (Methods), and we analyzed the model for the C-peptide concentration, respectively, directly given by the remaining 111 subjects (47 NGT, 17 borderline type, and 47 T2DM) measurement, and X is an initial value of X to be estimated. (Supplementary Table S4). Equation 1 describes how insulin provision rate Y increases according to αβ(G − h) when G > h, and decreases with αY. This Changes in opposite direction of hepatic and peripheral insulin means that provision of X, stored amounts of insulin and C- clearance from NGT to borderline type and T2DM peptide, depends on parameters α and β, and stimulated only We statistically compared the model parameters among the NGT, when the plasma glucose concentration exceeds the threshold borderline type, and T2DM groups (Fig. 2b and Methods). Four of value, h, which corresponds to FPG. the nine parameters, k , k , h, and X , were signiﬁcantly Equation 2 describes how X increases according to the provision Iout ratio b different. rate Y and decreases according to the insulin and C-peptide The parameter k is the degradation rate of serum insulin and secretion v . v is X secreted at the rate m when G > h. Since Iout CPin CPin corresponds to peripheral insulin clearance. The value of k in X , which is the initial value of X, relates to the insulin and C- Iout the NGT subjects was higher than that in the borderline type and peptide secretion when G > h for the ﬁrst time during hypergly- T2DM subjects (Fig. 2c), indicating that peripheral clearance cemic clamp, X is responsible for the ﬁrst-phase secretion. decreases in development of glucose intolerance, which is Equation 3 describes how serum insulin concentration I 30,40 consistent with previous studies. increases according to the post-hepatic insulin delivery, k · ratio The parameter k is the ratio of post-hepatic insulin to C- , and decreases according to peripheral insulin clearance v . ratio CPin Iout I also increases according to infused insulin, inﬂux. k · v is peptide, and (1 − k ) corresponds to the insulin extracted by ratio ratio CPin the liver, that is, hepatic insulin clearance. The value of (1 − k ) expanded as k · m · X, which corresponds to insulin delivered ratio ratio into peripheral circulation after passage through the liver when G in the NGT subjects was lower than that in the borderline type and > h. The parameter k is the molar ratio of post-hepatic insulin T2DM subjects (Fig. 2c), indicating the increase of hepatic insulin ratio clearance in the borderline type and T2DM subjects. This is to C-peptide, which represents the fraction of insulin delivered to the peripheral circulation without being extracted by the liver. consistent with an earlier clinical observation. Given that C-peptide is not extracted by the liver, k can The parameter h is the threshold of plasma glucose concentra- ratio represent the remaining fraction of insulin after the extraction by tion for the insulin secretion and corresponds to FPG. This the liver over the total amount of secreted insulin, and ranges parameter in the T2DM subjects was signiﬁcantly higher than that from 0 to 1. Therefore, (1 − k ) represents the fraction of insulin in the NGT subjects (Fig. 2b), consistent with the fact that FPG is ratio 9,10 extracted by the liver and not delivered to the peripheral higher in T2DM. circulation and corresponds to hepatic insulin clearance; inﬂux is The parameter X is the initial value of X, which corresponds to the insulin infusion rate during hyperinsulinemic-euglycemic the stored amounts of insulin and C-peptide or β-cell masses clamp. The infusion rate at time t is represented by the function before the start of the hyperglycemic clamp. This parameter in the f(t) (Methods). v represents serum insulin degradation with the T2DM subjects was signiﬁcantly lower than that in the NGT Iout rate parameter k . Therefore, k represents insulin degradation subjects (Fig. 2b), consistent with observations that β-cell masses Iout Iout 42–44 in the periphery and corresponds to peripheral insulin clearance. and stored insulin decrease in T2DM patients. Equation 4 describes how serum C-peptide concentration CP Using the same clamp data, we previously showed that insulin 14,30 increases according to the C-peptide secretion v and decreases secretion decreases from NGT to borderline type to T2DM. In CPin according to peripheral C-peptide clearance v . v is C- this study, however, the parameters α and β, related to insulin CPout CPin peptide secreted and delivered to peripheral serum without secretion, did not show any signiﬁcant differences among the hepatic clearance. v represents serum C-peptide degradation NGT, borderline type, and T2DM subjects, possibly because CPout with the rate parameter k . previously deﬁned insulin secretion is described by insulin CPout npj Systems Biology and Applications (2018) 14 Published in partnership with the Systems Biology Institute Increase in hepatic and decrease in peripheral K Ohashi et al. Fig. 2 Mathematical model of serum insulin and C-peptide. a The structure of the model (see also Eqs. 1–4 and Model VI in Supplementary Figure S2). I and CP are serum insulin and C-peptide concentration, respectively. X is the amount of stored insulin and C-peptide, and Y is the provision rate controlled by plasma glucose concentration, G. Arrows indicate ﬂuxes with corresponding parameters (red). b The estimated parameters for the NGT (green), borderline type (red), and T2DM (blue) subjects. Each dot corresponds to the indicated parameter for an individual subject. c The parameters of k and (1 − k ), corresponding to peripheral and hepatic insulin clearance, respectively. *P < 0.05, Iout ratio **P < 0.01, NS not signiﬁcant (two-sided Wilcoxon rank sum test with FDR-correction). Post-hoc statistical power analysis is shown in Supplementary Table S5. The bar and error bar show the median and lower and upper quartiles, respectively. Each dot corresponds to the indicated parameter for an individual subject secretion and delivery in this model, which depends on other ﬁnding that peripheral insulin clearance is highly correlated with parameters such as h, m, X , and k , and the parameters ISI and MCR. k is the degradation rate of serum insulin, which Iout b ratio depends on the number of insulin receptors on target tissues, involved in insulin secretion and delivery are too diverse. indicating that serum insulin degradation and insulin sensitivity The parameters k , k , k , h, and X show smaller ratio Iout CPout b are mutually correlated. Therefore, it is reasonable that k is variations than others (Fig. 2b). This is probably because Iout correlated not only with MCR but also with ISI. these parameters are directly related to the measured concentra- The model parameter showing the highest correlation with tions of serum insulin and C-peptide and plasma glucose, and insulin secretion during the ﬁrst phase, AUC (see Methods), therefore can be accurately estimated, whereas other parameters IRI10 which is the index of insulin secretion, was k (r = 0.425, P < ratio are not, resulting in large variation possibly due to inaccurate 0.01). Note that (1 − k ) corresponds to hepatic insulin ratio estimation. clearance. Because the parameter k is the fraction of insulin ratio remaining after the hepatic extraction, its correlation with insulin Relationship between hepatic and peripheral insulin clearance secretion is reasonable. parameters and clinical indices of serum insulin regulation In addition, the model parameter showing the highest We examined the correlation of the estimated model parameters correlation with both FPG and 2-h PG, the main indices of glucose with clinical indices of circulating insulin regulation among tolerance, was h (r = 0.448 and 0.504, respectively, both P < 0.001), 111 subjects (Fig. 3, Supplementary Table S6). The model which is the threshold glucose concentration for insulin secretion. parameter showing the highest correlation with insulin sensitivity This ﬁnding is consistent with h corresponding to FPG. The model index (ISI) and with the metabolic clearance rate (MCR), which is parameter showing the highest correlation with the clamp the index of insulin clearance (see Methods for details), was disposition index, clamp DI, which is calculated as the peripheral insulin clearance, k (r = 0.761 and 0.790, respectively, product of insulin secretion AUC and ISI and is the index of Iout IRI10 both P < 0.001). This correlation is consistent with our previous glucose tolerance, was k · k (r = 0.540, P < 0.001). ratio Iout Published in partnership with the Systems Biology Institute npj Systems Biology and Applications (2018) 14 Increase in hepatic and decrease in peripheral K Ohashi et al. Fig. 3 Model parameters showing the highest correlation with clinical indices. a Scatter plots for the indicated measured clinical indices versus the highest correlated model parameters (Supplementary Table S6). ISI insulin sensitivity index, MCR metabolic clearance rate, AUC IRI10 amount of insulin secretion during the ﬁrst 10 min of hyperglycemic clamp. Each dot indicates the value of an individual subject. The correlation coefﬁcient, r, and the P value for testing the hypothesis of no correlation are shown. The partial correlation coefﬁcients among k , ISI, and MCR are shown in Supplementary Figure S5. b Summary of the model parameters k and k showing the highest correlation Iout Iout ratio with the indicated clinical indices Considering that k is related to post-hepatic insulin delivery, secretion. Note that the decrease in k also increases the ratio Iout and k is related to insulin sensitivity, which depends on the amplitude of I. Iout Because both k and k decreased from NGT to borderline number of insulin receptors on target organs, it is reasonable that ratio Iout type and T2DM (Fig. 2b), we examined the effect of the the product k · k shows the highest correlation with clamp ratio Iout simultaneous changes of k and k on the amplitude and ratio Iout DI, which is also the product of clinically estimated insulin transient/sustained patterns of I. When both k and k ratio Iout secretion and sensitivity. increased with the same ratio, I increased during ﬁrst-phase secretion (0–10 min), whereas I decreased during second-phase Selective regulation of amplitude and temporal patterns of serum secretion (10–30 min) (Fig. 4a, right panel, red line). Thus, insulin concentration by hepatic and peripheral insulin clearance simultaneous increase of k and k results in the increase of ratio Iout Because k and k were the parameters showing the highest Iout ratio peak amplitude of I and in changes in the temporal pattern of I correlation with clinical indices of insulin sensitivity and secretion, from sustained to transient. respectively, both of which are related to the progression of We quantiﬁed the role of k and k in the peak amplitude ratio Iout glucose intolerance and T2DM, we analyzed the roles of k and ratio and temporal patterns of I.Wedeﬁned the index ipeak k in the temporal changes of serum insulin concentration (Fig. (incremental peak) for the peak amplitude of I, and the index Iout 4). We changed the originally estimated values of k or k or iTPI (incremental transient peak index; modiﬁed from Kubota ratio Iout −1 1 46 both by 2 to 2 times and simulated the time course of I, serum et al. ) for the temporal pattern of I (Fig. 4b), as follows: insulin concentration, during hyperglycemic clamp for each ipeak ¼ ItðÞ IðÞ 0 ; ItðÞ>IðÞ t ; (5) local max local max local max next subject (Supplementary Figure S6). Similar temporal changes of I versus changes in the parameters were observed in all 111 sub- Iðt ÞIðt Þ local max local min iTPI ¼ ; jects, so only the simulation result of subject #3 (NGT) is shown ipeak (6) (Fig. 4a). Iðt Þ<Iðt Þ; t >t ; local min local min next local min local max The time course of I with the original parameters in the model where I(t) represents I at time t, t is the time at which I local_max of subject #3 showed the transient increase (Fig. 4a, black line). As stops increasing for the ﬁrst time from 0 min, t is the local_max_next k increased, I increased without changing the transient pattern ratio next sampling time of t , t is the time at which I local_max local_min (Fig. 4a, left panel, red line). Indeed, an increase of k affects the ratio stops decreasing for the ﬁrst time after t , and t local_max local_min_next value of I similarly at any time point, because k controls the ratio is the next sampling time of t . local_min gain of time derivative of I.As k increased, I decreased and the Iout The index ipeak is the difference in I between the local temporal pattern became more transient with an earlier peak time maximum I(t ) and the initial fasting concentration I(0) and local_max (Fig. 4a, middle panel, red line). Conversely, as k decreased, I Iout represents the peak amplitude of I during the ﬁrst-phase increased and the temporal pattern became more sustained with secretion. The index iTPI is the ratio of the difference of I between a delayed peak time (Fig. 4a, middle panel, blue line). This result the local maximum I(t ) and the local minimum I(t ) local_max local_min suggests that k controls the shift in the temporal patterns of I Iout of I against ipeak, which reﬂects the ratio of I during the ﬁrst- and from transient to sustained. These changes in the temporal second-phase secretions. As iTPI approaches 1, the difference in I pattern of I are characterized by a relative decrease in the ﬁrst- between the ﬁrst- and second-phase secretions becomes larger, phase secretion and relative increase in the second-phase meaning that the temporal change of I becomes more transient. npj Systems Biology and Applications (2018) 14 Published in partnership with the Systems Biology Institute Increase in hepatic and decrease in peripheral K Ohashi et al. Fig. 4 The roles of k and k in the amplitude and temporal patterns of serum insulin concentration. a Simulated time course of serum ratio Iout insulin concentration I during hyperglycemic clamp of subject #3 by changing k or k or both by scaling the ﬁtted parameter value with ratio Iout −1.0 −0.5 0.5 1.0 2 ,2 ,1,2 , and 2 (see Methods). Dotted arrows indicate the direction of the change in the temporal pattern as the parameter increases. b The deﬁnition of ipeak (incremental peak) and iTPI (incremental transient peak index), reﬂecting the peak amplitude and the temporal pattern of serum insulin concentration I. c ipeak and iTPI of I of subject #3 by changing k or k or both ratio Iout Conversely, as iTPI approaches 0, the difference in I between the ﬁrst- and second-phase secretions becomes smaller, meaning that the temporal change of I becomes more sustained. We calculated ipeak and iTPI from the simulated time courses of −1 I by changing the original estimates of k or k or both by 2 ratio Iout to 2 times. As k increased, ipeak increased but iTPI did not ratio change (Fig. 4c, left panel), indicating that increasing k ratio increases the peak amplitude of I during the ﬁrst-phase secretion without changing its temporal pattern. As k increased, iTPI Iout increased and ipeak decreased (Fig. 4c, middle panel), indicating that increasing k changes the temporal patterns of I from Iout sustained to transient and decreases the peak amplitude of I during the ﬁrst-phase secretion. When both k and k increased at the same ratio, both ratio Iout ipeak and iTPI increased (Fig. 4c, right panel), indicating that increasing both k and k increases the peak amplitude of I ratio Iout and changes the temporal pattern from sustained to transient. The increase in ipeak means that the effect of k , which increases ratio ipeak, is stronger than that of k , which decreases ipeak. Given Iout that both k and k decrease from NGT to borderline type and ratio Iout T2DM, both ipeak and iTPI decrease (Fig. 5). This ﬁnding is consistent with earlier clinical observations that the peak amplitude of circulating insulin concentration during the ﬁrst- phase secretion decreases and the temporal pattern becomes 2–4 more sustained during the progression of glucose intolerance. Fig. 5 Overview of our study and main results. Mathematical We performed parameter sensitivity analysis on ipeak and iTPI in modeling based on hyperglycemic and hyperinsulinemic- the simulation for each model parameter (Table 2, Methods). We euglycemic clamp (glucose and insulin clamp) data in subjects compared the median of the parameter for all 111 subjects as the showed changes in opposite direction of hepatic and peripheral parameter sensitivity index (Table 2). For ipeak, the k had the ratio insulin clearance from NGT to T2DM. Hepatic insulin clearance (1 signiﬁcantly highest median, and for iTPI, k showed the Iout −k ) increases and peripheral insulin clearance k decreases, ratio Iout signiﬁcantly highest median, indicating that hepatic insulin characterizing the decrease in peak amplitude and the change in the temporal pattern of serum insulin concentration from transient clearance and peripheral insulin clearance are the most critical to sustained, respectively parameters controlling the peak amplitude and temporal patterns of serum insulin concentration, respectively. The measured temporal changes of the serum insulin concen- tration during hyperglycemic clamp (0–90 min) showed no clear suggesting that hepatic and peripheral insulin clearance are not difference between the NGT and borderline type subjects (Fig. 1). the only parameters responsible for the peak amplitude and However, the estimated k and k in the NGT subjects were temporal patterns of serum insulin concentration, respectively. ratio Iout signiﬁcantly higher than those in the borderline type subjects, Other parameters such as insulin secretion, which also affects the Published in partnership with the Systems Biology Institute npj Systems Biology and Applications (2018) 14 Increase in hepatic and decrease in peripheral K Ohashi et al. Table 2. Parameter sensitivity analysis for ipeak and iTPI Rank ipeak iTPI Median P Median P −1 1 k 1.00 k 4.64 × 10 ratio Iout −1 −38 −1 −6 2 m 3.52 × 10 6.26 × 10 β −2.53 × 10 1.30 × 10 −1 −36 −1 −15 3 k −2.74 × 10 1.23 × 10 α −1.42 × 10 5.36 × 10 Iout −4 −34 −1 −7 4 h −3.64 × 10 4.04 × 10 h 1.38 × 10 8.70 × 10 −4 −36 −2 −9 5 β 2.59 × 10 1.23 × 10 m 7.18 × 10 2.56 × 10 −4 −36 −15 −35 6 α 1.61 × 10 1.23 × 10 k 8.28 × 10 2.62 × 10 ratio Medians of the indicated parameters for all 111 subjects were used for parameter sensitivity analysis for ipeak and iTPI (see Methods). The higher the absolute value of the parameter, the higher the sensitivity. P values relative to the median for the top-ranked parameter were determined by two-sided Wilcoxon rank –3 sum test, and the value of <4.17 × 10 (=0.05/12, corrected by the number of tests, divided by 12) is considered statistically signiﬁcant temporal changes of serum insulin concentration, may compen- clearance and the temporal pattern changes from transient to sate for the temporal changes by insulin clearance between the sustained occur because of a decrease in peripheral insulin NGT and borderline type subjects. This also means that changes in clearance (Fig. 5). Importantly, the decrease in peripheral insulin the hepatic and peripheral insulin clearance from NGT to clearance alone can explain only the temporal change of serum borderline type and T2DM cannot be directly assessed from the insulin concentration, not the decrease of peak amplitude. Thus, measured time course of serum insulin concentration, but must be the increase of hepatic insulin clearance and decrease of evaluated with a mathematical model. peripheral insulin clearance simultaneously cause the decrease From Eq. 3, the parameter k directly reﬂects post-hepatic in the peak amplitude of serum insulin concentration during the ratio insulin delivery and is involved in the increase in gain of I. ﬁrst-phase secretion and change in temporal pattern from Therefore, the change of k is directly reﬂected in the peak transient to sustained. Our result demonstrates that, in addition ratio 3,4 amplitude, so the sensitivity to ipeak becomes 1. This means that to the decrease in insulin secretion, the increase in hepatic hepatic insulin clearance is more responsible for the peak clearance also contributes to the decrease in peak amplitude of amplitude of serum insulin concentration than the pre-hepatic serum insulin concentration in the ﬁrst-phase secretion from NGT insulin secretion before extraction by the liver. to borderline type and T2DM. The parameter k corresponds to peripheral insulin clearance In our model, as k , the ratio of post-hepatic insulin compared Iout ratio and is the degradation rate of I, meaning that k is the time to C-peptide, increased, ipeak, the peak amplitude of peripheral Iout constant of serum insulin degradation. k is the parameter insulin concentration, increased (Fig. 4c). According to clinical Iout directly responsible for temporal conversion of input X, delivered measurements, k was also correlated with ipeak calculated ratio insulin after the extraction by the liver, into output, I. Thus, k is directly from the serum insulin concentration measured during Iout the ﬁrst-phase secretion in hyperglycemic clamp (Supplementary the most sensitive parameter for iTPI corresponding to the shift Figure S8a, r = 0.423, P < 0.001), indicating that hepatic insulin between the transient and sustained temporal pattern of serum insulin concentration. clearance is pathologically correlated with the peak amplitude in the ﬁrst-phase secretion from NGT to borderline type and T2DM. On the other hand, in our model, as k , the peripheral insulin Iout DISCUSSION clearance, increased, iTPI, representing the temporal pattern of We developed several alternative mathematical models using peripheral insulin concentration, increased (Fig. 4c). However, in concentrations of plasma glucose, serum insulin, and C-peptide clinical measurements, k was not highly correlated with iTPI Iout during consecutive hyperglycemic and hyperinsulinemic- calculated directly from the serum insulin concentration measured euglycemic clamps, and selected the model showing the best ﬁt during hyperglycemic clamp (Supplementary Figure S8a, r = for most subjects. Although Model VI was selected for 76 of 0.297, P < 0.01). The reason for this lack of correlation between 121 subjects, 45 subjects were not optimal for Model VI. This k and iTPI in clinical measurement remains unclear; however, it Iout suggests that some of the parameters of Model VI were may be because little insulin was secreted during hyperglycemic unnecessary in subjects whose selected model is Model I, II, IV, clamp in some borderline type and T2DM subjects, and iTPI or V by comparing the structure with Model VI. However, no cannot be estimated accurately because of low concentration of parameter of Model VI showed signiﬁcant difference between serum insulin. subjects who selected Model I, II, IV,or V and subjects who Many studies have shown that insulin clearance decreases in 18–21,47,48 selected Model VI (Supplementary Figure S7), suggesting that T2DM patients. However, the change in hepatic insulin there is no biased feature on the structure of the control of clearance in this condition has been controversial, with some circulating insulin concentration in subjects who were not optimal studies ﬁnding an increase in T2DM subjects and others a 18,23 for Model VI, and Model VI can be applied to all subjects. decrease. We previously developed a mathematical model During the progression of glucose intolerance, it has been using data gathered during hyperglycemic and hyperinsulinemic- shown that the peak amplitude of circulating insulin concentra- euglycemic clamps, and peripheral insulin clearance signiﬁcantly tion during the ﬁrst-phase secretion decreases and the temporal decreased from NGT to borderline type to T2DM. However, 2–4 pattern becomes more sustained. In this study, we found that hepatic and peripheral insulin clearances were not estimated both k , corresponding to peripheral insulin clearance, and k separately because we did not use C-peptide data. Recently, Iout ratio decrease from NGT to borderline type and T2DM. Given that (1 − Polidori et al. estimated both hepatic and peripheral insulin k ), corresponding to hepatic insulin clearance, increases as the clearance by modeling analysis using plasma insulin and C- ratio k decreases, our ﬁnding strongly suggests that, from NGT to peptide concentrations obtained from the insulin-modiﬁed ratio borderline type and T2DM, the peak amplitude of serum insulin frequently sampled IVGTT. They found that the peripheral insulin concentration decreases due to the increase in hepatic insulin clearance signiﬁcantly decreased in borderline type subjects npj Systems Biology and Applications (2018) 14 Published in partnership with the Systems Biology Institute Increase in hepatic and decrease in peripheral K Ohashi et al. compared with NGT subjects, whereas hepatic insulin clearance circulating insulin concentration selectively regulate insulin did not signiﬁcantly differ between the borderline type and NGT actions on the target tissues. Given that hepatic and peripheral subjects ; the former ﬁnding is consistent with our result that insulin clearances are responsible for the amplitude and temporal peripheral insulin clearance decreases from NGT to borderline pattern of circulating insulin concentration, these clearances are type and T2DM. We demonstrated that hepatic insulin clearance likely to be involved in selective control of insulin action, glucose signiﬁcantly increases, whereas peripheral insulin clearance homeostasis, and the pathogenesis of T2DM. signiﬁcantly decreases from NGT to borderline type and T2DM. We previously developed a mathematical model for concentra- One difference between the study by Polidori et al. and our study tions of plasma glucose and serum insulin measured during is C-peptide kinetics. They used the reported two-compartment consecutive hyperglycemic and hyperinsulinemic-euglycemic model of C-peptide kinetics for calculating insulin secretion rate clamps and found signiﬁcant decreases in insulin secretion, by deconvolution, while we selected the structure of C-peptide sensitivity, and peripheral insulin clearance from NGT to border- kinetics that ﬁtted for our data, which may improve the accuracy line type to T2DM. The differences between our previous study of the parameter estimation of hepatic insulin clearance, and this study are the model structure and C-peptide data. The estimated by use of serum insulin and C-peptide concentration. previous model consisted of plasma glucose and serum insulin The increase in hepatic insulin clearance may be caused by and required only glucose and insulin infusion as inputs. The impaired suppression of endocytosis of insulin receptors on the model in this study does not have plasma glucose concentration liver, and the decrease in peripheral insulin clearance may be but includes serum insulin and C-peptide concentrations, while caused by a decrease of the number of insulin receptors on target plasma glucose concentration and insulin infusion are used as 45 40 tissues. Polidori et al. also found that hepatic and peripheral inputs (Fig. 2a, Supplementary Figure S2). In the previous study, insulin clearances were not highly correlated. Consistent with their only peripheral insulin clearance, but not hepatic insulin clearance, results, in our analysis, the insulin clearance parameters k and was estimated because C-peptide data were not used. The ratio k were not highly correlated (Supplementary Figure S8b, r = decrease of insulin clearance from NGT to T2DM in the previous Iout 0.296, P < 0.01), suggesting that both insulin clearances are study is consistent with the decrease of peripheral insulin independently regulated. clearance from NGT to T2DM in this study. In the previous study, We are aware that some of the results of this analysis only hold the parameter corresponding to insulin secretion in the NGT and if the parameters are identiﬁable based on our serum insulin and borderline type subjects was signiﬁcantly higher than that in the C-peptide data. We performed 20 trials of parameter estimation T2DM subjects; however, the parameter related to insulin for each subject (Methods), but most subjects (107 subjects) had secretion did not show a signiﬁcant difference between the only one trial which minimized RSS. The values of estimated NGT, borderline type, and T2DM subjects in this study, possibly parameters and RSS varied among the 20 trials of each subject. For because previously deﬁned insulin secretion is described by the remaining four subjects, estimated parameters varied among insulin secretion and delivery in this model, and the parameters trials that returned the same RSS, especially the parameters α and related to insulin secretion and delivery (α, β, h, m, X , and k ) b ratio β differed to a large extent, while the parameters k and k are too diversiﬁed. The parameter corresponding to insulin Iout ratio did not largely differ (Supplementary Figure S9). If the number of sensitivity was not incorporated in this study. estimated trials, parents, and generations of evolutionary pro- Many mathematical models to reproduce circulating C-peptide gramming increases, a trial that gives a different parameter concentration have been developed. A two-compartment model solution with smaller RSS than that reported in this study might be for C-peptide kinetics was originally proposed. A combined obtained. Structural or a priori identiﬁability of parameters based model that included both circulating insulin and C-peptide on the system equations, which tests if model parameters can kinetics described by a single compartment structure was be determined from the available data, was not performed in this introduced to estimate hepatic insulin clearance. The C- study. Large variability in the ﬁtted parameters, like for instance in peptide minimal model describing peripheral insulin and C- α and β, could be due to the identiﬁability of the parameters and peptide appearance and kinetics was also developed to assess 33–37 not due to biological variance, and interpretation of the results has hepatic insulin clearance, and several other model structures 38,39 to take this into account. for circulating C-peptide concentration were reported. One Insulin selectively regulates various functions, such as signaling difference between others’ and our studies is the experimental activities, metabolic control, and gene expression, depending on protocol in which data were applied to parameter estimation. its temporal patterns. For example, we previously reported that IVGTT or hyperglycemic clamp were performed for parameter pulse stimulation of insulin in rat hepatoma Fao cells, resembling estimation in models of circulating C-peptide concentration, the ﬁrst-phase secretion, selectively regulated glycogen synthase whereas we used hyperglycemic and hyperinsulinemic- kinase-3β (GSK3β), which regulates glycogenesis, and S6 kinase, euglycemic clamps, which may improve the accuracy of the which regulates protein synthesis, whereas ramp stimulation of parameter estimation of peripheral insulin clearance, k . Iout insulin, resembling the second-phase secretion, selectively regu- Recently, a model of plasma insulin concentration including lated GSK3β and glucose-6-phosphatase (G6Pase), which regulates hepatic and peripheral insulin clearance and the delivery of insulin gluconeogenesis. We also found that insulin-dependent meta- from the systemic circulation to the liver during the insulin- bolic control and gene expression are selectively regulated by modiﬁed IVGTT was proposed. In that model, the parameter of 50,51 temporal patterns and doses of insulin in FAO cells. Sustained hepatic insulin clearance was negatively correlated with acute stimulation of insulin suppressed the expression of insulin insulin secretion in response to glucose, and the parameter of 52–54 receptors, leading to reduced insulin sensitivity in FAO cells. peripheral insulin clearance was correlated with insulin sensitiv- Likewise, phosphorylation of the insulin receptor substrate (IRS)-1/ ity, consistent with the results in this study (Fig. 3). Since the age 2 in rat liver increased when pulsatile (rather than continuous) of subjects in our study differed between groups with NGT, stimulation of insulin was imposed in the portal circulation. This borderline type, and T2DM (Supplementary Table S4), the may have occurred through the negative feedback within the correlations between the parameters and clinical indices may be insulin signaling pathway, the phosphatidylinositide (PI) 3-kinase/ affected by age. However, the parameters showing the highest 53,56 Alt pathway, targeting IRS-1/2. In addition, IRS-2, rather than correlation with clinical indices of insulin secretion, AUC , IRI10 IRS-1, mainly regulates hepatic gluconeogenesis through its rapid insulin sensitivity, ISI, and insulin clearance, MCR, were not downregulation by insulin, suggesting the selective roles of IRS- changed with conditioning of age (Supplementary Table S7). 1/2 in response to temporal patterns of plasma insulin. These The high correlation between the parameter of hepatic insulin ﬁndings indicate that the amplitude and temporal pattern of clearance, k , and the clinical index of insulin secretion, AUC , ratio IRI10 Published in partnership with the Systems Biology Institute npj Systems Biology and Applications (2018) 14 Increase in hepatic and decrease in peripheral K Ohashi et al. suggests the possibility that hepatic insulin clearance considerably models, I represents serum insulin concentration (pM), and CP and CP represent serum C-peptide concentration (pM) including insulin and C- affects the clinical index of insulin secretion measured by peptide secretion and hepatic and peripheral clearance. We used a peripheral insulin concentration because the clinical index of conversion factor of insulin (6.00 nmol/U) and the molecular weights of insulin secretion, AUC , was measured by the post-hepatic IRI10 glucose (180.16 g/mol) and C-peptide (3020.3 g/mol) to convert the unit of insulin delivery, and therefore reﬂects both insulin secretion and serum insulin, plasma glucose, and serum C-peptide, respectively. We used hepatic insulin clearance. This suggests that insulin secretion plasma glucose concentration G (mM) as input in the models, which was per se in the clinical index of insulin secretion may be determined by stepwise interpolation of the measured plasma glucose overestimated because of the involvement of hepatic insulin data. Note that plasma glucose data were obtained as the 5-min average clearance. Further study is necessary to address this issue. values, and each sampling time was reduced by 2 min in the calculation of In conclusion, using the mathematical model for serum insulin stepwise interpolation. The actual insulin infusion rate (IIR, mU/kg/min) was converted to the and C-peptide concentrations during consecutive hyperglycemic corresponding serum concentrations (cIIR) as follows: and hyperinsulinemic-euglycemic clamps, we determined the quantitative structure of the control of circulating insulin IIR ðmU=kg=minÞ 6:00 10 ðpmol=mUÞ (7) cIIRðÞ pM=min¼ ; concentration. The estimated model parameters revealed the 3 BV 10 increase of hepatic insulin clearance and decrease of peripheral where BV denotes blood volume (75 and 65 mL/kg for men and women, insulin clearance from NGT to borderline type and T2DM, and respectively ). these changes selectively regulate the amplitude and temporal In the models, insulin infusions are represented by inﬂux. This ﬂux patterns of serum insulin concentration, respectively. The changes follows the nonlinear function f that predicts insulin infusion concentra- tions. Given that insulin infusion was performed only during the in opposite direction of both types of clearance shed light on the hyperinsulinemic-euglycemic (from 100 to 220 min) clamp, the function f pathological mechanism underlying the abnormal temporal was given by the following equations: patterns of circulating insulin concentration from NGT to border- line type and T2DM. 0 ðt 100Þ fðtÞ¼ ; (8) ii expðii ðt 100ÞÞ þ ii ðt>100Þ 1 2 3 where the parameters ii (j = 1, 2, 3) are estimated to reproduce cIIR for MATERIALS AND METHODS j each subject with a nonlinear least squares technique. Parameters for all Subjects and measurements subjects are shown in Supplementary Table S9. The plasma and serum measurement data originated from our previous 14,30 research. This metabolic analysis was approved by the ethics Parameter estimation committee of Kobe University Hospital and was registerd with the University hospital Medical Information Network (UMIN000002359), and The model parameters for each subject were estimated to reproduce the written informed consent was obtained from all subjects. In brief, 50 NGT, experimentally measured time course by a meta-evolutionary program- 18 borderline type, and 53 T2DM subjects underwent the consecutive ming method to approach the neighborhood of the local minimum, clamp analyses. From 0 to 90 min, a hyperglycemic clamp was applied by followed by application of the nonlinear least squares technique to reach 2 61 intravenous infusion of a bolus of glucose (9622 mg/m ) within 15 min the local minimum. Each parameter was estimated in the range from −6 4 followed by that of a variable amount of glucose to maintain the plasma 10 to 10 . For these methods, the model parameters were estimated to glucose level at 200 mg/dL. Ten minutes after the end of the minimize the objective function value, which is deﬁned as the RSS between the actual time course obtained by clamp analyses and the hyperglycemic clamp, a 120-min hyperinsulinemic-euglycemic clamp was model trajectories. RSS is given by: initiated by intravenous infusion of human regular insulin (Humulin R, Eli Lilly Japan K.K.) at a rate of 40 mU/m /min and with a target plasma 2 2 X X IðtÞ I ðtÞ CPðtÞ CP ðtÞ sim sim glucose level of 90 mg/dL. For the NGT and borderline type subjects whose RSS ¼ þ ; (9) I CP plasma glucose levels were <90 mg/dL, the plasma glucose concentration mean mean points points was clamped at the fasting level. We measured the plasma glucose level where every 1 min during the clamp analyses and obtained the 5-min average P P values. We also measured insulin and C-peptide level in serum samples IðtÞ points collected at 5, 10, 15, 60, 75, 90, 100, 190, and 220 min after the onset of subjects I ¼ ; (10) mean the tests. First-phase insulin secretion during the hyperglycemic clamp was points subjects deﬁned as the incremental area under the immunoreactive insulin (IRI) concentration curve (μU/mL/min) from 0 to 10 min (AUC ). The ISI IRI10 P P derived from the hyperinsulinemic-euglycemic clamp was calculated by CPðtÞ subjects points dividing the mean glucose infusion rate during the ﬁnal 30 min of the CP ¼ : (11) mean points clamp (mg/kg/min) by both the plasma glucose (mg/dL) and serum insulin subjects (μU/mL) levels at the end of the clamp and then multiplying the result by 100. A clamp-based analog of the disposition index, the clamp disposition I(t) and CP(t) are the serum insulin and C-peptide concentration, and index (clamp DI), was calculated as the product of AUC and ISI, as IRI10 I (t) and CP (t) are simulated serum insulin and C-peptide concentra- sim sim 14 13 described previously. The MCR, an index of insulin clearance, was tions at t min, respectively. Serum insulin and C-peptide concentrations calculated by dividing the insulin infusion rate at the steady state were normalized by dividing them by the averages of serum concentra- (1.46 mU/kg/min) by the increase in insulin concentration above the basal tions over all time points of all subjects of insulin (I , 302.7 pM) and C- mean level in the hyperinsulinemic-euglycemic clamp : 1.46 (mU/kg/min) × peptide (CP , 1475 pM), respectively. The numbers of parents and mean body weight (kg) × body surface area (m ) / (end IRI− fasting IRI) (μU/mL), generations in the meta-evolutionary programming were 400 and 4000, 1/2 where body surface area is deﬁned as (body weight (kg)) × (body height respectively. Parameter estimation was tried 20 times by changing the 1/2 (cm)) / 60 (Mosteller formula). Since this study is a retrospective analysis initial parameter values for each subject, and the parameter with the of previously collected data, randomization and blinding of the groups smallest RSS among 20 trials was taken as the estimated solution of each with NGT, borderline type, and T2DM was not performed. The actual data subject. Model parameters for all subjects are shown in Supplementary for all 121 subjects are shown in Supplementary Figure S10 and Table S9. Supplementary Table S8. Model selection Mathematical models The model was chosen among the six models according to the AIC. For a We developed six mathematical models based on the proposed models in given model and a single subject, AIC was calculated as follows: order to choose the best model for reproducing our measurement of 2π RSS serum insulin and C-peptide during consecutive hyperglycemic and AIC ¼ n ln þ n þ 2K ; (12) hyperinsulinemic-euglycemic clamps (Supplementary Figure S2). In these npj Systems Biology and Applications (2018) 14 Published in partnership with the Systems Biology Institute Increase in hepatic and decrease in peripheral K Ohashi et al. where n is the total number of sampling time points of serum insulin and REFERENCES C-peptide, and K is the number of estimated parameters of the model. 1. DeFronzo, R. A., Bonadonna, R. C. & Ferrannini, E. Pathogenesis of NIDDM. A balanced overview. Diabetes Care 15, 318–368 (1992). 2. Cerasi, E. & Luft, R. The plasma insulin response to glucose infusion in healthy Determination of parameter outliers subjects and in diabetes mellitus. Acta Endocrinol. (Copenh) 55, 278–304 (1967). The outliers of RSS and model parameters were detected by the adjusted 3. Del Prato, S. & Tiengo, A. The importance of ﬁrst-phase insulin secretion: impli- 62 3MC outlyingness (AO). The cutoff value of AO was Q + 1.5e · IQR, where cations for the therapy of type 2 diabetes mellitus. Diabetes Metab. Res. Rev. 17, Q , MC, and IQR are the third quartile, medcouple, and interquartile range, 164–174 (2001). respectively. The medcouple is a robust measure of skewness. The 4. Seino, S., Shibasaki, T. & Minami, K. Dynamics of insulin secretion and the clinical number of directions was set at 8000. Subjects found to have outlier implications for obesity and diabetes. J. Clin. Invest. 121, 2118–2125 (2011). parameters (one NGT, one borderline type, and ﬁve T2DM subjects) were 5. Lindsay, J. R. et al. Meal-induced 24-hour proﬁle of circulating glycated insulin in excluded from further study. type 2 diabetic subjects measured by a novel radioimmunoassay.Metabolism 52, 631–635 (2003). 6. Polonsky, K. S., Given, B. D. & Van Cauter, E. Twenty-four-hour proﬁles and pul- Parameter sensitivity analysis satile patterns of insulin secretion in normal and obese subjects. J. Clin. Invest. 81, We deﬁned the individual model parameter sensitivity for each subject as 442–448 (1988). follows: 7. Stumvoll, M. et al. Use of the oral glucose tolerance test to assess insulin release and insulin sensitivity. Diabetes Care 23, 295–301 (2000). ∂ log fðxÞ x ∂fðxÞ 8. Seino, Y. et al. Report of the committee on the classiﬁcation and diagnostic SðfðxÞ; xÞ¼ ¼ ; (13) ∂ log x fðxÞ ∂x criteria of diabetes mellitus. J. Diabetes Investig. 1, 212–228 (2010). 9. Hayashi, T. et al. Patterns of insulin concentration during the OGTT predict the where x is the parameter value and f(x)is ipeak or iTPI. The differentiation is risk of type 2 diabetes in Japanese Americans. Diabetes Care 36, 1229–1235 ∂fðxÞ fðxþΔxÞfðxΔxÞ numerically approximated by central difference , and x ∂x 2Δx (2013). + Δx and x − Δx were set so as to be increased [x (1.1x)] or decreased [x 10. Abdul-Ghani, M. A., Tripathy, D. & DeFronzo, R. A. Contributions of beta-cell (0.9x)] by 10%, respectively. Finally, we deﬁned the parameter sensitivity by dysfunction and insulin resistance to the pathogenesis of impaired glucose tol- the median of the individual parameter sensitivity for all subjects. We erance and impaired fasting glucose. Diabetes Care 29, 1130–1139 (2006). examined the parameter sensitivity for six parameters of the rate constant 11. Perley, M. J. & Kipnis, D. M. Plasma insulin responses to oral and intravenous related to serum insulin concentration, except X and k . The higher the b CPout glucose: studies in normal and diabetic sujbjects. J. Clin. Invest. 46, 1954–1962 absolute value of parameter sensitivity, the larger the effect of the (1967). parameter on ipeak or iTPI. 12. Pfeifer, M. A., Halter, J. B. & Porte, D. Insulin secretion in diabetes mellitus. Am. J. Med. 70, 579–588 (1981). 13. DeFronzo, R. A., Tobin, J. D. & Andres, R. Glucose clamp technique: a method for Statistical analysis quantifying insulin secretion and resistance. Am. J. Physiol. 237, E214–E223 Unless indicated otherwise, data are expressed as the median with ﬁrst and (1979). third quartiles. Medians of parameter values were compared among the 14. Okuno, Y. et al. Postprandial serum C-peptide to plasma glucose concentration NGT, borderline type, and T2DM subjects with the use of the two-sided ratio correlates with oral glucose tolerance test- and glucose clamp-based dis- Wilcoxon rank sum test with Benjamini Hochberg FDR multiple testing position indexes. Metabolism 62, 1470–1476 (2013). correction. An FDR-corrected P value <0.05 was considered statistically 15. Sato, H., Terasaki, T., Mizuguchi, H., Okumura, K. & Tsuji, A. Receptor-recycling signiﬁcant. model of clearance and distribution of insulin in the perfused mouse liver. Dia- betologia 34, 613–621 (1991). 16. Duckworth, W. C., Hamel, F. G. & Peavy, D. E. Hepatic metabolism of insulin. Am. J. Data availability Med. 85,71–76 (1988). The SBToolbox2 (http://www.sbtoolbox2.org/main.php) was used 17. Rabkin, R. & Kitaji, J. Renal metabolism of peptide hormones. Miner. Electrolyte together with MATLAB R2015a (http://mathworks.com/) in the mathema- Metab. 9, 212–226 (1983). tical modeling. The code ﬁles implementing the 6 analyzed models and 18. Marini, M. A. et al. Differences in insulin clearance between metabolically healthy used in the simulation are freely available at http://kurodalab.bs.s.u-tokyo. and unhealthy obese subjects. Acta Diabetol. 51, 257–261 (2014). ac.jp/info/. 19. Lee, C. C. et al. Insulin clearance and the incidence of type 2 diabetes in Hispanics and African Americans: the IRAS Family Study. Diabetes Care 36, 901–907 (2013). 20. Rudovich, N. N., Rochlitz, H. J. & Pfeiffer, A. F. Reduced hepatic insulin extraction ACKNOWLEDGEMENTS in response to gastric inhibitory polypeptide compensates for reduced insulin We thank fellow laboratory members for critical reading of the manuscript and for secretion in normal-weight and normal glucose tolerant ﬁrst-degree relatives of technical assistance with the analysis. The computations for this work were type 2 diabetic patients. Diabetes 53, 2359–2365 (2004). performed in part on the NIG supercomputer system at ROIS National Institute of 21. Jones, C. N. et al. Alterations in the glucose-stimulated insulin secretory dose- Genetics. This work was supported by the Creation of Fundamental Technologies for response curve and in insulin clearance in nondiabetic insulin-resistant indivi- duals. J. Clin. Endocrinol. Metab. 82, 1834–1838 (1997). Understanding and Control of Biosystem Dynamics, CREST (JPMJCR12W3), of the 22. Tamaki, M. et al. The diabetes-susceptible gene SLC30A8/ZnT8 regulates hepatic Japan Science and Technology Agency (JST); Japan Diabetes Foundation; Ono insulin clearance. J. Clin. Invest. 123, 4513–4524 (2013). Medical Research Foundation; and the Japan Society for the Promotion of Science 23. Bonora, E., Zavaroni, I., Coscelli, C. & Butturini, U. Decreased hepatic insulin (JSPS) KAKENHI Grant Number (17H06300). extraction in subjects with mild glucose intolerance. Metabolism 32, 438–446 (1983). 24. Saisho, Y. et al. Postprandial serum C-peptide to plasma glucose ratio as a pre- AUTHOR CONTRIBUTIONS dictor of subsequent insulin treatment in patients with type 2 diabetes. Endocr. J. K.O., M.F., W.O., and S.K. conceived the project; H.Ko., K.S., and W.O. designed and 58, 315–322 (2011). performed the experiments; K.O. and M.F. developed the computational model; K.O., 25. Ahrén, B. & Thorsson, O. Increased insulin sensitivity is associated with reduced M.F., S.U., and H.Ku. analyzed the data; K.O., W.O., and S.K. wrote the manuscript. insulin and glucagon secretion and increased insulin clearance in man. J. Clin. Endocrinol. Metab. 88, 1264–1270 (2003). 26. Breda, E., Cavaghan, M. K., Toffolo, G., Polonsky, K. S. & Cobelli, C. Oral glucose ADDITIONAL INFORMATION tolerance test minimal model indexes of beta-cell function and insulin sensitivity. Supplementary information accompanies the paper on the npj Systems Biology and Diabetes 50, 150–158 (2001). Applications website (https://doi.org/10.1038/s41540-018-0051-6). 27. Picchini, U., De Gaetano, A., Panunzi, S., Ditlevsen, S. & Mingrone, G. A mathe- matical model of the euglycemic hyperinsulinemic clamp. Theor. Biol. Med. Model Competing interests: The authors declare no competing interests. 2, 44 (2005). 28. Cobelli, C. et al. The oral minimal model method. Diabetes 63, 1203–1213 (2014). 29. Bergman, R. N., Phillips, L. S. & Cobelli, C. Physiologic evaluation of factors con- Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims trolling glucose tolerance in man: measurement of insulin sensitivity and beta- in published maps and institutional afﬁliations. Published in partnership with the Systems Biology Institute npj Systems Biology and Applications (2018) 14 Increase in hepatic and decrease in peripheral K Ohashi et al. cell glucose sensitivity from the response to intravenous glucose. J. Clin. Invest. 50. Noguchi, R. et al. The selective control of glycolysis, gluconeogenesis and gly- 68, 1456–1467 (1981). cogenesis by temporal insulin patterns. Mol. Syst. Biol. 9, 664 (2013). 30. Ohashi, K. et al. Glucose homeostatic law: insulin clearance predicts the pro- 51. Sano, T. et al. Selective control of up-regulated and down-regulated genes by gression of glucose intolerance in humans. PLoS ONE 10, e0143880 (2015). temporal patterns and doses of insulin. Sci. Signal 9, ra112 (2016). 31. Eaton, R. P., Allen, R. C., Schade, D. S., Erickson, K. M. & Standefer, J. Prehepatic 52. Goodner, C. J., Sweet, I. R. & Harrison, H. C. Rapid reduction and return of surface insulin production in man: kinetic analysis using peripheral connecting peptide insulin receptors after exposure to brief pulses of insulin in perifused rat hepa- behavior. J. Clin. Endocrinol. Metab. 51, 520–528 (1980). tocytes. Diabetes 37, 1316–1323 (1988). 32. Vølund, A., Polonsky, K. S. & Bergman, R. N. Calculated pattern of intraportal 53. Hirashima, Y. et al. Insulin down-regulates insulin receptor substrate-2 expression insulin appearance without independent assessment of C-peptide kinetics. Dia- through the phosphatidylinositol 3-kinase/Akt pathway. J. Endocrinol. 179, betes 36, 1195–1202 (1987). 253–266 (2003). 33. Cobelli, C. & Pacini, G. Insulin secretion and hepatic extraction in humans by 54. Hori, S. S., Kurland, I. J. & DiStefano, J. J. Role of endosomal trafﬁcking dynamics minimal modeling of C-peptide and insulin kinetics. Diabetes 37, 223–231 (1988). on the regulation of hepatic insulin receptor activity: models for Fao cells. Ann. 34. Grodsky, G. M. A threshold distribution hypothesis for packet storage of insulin Biomed. Eng. 34, 879–892 (2006). and its mathematical modeling. J. Clin. Invest. 51, 2047–2059 (1972). 55. Matveyenko, A. V. et al. Pulsatile portal vein insulin delivery enhances hepatic 35. Ličko, V. & Silvers, A. Open-loop glucose-insulin control with threshold secretory insulin action and signaling. Diabetes 61, 2269–2279 (2012). mechanism: analysis of intravenous glucose tolerance tests in man. Math. Biosci. 56. Sedaghat, A. R., Sherman, A. & Quon, M. J. A mathematical model of metabolic 27, 319–332 (1975). insulin signaling pathways. Am. J. Physiol. Endocrinol. Metab. 283, E1084–E1101 36. Toffolo, G. et al. Quantitative indexes of beta-cell function during graded (2002). up&down glucose infusion from C-peptide minimal models. Am. J. Physiol. 57. Kubota, N. et al. Dynamic functional relay between insulin receptor substrate 1 Endocrinol. Metab. 280,E2–E10 (2001). and 2 in hepatic insulin signaling during fasting and feeding. Cell Metab. 8,49–64 37. Toffolo, G., Campioni, M., Basu, R., Rizza, R. A. & Cobelli, C. A minimal model of (2008). insulin secretion and kinetics to assess hepatic insulin extraction. Am. J. Physiol. 58. Vølund, A. et al. In vitro and in vivo potency of insulin analogues designed for Endocrinol. Metab. 290, E169–E176 (2006). clinical use. Diabet. Med. 8, 839–847 (1991). 38. Chase, J. G. et al. A three-compartment model of the C-peptide-insulin dynamic 59. Choi, E. & Ahn, W. A new mixture ratio of heparin for the cell salvage device. during the DIST test. Math. Biosci. 228, 136–146 (2010). Korean J. Anesthesiol. 60, 226 (2011). 39. Mari, A., Tura, A., Gastaldelli, A. & Ferrannini, E. Assessing insulin secretion by 60. Lagarias, J., Reeds, J., Wright, M. & Wright, P. Convergence properties of the modeling in multiple-meal tests: role of potentiation. Diabetes 51(Suppl. 1), Nelder-Mead simplex method in low dimensions. Siam J. Optim. 9, 112–147 S221–S226 (2002). (1998). 40. Polidori, D. C., Bergman, R. N., Chung, S. T. & Sumner, A. E. Hepatic and extra- 61. Fujita, K. A. et al. Decoupling of receptor and downstream signals in the Akt hepatic insulin clearance are differentially regulated: results from a novel model- pathway by its low-pass ﬁlter characteristics. Sci. Signal 3, ra56 (2010). based analysis of intravenous glucose tolerance data. Diabetes 65, 1556–1564 62. Hubert, M. & der Van der Veeken, S. Outlier detection for skewed data. J. Che- (2016). mom. 22, 235–246 (2008). 41. Akaike, H. In Proc. 2nd International Symposium on Information Theory (eds. Pet- 63. Brys, G., Hubert, M. & Struyf, A. A robust measure of skewness. J. Comput. Graph. rov, B. N. & Csáki, F.) 267–281 (Akademiai Kiado, Budapest, Hungary, 1973). Stat. 13, 996–1017 (2004). 42. Butler, A. E. et al. Beta-cell deﬁcit and increased beta-cell apoptosis in humans 64. Benjamini, Y. & Hochberg, Y. Controlling the false discovery rate: a practical and with type 2 diabetes. Diabetes 52, 102–110 (2003). powerful approach to multiple testing. J. R. Stat. Soc. B 57, 289–300 (1995). 43. Inaishi, J. et al. Effects of obesity and diabetes on α- and β-cell mass in surgically 65. Schmidt, H. & Jirstrand, M. Systems Biology Toolbox for MATLAB: a computational resected human pancreas. J. Clin. Endocrinol. Metab. 101, 2874–2882 (2016). platform for research in systems biology. Bioinformatics 22, 514–515 (2006). 44. Mizukami, H. et al. Involvement of oxidative stress-induced DNA damage, endoplasmic reticulum stress, and autophagy deﬁcits in the decline of β-cell mass in Japanese type 2 diabetic patients. Diabetes Care 37, 1966–1974 Open Access This article is licensed under a Creative Commons (2014). Attribution 4.0 International License, which permits use, sharing, 45. Duckworth, W. C., Bennett, R. G. & Hamel, F. G. Insulin degradation: progress and adaptation, distribution and reproduction in any medium or format, as long as you give potential. Endocr. Rev. 19, 608–624 (1998). appropriate credit to the original author(s) and the source, provide a link to the Creative 46. Kubota, H. et al. Temporal coding of insulin action through multiplexing of the Commons license, and indicate if changes were made. The images or other third party AKT pathway. Mol. Cell 46, 820–832 (2012). material in this article are included in the article’s Creative Commons license, unless 47. Benzi, L. et al. Insulin degradation in vitro and in vivo: a comparative study in indicated otherwise in a credit line to the material. If material is not included in the men. Evidence that immunoprecipitable, partially rebindable degradation pro- article’s Creative Commons license and your intended use is not permitted by statutory ducts are released from cells and circulate in blood. Diabetes 43, 297–304 (1994). regulation or exceeds the permitted use, you will need to obtain permission directly 48. Polonsky, K. S. et al. Quantitative study of insulin secretion and clearance in from the copyright holder. To view a copy of this license, visit http://creativecommons. normal and obese subjects. J. Clin. Invest. 81, 435–441 (1988). org/licenses/by/4.0/. 49. Raue, A., Karlsson, J., Saccomani, M. P., Jirstrand, M. & Timmer, J. Comparison of approaches for parameter identiﬁability analysis of biological systems. Bioinfor- © The Author(s) 2018 matics 30, 1440–1448 (2014). npj Systems Biology and Applications (2018) 14 Published in partnership with the Systems Biology Institute

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Increase in hepatic and decrease in peripheral insulin clearance characterize abnormal temporal patterns of serum insulin in diabetic subjects

Increase in hepatic and decrease in peripheral insulin clearance characterize abnormal temporal patterns of serum insulin in diabetic subjects

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Increase in hepatic and decrease in peripheral insulin clearance characterize abnormal temporal patterns of serum insulin in diabetic subjects

Increase in hepatic and decrease in peripheral insulin clearance characterize abnormal temporal patterns of serum insulin in diabetic subjects

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