Multiscale Mathematical Model of Drug-Induced Proximal Tubule Injury: Linking Urinary Biomarkers to Epithelial Cell Injury and Renal Dysfunction

Multiscale Mathematical Model of Drug-Induced Proximal Tubule Injury: Linking Urinary Biomarkers... Abstract Drug-induced nephrotoxicity is a major cause of acute kidney injury, and thus detecting the potential for nephrotoxicity early in the drug development process is critical. Various urinary biomarkers exhibit different patterns following drug-induced injury, which may provide greater information than traditional biomarkers like serum creatinine. In this study, we developed a multiscale quantitative systems pharmacology model relating drug exposure to proximal tubule (PT) epithelial cell injury and subsequently to expression of multiple urinary biomarkers and organ-level functional changes. We utilized urinary kidney injury molecule-1 (Kim-1), alpha glutathione S-transferase, albumin (αGST), glucose, and urine volume time profiles as well as serum creatinine and histopathology data obtained from rats treated with the nephrotoxicant cisplatin to develop the model. Although the model was developed using single-dose response to cisplatin, the model predicted the serum creatinine response to multidose cisplatin regimens. Further, using only the urinary Kim-1 response to gentamicin (a nephrotoxicant with a distinctly different injury time course than cisplatin), the model detected and predicted mild to moderate PT injury, as confirmed with histopathology, even when serum creatinine was unchanged. Thus, the model is generalizable, and can be used to deconvolute the underlying degree and time course of drug-induced PT injury and renal dysfunction from a small number of urinary biomarkers, and may provide a tool to determine optimal dosing regimens that minimize renal injury. quantitative systems pharmacology, acute kidney injury, nephrotoxicity, biomarker, proximal tubular injury, multiscale model Failure to detect and understand the time course of drug-induced acute kidney injury (AKI) is a challenging problem in both drug development and clinical treatment of critically ill patients (Alge and Arthur, 2015; Schetz et al., 2005). Missed or misunderstood preclinical toxicity due to the poor sensitivity of traditional biomarkers (serum creatinine and blood urea nitrogen [BUN]) can put clinical trial subjects at unnecessary risk and also lead to expensive late-stage drug failures (Han et al., 2002). Clinically, it can result in delayed action to mitigate injury. Multiple novel urinary biomarkers (eg, alpha glutathione S-transferase [αGST] [Pinches et al., 2012], kidney injury molecule-1 [Kim-1] [Bonventre, 2009; Han et al., 2002], albumin [Pinches et al., 2012], and others [Parikh et al., 2013]) are promising for early detection and more accurate prediction of drug-induced renal injury (de Geus et al., 2012; Ostermann et al., 2012). However, the time courses of expression vary widely between biomarkers and among different nephrotoxicants, making interpretation challenging. The proximal tubule (PT) is the most common site of drug-induced AKI. Because of their role in active transportation and metabolism of drugs, PT epithelial cells (EpCs) are vulnerable to nephrotoxicants (Lohr et al., 1998; Morrissey et al., 2013; Tiong et al., 2014). Although the process of EpC injury remains incompletely understood, Figure 1 illustrates the currently accepted conceptual framework of AKI pathophysiology (Charlton et al., 2014; Devarajan, 2006, 2010). Initially, subtle and largely reversible cellular structural changes such as loss of brush border and altered cellular polarity occur (Devarajan, 2006). Injured cells may either recover back to normal cells or, if the injury is severe enough, experience irreversible changes that lead to cell death. As tubular cells die, neighboring viable cells de-differentiate and proliferate, resulting in regeneration of a normal epithelium (Devarajan, 2006). As these processes occur, they alter EpC expression and release signaling molecules (eg, upregulation of Kim-1), impair EpC reabsorption/secretion (eg, reduced albumin reabsorption), or release cytosolic content into the tubule lumen (eg, αGST [McDuffie et al., 2013; McMahon and Waikar, 2013]), resulting in observable changes in urinary biomarkers. Thus, although biomarkers such as BUN and serum creatinine reflect whole-organ function, biomarkers such as urinary Kim-1, αGST, albumin, and glucose may each provide specific information on alterations in cellular-level processes. Figure 1. View largeDownload slide Processes of proximal tubule epithelial cell injury, death, recovery, and regeneration during acute kidney injury (adapted from Devarajan, 2006). Figure 1. View largeDownload slide Processes of proximal tubule epithelial cell injury, death, recovery, and regeneration during acute kidney injury (adapted from Devarajan, 2006). Pinches et al. (2012) and Vaidya et al. (2010) have demonstrated that the magnitudes of biomarkers like urinary Kim-1, albumin, glucose, and others are related to histopathological injury severity. In particular, Vaidya et al. (2010) showed that Kim-1 is a sensitive and specific predictor of injury. These studies also demonstrated varying temporal patterns for different biomarkers and in response to different drugs. This suggests it may be possible to extract greater information from these biomarkers on the mechanism, extent, and time course of renal injury and organ-level dysfunction. A quantitative framework that relates observed drug-induced changes in novel urinary biomarkers to latent pathophysiological processes that manifest at the cellular, organ, and systems levels would allow evaluation of the mechanism, extent, and time course of both local injury and organ-level dysfunction. This could facilitate improved preclinical evaluation and benchmarking of drug candidates, optimization of dosing regimens to minimize injury, and potentially translation of preclinical findings to predict clinical risk. In this study, we developed a multiscale mathematical model that temporally relates drug exposure to pathophysiological processes of PT EpC injury and repair and subsequently to the expression of multiple urinary biomarker responses (Kim-1, αGST, albumin, glucose, urine volume) and to organ-level functional changes as indicated by serum creatinine. MATERIALS AND METHODS Experimental Data Development Data For model development, we utilized urinary biomarker and renal histopathology data previously collected in male HsdHan:WIST (Harlan UK) strain rats treated with a single intraperitoneal (IP) administration of 0, 0.1, 1.0, or 2.5 mg/kg cisplatin (Pinches et al., 2012). Pharmacokinetic data that are used as driver for PT injury were collected for 2.5 mg/kg dose for 5 days at 1, 3, 18, 42, 66, and 90 h. Urinary biomarkers including Kim-1, αGST, glucose, albumin, and volume were collected at baseline and daily starting 2 days postdose. Serum creatinine was measured on days 5, 7, 8, and 22. Rats were sacrificed on day 5, 8, or 22 for histopathology, including scoring of necrosis and regeneration in the PT S3 segment by an independent pathologist. Due to their intrinsic metabolic behavior, compared with the proximal convoluted tubule S1 and S2 segments, cells in the proximal straight tubule S3 segment are selectively susceptible to necrosis when exposed to noxious stimuli (Venkatachalam et al., 1978). Histopathological severity scores for PT S3 necrosis and regeneration were calculated as the sum of severity grades (1 through 4, with 1 being normal and 4 being most severe) weighted by the fraction of animals with that severity. As shown in Figures 2A and 2B, the urinary biomarker time courses revealed 2 distinct biomarker groups: (1) αGST, albumin, and glucose showed steep narrow peaks that did not begin to rise until day 4 and had returned to normal again by day 7 and (2) Kim-1 and urine volume showed a broader peak, beginning to rise by day 2 and remaining elevated on day 7. These trends are similar in both doses, although Kim-1 peaked later in the 2.5 mg/kg dose group. Trends in PT necrosis coincided with the first biomarker group. At the lower dose, regeneration coincided with the biomarker peaks, although at the higher dose it peaked later. Figure 2. View largeDownload slide Time courses of fold increase (from predose values) of a panel of urinary biomarkers, as well as histopathologic severity scored for PT S3 necrosis and regeneration, in rats treated with 2.5 mg/kg (A) and 1.0 mg/kg (B) cisplatin. Figure 2. View largeDownload slide Time courses of fold increase (from predose values) of a panel of urinary biomarkers, as well as histopathologic severity scored for PT S3 necrosis and regeneration, in rats treated with 2.5 mg/kg (A) and 1.0 mg/kg (B) cisplatin. Data for Model Applications Two previously published studies were used for testing model generalizability to multiple doses and a different drug mechanism. In the study of Kobayashi et al. (2000), male Donryu rats were exposed to a weekly high dose of 5 mg/kg or a daily lower dose of 1.2 mg/kg cisplatin over 3 weeks, and serum creatinine was measured at the end of the study (the authors state that these doses were selected because animals died when the high dose of 5 mg/kg was administered more frequently, and daily doses of 1 mg/kg or less had minimal anticancer effect) (Kobayashi et al., 2000). In the study of Vaidya et al. (2010), male Sprague Dawley rats were treated with daily IP administration of gentamicin (20, 80, or 240 mg/kg/day) for 15 days. Urinary Kim-1 and serum creatinine were collected on days 3, 9, and 15, along with day 12 for 240 mg/kg. Animals were sacrificed on days 3, 9, and 15 for histopathologic analysis and were assigned a composite PT severity score ranging from 0 to 5, 5 being the highest (Vaidya et al., 2010). For our analysis, the mean histopathology severity score for each day was calculated and normalized by the highest severity level, 5, to scale the range of severity from 0 to 1, to facilitate comparison with model-predicted cell injury. Because gentamicin plasma concentrations were not reported, pharmacokinetic data were extracted from a separate study (Engineer et al., 1987). Relating Urinary Biomarkers to PT EpC Injury and Death The biomarker and histopathology data following a single cisplatin dose shown in Figure 2 informed key assumptions in developing the drug-induced PT injury model. Based on the distinct temporal behaviors of the 2 classes of biomarkers and related histopathology, we hypothesized that: (1) the early rise and broad peak in the magnitudes of urinary Kim-1 and urine volume were indicative of EpC injury (brush-border loss and depolarization) and (2) the delayed rise and narrow peak in the magnitudes of urinary αGST, albumin, and glucose were indicative of acute EpC death, quickly followed by regeneration. These hypotheses follow from our understanding of the biology of EpC and each of the biomarkers. Alpha glutathione S-transferase is normally present in the cytoplasm and is likely released into the lumen upon EpC death (McDuffie et al., 2013). Kidney injury molecule-1 is upregulated in response to cellular injury and serves to attract macrophages to remove debris and protect cells from further inflammatory injury (Bonventre, 2009; Ichimura et al., 2008; Lim et al., 2013). Proximal tubule EpCs normally reabsorb large quantities of sodium and water through the brush-border microvilli, and brush-border loss would be expected to reduce reabsorptive capacity and increase excretion of sodium and water. The relatively smaller quantities of albumin and glucose filtered through the glomerulus normally almost completely reabsorbed by the PT via an endocytic mechanism (Birn et al., 2000; Zhai et al., 2000), and the tubule has sufficient endocytic capacity to sustain brush-border loss and still maintain albumin and glucose reabsorption. However, death of a significant number of cells would result in insufficient reabsorptive capacity and lead to increased excretion of these biomarkers. With these concepts in mind, the sudden rise in αGST, albumin, and glucose around day 5 (at both doses) suggests an acute period of cell death resulting in loss of EpC reabsorptive capacity and release of cytosol content into the lumen. This is consistent with histopathology scores, which were highest at day 5, much lower by day 8, and normal by day 22. The equally rapid fall in these biomarkers suggests that the functional capacity of these cells is quickly recovered, likely through hypertrophy and hyperplasia of surrounding cells. This is consistent with the histopathologic scores for PT regeneration. The persistence of histologic signs of regeneration at the higher dose after the functional biomarkers have recovered, as well as the persistent elevation in Kim-1 and urine volume, suggests that cell regeneration (replication and differentiation) may be a prolonged process, which continues after these basic functions have been restored. Multiscale Mathematical Model Model Scope As illustrated in Figure 3, the multiscale mathematical model is comprised of interlinked submodels: a cellular-level model of EpC injury/death and an organ/systems-level model of renal physiology and volume regulation. Changes in PT function resulting from drug-induced EpC injury/death provide the links between the 2 submodels. At the cellular level (left panel), the concentration-time profile of cisplatin drives cellular injury and death. Drug-induced injury and death at the cellular level lead directly to biomarker expression (Kim-1) and release (αGST), as well as to loss of function (Na, water, glucose, and albumin reabsorption) at the tubule level, resulting in changes in urine volume, glucose, and albumin. At the systems level (right panel), impaired tubular Na and water reabsorption indirectly cause alterations in the renal (right panel, top) and systemic hemodynamics (right panel, bottom), which ultimately result in changes in glomerular filtration rate (GFR) and serum creatinine. The details of each submodel, as well as how they are interconnected, are described below. Additional details can be found in the Supplementary materials. Figure 3. View largeDownload slide Model overview. Drug pharmacokinetic exposure drives injury and death at the cellular level, producing impairments in reabsorption at the tubular level, which then affect changes at the organ/systems level (increased tubular pressure, TGF, and ultimately reduced GFR). Biomarkers like urinary Kim-1 and αGST are increased as a result of cellular-level injury; glucose and albumin are increased as a result of tubular-level impairment; serum creatinine reflects the systems-level consequences of tubular impairment leading to reduced GFR; urine volume reflects both reduced reabsorption and subsequent reduced renal filtration. TGF, tubuloglomerular feedback; TPR, total peripheral resistance; MAP, mean arterial pressure. Figure 3. View largeDownload slide Model overview. Drug pharmacokinetic exposure drives injury and death at the cellular level, producing impairments in reabsorption at the tubular level, which then affect changes at the organ/systems level (increased tubular pressure, TGF, and ultimately reduced GFR). Biomarkers like urinary Kim-1 and αGST are increased as a result of cellular-level injury; glucose and albumin are increased as a result of tubular-level impairment; serum creatinine reflects the systems-level consequences of tubular impairment leading to reduced GFR; urine volume reflects both reduced reabsorption and subsequent reduced renal filtration. TGF, tubuloglomerular feedback; TPR, total peripheral resistance; MAP, mean arterial pressure. Cellular-Level Model of EpC Injury The cellular EpC injury model (Figure 3, bottom left) describes the processes of cell injury, death, recovery, and regeneration resulting from exposure to a nephrotoxicant, as illustrated in Figure 1 (Devarajan, 2010; Lim et al., 2013). The model describes 3 mutually exclusive sets of EpCs: functional, injured, and dead. At any particular time t, the fractions of the total EpC population that belongs to each of the functional, injured, and dead EpCs are represented by F(t), I(t), and N(t), respectively, and always sum to one. Cells move between populations through 4 processes: injury, recovery, death, and regeneration. The governing differential equations are as follows:   ddtI=RInjuryt-RRecoveryt-RDeatht, (1)  ddtF=-RInjuryt+RRecoveryt+RRegenerationt,  (2)  ddtN=RDeatht-RRegenerationt, (3) where RInjury, RRecovery, RDeath, and RRegenration are the injury, recovery, death, and regeneration rates, respectively. Cell injury represents brush-border loss and loss of polarity, so that cell functions that rely on microvilli, such as sodium and water reabsorption, are impaired. The injury rate Rinjury is proportional to the functional cell fraction F(t) and the effective drug exposure driving injury, Cinjury, as given in equation 4. kinjury is the proportional injury rate constant, and thresholdinjury the effective exposure below which no injury is observed.   RInjuryt=kinjury*maxCinjuryt-thresholdinjury, 0*Ft. (4) Cell recovery represents restoration of normal cell function as the brush border and polarity are restored. The rate of cell recovery RRecovery is related to the fraction of injured cells via a proportional rate constant krecovery:   RRecoveryt=krecovery*It. (5) Cell death represents a complete loss of cell viability, so that cytoplasmic content (including αGST) is released into the tubule lumen, and cell function (including albumin and glucose reabsorption) is completely lost. The cell death rate RDeath is modeled as a sigmoidal function of the delayed cisplatin concentration Cdeath, which accounts for an additional time lag in cellular death relative to injury.   RDeatht=kdeath*CdeathγtIC50Deathγ+Cdeathγt*It. (6) The sigmoidal function was motivated by the sharp delayed rise in αGST, albumin, and glucose. Cellular regeneration represents recovery of the function of dead cells due to hypertrophy and hyperplasia of surrounding cells. Cell proliferation is inhibited by contact with other cells (McClatchey and Yap, 2012), and thus as the number of dead cells increases, the number of EpC cell-cell contacts will decrease, and the proliferation rate may be expected to increase. Indeed, we found that describing the regeneration rate RRegeneration as a power law function of the dead cell fraction, where the rate constant kregeneration and the power constant p were determined by optimization, provided a better fit to the experimental data, as compared with a linear model.   RRegenerationt=kregeneration*Npt. (7) Systems Model of Renal Physiology and Volume Homeostasis We utilized a previously developed mechanistic model of renal function and volume homeostasis (Hallow et al., 2017). Briefly, as illustrated in Figure 3, this model describes the processes of glomerular filtration, reabsorption along each tubular segment, and excretion of unabsorbed substances at the single-nephron level. The kidney is modeled as a set of N nephrons in parallel. The outputs of the nephron model—sodium and water excretion—feed into a model of volume homeostasis, where the balance between sodium and water intake and excretion determine blood volume, extracellular fluid volume, and blood pressure. Blood pressure and blood sodium concentration then feed back to the kidney submodel. The model also incorporates key intrinsic as well as neurohumoral feedback mechanisms, including tubuloglomerular feedback (TGF), vasopressin, and the renin-angiotensin-aldosterone system. Full equations of the model are given elsewhere (Hallow and Gebremichael, 2017a,b; Hallow et al., 2017), and key equations are provided in the Supplementary materials. Linking EpC Cell Injury Model to System Behavior and Biomarker Responses EpC injury and death fractions were used to drive changes in tubular function and biomarker expression. Each effect E then multiplies the associated nominal release/production rate or fractional reabsorption rate. The βs in each equation are scaling factors estimated by fitting model biomarker outputs to the observed biomarker time courses. Alpha glutathione S-transferase Urinary excretion of αGST is normally quite small, but increases many fold during AKI. We assumed that all αGST released into the tubule lumen is excreted, and the effect of cell death on αGST excretion EαGST is related to the fraction N of dead cells:   EαGST=1+βαGST*N. (8) The rate of urinary αGST excretion is thus determined by scaling the nominal αGST excretion rate X˙αGST0 by the effect EαGST:   X˙αGSTt=X˙αGST0*EαGSTt=X˙αGST0*1+βαGST*N. (9) Albumin Nearly all filtered albumin is normally reabsorbed by the PT via an endocytic mechanism; however, dead cells cannot reabsorb albumin. The effect of cell death on PT albumin reabsorption Ealb is related to the dead cell fraction N:   Ealb=1-βalb*N. (10) Proximal tubule albumin reabsorption fraction ηalbt is then determined by scaling the nominal albumin reabsorption fraction ηalb0 with the effect Ealb:   ηalbt=ηalb0*Ealb. (11) ηalb, in turn, affects the urinary albumin excretion rate X˙alb(t):   X˙albt=GFRt*Salb*ϑ*1-ηalbt, (12) where  [Salb] is the serum albumin concentration (treated as a constant) and ϑ is the albumin sieving coefficient. Glucose Similarly, nearly all filtered glucose is normally reabsorbed by the PT (approximately 90%–97% at the S1 segment and approximately 3%–10% at the S3 segment via the sodium cotransporters SGLT2 and SGLT1, respectively [Gorboulev et al., 2012; Novikov and Vallon, 2016; Rieg et al., 2014; Vallon, 2011]). However, dead cells cannot reabsorb glucose. As with albumin, we assumed PT glucose reabsorption impairment is related to cell death fraction. However, relative to the changes in αGST and albumin, the fold-change of urinary glucose excretion at 1 mg/kg dose of cisplatin was much lower versus the 2.5 mg/kg dose. The PT possesses excess glucose reabsorptive capacity (DeFronzo et al., 2017), and we hypothesized that when the degree of cell death is small (the lower dose) this excess capacity is able to compensate to a greater extent. The effect of cell death on PT glucose reabsorption rate Eglu is thus related to dead cells fraction by the following nonlinear relationship:   Eglu=1-βglu*Nα, (13) where α is a fitting constant, determined by optimization, and accounts for the increase in glucose excretion as cell death increases and the excess capacity becomes overwhelmed. Because most necrosis is reported to be on the S3 segment (Pinches et al., 2012), the drug-induced change of the urinary glucose excretion rate X˙glu is determined by scaling the nominal S3 segment glucose reabsorption fraction ηS30 with the effect Eglu as:   X˙glut=GFRt*Sglu*1-ηS10-ηS30*Eglu, (14) where  [Sglu] is the serum glucose concentration (assumed constant) and ηS10 is the nominal S1 glucose reabsorption fraction. Kidney injury molecule-1 Urinary Kim-1 is normally negligible, but increases significantly during AKI. The observed time course of Kim-1 exhibited an early onset and a delayed peak. The early rise was assumed to be due to EpC injury, whereas the continued increase suggests additional expression following cellular death. Thus, the effect on Kim-1 expression, EKkim1, is modeled as a function of both dead and injured cell fractions:   EKim1=βKim1*I+N. (15) The urinary Kim-1 peak was delayed compared with the peak in cellular death marked by urinary αGST, albumin, and glucose. This may reflect the time required for signal transduction and upregulation of expression by neighboring living cells, or it may reflect Kim-1 released by regenerating cells that have already regained their ability to reabsorb albumin and glucose but are not fully differentiated and functioning as normal cells. To reproduce the observed delayed Kim-1 signal, we implemented a single transit compartment, a common approach in signal transduction models (Felmlee et al., 2012), based upon best fit of the data:   dM1dt=1τ*EKim1-M1,  (16) where M1 is the effect in the transit compartment and τ is the mean transit time through the compartment. The urinary excretion rate X˙Kim1 of Kim-1 is then:   X˙Kim1t=X˙Kim10*1+M1, (17) where X˙Kim10 is the nominal excretion rate of Kim-1. Urine volume PT reabsorption is isosmotic, and thus PT water reabsorption passively follows Na reabsorption through osmosis. Loss of microvilli during cell injury and/or death reduces PT EpCs’ ability to reabsorb sodium; this effect, Esodium, is expressed as:   Esodium=1-βsod*I+N. (18) This term modifies the PT sodium reabsorption fraction ηptsodreabs:   ηptsodreabs=ηptsodreabs0*Esodium, (19) where ηptsodreabs0 is the nominal sodium reabsorption fraction. ηptsodreabs is explicitly represented in the systems-level renal physiology model, where reducing sodium and water reabsorption alters renal hemodynamics and ultimately GFR. Reduced water reabsorption in the PT increases PT and Bowman’s space pressure, which opposes filtration pressure and lowers GFR. In addition, when less sodium is reabsorbed proximally, more is delivered to the macula densa, triggering TGF that constricts the afferent arteriole and lowers GFR further. Thus, injury-induced reductions in PT sodium and water reabsorption tend to directly increase urine excretion, but the indirect effects on GFR tend to lower urine excretion. The model-predicted total urine volume reflects the combined effect of both mechanisms. Serum creatinine Creatinine is filtered freely through the glomerulus, and approximately 15% (Samra and Abcar, 2012) of excreted creatinine is due to secretion from PT EpCs into the tubule lumen. Creatinine is not reabsorbed in the tubule. Cisplatin-induced PT injury increases serum creatinine in 2 ways: (1) Injury-induced changes in PT sodium and water reabsorption cause renal hemodynamic changes that suppress GFR and reduce renal filtration of creatinine and (2) cisplatin directly reduces tubular secretion of creatinine by interfering with the transporter, Organic Cation Transporter 2 (Ciarimboli et al., 2012). The effect of PT injury on GFR and thus on creatinine filtration is captured implicitly through the systems-level model, as a consequence of impaired tubular Na and water reabsorption, as described above. We also modeled the direct effect of cisplatin on PT creatinine secretion, employing a sigmoid Emax model, which accounts for cisplatin-induced pharmacodynamic effect on PT creatinine secretion. A complete description of serum creatinine dynamics is provided in the Supplementary materials. Drug Exposure Model For both cisplatin and gentamicin, plasma drug concentration-time profile was modeled using a standard 2-compartment model. To account for the time delays between plasma drug exposure and onset of changes in biomarkers reflecting cell injury or death, a transit compartment construct was used to produce delayed signals Cinjury and Cdeath. More details are provided in the Supplementary materials. Software Implementation The model was implemented in R 3.1.2 using the RxODE package (https://cran.r-project.org/web/packages/RxODE/index.html), a tool for simulating differential equation models in R (Wang et al., 2016). The cellular injury model features a total of 19 parameters, which were simultaneously fitted to reproduce the time profiles of biomarkers obtained from the animal study, using a global optimization method based on a genetic algorithm method, supplemented by R shiny app (https://shiny.rstudio.com/) visualization tool for initialization and fine tuning. More details can be found in Supplementary materials. RESULTS Model Development: Fitting to Cisplatin-Induced Biomarker Responses Figure 4 summarizes the model fit of biomarker responses to single-dose cisplatin-induced PT injury at each dose. Estimated model parameters are given in Supplemental Table 3. The top left in each panel of Figure 4 shows the model fit to the plasma cisplatin concentration-time profile. Because there is a time delay between exposure and initiation of cell injury and death, as indicated by the biomarker time profiles, time-delayed concentration profiles ( Cinjury and Cdeath) were used as the signals driving cell injury and death. The model captures the magnitude and time course of each biomarker at each dose, including the steep narrow peak (near day 5) of αGST, albumin, and glucose and the broad peak of Kim-1, water excretion, and serum creatinine. Figure 4. View largeDownload slide Model fit of biomarker responses following cisplatin doses of 2.5 mg/kg (A) and 1.0 mg/kg (B). For each dose, cisplatin exposure (top left) drives cellular injury and death (bottom left), which then produce biomarker responses shown on the right. Blue, simulation; red diamonds, median, experimental data; black dashed lines, experimental data first and fourth quartiles; green triangles, digitized data from Fukushima et al. (2016). Figure 4. View largeDownload slide Model fit of biomarker responses following cisplatin doses of 2.5 mg/kg (A) and 1.0 mg/kg (B). For each dose, cisplatin exposure (top left) drives cellular injury and death (bottom left), which then produce biomarker responses shown on the right. Blue, simulation; red diamonds, median, experimental data; black dashed lines, experimental data first and fourth quartiles; green triangles, digitized data from Fukushima et al. (2016). Model-Estimated EpC Injury and Death The fractions of functional F, injured I, and dead N cells (Figure 4, bottom left in each panel) are latent variables that drive the biomarker responses, and whose magnitudes and time courses were determined by fitting model parameters to the observed biomarker time courses. Although all data were fit simultaneously, the shape and magnitude of cell death were constrained primarily by αGST, albumin, and glucose, whereas cell injury was constrained primarily by Kim-1, urine volume, and serum creatinine. These simulations indicate that, at both doses, cell injury begins and peaks early, whereas the initiation of cell death is delayed and the peak occurs later, around day 5. There is substantial cell injury at both doses, although maximum cell injury is 132% higher at the higher dose than the lower dose (51% vs 22%). There is significant cell death (48% at peak) at the higher dose, whereas cell death is much reduced at the lower dose (3.5% maximum). Biomarkers Indicative of Cell Death As seen in Figure 4 (bottom-right rows in each panel), the time courses of αGST, albumin, and glucose all closely follow the time course of cell death. At both doses, the model reproduces the delayed and sharp rise and fall of these biomarkers at day 5. The magnitudes of urinary αGST and albumin responses were proportional to the increase in cell death at each dose. However, the ratio of glucose excretion at the lower dose relative to the higher dose was much smaller than the ratio of cell death. The power law equation for glucose reabsorption impairment (equation 14) allowed the model to capture this behavior. As mentioned above, the PT possesses excess capacity for glucose reabsorption (DeFronzo et al., 2017), and thus it is likely that at low levels of EpC death, the remaining cells are able to compensate. However, as cell death increases, the excess capacity is overwhelmed and glucose excretion accelerates. Biomarkers Indicative of Both Cell Injury and Death In Figure 4, the top-right rows in each panel show the observed and simulated responses of markers that arise from a combined effect of cellular injury and death. Kidney injury molecule-1 As described earlier, the urinary Kim-1 response was hypothesized to increase due to both EpC injury and EpC death. The model captured the early rise, as well as the delayed broad peak in Kim-1, around day 7, of the 2.5 mg/kg dose. For the 1 mg/kg dose, the Kim-1 response was smaller and more variable. The model-predicted rise in Kim-1 was slower than the observed median response, but still fell within the 25%–75% quartiles of the response. Urine volume As described earlier, injured cells lose their brush border and microvilli, diminishing their ability to reabsorb large amounts of sodium and water and resulting in excess excretion. Dead cells obviously lose these functions as well. Changes in urine volume reflect both impaired water reabsorption due to dead and injured cells (which tends to increase excretion), as well as reduced glomerular filtration at the organ level (which tends to decrease excretion). Urine volume data were highly variable, possibly due to variability in water intake, voiding times, and other experimental factors. However, for both doses, the model adequately reproduced observed urinary volume responses. At the low dose, the model predicted minimal cell death, and thus the peak in urine volume paralleled the cell injury peak. At the higher dose, the model predicts significant cell death and injury, and the broader peak parallels the combined effect of cellular injury and death. Serum creatinine Because serum creatinine was not measured in our study until day 5, we supplemented our data with daily serum creatinine measurements from Fukushima et al. (2016). As shown in Figure 4, the simulated serum creatinine time profile closely matched the observed data. The peak in serum creatinine occurred near day 5 for both doses, reflecting the combined effect of GFR decline and PT creatinine secretion dysfunction arising from EpC injury and death. Model Application: Multidose Administration and Evaluation of Cisplatin Dosing Regimen The model was developed using the response to a single dose of cisplatin, but we also tested its ability to predict the response to repeated cisplatin dosing. As shown in Figure 5 (blue lines), the model-predicted changes in serum creatinine after 21 days following weekly dosing of 5 mg/kg (top row) or daily dosing of 1.2 mg/kg (bottom row) were consistent with the range of changes observed in experimental serum creatinine (Kobayashi et al., 2000). Figure 5. View largeDownload slide Responses to repeated cisplatin administration. Upper panels: responses following weekly administrations at various doses. Lower panels: responses to changes in dosing frequencies, for a 1.2 mg/kg dose. In both panels, brown triangle symbols are the observed fold increase of serum creatinine for each group of rats studied in Kobayashi et al. (2000), and blue curves are the corresponding simulation, for weekly 5 mg/kg (upper panel) and daily 1.2 mg/kg (lower panel) cisplatin dosing. Figure 5. View largeDownload slide Responses to repeated cisplatin administration. Upper panels: responses following weekly administrations at various doses. Lower panels: responses to changes in dosing frequencies, for a 1.2 mg/kg dose. In both panels, brown triangle symbols are the observed fold increase of serum creatinine for each group of rats studied in Kobayashi et al. (2000), and blue curves are the corresponding simulation, for weekly 5 mg/kg (upper panel) and daily 1.2 mg/kg (lower panel) cisplatin dosing. The model also predicted that both dosing regimens tested in the study of Kobayashi et al. (2000) would result in extensive (approximately 75%) EpC death. Although injured cells may easily recover, cell death may be more detrimental to long-term renal function, especially when cells are not allowed to recover and regenerate between dosing cycles. The model can be applied to identify regimens that minimize EpC death while maximizing drug exposure. The model provides a tool for quantifying and visualizing injury under different regimens, to guide dosing decisions. Figure 5 shows additional simulated response to different doses and regimens. For weekly dosing (top row), the model predicts that a dose of 2 mg/kg or less would maintain cell death below 50%. For a fixed dose of 1.2 mg/kg (Figure 5, bottom row), every 3-day dosing instead of daily would keep cell death below 50%. Interestingly, reducing the dosing frequency further (eg, once every 4 days), cut cell death in half, down to about 25%. Yet, the difference in serum creatinine change between these 2 scenarios was minimal, illustrating the lack of sensitivity of serum creatinine for quantifying cellular toxicity. In these simulations, as expected, patterns of Kim-1 excretion depended upon dose and dosing frequency. However, for a weekly 1.2 mg/kg dosing (and, to some degree, for other dosing scenarios), Kim-1 excretion remained elevated at the times when the dead cell fraction as well as serum creatinine tended to return to normal, thereby providing a unique signature for Kim-1. This behavior can be partly associated with the delayed peak responses of Kim-1 that may not be in accord with the brief cellular recovery between subsequent drug administrations and may lead to further Kim-1 accumulation with each cycle. Readers may explore additional administration protocols using the web-based model interface provided at http://qsp.engr.uga.edu:3838/AKI_regimen/. Model Application: Prediction of Gentamicin-Induced Injury The model was developed using cisplatin response data, but to be truly useful, it should be generalizable to PT injury by other compounds. Pharmacokinetics as well as the magnitude and time course of drug-induced EpC injury/death may vary widely among nephrotoxic agents. However, although the relationship between drug exposure and cell injury and death is compound-specific, the relationships between cell injury and death and subsequent effects on tubular dysfunction, biomarker expression, and organ-level dysfunction should be independent of the injury mechanism. This implies that, to model a new compound, only the drug pharmacokinetics and parameters defining rates of cell injury and death need to be re-estimated; the remaining downstream equations and parameters governing the consequences of cell injury and death should not change. If this is the case, then by fitting the model to a panel of biomarker responses arising from a new compound, the model should be able to deconvolute the underlying cell injury/death from observed biomarkers. To test this idea, we applied the model to published data from a previously conducted preclinical study of gentamicin (Vaidya et al., 2010), which is known to cause PT injury with repeated dosing (Ali et al., 2011). This study measured urinary Kim-1 and serum creatinine in response to daily gentamicin treatment, but unfortunately did not measure other biomarkers utilized in our model. We replaced the cisplatin pharmacokinetics with gentamicin pharmacokinetics (Engineer et al., 1987) and re-estimated parameters governing the cell injury and cell death response to gentamicin exposure (parameters in equations 4 and 6) by simultaneously fitting to the urinary Kim-1 response to daily dosing of 20, 80, or 240 mg/kg gentamicin (Vaidya et al., 2010). Urinary Kim-1 reflects both cell injury and cell death, but without an additional biomarker like αGST, albumin, or glucose that is specific to cellular death, the ability to distinguish between injury and death was limited. As a simplifying assumption, the ratio between kinjury and kdeath was constrained to be the same for gentamicin and cisplatin. All other parameters, including cell recovery and regeneration rates, were fixed at previously estimated values. We then simulated the cell injury/death and serum creatinine time courses for each dose, as shown in Figure 6. We compared the simulated sum of injured and dead cell fractions with the observed histopathologic scores, recognizing that the ability to further distinguish between injury and death was limited by the lack of additional biomarker data. Figure 6. View largeDownload slide Simulated response to gentamicin-induced renal injury. Left panel: concentration-time profile of gentamicin for 20, 80, and 240 mg/kg doses. From top to bottom shows concentration-time profile for single dose, daily dosing, and cellular injury and cellular death compartments. Right panel: first column, model parameters were constrained to fit the observed urinary Kim-1; second column, simulated serum creatinine compared with observed response; third column, the simulated sum of injured and dead cell fractions (I + N), compared with observed mean histopathology severity. Data obtained from Vaidya et al. (2010). Kim-1, kidney injury molecule-1. Figure 6. View largeDownload slide Simulated response to gentamicin-induced renal injury. Left panel: concentration-time profile of gentamicin for 20, 80, and 240 mg/kg doses. From top to bottom shows concentration-time profile for single dose, daily dosing, and cellular injury and cellular death compartments. Right panel: first column, model parameters were constrained to fit the observed urinary Kim-1; second column, simulated serum creatinine compared with observed response; third column, the simulated sum of injured and dead cell fractions (I + N), compared with observed mean histopathology severity. Data obtained from Vaidya et al. (2010). Kim-1, kidney injury molecule-1. For both 20 and 80 mg/kg gentamicin, the model described the urinary Kim-1 response well and predicted the quite small changes in serum creatinine. Importantly, the model-predicted measure of combined cell injury and death also agreed very well with both the time course and magnitude of histopathologic PT injury, indicating that the model is indeed able to determine the degree of underlying PT injury from the observed Kim-1 biomarker response, even when serum creatinine remains practically unchanged from baseline. For the 240 mg/kg dose, the model predicted the extensive PT injury observed at this dose, but did not fully capture the rise in Kim-1, and did not capture the very large increase in serum creatinine (5-fold by day 9) at this dose. Such a large change in creatinine reflects a massive loss of renal function. We speculate that at very high doses, the injurious effects of gentamicin extend beyond the dysfunction in PT reabsorption captured by the model. Because the dataset used in model development did not include such severe injury, the model in its current form does not capture these additional mechanisms and may be best suited for modeling mild to moderate renal injury. DISCUSSION In this study, we developed a multiscale systems pharmacology model of drug-induced PT injury. By coupling observed time profiles for a panel of biomarkers and histopathologic observations with knowledge of EpC biology, renal physiology, and the physiologic processes involved in expression of each biomarker, we formulated a model that provides a mechanistic, quantitative framework for relating observable biomarker time courses to unobservable cellular-level processes of EpC injury and death and subsequently to alterations in organ-level function (GFR, as indicated by serum creatinine). Although the model was developed with cisplatin data, it was able to use the Kim-1 response to a different compound, gentamicin, to predict the magnitude and time course of underlying PT damage. After identifying 2 groups of biomarkers in our development dataset, we considered known physiology regarding each biomarker’s EpC expression/regulation, as well as the observed PT necrosis and regeneration histopathology scores, and hypothesized that the 2 classes represent distinct processes of cell injury (broad-peak biomarkers with early onset) and cell death (narrow-peak biomarkers). We further related cell injury and death with changes in EpC functional capacity—ie, injured cells lose the ability to reabsorb large amounts of sodium and water, while retaining the ability to reabsorb albumin and glucose; dead cells lose all reabsorptive capacity. We then related these cellular-level changes in function and viability to organ-level changes in renal function. We believe that the multiscale model presented here is the first to quantitatively relate urinary biomarker dynamics to underlying PT EpC injury and to organ-level renal impairment. We also demonstrated generalizability that, to model a new compound, only the drug pharmacokinetics and parameters defining rates of cell injury and death need to be re-estimated; the remaining downstream equations and parameters governing the consequences of cell injury and death are compound-independent. For gentamicin, the model was then able to predict the degree of underlying PT EpC injury based on the observed urinary Kim-1 response. Because biomarkers like urinary αGST or albumin that reflect cell death were not available, we were not able to determine the relative contribution of cell injury versus cell death with certainty, although this could be done in future studies in which cell death biomarkers are measured. This distinction may be important, because tubules may recover more easily when cells are injured than when a large number of cells are killed. Thus, in future studies, the model may be used to deconvolute the underlying degree and time course of PT injury and renal dysfunction from a small number of urinary biomarkers. The model predicted PT EpC injury from urinary Kim-1, even when serum creatinine changes were negligible, illustrating the power to detect mild injury, and the limitations of serum creatinine as an indicator of renal injury. The model performed less well in predicting serum creatinine changes in the setting of severe gentamicin-induced injury. The model currently only accounts for drug-induced changes in PT reabsorption, and we speculate that when injury is severe, other changes may occur as well—eg, tubular blockage, vasoconstriction, or glomerular injury. The development dataset did not include such severe injury, and thus the model currently does not capture these additional mechanisms. However, the renal physiology model is equipped to accommodate these additional mechanisms, and in future studies the model may be extended by utilizing datasets under more severe injury conditions. The present model may be best suited for modeling mild to moderate renal injury, but this is perhaps the most critical domain, because this type of injury is more difficult to detect by serum creatinine changes. Although the model was developed using single-dose creatinine response data, it predicted creatinine responses following multiple doses under 2 different dosing regimens. We also illustrated how the model can be used to evaluate different, experimentally untested dosing regimens, to identify regimens that minimize cell death. Such analysis, combined with efficacy dose-response data, could be applied in drug development to determine optimal dosing regimens that maximize efficacy while minimizing renal injury. In particular, the model may provide more quantitative information for evaluating biomarker evidence for renal toxicity, especially PT injury, when making decisions on whether to move compounds forward in new drug development. For example, if the time course of a panel of biomarkers that are indicative of cellular injury and death are measured, then the model can be used to deconvolute the underlying cellular injury and death in a manner similar to that done for gentamicin. Once a set of key parameters specific to the new drug has been identified, varying dosing regimens can be explored for safety analysis. On the other hand, when circumstances do not permit for such rigorous analysis, one may use the web-based model interface to compare biomarkers signal from the new drug with that of cisplatin and qualitatively benchmark the extent of cellular injury/death to inform decision-making. This model represents a major step in the development of a comprehensive model of drug-induced renal injury, but model development is a continuous and iterative process. The model currently represents only PT injury—the most common site of drug-induced injury. Future work will incorporate biomarker responses to other sites of injuries, including distal nephron, glomerular, and vascular injury, to the underlying pathophysiological and cellular changes. Going forward, we will also evaluate the model’s translational ability to predict clinical AKI based on preclinical biomarker responses. In addition, the model currently focuses on acute injury, but repeated mild injury can contribute to progression from AKI to CKD (Sharp et al., 2016). In future iterations, we plan to link acute injury/recovery with long-term disease progression. 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Published by Oxford University Press on behalf of the Society of Toxicology. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Toxicological Sciences Oxford University Press

Multiscale Mathematical Model of Drug-Induced Proximal Tubule Injury: Linking Urinary Biomarkers to Epithelial Cell Injury and Renal Dysfunction

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Abstract

Abstract Drug-induced nephrotoxicity is a major cause of acute kidney injury, and thus detecting the potential for nephrotoxicity early in the drug development process is critical. Various urinary biomarkers exhibit different patterns following drug-induced injury, which may provide greater information than traditional biomarkers like serum creatinine. In this study, we developed a multiscale quantitative systems pharmacology model relating drug exposure to proximal tubule (PT) epithelial cell injury and subsequently to expression of multiple urinary biomarkers and organ-level functional changes. We utilized urinary kidney injury molecule-1 (Kim-1), alpha glutathione S-transferase, albumin (αGST), glucose, and urine volume time profiles as well as serum creatinine and histopathology data obtained from rats treated with the nephrotoxicant cisplatin to develop the model. Although the model was developed using single-dose response to cisplatin, the model predicted the serum creatinine response to multidose cisplatin regimens. Further, using only the urinary Kim-1 response to gentamicin (a nephrotoxicant with a distinctly different injury time course than cisplatin), the model detected and predicted mild to moderate PT injury, as confirmed with histopathology, even when serum creatinine was unchanged. Thus, the model is generalizable, and can be used to deconvolute the underlying degree and time course of drug-induced PT injury and renal dysfunction from a small number of urinary biomarkers, and may provide a tool to determine optimal dosing regimens that minimize renal injury. quantitative systems pharmacology, acute kidney injury, nephrotoxicity, biomarker, proximal tubular injury, multiscale model Failure to detect and understand the time course of drug-induced acute kidney injury (AKI) is a challenging problem in both drug development and clinical treatment of critically ill patients (Alge and Arthur, 2015; Schetz et al., 2005). Missed or misunderstood preclinical toxicity due to the poor sensitivity of traditional biomarkers (serum creatinine and blood urea nitrogen [BUN]) can put clinical trial subjects at unnecessary risk and also lead to expensive late-stage drug failures (Han et al., 2002). Clinically, it can result in delayed action to mitigate injury. Multiple novel urinary biomarkers (eg, alpha glutathione S-transferase [αGST] [Pinches et al., 2012], kidney injury molecule-1 [Kim-1] [Bonventre, 2009; Han et al., 2002], albumin [Pinches et al., 2012], and others [Parikh et al., 2013]) are promising for early detection and more accurate prediction of drug-induced renal injury (de Geus et al., 2012; Ostermann et al., 2012). However, the time courses of expression vary widely between biomarkers and among different nephrotoxicants, making interpretation challenging. The proximal tubule (PT) is the most common site of drug-induced AKI. Because of their role in active transportation and metabolism of drugs, PT epithelial cells (EpCs) are vulnerable to nephrotoxicants (Lohr et al., 1998; Morrissey et al., 2013; Tiong et al., 2014). Although the process of EpC injury remains incompletely understood, Figure 1 illustrates the currently accepted conceptual framework of AKI pathophysiology (Charlton et al., 2014; Devarajan, 2006, 2010). Initially, subtle and largely reversible cellular structural changes such as loss of brush border and altered cellular polarity occur (Devarajan, 2006). Injured cells may either recover back to normal cells or, if the injury is severe enough, experience irreversible changes that lead to cell death. As tubular cells die, neighboring viable cells de-differentiate and proliferate, resulting in regeneration of a normal epithelium (Devarajan, 2006). As these processes occur, they alter EpC expression and release signaling molecules (eg, upregulation of Kim-1), impair EpC reabsorption/secretion (eg, reduced albumin reabsorption), or release cytosolic content into the tubule lumen (eg, αGST [McDuffie et al., 2013; McMahon and Waikar, 2013]), resulting in observable changes in urinary biomarkers. Thus, although biomarkers such as BUN and serum creatinine reflect whole-organ function, biomarkers such as urinary Kim-1, αGST, albumin, and glucose may each provide specific information on alterations in cellular-level processes. Figure 1. View largeDownload slide Processes of proximal tubule epithelial cell injury, death, recovery, and regeneration during acute kidney injury (adapted from Devarajan, 2006). Figure 1. View largeDownload slide Processes of proximal tubule epithelial cell injury, death, recovery, and regeneration during acute kidney injury (adapted from Devarajan, 2006). Pinches et al. (2012) and Vaidya et al. (2010) have demonstrated that the magnitudes of biomarkers like urinary Kim-1, albumin, glucose, and others are related to histopathological injury severity. In particular, Vaidya et al. (2010) showed that Kim-1 is a sensitive and specific predictor of injury. These studies also demonstrated varying temporal patterns for different biomarkers and in response to different drugs. This suggests it may be possible to extract greater information from these biomarkers on the mechanism, extent, and time course of renal injury and organ-level dysfunction. A quantitative framework that relates observed drug-induced changes in novel urinary biomarkers to latent pathophysiological processes that manifest at the cellular, organ, and systems levels would allow evaluation of the mechanism, extent, and time course of both local injury and organ-level dysfunction. This could facilitate improved preclinical evaluation and benchmarking of drug candidates, optimization of dosing regimens to minimize injury, and potentially translation of preclinical findings to predict clinical risk. In this study, we developed a multiscale mathematical model that temporally relates drug exposure to pathophysiological processes of PT EpC injury and repair and subsequently to the expression of multiple urinary biomarker responses (Kim-1, αGST, albumin, glucose, urine volume) and to organ-level functional changes as indicated by serum creatinine. MATERIALS AND METHODS Experimental Data Development Data For model development, we utilized urinary biomarker and renal histopathology data previously collected in male HsdHan:WIST (Harlan UK) strain rats treated with a single intraperitoneal (IP) administration of 0, 0.1, 1.0, or 2.5 mg/kg cisplatin (Pinches et al., 2012). Pharmacokinetic data that are used as driver for PT injury were collected for 2.5 mg/kg dose for 5 days at 1, 3, 18, 42, 66, and 90 h. Urinary biomarkers including Kim-1, αGST, glucose, albumin, and volume were collected at baseline and daily starting 2 days postdose. Serum creatinine was measured on days 5, 7, 8, and 22. Rats were sacrificed on day 5, 8, or 22 for histopathology, including scoring of necrosis and regeneration in the PT S3 segment by an independent pathologist. Due to their intrinsic metabolic behavior, compared with the proximal convoluted tubule S1 and S2 segments, cells in the proximal straight tubule S3 segment are selectively susceptible to necrosis when exposed to noxious stimuli (Venkatachalam et al., 1978). Histopathological severity scores for PT S3 necrosis and regeneration were calculated as the sum of severity grades (1 through 4, with 1 being normal and 4 being most severe) weighted by the fraction of animals with that severity. As shown in Figures 2A and 2B, the urinary biomarker time courses revealed 2 distinct biomarker groups: (1) αGST, albumin, and glucose showed steep narrow peaks that did not begin to rise until day 4 and had returned to normal again by day 7 and (2) Kim-1 and urine volume showed a broader peak, beginning to rise by day 2 and remaining elevated on day 7. These trends are similar in both doses, although Kim-1 peaked later in the 2.5 mg/kg dose group. Trends in PT necrosis coincided with the first biomarker group. At the lower dose, regeneration coincided with the biomarker peaks, although at the higher dose it peaked later. Figure 2. View largeDownload slide Time courses of fold increase (from predose values) of a panel of urinary biomarkers, as well as histopathologic severity scored for PT S3 necrosis and regeneration, in rats treated with 2.5 mg/kg (A) and 1.0 mg/kg (B) cisplatin. Figure 2. View largeDownload slide Time courses of fold increase (from predose values) of a panel of urinary biomarkers, as well as histopathologic severity scored for PT S3 necrosis and regeneration, in rats treated with 2.5 mg/kg (A) and 1.0 mg/kg (B) cisplatin. Data for Model Applications Two previously published studies were used for testing model generalizability to multiple doses and a different drug mechanism. In the study of Kobayashi et al. (2000), male Donryu rats were exposed to a weekly high dose of 5 mg/kg or a daily lower dose of 1.2 mg/kg cisplatin over 3 weeks, and serum creatinine was measured at the end of the study (the authors state that these doses were selected because animals died when the high dose of 5 mg/kg was administered more frequently, and daily doses of 1 mg/kg or less had minimal anticancer effect) (Kobayashi et al., 2000). In the study of Vaidya et al. (2010), male Sprague Dawley rats were treated with daily IP administration of gentamicin (20, 80, or 240 mg/kg/day) for 15 days. Urinary Kim-1 and serum creatinine were collected on days 3, 9, and 15, along with day 12 for 240 mg/kg. Animals were sacrificed on days 3, 9, and 15 for histopathologic analysis and were assigned a composite PT severity score ranging from 0 to 5, 5 being the highest (Vaidya et al., 2010). For our analysis, the mean histopathology severity score for each day was calculated and normalized by the highest severity level, 5, to scale the range of severity from 0 to 1, to facilitate comparison with model-predicted cell injury. Because gentamicin plasma concentrations were not reported, pharmacokinetic data were extracted from a separate study (Engineer et al., 1987). Relating Urinary Biomarkers to PT EpC Injury and Death The biomarker and histopathology data following a single cisplatin dose shown in Figure 2 informed key assumptions in developing the drug-induced PT injury model. Based on the distinct temporal behaviors of the 2 classes of biomarkers and related histopathology, we hypothesized that: (1) the early rise and broad peak in the magnitudes of urinary Kim-1 and urine volume were indicative of EpC injury (brush-border loss and depolarization) and (2) the delayed rise and narrow peak in the magnitudes of urinary αGST, albumin, and glucose were indicative of acute EpC death, quickly followed by regeneration. These hypotheses follow from our understanding of the biology of EpC and each of the biomarkers. Alpha glutathione S-transferase is normally present in the cytoplasm and is likely released into the lumen upon EpC death (McDuffie et al., 2013). Kidney injury molecule-1 is upregulated in response to cellular injury and serves to attract macrophages to remove debris and protect cells from further inflammatory injury (Bonventre, 2009; Ichimura et al., 2008; Lim et al., 2013). Proximal tubule EpCs normally reabsorb large quantities of sodium and water through the brush-border microvilli, and brush-border loss would be expected to reduce reabsorptive capacity and increase excretion of sodium and water. The relatively smaller quantities of albumin and glucose filtered through the glomerulus normally almost completely reabsorbed by the PT via an endocytic mechanism (Birn et al., 2000; Zhai et al., 2000), and the tubule has sufficient endocytic capacity to sustain brush-border loss and still maintain albumin and glucose reabsorption. However, death of a significant number of cells would result in insufficient reabsorptive capacity and lead to increased excretion of these biomarkers. With these concepts in mind, the sudden rise in αGST, albumin, and glucose around day 5 (at both doses) suggests an acute period of cell death resulting in loss of EpC reabsorptive capacity and release of cytosol content into the lumen. This is consistent with histopathology scores, which were highest at day 5, much lower by day 8, and normal by day 22. The equally rapid fall in these biomarkers suggests that the functional capacity of these cells is quickly recovered, likely through hypertrophy and hyperplasia of surrounding cells. This is consistent with the histopathologic scores for PT regeneration. The persistence of histologic signs of regeneration at the higher dose after the functional biomarkers have recovered, as well as the persistent elevation in Kim-1 and urine volume, suggests that cell regeneration (replication and differentiation) may be a prolonged process, which continues after these basic functions have been restored. Multiscale Mathematical Model Model Scope As illustrated in Figure 3, the multiscale mathematical model is comprised of interlinked submodels: a cellular-level model of EpC injury/death and an organ/systems-level model of renal physiology and volume regulation. Changes in PT function resulting from drug-induced EpC injury/death provide the links between the 2 submodels. At the cellular level (left panel), the concentration-time profile of cisplatin drives cellular injury and death. Drug-induced injury and death at the cellular level lead directly to biomarker expression (Kim-1) and release (αGST), as well as to loss of function (Na, water, glucose, and albumin reabsorption) at the tubule level, resulting in changes in urine volume, glucose, and albumin. At the systems level (right panel), impaired tubular Na and water reabsorption indirectly cause alterations in the renal (right panel, top) and systemic hemodynamics (right panel, bottom), which ultimately result in changes in glomerular filtration rate (GFR) and serum creatinine. The details of each submodel, as well as how they are interconnected, are described below. Additional details can be found in the Supplementary materials. Figure 3. View largeDownload slide Model overview. Drug pharmacokinetic exposure drives injury and death at the cellular level, producing impairments in reabsorption at the tubular level, which then affect changes at the organ/systems level (increased tubular pressure, TGF, and ultimately reduced GFR). Biomarkers like urinary Kim-1 and αGST are increased as a result of cellular-level injury; glucose and albumin are increased as a result of tubular-level impairment; serum creatinine reflects the systems-level consequences of tubular impairment leading to reduced GFR; urine volume reflects both reduced reabsorption and subsequent reduced renal filtration. TGF, tubuloglomerular feedback; TPR, total peripheral resistance; MAP, mean arterial pressure. Figure 3. View largeDownload slide Model overview. Drug pharmacokinetic exposure drives injury and death at the cellular level, producing impairments in reabsorption at the tubular level, which then affect changes at the organ/systems level (increased tubular pressure, TGF, and ultimately reduced GFR). Biomarkers like urinary Kim-1 and αGST are increased as a result of cellular-level injury; glucose and albumin are increased as a result of tubular-level impairment; serum creatinine reflects the systems-level consequences of tubular impairment leading to reduced GFR; urine volume reflects both reduced reabsorption and subsequent reduced renal filtration. TGF, tubuloglomerular feedback; TPR, total peripheral resistance; MAP, mean arterial pressure. Cellular-Level Model of EpC Injury The cellular EpC injury model (Figure 3, bottom left) describes the processes of cell injury, death, recovery, and regeneration resulting from exposure to a nephrotoxicant, as illustrated in Figure 1 (Devarajan, 2010; Lim et al., 2013). The model describes 3 mutually exclusive sets of EpCs: functional, injured, and dead. At any particular time t, the fractions of the total EpC population that belongs to each of the functional, injured, and dead EpCs are represented by F(t), I(t), and N(t), respectively, and always sum to one. Cells move between populations through 4 processes: injury, recovery, death, and regeneration. The governing differential equations are as follows:   ddtI=RInjuryt-RRecoveryt-RDeatht, (1)  ddtF=-RInjuryt+RRecoveryt+RRegenerationt,  (2)  ddtN=RDeatht-RRegenerationt, (3) where RInjury, RRecovery, RDeath, and RRegenration are the injury, recovery, death, and regeneration rates, respectively. Cell injury represents brush-border loss and loss of polarity, so that cell functions that rely on microvilli, such as sodium and water reabsorption, are impaired. The injury rate Rinjury is proportional to the functional cell fraction F(t) and the effective drug exposure driving injury, Cinjury, as given in equation 4. kinjury is the proportional injury rate constant, and thresholdinjury the effective exposure below which no injury is observed.   RInjuryt=kinjury*maxCinjuryt-thresholdinjury, 0*Ft. (4) Cell recovery represents restoration of normal cell function as the brush border and polarity are restored. The rate of cell recovery RRecovery is related to the fraction of injured cells via a proportional rate constant krecovery:   RRecoveryt=krecovery*It. (5) Cell death represents a complete loss of cell viability, so that cytoplasmic content (including αGST) is released into the tubule lumen, and cell function (including albumin and glucose reabsorption) is completely lost. The cell death rate RDeath is modeled as a sigmoidal function of the delayed cisplatin concentration Cdeath, which accounts for an additional time lag in cellular death relative to injury.   RDeatht=kdeath*CdeathγtIC50Deathγ+Cdeathγt*It. (6) The sigmoidal function was motivated by the sharp delayed rise in αGST, albumin, and glucose. Cellular regeneration represents recovery of the function of dead cells due to hypertrophy and hyperplasia of surrounding cells. Cell proliferation is inhibited by contact with other cells (McClatchey and Yap, 2012), and thus as the number of dead cells increases, the number of EpC cell-cell contacts will decrease, and the proliferation rate may be expected to increase. Indeed, we found that describing the regeneration rate RRegeneration as a power law function of the dead cell fraction, where the rate constant kregeneration and the power constant p were determined by optimization, provided a better fit to the experimental data, as compared with a linear model.   RRegenerationt=kregeneration*Npt. (7) Systems Model of Renal Physiology and Volume Homeostasis We utilized a previously developed mechanistic model of renal function and volume homeostasis (Hallow et al., 2017). Briefly, as illustrated in Figure 3, this model describes the processes of glomerular filtration, reabsorption along each tubular segment, and excretion of unabsorbed substances at the single-nephron level. The kidney is modeled as a set of N nephrons in parallel. The outputs of the nephron model—sodium and water excretion—feed into a model of volume homeostasis, where the balance between sodium and water intake and excretion determine blood volume, extracellular fluid volume, and blood pressure. Blood pressure and blood sodium concentration then feed back to the kidney submodel. The model also incorporates key intrinsic as well as neurohumoral feedback mechanisms, including tubuloglomerular feedback (TGF), vasopressin, and the renin-angiotensin-aldosterone system. Full equations of the model are given elsewhere (Hallow and Gebremichael, 2017a,b; Hallow et al., 2017), and key equations are provided in the Supplementary materials. Linking EpC Cell Injury Model to System Behavior and Biomarker Responses EpC injury and death fractions were used to drive changes in tubular function and biomarker expression. Each effect E then multiplies the associated nominal release/production rate or fractional reabsorption rate. The βs in each equation are scaling factors estimated by fitting model biomarker outputs to the observed biomarker time courses. Alpha glutathione S-transferase Urinary excretion of αGST is normally quite small, but increases many fold during AKI. We assumed that all αGST released into the tubule lumen is excreted, and the effect of cell death on αGST excretion EαGST is related to the fraction N of dead cells:   EαGST=1+βαGST*N. (8) The rate of urinary αGST excretion is thus determined by scaling the nominal αGST excretion rate X˙αGST0 by the effect EαGST:   X˙αGSTt=X˙αGST0*EαGSTt=X˙αGST0*1+βαGST*N. (9) Albumin Nearly all filtered albumin is normally reabsorbed by the PT via an endocytic mechanism; however, dead cells cannot reabsorb albumin. The effect of cell death on PT albumin reabsorption Ealb is related to the dead cell fraction N:   Ealb=1-βalb*N. (10) Proximal tubule albumin reabsorption fraction ηalbt is then determined by scaling the nominal albumin reabsorption fraction ηalb0 with the effect Ealb:   ηalbt=ηalb0*Ealb. (11) ηalb, in turn, affects the urinary albumin excretion rate X˙alb(t):   X˙albt=GFRt*Salb*ϑ*1-ηalbt, (12) where  [Salb] is the serum albumin concentration (treated as a constant) and ϑ is the albumin sieving coefficient. Glucose Similarly, nearly all filtered glucose is normally reabsorbed by the PT (approximately 90%–97% at the S1 segment and approximately 3%–10% at the S3 segment via the sodium cotransporters SGLT2 and SGLT1, respectively [Gorboulev et al., 2012; Novikov and Vallon, 2016; Rieg et al., 2014; Vallon, 2011]). However, dead cells cannot reabsorb glucose. As with albumin, we assumed PT glucose reabsorption impairment is related to cell death fraction. However, relative to the changes in αGST and albumin, the fold-change of urinary glucose excretion at 1 mg/kg dose of cisplatin was much lower versus the 2.5 mg/kg dose. The PT possesses excess glucose reabsorptive capacity (DeFronzo et al., 2017), and we hypothesized that when the degree of cell death is small (the lower dose) this excess capacity is able to compensate to a greater extent. The effect of cell death on PT glucose reabsorption rate Eglu is thus related to dead cells fraction by the following nonlinear relationship:   Eglu=1-βglu*Nα, (13) where α is a fitting constant, determined by optimization, and accounts for the increase in glucose excretion as cell death increases and the excess capacity becomes overwhelmed. Because most necrosis is reported to be on the S3 segment (Pinches et al., 2012), the drug-induced change of the urinary glucose excretion rate X˙glu is determined by scaling the nominal S3 segment glucose reabsorption fraction ηS30 with the effect Eglu as:   X˙glut=GFRt*Sglu*1-ηS10-ηS30*Eglu, (14) where  [Sglu] is the serum glucose concentration (assumed constant) and ηS10 is the nominal S1 glucose reabsorption fraction. Kidney injury molecule-1 Urinary Kim-1 is normally negligible, but increases significantly during AKI. The observed time course of Kim-1 exhibited an early onset and a delayed peak. The early rise was assumed to be due to EpC injury, whereas the continued increase suggests additional expression following cellular death. Thus, the effect on Kim-1 expression, EKkim1, is modeled as a function of both dead and injured cell fractions:   EKim1=βKim1*I+N. (15) The urinary Kim-1 peak was delayed compared with the peak in cellular death marked by urinary αGST, albumin, and glucose. This may reflect the time required for signal transduction and upregulation of expression by neighboring living cells, or it may reflect Kim-1 released by regenerating cells that have already regained their ability to reabsorb albumin and glucose but are not fully differentiated and functioning as normal cells. To reproduce the observed delayed Kim-1 signal, we implemented a single transit compartment, a common approach in signal transduction models (Felmlee et al., 2012), based upon best fit of the data:   dM1dt=1τ*EKim1-M1,  (16) where M1 is the effect in the transit compartment and τ is the mean transit time through the compartment. The urinary excretion rate X˙Kim1 of Kim-1 is then:   X˙Kim1t=X˙Kim10*1+M1, (17) where X˙Kim10 is the nominal excretion rate of Kim-1. Urine volume PT reabsorption is isosmotic, and thus PT water reabsorption passively follows Na reabsorption through osmosis. Loss of microvilli during cell injury and/or death reduces PT EpCs’ ability to reabsorb sodium; this effect, Esodium, is expressed as:   Esodium=1-βsod*I+N. (18) This term modifies the PT sodium reabsorption fraction ηptsodreabs:   ηptsodreabs=ηptsodreabs0*Esodium, (19) where ηptsodreabs0 is the nominal sodium reabsorption fraction. ηptsodreabs is explicitly represented in the systems-level renal physiology model, where reducing sodium and water reabsorption alters renal hemodynamics and ultimately GFR. Reduced water reabsorption in the PT increases PT and Bowman’s space pressure, which opposes filtration pressure and lowers GFR. In addition, when less sodium is reabsorbed proximally, more is delivered to the macula densa, triggering TGF that constricts the afferent arteriole and lowers GFR further. Thus, injury-induced reductions in PT sodium and water reabsorption tend to directly increase urine excretion, but the indirect effects on GFR tend to lower urine excretion. The model-predicted total urine volume reflects the combined effect of both mechanisms. Serum creatinine Creatinine is filtered freely through the glomerulus, and approximately 15% (Samra and Abcar, 2012) of excreted creatinine is due to secretion from PT EpCs into the tubule lumen. Creatinine is not reabsorbed in the tubule. Cisplatin-induced PT injury increases serum creatinine in 2 ways: (1) Injury-induced changes in PT sodium and water reabsorption cause renal hemodynamic changes that suppress GFR and reduce renal filtration of creatinine and (2) cisplatin directly reduces tubular secretion of creatinine by interfering with the transporter, Organic Cation Transporter 2 (Ciarimboli et al., 2012). The effect of PT injury on GFR and thus on creatinine filtration is captured implicitly through the systems-level model, as a consequence of impaired tubular Na and water reabsorption, as described above. We also modeled the direct effect of cisplatin on PT creatinine secretion, employing a sigmoid Emax model, which accounts for cisplatin-induced pharmacodynamic effect on PT creatinine secretion. A complete description of serum creatinine dynamics is provided in the Supplementary materials. Drug Exposure Model For both cisplatin and gentamicin, plasma drug concentration-time profile was modeled using a standard 2-compartment model. To account for the time delays between plasma drug exposure and onset of changes in biomarkers reflecting cell injury or death, a transit compartment construct was used to produce delayed signals Cinjury and Cdeath. More details are provided in the Supplementary materials. Software Implementation The model was implemented in R 3.1.2 using the RxODE package (https://cran.r-project.org/web/packages/RxODE/index.html), a tool for simulating differential equation models in R (Wang et al., 2016). The cellular injury model features a total of 19 parameters, which were simultaneously fitted to reproduce the time profiles of biomarkers obtained from the animal study, using a global optimization method based on a genetic algorithm method, supplemented by R shiny app (https://shiny.rstudio.com/) visualization tool for initialization and fine tuning. More details can be found in Supplementary materials. RESULTS Model Development: Fitting to Cisplatin-Induced Biomarker Responses Figure 4 summarizes the model fit of biomarker responses to single-dose cisplatin-induced PT injury at each dose. Estimated model parameters are given in Supplemental Table 3. The top left in each panel of Figure 4 shows the model fit to the plasma cisplatin concentration-time profile. Because there is a time delay between exposure and initiation of cell injury and death, as indicated by the biomarker time profiles, time-delayed concentration profiles ( Cinjury and Cdeath) were used as the signals driving cell injury and death. The model captures the magnitude and time course of each biomarker at each dose, including the steep narrow peak (near day 5) of αGST, albumin, and glucose and the broad peak of Kim-1, water excretion, and serum creatinine. Figure 4. View largeDownload slide Model fit of biomarker responses following cisplatin doses of 2.5 mg/kg (A) and 1.0 mg/kg (B). For each dose, cisplatin exposure (top left) drives cellular injury and death (bottom left), which then produce biomarker responses shown on the right. Blue, simulation; red diamonds, median, experimental data; black dashed lines, experimental data first and fourth quartiles; green triangles, digitized data from Fukushima et al. (2016). Figure 4. View largeDownload slide Model fit of biomarker responses following cisplatin doses of 2.5 mg/kg (A) and 1.0 mg/kg (B). For each dose, cisplatin exposure (top left) drives cellular injury and death (bottom left), which then produce biomarker responses shown on the right. Blue, simulation; red diamonds, median, experimental data; black dashed lines, experimental data first and fourth quartiles; green triangles, digitized data from Fukushima et al. (2016). Model-Estimated EpC Injury and Death The fractions of functional F, injured I, and dead N cells (Figure 4, bottom left in each panel) are latent variables that drive the biomarker responses, and whose magnitudes and time courses were determined by fitting model parameters to the observed biomarker time courses. Although all data were fit simultaneously, the shape and magnitude of cell death were constrained primarily by αGST, albumin, and glucose, whereas cell injury was constrained primarily by Kim-1, urine volume, and serum creatinine. These simulations indicate that, at both doses, cell injury begins and peaks early, whereas the initiation of cell death is delayed and the peak occurs later, around day 5. There is substantial cell injury at both doses, although maximum cell injury is 132% higher at the higher dose than the lower dose (51% vs 22%). There is significant cell death (48% at peak) at the higher dose, whereas cell death is much reduced at the lower dose (3.5% maximum). Biomarkers Indicative of Cell Death As seen in Figure 4 (bottom-right rows in each panel), the time courses of αGST, albumin, and glucose all closely follow the time course of cell death. At both doses, the model reproduces the delayed and sharp rise and fall of these biomarkers at day 5. The magnitudes of urinary αGST and albumin responses were proportional to the increase in cell death at each dose. However, the ratio of glucose excretion at the lower dose relative to the higher dose was much smaller than the ratio of cell death. The power law equation for glucose reabsorption impairment (equation 14) allowed the model to capture this behavior. As mentioned above, the PT possesses excess capacity for glucose reabsorption (DeFronzo et al., 2017), and thus it is likely that at low levels of EpC death, the remaining cells are able to compensate. However, as cell death increases, the excess capacity is overwhelmed and glucose excretion accelerates. Biomarkers Indicative of Both Cell Injury and Death In Figure 4, the top-right rows in each panel show the observed and simulated responses of markers that arise from a combined effect of cellular injury and death. Kidney injury molecule-1 As described earlier, the urinary Kim-1 response was hypothesized to increase due to both EpC injury and EpC death. The model captured the early rise, as well as the delayed broad peak in Kim-1, around day 7, of the 2.5 mg/kg dose. For the 1 mg/kg dose, the Kim-1 response was smaller and more variable. The model-predicted rise in Kim-1 was slower than the observed median response, but still fell within the 25%–75% quartiles of the response. Urine volume As described earlier, injured cells lose their brush border and microvilli, diminishing their ability to reabsorb large amounts of sodium and water and resulting in excess excretion. Dead cells obviously lose these functions as well. Changes in urine volume reflect both impaired water reabsorption due to dead and injured cells (which tends to increase excretion), as well as reduced glomerular filtration at the organ level (which tends to decrease excretion). Urine volume data were highly variable, possibly due to variability in water intake, voiding times, and other experimental factors. However, for both doses, the model adequately reproduced observed urinary volume responses. At the low dose, the model predicted minimal cell death, and thus the peak in urine volume paralleled the cell injury peak. At the higher dose, the model predicts significant cell death and injury, and the broader peak parallels the combined effect of cellular injury and death. Serum creatinine Because serum creatinine was not measured in our study until day 5, we supplemented our data with daily serum creatinine measurements from Fukushima et al. (2016). As shown in Figure 4, the simulated serum creatinine time profile closely matched the observed data. The peak in serum creatinine occurred near day 5 for both doses, reflecting the combined effect of GFR decline and PT creatinine secretion dysfunction arising from EpC injury and death. Model Application: Multidose Administration and Evaluation of Cisplatin Dosing Regimen The model was developed using the response to a single dose of cisplatin, but we also tested its ability to predict the response to repeated cisplatin dosing. As shown in Figure 5 (blue lines), the model-predicted changes in serum creatinine after 21 days following weekly dosing of 5 mg/kg (top row) or daily dosing of 1.2 mg/kg (bottom row) were consistent with the range of changes observed in experimental serum creatinine (Kobayashi et al., 2000). Figure 5. View largeDownload slide Responses to repeated cisplatin administration. Upper panels: responses following weekly administrations at various doses. Lower panels: responses to changes in dosing frequencies, for a 1.2 mg/kg dose. In both panels, brown triangle symbols are the observed fold increase of serum creatinine for each group of rats studied in Kobayashi et al. (2000), and blue curves are the corresponding simulation, for weekly 5 mg/kg (upper panel) and daily 1.2 mg/kg (lower panel) cisplatin dosing. Figure 5. View largeDownload slide Responses to repeated cisplatin administration. Upper panels: responses following weekly administrations at various doses. Lower panels: responses to changes in dosing frequencies, for a 1.2 mg/kg dose. In both panels, brown triangle symbols are the observed fold increase of serum creatinine for each group of rats studied in Kobayashi et al. (2000), and blue curves are the corresponding simulation, for weekly 5 mg/kg (upper panel) and daily 1.2 mg/kg (lower panel) cisplatin dosing. The model also predicted that both dosing regimens tested in the study of Kobayashi et al. (2000) would result in extensive (approximately 75%) EpC death. Although injured cells may easily recover, cell death may be more detrimental to long-term renal function, especially when cells are not allowed to recover and regenerate between dosing cycles. The model can be applied to identify regimens that minimize EpC death while maximizing drug exposure. The model provides a tool for quantifying and visualizing injury under different regimens, to guide dosing decisions. Figure 5 shows additional simulated response to different doses and regimens. For weekly dosing (top row), the model predicts that a dose of 2 mg/kg or less would maintain cell death below 50%. For a fixed dose of 1.2 mg/kg (Figure 5, bottom row), every 3-day dosing instead of daily would keep cell death below 50%. Interestingly, reducing the dosing frequency further (eg, once every 4 days), cut cell death in half, down to about 25%. Yet, the difference in serum creatinine change between these 2 scenarios was minimal, illustrating the lack of sensitivity of serum creatinine for quantifying cellular toxicity. In these simulations, as expected, patterns of Kim-1 excretion depended upon dose and dosing frequency. However, for a weekly 1.2 mg/kg dosing (and, to some degree, for other dosing scenarios), Kim-1 excretion remained elevated at the times when the dead cell fraction as well as serum creatinine tended to return to normal, thereby providing a unique signature for Kim-1. This behavior can be partly associated with the delayed peak responses of Kim-1 that may not be in accord with the brief cellular recovery between subsequent drug administrations and may lead to further Kim-1 accumulation with each cycle. Readers may explore additional administration protocols using the web-based model interface provided at http://qsp.engr.uga.edu:3838/AKI_regimen/. Model Application: Prediction of Gentamicin-Induced Injury The model was developed using cisplatin response data, but to be truly useful, it should be generalizable to PT injury by other compounds. Pharmacokinetics as well as the magnitude and time course of drug-induced EpC injury/death may vary widely among nephrotoxic agents. However, although the relationship between drug exposure and cell injury and death is compound-specific, the relationships between cell injury and death and subsequent effects on tubular dysfunction, biomarker expression, and organ-level dysfunction should be independent of the injury mechanism. This implies that, to model a new compound, only the drug pharmacokinetics and parameters defining rates of cell injury and death need to be re-estimated; the remaining downstream equations and parameters governing the consequences of cell injury and death should not change. If this is the case, then by fitting the model to a panel of biomarker responses arising from a new compound, the model should be able to deconvolute the underlying cell injury/death from observed biomarkers. To test this idea, we applied the model to published data from a previously conducted preclinical study of gentamicin (Vaidya et al., 2010), which is known to cause PT injury with repeated dosing (Ali et al., 2011). This study measured urinary Kim-1 and serum creatinine in response to daily gentamicin treatment, but unfortunately did not measure other biomarkers utilized in our model. We replaced the cisplatin pharmacokinetics with gentamicin pharmacokinetics (Engineer et al., 1987) and re-estimated parameters governing the cell injury and cell death response to gentamicin exposure (parameters in equations 4 and 6) by simultaneously fitting to the urinary Kim-1 response to daily dosing of 20, 80, or 240 mg/kg gentamicin (Vaidya et al., 2010). Urinary Kim-1 reflects both cell injury and cell death, but without an additional biomarker like αGST, albumin, or glucose that is specific to cellular death, the ability to distinguish between injury and death was limited. As a simplifying assumption, the ratio between kinjury and kdeath was constrained to be the same for gentamicin and cisplatin. All other parameters, including cell recovery and regeneration rates, were fixed at previously estimated values. We then simulated the cell injury/death and serum creatinine time courses for each dose, as shown in Figure 6. We compared the simulated sum of injured and dead cell fractions with the observed histopathologic scores, recognizing that the ability to further distinguish between injury and death was limited by the lack of additional biomarker data. Figure 6. View largeDownload slide Simulated response to gentamicin-induced renal injury. Left panel: concentration-time profile of gentamicin for 20, 80, and 240 mg/kg doses. From top to bottom shows concentration-time profile for single dose, daily dosing, and cellular injury and cellular death compartments. Right panel: first column, model parameters were constrained to fit the observed urinary Kim-1; second column, simulated serum creatinine compared with observed response; third column, the simulated sum of injured and dead cell fractions (I + N), compared with observed mean histopathology severity. Data obtained from Vaidya et al. (2010). Kim-1, kidney injury molecule-1. Figure 6. View largeDownload slide Simulated response to gentamicin-induced renal injury. Left panel: concentration-time profile of gentamicin for 20, 80, and 240 mg/kg doses. From top to bottom shows concentration-time profile for single dose, daily dosing, and cellular injury and cellular death compartments. Right panel: first column, model parameters were constrained to fit the observed urinary Kim-1; second column, simulated serum creatinine compared with observed response; third column, the simulated sum of injured and dead cell fractions (I + N), compared with observed mean histopathology severity. Data obtained from Vaidya et al. (2010). Kim-1, kidney injury molecule-1. For both 20 and 80 mg/kg gentamicin, the model described the urinary Kim-1 response well and predicted the quite small changes in serum creatinine. Importantly, the model-predicted measure of combined cell injury and death also agreed very well with both the time course and magnitude of histopathologic PT injury, indicating that the model is indeed able to determine the degree of underlying PT injury from the observed Kim-1 biomarker response, even when serum creatinine remains practically unchanged from baseline. For the 240 mg/kg dose, the model predicted the extensive PT injury observed at this dose, but did not fully capture the rise in Kim-1, and did not capture the very large increase in serum creatinine (5-fold by day 9) at this dose. Such a large change in creatinine reflects a massive loss of renal function. We speculate that at very high doses, the injurious effects of gentamicin extend beyond the dysfunction in PT reabsorption captured by the model. Because the dataset used in model development did not include such severe injury, the model in its current form does not capture these additional mechanisms and may be best suited for modeling mild to moderate renal injury. DISCUSSION In this study, we developed a multiscale systems pharmacology model of drug-induced PT injury. By coupling observed time profiles for a panel of biomarkers and histopathologic observations with knowledge of EpC biology, renal physiology, and the physiologic processes involved in expression of each biomarker, we formulated a model that provides a mechanistic, quantitative framework for relating observable biomarker time courses to unobservable cellular-level processes of EpC injury and death and subsequently to alterations in organ-level function (GFR, as indicated by serum creatinine). Although the model was developed with cisplatin data, it was able to use the Kim-1 response to a different compound, gentamicin, to predict the magnitude and time course of underlying PT damage. After identifying 2 groups of biomarkers in our development dataset, we considered known physiology regarding each biomarker’s EpC expression/regulation, as well as the observed PT necrosis and regeneration histopathology scores, and hypothesized that the 2 classes represent distinct processes of cell injury (broad-peak biomarkers with early onset) and cell death (narrow-peak biomarkers). We further related cell injury and death with changes in EpC functional capacity—ie, injured cells lose the ability to reabsorb large amounts of sodium and water, while retaining the ability to reabsorb albumin and glucose; dead cells lose all reabsorptive capacity. We then related these cellular-level changes in function and viability to organ-level changes in renal function. We believe that the multiscale model presented here is the first to quantitatively relate urinary biomarker dynamics to underlying PT EpC injury and to organ-level renal impairment. We also demonstrated generalizability that, to model a new compound, only the drug pharmacokinetics and parameters defining rates of cell injury and death need to be re-estimated; the remaining downstream equations and parameters governing the consequences of cell injury and death are compound-independent. For gentamicin, the model was then able to predict the degree of underlying PT EpC injury based on the observed urinary Kim-1 response. Because biomarkers like urinary αGST or albumin that reflect cell death were not available, we were not able to determine the relative contribution of cell injury versus cell death with certainty, although this could be done in future studies in which cell death biomarkers are measured. This distinction may be important, because tubules may recover more easily when cells are injured than when a large number of cells are killed. Thus, in future studies, the model may be used to deconvolute the underlying degree and time course of PT injury and renal dysfunction from a small number of urinary biomarkers. The model predicted PT EpC injury from urinary Kim-1, even when serum creatinine changes were negligible, illustrating the power to detect mild injury, and the limitations of serum creatinine as an indicator of renal injury. The model performed less well in predicting serum creatinine changes in the setting of severe gentamicin-induced injury. The model currently only accounts for drug-induced changes in PT reabsorption, and we speculate that when injury is severe, other changes may occur as well—eg, tubular blockage, vasoconstriction, or glomerular injury. The development dataset did not include such severe injury, and thus the model currently does not capture these additional mechanisms. However, the renal physiology model is equipped to accommodate these additional mechanisms, and in future studies the model may be extended by utilizing datasets under more severe injury conditions. The present model may be best suited for modeling mild to moderate renal injury, but this is perhaps the most critical domain, because this type of injury is more difficult to detect by serum creatinine changes. Although the model was developed using single-dose creatinine response data, it predicted creatinine responses following multiple doses under 2 different dosing regimens. We also illustrated how the model can be used to evaluate different, experimentally untested dosing regimens, to identify regimens that minimize cell death. Such analysis, combined with efficacy dose-response data, could be applied in drug development to determine optimal dosing regimens that maximize efficacy while minimizing renal injury. In particular, the model may provide more quantitative information for evaluating biomarker evidence for renal toxicity, especially PT injury, when making decisions on whether to move compounds forward in new drug development. For example, if the time course of a panel of biomarkers that are indicative of cellular injury and death are measured, then the model can be used to deconvolute the underlying cellular injury and death in a manner similar to that done for gentamicin. Once a set of key parameters specific to the new drug has been identified, varying dosing regimens can be explored for safety analysis. On the other hand, when circumstances do not permit for such rigorous analysis, one may use the web-based model interface to compare biomarkers signal from the new drug with that of cisplatin and qualitatively benchmark the extent of cellular injury/death to inform decision-making. This model represents a major step in the development of a comprehensive model of drug-induced renal injury, but model development is a continuous and iterative process. The model currently represents only PT injury—the most common site of drug-induced injury. Future work will incorporate biomarker responses to other sites of injuries, including distal nephron, glomerular, and vascular injury, to the underlying pathophysiological and cellular changes. Going forward, we will also evaluate the model’s translational ability to predict clinical AKI based on preclinical biomarker responses. In addition, the model currently focuses on acute injury, but repeated mild injury can contribute to progression from AKI to CKD (Sharp et al., 2016). In future iterations, we plan to link acute injury/recovery with long-term disease progression. 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Toxicological SciencesOxford University Press

Published: Mar 1, 2018

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