Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Cell Cycle And The Concept Of Physiological Age With Special Reference To Pyruvate Kinase Activity In Wi-38 Cells

Cell Cycle And The Concept Of Physiological Age With Special Reference To Pyruvate Kinase... Section of Cancer Biology, Division of Radiation Oncology, Mallinckrodt Institute of Radiologv, Washington University School of Medicine, St Louis, Missouri, and *Department of Biology, City of Hope National Medical Center, Duarte, California, U.S.A. (Receiued 13 June 1977: rel>ision accepted 13 October 1977) ABSTRACT WI-38 cells were synchronized by mitotic collection and periodically assayed for pyruvate kinase activity. The kinetics of the synchronous cohort were determined by continuous labelling index and by mitotic index. The experimental data were analysed by computer using a state vector model to yield the probability density functions for phase transit times and for cell physiological ages. Pyruvate kinase activity for these cells as a function of physiological age was then examined using the computer model. Considering DNA synthesis, pyruvate kinase activity and mitosis to be markers of physiological age, it was found that a model which assumes that a cohort of synchronized cells desynchronizes irreversibly and uniformly from one age marker to the next is incompatible with the experimental data. For example, the times over which cells entered the S phase were too widely distributed to be consistent with the mitotic index data. Also, for pyruvate kinase activity to be a function of physiological age alone, the cell ages were probably too dispersed to be compatible with the experimental enzyme data. Alternative models for cell physiological ageing are presented, which are compatible with the experimental data. Synchronous cell cultures are often used to study variations in biochemical and cellular functions as the cells progress through the cycle. While several methods of obtaining synchronous cell populations have been developed (Mitchison, 197 l), when biochemical studies are to be performed mitotic collection (Terasima & Tolmach, 1963) is often the method of choice, since it is biochemically the least disruptive to the cells. Since mitotic time is such a short part of the total cell cycle, the age distribution is quite narrow when the cells are initially collected. However, the initial synchrony of this age cohort decays as the cells t Present address: University of California. School of Medicine. Laboratory of Radiobiology, San Francisco. California 94143, U.S.A. Correspondence: Dr P. G. Steward, Veterans Administration Hospital, Radiation Therapy Department (1 14A JC), St Louis, Missouri 63 125. U.S.A. 0008-8730/78/1100-0623$02.00 0 1978 Blackwell Scientific Publications P. G. Steward, L. N . Kapp and R. R . Klevecz progress through the cell cycle, since some cells approach the subsequent mitosis more rapidly than others. Thus, as the chronological age of the cohort increases, the physiological age distribution of the cohort broadens.* This makes the interpretation of the experiments utilizing synchronous cultures ambiguous. For example, a small measured response is compatible with both a weak response from every cell in a sample, or with a strong response from a few cells in the sample which fall within a very narrow physiological age interval. The experimentally observed response at time t , E(t),of a cell population is E ( t )= j A ( a ) S ( t , a ) d a ; (1) where A ( a ) is the response of cells at physiological age a, S ( f , a) is the physiological age density distribution at time t, i.e. the number of cells at age a per unit physiological age interval t time units following mitotic collection, and cells are defined to be of physiological age a = 0 immediately following mitosis and of age a = 1 at mitosis. The goal in synchrony experiments is usually to obtain the function A(a), but the response or parameter experimentally observable is E(t). Ideally, desynchronization would not occur and the age distribution would be infinitely narrow; S(t, a) would then be the delta function d ( t - a).? If this was the case then A ( t ) = E(t). so that the desired function would be experimentally observable and the ambiguity referred to above would no longer exist. The ambiguity in interpreting synchrony experiments stems from the fact that S(t, a) is not a 6 function and that this age distribution broadens with time. The analysis required to obtain A(a) is rarely performed due to the difficulties involved. However, computer simulation of the broadening physiological age distribution of mitotically collected cells with time has been used to analyse the experimental age response for cell lethality following exposure to various drugs (Steward & Hahn, 1971). We report here a similar analysis of the age response for pyruvate kinase activity, and we show that the activity of this enzyme is not likely to be a function of physiological age alone. MATERIALS A N D METHODS Cell line WI-38 human embryonic lung fibroblasts were obtained from Dr L. Hayflick at the thirteenth passage. These were maintained as a monolayer culture in McCoy's 5a medium with 15% foetal calf serum, neomycin and 10 mM HEPES. Synchrony Cells were grown in roller bottles and maintained at 0.5 rev/min. To select mitotic cells, the roller speed was increased to 200 rev/min for 5 min and the medium plus mitotic cells were then pumped out of the rollers and into Falcon T C flasks. This process was repeated hourly until the necessary number of samples had been collected (Klevecz & Kapp, 1973). Synchronized cells were collected at passages 20 to 25. * Chronological age is defined as the time elapsed since the previous mitosis. Physiological age is defined as the extent of biochemical progression towards the next mitosis. 6(x) dx = 1.O. 'f A 6 function is defined such that 6(x) = 0 for x # 0 and Pyruvate kinase activity in WI-38 cells E nzvme activity Pyruvate kinase activity was measured as described by Shonk & Boxer (1964). Cells were washed, trypsinized and sonicated for 30 sec (Sonifier, Heat Systems Inc.). An aliquot of the sonicate was then incubated in a reaction mixture containing 0.05 M Tris-HC1, 0.01 M MgCI,, 0.2 m M NADH, 3.0 mM phosphoenolpyruvic acid and 1 u/ml L D H at p H 7.5. The optical density change of the reaction mixture was followed at 340 nm with a Gilford model 2400 spectrophotometer. The slope of a line which was optical density plotted as a function of time was proportional to the enzyme activity. Computer simulation o the synchrony f The mathematical technique used to simulate the progression of cells about the cell cycle is a slight modification of that developed by Hahn ( 1 966. 1970). Slight variations of this model have also been used by Young & Fowler ( I 969) to study repair of sublethal damage following X-irradiation: by Roti Roti & Okada (1971) to analyse cell cycle synchrony produced by exposure to excess thymidine and to colcemid: by Niederer & Cunningham (1976) to study the effect on cell populations of sequential X-ray doses: by Gray (1976) to anaiyse D N A histograms: and Kim. Bahrami & Woo ( 1974) have proposed this model to study cell size. age and DNA distributions. The cell cycle is divided into 17 physiological age intervals and the physiological age distribution is represented as a n dimensional vector called the state vector. For example, the initial physiological age distriubtion, So (0). is represented as: mi where m , is the number of cells in the first physiological age interval of G , phase, i n , is the cell number in the ith age interval, and m, is the number of cells in the nth age interval which, by our convention, are the mitotic cells, all at time t = 0. The ageing of the population represented in equation 2 is simulated by advancing cells down the state vector into mitosis, doubling the number of mitotic cells which are then entered into the first age interval. This rotation process occurs in discrete steps. the implementation of each simulates the passage of one time interval A t . Since all cells do not age physiologically at the same rate, following each time interval At, the cell fraction q,, a'? a,, and a,are advanced by 0, 1, 2. and 3 physiological age intervals respectively. The probability of a cell's progressing by more than 3 physiological age intervals in the time A t is presumed to be negligible for the simulations described below. For the number of cells in a population to neither increase nor decrease as they pass through an age interval, a,, + a,+ cr, -I- a, = 1 for that interval. The distribution of cell generation times is determined by the number of age intervals and the values chosen for the as. In order to permit cell kinetic behaviour t o vary from one phase of the cell cycle to the next. one set of as can be chosen for all of the age P. G. Steward, L. N . Kapp and R . R. Klevecz intervals of the G I phase, another set for all of the age intervals of the S phase and a third set for the age intervals of the G2phase and mitosis. Formally, the ageing process is incorporated into the model by means of a matrix operator H. such that the physiological age distribution at the time t = At is S,(A t ) = HSJO), and at time iAt the age distribution is S,(iAt) = H”S,(O). (3) The matrix operator H,for the special case when two age intervals are assigned to each of the G,, S and G2phases and one interval is assigned to mitosis, is: ‘OG, rCC3G,M ‘OG, “2G,M “3G,M raIG,M “2G,M ‘lG, H= (4) ax a2s a3S ~IG,M a2GZM ~OG,M ‘lG,M ‘OG,M where r - 1 is the number of cells added to the population per mitotic event and the (IS are defined as above. Equation 4 differs slightly from the operator developed by Hahn (1970) for the state vector model, but is similar to the one used by Steward (1975). RESULTS The age distribution of a cycling cell population as a function of time can be computed by means of the state vector model described above. Three characteristics ofthe population must be known, however: firstly, the initial age distribution, i.e. the ms of equation 2; secondly, the rate at which cells enter and exit from the population or, in our case, the r of equation 4: and thirdly. the probability density distribution for the cell transit times through each phase of the cell cycle, i.e. the as and the number of age intervals for each phase as utilized in equation 4. With these parameters known, the age distribution can be found by means of equation 3 for any integral number of time intervals A t . Since, immediately following mitotic collection, the mitotic index of the WI-38 cells used in these experiments was found to be 85%, we assume that the initial age distribution is characterized by 85% of the cells being in mitosis and the other 15% being distributed uniformly throughout the cell cycle. When we placed these 15% in the first age interval of the G I phase, the conclusions of this study were unchanged, indicating that the disposition of this 15% is not critical. We assume that cells enter or exit the cell cycle only at mitosis. For the case where r of equation 4 is 2, two cells enter G, phase for each cell passing through mitosis. If r = 1, then the cycling population is just self-maintaining and one cell exists from this population for each cell passing through mitosis. For 1 < r < 2, the population is expanding and cell loss (from the cycling population) is occurring. The continuous labelling index curve of Fig. 1 indicates Pyruvate kinase activity in WI-38 cells that only about 70% of the mitotically collected cells enter S phase. The viability of cells in the population was determined by taking samples at various times following collection and staining with 0.5% eosin. In each sample only 2-3% of the cells were stained (data not shown), implying that although 97-98% of the cells were alive by this assay (Watanabe & Okada, 1967), only about 70% entered DNA synthesis. On the basis of these experiments we chose an r of either 1.46 or 1-5, which is 73 or 75% respectively of the r value corresponding to no cell loss. The final characteristics of the cycling population required in order t o compute the age density distribution as a function of time following mitotic collection are the transit time I2 Time after collection ihri FIG. 1. Labelling index as a function of time after mitotic collection. WI-38 cells at passage 25 were exposed continuously to ['HITdR (5.0 pCi/ml, 6.0 Ci/mmol) from the time of collection until they were fixed for autoradiography. Points were taken from Kapp & Klevecz (1976). The line is computed for the cell population characterized in Table 1. distributions for segments of the cell cycle. These are estimated from the continuous labelling index data and the mitotic index data of Figs 1 and 2b respectively. The slope of the labelling index curve (Fig. 1) yields the rate of entry into S phase of mitotically collected cells, i.e. it is a measure primarily of the G I phase transit time distribution. The mitotic index data (Fig. 2b) determine the distribution of transit times for the cell cycle in the first generation following mitotic coliection. The data of Figs 1 and 2b were analysed by computer to yield the required transit time distributions. This was accomplished by simulating, by means of the computer model, the experiments which produced these data. For the continuous labelling experiment, 85% of the cells were placed in mitosis, the remainder were distributed equally among the other age intervals, and r was set to 1.5. The cells were accumulated in the first age interval of S phase. The cell fraction accumulated, presented as the line in Fig. 1, represents the labelling index. Since most of the cells transited only the G I phase before being accumulated, it was primarily the CIS and nG,for G, phase (i.e. the G , phase transit time distribution) which were determined by this simulation. The parameters found for the G,phase are given in line l'of Table 1. The resulting mean transit time and its standard deviation and coefficient of variation are also given. T o simulate the experiment producing the mitotic index data, again 85% of the cells were initially placed in mitosis and the remaining 15% distributed equally among the other age intervals. In the experiment, a 2 hr colcemid block preceded the determination of each P. G. Steward, L . N . Kapp and R. R. Klevecz 0. I .c 0. I 0.0: 0.1: o.oe Time after collection (hr) Time ( h r ) FIG.2. FIG.3. Flti. 2. Mitotic index as a function of time after mitotic collection. (a) Computed for the population characterized in Table 1 as described in the text. For this computer simulation, r = 1.2 (see equation 4), implying that 60% of the collected cells were observed to enter the subsequent mitosis. (b) WI-38 cells at passage 25 were exposed to colcemid for the 2 hr indicated by the bars before determining the mitotic index (redrawn from Kapp & Klevecz, 1976). FIG.3. Probability density distributions for cell transit times computed for the population characterized in Table 1. (a) G , phase; (b) S plus G, plus M phases; (c) cell cycle. mitotic index. For purposes of the simulation, cells in mitosis when the drug is administered are not blocked and thus, in effect, we assume a 0.5 hr delay in the blocking action of the drug, such as has been reported for colchicine (Bertalanffy, 1964). With this assumption the TABLE Characteristics of cell population 1 1. ~ ~~ ~~~~ ~~ ~~ ~~ ~~ ~~ ~ Cell cycle interval GI S plus G, plus M Entire cycle Mean transit time (hr) Standard deviation (hr) Coefficient ofvariation a, 0.59 0 - a, 0.31 1 - a, 0.05 0 - a, 0.05 0 - Pyruvate kinase activity in WI-38 cells experimental mitotic index data indicates that only about 55% of the collected cells were experimentally observed at the subsequent mitosis. Thus, to simulate the mitotic index experiments, it was necessary to reduce the value of r to about 1.0 in order to match the peak heights of the simulated mitotic index curves with the peak height of the experimental curve. This reduction in r from 1.5 to about 1.O for simulation of this mitotic index experiment does not necessarily mean that cells are lost from cycle in the S or G, phase since it is likely, due to their reduced adhesion and increased mechanical fragility, that mitotic cells were selectively lost during the preparation of the slides analysed. Since the shapes of our mitotic index curves have been reproducible, we believe that the frequency of mitotic cell loss is approximately constant for all preparations, so the distribution, although not the amplitude, of these curves is accurate. Thus the reduction in r is artificial and does not affect our computation of the age distribution of cycling cells. The exact value of r for each mitotic index simulation is given in the corresponding figure. The narrowest possible mitotic index curve would be simulated by assuming a deterministic progression of cells through the S phase, the G, phase and mitosis, i.e. by assuming that cells in these phases age physiologically and chronologically at the same rate. This assumption, although biologically unreasonable, does represent a limiting case with respect to the dispersion of a synchronous age cohort traversing these phases. Even with this assumption the simulated mitotic index curve, presented as Fig. 2a, apears to be at least as broad as the experimental curve of Fig. 2b. On this basis we accept for now a deterministic progression through these phases as indicated in line 2 of Table 1. Characteristics of the resulting cell cycle are presented in line 3. Since the mean generation time that we derived from the experimental mitotic index data was about 18.4 hr, we have restricted our simulated populations also to this mean. Transit time distributions computed using the parameters of Table 1 are presented in Fig. 3. Age density distributions have been computed by means of the state vector model incorporating the parameters of Table 1. Selected examples of these distributions are illustrated in Fig. 4.The initial age distribution is presented as the one at 0.25 hr, since it is presumed to exist over the first 0.5 hr time interval. The age distribution, although initially narrow, is seen to broaden significantly as it penetrates the G, phase; it broadens no further as it transits the rest of the cell cycle. At 17.25 hr some cells have passed through mitosis and are seen to be re-entering the G, phase. The physiological age unit used as the abscissa scale is defined such that 10 units are awarded t o GI phase, 28 to the S and G, phases and 1 to mitosis. The physiological age intervals as utilized by the state vector model are indicated at their corresponding age unit. If the activity of a particular enzyme in an individual cell varies as a function of its physiological age, then this enzyme activity, when measured in a population of a large number of cells, is a function of the distribution of cell ages. As an example, take the case illustrated in Fig. 5. In Fig. 5 a the age distribution of cells is a 6 function, i.e. cells of only one age are present and this age increases with time. The enzyme activity as a function of time for the population accurately reflects the enzyme activity as a function of age for the cells. If, however, as illustrated in Fig. 5b, only cells of age a, manifest any enzyme activity and the cell population is somewhat distributed in ages, then the measured activity as a function of time reflects the age distribution of cells within the population rather than the age distribution of the enzyme activity. If both the cell population and enzyme activity are distributed in age then. of course, the enzyme activity for the population measured as a function of time must necessarily be broader than if one or the other was a 6 function. Explicitly, the enzyme p;w P. G. Steward, L . N. Kapp and R . R . Klevecz Physiological oge inlervol (4.25 hr; NC.025) (9.25 hr;NC=0.26) (13.25 h r ; N C = 0 . 2 6 ) Physiologicol oge unit FIG. 4. FIG. 5 FIG.4. Age density distributions computed for the cell population characterized in Table 1 at the indicated times after mitotic collection. Illustrated are the critical distributions corresponding to the times of peak enzyme activity (Fig. 6 ) . The fraction of cells not cycling (NC), due to the fact that r < 2, is indicated for each distribution. The ‘physiological age unit’ is defined in order to permit direct visual comparison between these distributions and those of Fig. 10. The corresponding physiological age intervals are indicated. FIG. 5. Representations of the experimentally determinable enzyme activities under two extreme conditions. (a) The cell population maintains perfect synchrony as it ages with increasing time, while the enzyme activity is distributed. (b) The cell population is distributed in age. while only cells of a single age have any enzyme activity. Pyruvate kinase activity in WI-38 cells activity E ( t ) is given by equation 1, where A ( a ) is the enzyme activity per cell as a function of physiological age. The enzyme activity as a function of time following mitotic collection was determined experimentally for the WI-38 cell population and is given as the solid line in Fig. 6a.* Using for E ( t ) these experimental data of Fig. 6 a and for the function S(t, a) the computed age distributions which were sampled for Fig. 4, equation 1 was solved indirectly for A(a) as " 0 a, Ln Tlme after collection (hr) Physiological age interval FIG. 6. (a) Pyruvate kinase activity. E(r) (nmol substrate utilized/min/106 cells) as a function of or time after mitotic collection determined experimentally (0) computed (----). (b) Pyruvate kinase, A ( a ) (nmol substrate utilized/min/106 cells in the indicated age interval) as a function of the physiological age intervals as incorporated by the state vector model. outlined below. A program was written for the PC 12/7 computer which solved equation 1 for E(t). The enzyme activity as a function of the physiological age interval, A (a), was adjusted by the operator ysing the computer analogue inputs until the computed E(t), which was continuously flashed onto the display scope, followed as closely as possible the experimental data points which were simultaneously imaged on the screen. In all simulations reported here it was found advantageous to give the cells in only four age intervals a non-zero enzyme activity, one interval corresponding to each of the prominent peaks mapped by the data points of Fig. 6a. The value of A ( a )chosen as yielding the E(t)most closely approximating the * Although the data presented in Fig. 6a are from a single experiment, the shape and relative position of the peaks were found to be reproducible in two other experiments. Due to slight temporal shifts in the maxima from experiment to experiment. averaging data for more than one experiment changes the shape of these peaks. This has been found for other enzymes and has been discussed previously (Klevecz & Kapp, 1973). Therefore, for purposes of the computer analysis presented here. it was thought best to work with data from a single, representative experiment. P. G. Steward, L . N . Kapp and R. R. Klevecz data is presented in Fig. 6b, and the resulting E(t) is plotted as the dashed line in Fig. 6a. Clearly the age distribution at the times of peak enzyme activities (illustrated in Fig. 4) are too broad to permit simulation of the experimental data, even though it was assumed that after leaving the G, phase no further dispersion of the synchronous age cohort occurs. It was a matter of some concern to us that the mitotic index data and the corresponding simulation presented in Fig. 2 do not match well. The data indicates that the distribution of generation times for this population is skewed to the left. The simulation by the state vector model skews this distribution to the right, in agreement with what is generally thought to be Time ofter collection lhr) FIG.7. Continuous labelling index. Points are the same as in Fig. 1. The line is computed for the cell populations characterized in Tables 2 and 3. the case for most cell populations. Also, the main part of the peak for the mitotic index data (Fig. 2b) is narrower than that of the simulation (Fig. 2a), indicating that the age cohort as it reaches mitosis may not be distributed as broadly as that of our simulated population. Therefore, since our simulated cell population is compatible with the labelling index data of Fig. 1, and the deterministic progression through S and G , phases permits no further desynchrony, an incompatibility between the labelling index data and the mitotic index data could be indicated unless, of course, the population becomes more synchronous after entering S phase. In an attempt to resolve these inconsistencies, we examined the characteristics of a simulated cell population which are compatible with our state vector model and which TABLE Characteristics of cell population 2 2. Mean transit time (hr) Cell cycle interval Standard deviation (hr) Coefficient ofvariation a . a, a, 0.2 0 - a, 0.2 0 - tl G, S plus G, plus M Entire cycle 0.2 1 - Pyruvate kinase activity in WI-38 cells minimize the incompatibility of all of the experimental data. The computer-generated labelling index of this population is compared with the corresponding experimental data points in Fig. 7. Other characteristics of the population are tabulated in Table 2 . Note that again no dispersion of the age cohort is permitted as it traverses the S and G, phases. With this unrealistic assumption, the mitotic index data are computed and presented in Fig. 8a; the Time after collection (hr) Time (hr) FIG. 8. FIG. 9. FIG.8. Mitotic index as a function of time after mitotic collection. (a) Computed for the population characterized in Table 2. Here r = 0.8, implying that 40% of the collected cells were observed to enter the subsequent mitosis. (b) Experimental (the same as Fig. 2b). (c) Computed for the population characterized in Table 3. Here r = 1.1, implying that 55% of the collected cells were observed in the subsequent mitosis. FIG. 9. Probability density distributions for cell transit times computed for the populations and 3 (-----). (a) G, phase: (b) S plus G , plus M phases: (c) cell characterized in Tables 2 () cycle. experimental data are presented for comparison in Fig. 8b. The probability density functions for transit times and physiological ages are given as the solid lines in Figs 9 and 10 respectively. Since the age distributions of Fig. 10 are much narrower than those of Fig. 4, the computer program described above can approximate the experimental enzyme activity data much more closely than before. Age distributions of the present cell population, of which the solid curves P. G. Steward, L. N. Kapp and R. R. Klevecz + x z .+ Time after " 0 collection ( h r ) W + 2. 2 a (17.25 hr; NC: 0.301 Physiological age interval 10 20 30 40 Physiological age interval FIG. 10. FIG. 1 1 FIG.10. Age density distributions computed for the cell populations characterized in Tables 2 () and 3 (----) at the indicated times after mitotic collection. Illustrated are the critical distributions corresponding to the times of peak enzyme activity (Fig. 11). The fraction of cells not cycling (NC) is indicated for each distribution. The abscissa scale is the physiological age intervals incorporated into the state vector model. FIG.11. (a) Pyruvate kinase activity, E ( t ) (nmol substrate utilized/min/106 cells) as a function of (same as in Fig. 6 ) . or computed for time after mitotic collection determined experimentally (0) the cell population characterized in Tables 2 (----) and 3 (.....), (b) Pyruvate kinase activity, A ( a ) (nmol substrate utilized/min/106 cells in the indicated age interval) as a function of the physiological age intervals as incorporated into the state vector model. This function was used for computing each of the two functions E ( t ) presented in Fig. 1 la. Pyruvate kinase activity in WI-38 cells TABLE Characteristics of cell population 3 3. Mean transit time (hr) 4.2 14.3 18.4 Cell cycle interval G, S plus G, plus M Entire cycle Standard deviation (hr) Coefficient of variation a,, al 0.2 0.8 - a 2 1.5 1.2 I .9 0 - of Fig. 10 are examples, were used to compute the enzyme activities indicated by the dashed line in Fig. 1 l a . This is a reasonably close approximation, particularly for the activity peaks at 13 and 17 hr, to the experimental data (solid line of Fig. l l a ) . The corresponding enzyme activity as a function of physiological age is shown in Fig. 1 lb. Since we believe that deterministic progression of cells through S and G , phases is biologically unrealistic, we re-examined this cell population after introducing a slight dispersion of the age cohort as it transversed these phases. Characteristics of this revised cell population are tabulated in Table 3 and the corresponding computed mitotic index curve is presented in Fig. 8c. This curve appears somewhat broader than the experimental curve (Fig. 8b). The resulting probability density functions for transit times and physiological ages are given as dashed lines in Figs 9 and 10 respectively. Even though the age distributions are only slightly broader than before, the computed enzyme activities as a function of time after mitotic collection, presented as the dotted line in Fig. 1la, fit the experimental data poorly. The enzyme activity as a function of physiological age is again that illustrated in Fig. 1 1b. In order to compare the kinetics of the WI-38 cell populations used in our simulations with the kinetics of this cell line as reported by others, we have analysed, by means of the state vector model, the PLM curve for passage 18 WI-38 cells reported by Macieira-Coelho, Ponten & Philipson (1 966). The results of this analysis are presented in Table 4 and can be compared with the characteristics of our three cell populations tabulated in Tables 1, 2 and 3. Note that for each phase of the cell cycle the coefficient of variation, which is here a measure of the rate at which a synchronous subpopulation will disperse, is greater for the asynchronous population of Macieira-Coelho et al. (1966) than for our synchronized populations. This reinforces our impression that we have not over-estimated the rate of desynchronization for the population characterized in Table 3, and that our experimental enzyme activity data and our theoretical model are prclbably incompatible. TABLE Characteristics of a WI-38 cell population obtained by 4. analysis of a pulse-labelled mitoses curve (see text) Mean transit time (hr) Cell cycle interval G, S plus G, plus M Entire cycle Standard deviation (hr) Coefficient of variation P. G. Steward, L . N . Kapp and R. R. Klevecz DISCUSSION We have described a theoretical analysis of the desynchronization of a mitotically collected WI-38 cell population. It is shown that a hypothetical population which traverses the G, phase in a manner maximally consistent with continuous labelling index data (Fig. 1) is probably incompatible with the mitotic index data (Fig. 2). Presuming pyruvate kinase activity to be a function of physiological age alone, there is no question that the age distributions of this cell population are too broad to be compatible with the experimental pyruvate kinase activity data (Fig. 6). We then identified a hypothetical cell population which is consistent with our pyruvate kinase activity data, and also with our presumption that this activity is a function of only a cell’s physiological age. This was done by reducing the rate of desynchronization through G I barely enough t o provide age distributions which were sufficiently narrow, in the absence of any further desynchronization in S and G, phases, so that enzyme activities of the theoretical and actual populations could agree (Fig. 11, dashed line). Although the experimental mitotic index data (Fig. 8a) is not seriously incompatible with that of this hypothetical population (Table 2 and Fig. 8b), the continuous labelling index for this population appears to increase somewhat more abruptly than the experimental data (Fig. 7). It may seem encouraging that we were nearly successful in identifying a cell population tor which our computer simulations agree with the experimental labelling and mitotic indexes and with the enzyme activity data. However, these simulations incorporate two improbable assumptions. Firstly, it is unlikely that the enzyme activity as a function of cell age, A(a), changes as abruptly as indicated in Fig. 1 Ib. Secondly, it is biologically unrealistic to presume that no stochastic processes to occur in S and G, phases. Unfortunately, introducing even a slight further dispersion of the age cohort as it traverses these phases causes the age distributions to be so broad that they are incompatible with the experimental pyruvate kinase activity data (Fig. 11, dotted line). We conclude that a cell population which is compatible with the pyruvate kinase activity data and is also biologically realistic would have a continuous labelling index curve which rises even more abruptly than that shown in Fig. 7, and is thus inconsistent with the experimental labelling index data. It is not clear, though, that this enzyme activity is also incompatible with the mitotic index data. Our analysis of the PLM curve of Macieira-Coelho et al. (1966), presented in Table 4, indicates that a synchronous subpopulation of her asynchronous WI-38 cells would desynchronize much faster than our hypothetical populations, which yield age distributions already too broad to be consistent with the enzyme activity data. For example, from Tables 3 and 4 it is seen that the population. which in Fig. 1 l a is shown to be incompatible with the enzyme data, has coefficients of variation of 0.35 and 0 . 1 for the G, phase and the cell cycle respectively, compared to 0.59 and 0.18 for the asynchronous population of MacieiraCoelho et al. (1 966). It appears that either our presumption that pyruvate kinase activity is a function only of cell age, or our presumption that cells age in a manner consistent with the state vector model, or both of these, is incompatible with our experimental data as well as with this PLM curve. We believe our experimental techniques and our data t o be valid. The automated synchrony system used here has been previously described (Klevecz & Kapp, 1973). Such a system avoids use of drugs or inhibitors, lowered temperatures and centrifugation, and thus minimizes manipulation of the cells during the synchronizing process. In addition, oscillatory Pyruvate kinase activity in WI-38 cells or multiple peak enzyme patterns, similar t o those reported here for pyruvate kinase. have been reported for lactate dehydrogenase in Chinese hamster cells (Klevecz & Ruddle, 1968). acid phosphatase in mouse cells (Kapp & Okada, 1972), serine dehydratase in hamster cells (Kapp, Remington & Klevecz, 1973), lactate dehydrogenase in human cells (Klevecz & Kapp, 1973) and for other enzymes in other cell lines (Klevecz & Forrest, 1977). In view of this it appears that it may be necessary t o examine the cell cycle concepts incorporated into the theoretical model in order t o explain the discrepancies between the experimental results and the theoretically predicted results. For example, the experimental generation time distribution (Fig. 2b) appears skewed to the left. However, our theoretical model is adapted to the more usual finding that cell transit time distributions are skewed to the right, presumably because a minimum time is required for the biochemical synthesis necessary t o advance to the next cell cycle stage, but a few cells may take much more time than this minimum. Detailed inspection of Fig. 2b reveals what could be bursts of mitoses at about 12, 17 and 20 hr after collection with the overall envelope, resulting in the appearance of a single distribution skewed to the left. Klevecz (1976) has collected some evidence to support his suggestion that cells can enter the S phase only after residing in the G, phase for an integral number of 4 hr intervals. Thus the age distribution late in the cell cycle for a population synchronized in mitosis could appear to be a series of age distributions with cells clustered about modes spaced 4 hr apart. Were this the case, these three bursts of mitoses could be three of these subpopulations passing through mitosis, and this would identify a departure of the behaviour of these cells from the concepts incorporated into the model. Consider our concept of physiological age. We have assumed that physiological age can be defined in terms of a sequence of biochemical activities which progress systematically and irreversibly from one mitosis towards the next. Furthermore, we have assumed that the onset and decline of D N A synthesis, pyruvate kinase activity and mitosis all have discrete positions within this sequence. Alternatively, within each cell there may be more than one sequence of biochemical activities, and progression along these toward mitosis may occur somewhat independently of one another (Kapp & Okada, 1972). Such a possibility identifies a potential ambiguity in the definition of physiological age. If DNA synthesis were in one sequence and pyruvate kinase in another, a cell population could be quite synchronous with respect to pyruvate kinase activity and less so with respect to D N A synthesis. A second possibility is that pyruvate kinase is not a part of any biochemical sequence determining physiological age. It may be a part of a sequence which can be initiated anywhere within a set of physiological age intervals and, once initiated, progression along the sequence toward a pyruvate kinase activity peak may not be tied to progression in physiological age. Essentially, it is assumed in our modelling that a cohort of cells, synchronized with respect to physiological age, will desynchronize at a uniform rate from one physiological age marker t o the next. If there were some factor responsible for communicating, throughout a cell culture, information resulting in a peak of pyruvate kinase activity, then the activiy peak or peaks would not be a function of only the cell’s physiological age. Some evidence indicating something of this nature t o exist for the initiation of D N A synthesis in synchronous cultures has been reported by Dewey, Miller & Nagasawa (1 973), who have shown that conditioned medium from synchronized cells entering the S phase, or the proximity of S phase cells, can cause a synchronized G, population to enter S phase as much as 1.5 t o 2.5 hr earlier than would be expected for an isolated G, population. Similarly, Rao & Johnson (1970) have P. G. Steward, L. N . Kapp and R. R. Klevecz reported that a G, nucleus fused t o an S phase nucleus enters S phase earlier than either two fused G, nuclei or an isolated G, cell. Hormonally regulated enzyme synthesis has been reported which permits the intracellular enzyme activity to be somewhat independent of cell age. Consider, for example, the model for control of tyrosine aminotransferase (TAT) synthesis in cultured hepatoma cells proposed by Tomkins et al. (1972).* Here, translation of the T A T message is suppressed by a labile repressor. The enzyme inducer in this case inactivates the repressor, permitting translation of the already present message. Conversely, the enzyme synthesis is suppressed by withdrawing the inducer, thus reactivating the repressor. If the enzyme itself were sufficiently labile or actively degraded, such a post-transcriptional control mechanism could provide, as a function of time, very sharp peaks in enzyme activity. One way of adapting such concepts to our culture conditions could be the following. Suppose the concentration of a humoral inducer for pyruvate kinase in a synchronized culture increases in an age-dependent fashion. As the synchronized culture ages, the cohort desynchronizes yet, as the inducer concentration in the nutrient medium reaches sufficient levels, the cells begin translating the pyruvate kinase message in synchrony. If feedback exists such that a repressor is activated by a sufficient enzyme concentration, repeating synchronous bursts of enzyme translation could occur. Thus short bursts of enzyme activity could be assayed which would be independent of the culture’s physiological age distribution as defined by D N A synthetic and morphological age markers. We d o not claim that the above outline actually represents the control for pyruvate kinase in synchronous cultures. However, in the context of such post-transcriptional control mechanisms, it is not surprising that the bursts of enzyme activity observed by us d o not represent only age-dependent changes in individual cells. We conclude that pyruvate kinase activity is not a function of physiological cell age alone. Furthermore, we conclude that there exists no unique and non-trivial definition of physiological age. This is true because no matter what sequence of age markers one adopts in order to define physiological age, individuals of the same age can exhibit different biochemical activities and can, therefore, be heterogeneous in their response to some chemical or physical probes. In contrast to this, the usual concept of physiological age is defined in terms of mitosis and the initiation and completion of D N A synthesis, because these markers can be conveniently measured morphologically o r biochemically, and any other physiological function or status must fit as a sequence with these markers. Age cohorts would be expected to desynchronize uniformly and irreversibly from one marker to the next. It is this latter concept of physiological age which is incorporated into our model and most other theoretical models which are currently used to describe the progression of cells through the cell cycle. Although this may be an acceptable concept when applied to some cellular processes, clearly it may be a deceptive oversimplification when applied to others. One common application of theoretical models incorporating the concept of physiological age is in the field of cancer biology. Here one simulates the response of a cell population t o sequential administrations of physical agents (e.g. radiation) or chemical agents (e.g. phasespecific drugs). In this case the problems of applying the concept of physiological age are compounded, since these agents have the sub-lethal effect of altering the ageing rate, and it is likely that this perturbation is greater for some biochemical processes than for others. Physiological age then becomes little more than a construct of the theoretical model since the * By citing this well-known model, we are making no assertion regarding how strictly it conforms to reality. Pyruvate kinase activity in WI-38 cells relationship between cell age (however defined) and cell response to further administrations of cytotoxic agents may well be lost. ACKNOWLEDGMENT This investigation was supported by grant No. 5POlCA13053-05, awarded by the National Cancer Institute, DHEW, and by grant No. H004699, awarded by the National Institutes for Child Health and Human Development, DHEW. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Cell Proliferation Wiley

Cell Cycle And The Concept Of Physiological Age With Special Reference To Pyruvate Kinase Activity In Wi-38 Cells

Cell Proliferation , Volume 11 (6) – Nov 1, 1978

Loading next page...
 
/lp/wiley/cell-cycle-and-the-concept-of-physiological-age-with-special-reference-zSCbIvhhuH

References (32)

Publisher
Wiley
Copyright
1978 Blackwell Science Limited
ISSN
0960-7722
eISSN
1365-2184
DOI
10.1111/j.1365-2184.1978.tb00835.x
Publisher site
See Article on Publisher Site

Abstract

Section of Cancer Biology, Division of Radiation Oncology, Mallinckrodt Institute of Radiologv, Washington University School of Medicine, St Louis, Missouri, and *Department of Biology, City of Hope National Medical Center, Duarte, California, U.S.A. (Receiued 13 June 1977: rel>ision accepted 13 October 1977) ABSTRACT WI-38 cells were synchronized by mitotic collection and periodically assayed for pyruvate kinase activity. The kinetics of the synchronous cohort were determined by continuous labelling index and by mitotic index. The experimental data were analysed by computer using a state vector model to yield the probability density functions for phase transit times and for cell physiological ages. Pyruvate kinase activity for these cells as a function of physiological age was then examined using the computer model. Considering DNA synthesis, pyruvate kinase activity and mitosis to be markers of physiological age, it was found that a model which assumes that a cohort of synchronized cells desynchronizes irreversibly and uniformly from one age marker to the next is incompatible with the experimental data. For example, the times over which cells entered the S phase were too widely distributed to be consistent with the mitotic index data. Also, for pyruvate kinase activity to be a function of physiological age alone, the cell ages were probably too dispersed to be compatible with the experimental enzyme data. Alternative models for cell physiological ageing are presented, which are compatible with the experimental data. Synchronous cell cultures are often used to study variations in biochemical and cellular functions as the cells progress through the cycle. While several methods of obtaining synchronous cell populations have been developed (Mitchison, 197 l), when biochemical studies are to be performed mitotic collection (Terasima & Tolmach, 1963) is often the method of choice, since it is biochemically the least disruptive to the cells. Since mitotic time is such a short part of the total cell cycle, the age distribution is quite narrow when the cells are initially collected. However, the initial synchrony of this age cohort decays as the cells t Present address: University of California. School of Medicine. Laboratory of Radiobiology, San Francisco. California 94143, U.S.A. Correspondence: Dr P. G. Steward, Veterans Administration Hospital, Radiation Therapy Department (1 14A JC), St Louis, Missouri 63 125. U.S.A. 0008-8730/78/1100-0623$02.00 0 1978 Blackwell Scientific Publications P. G. Steward, L. N . Kapp and R. R . Klevecz progress through the cell cycle, since some cells approach the subsequent mitosis more rapidly than others. Thus, as the chronological age of the cohort increases, the physiological age distribution of the cohort broadens.* This makes the interpretation of the experiments utilizing synchronous cultures ambiguous. For example, a small measured response is compatible with both a weak response from every cell in a sample, or with a strong response from a few cells in the sample which fall within a very narrow physiological age interval. The experimentally observed response at time t , E(t),of a cell population is E ( t )= j A ( a ) S ( t , a ) d a ; (1) where A ( a ) is the response of cells at physiological age a, S ( f , a) is the physiological age density distribution at time t, i.e. the number of cells at age a per unit physiological age interval t time units following mitotic collection, and cells are defined to be of physiological age a = 0 immediately following mitosis and of age a = 1 at mitosis. The goal in synchrony experiments is usually to obtain the function A(a), but the response or parameter experimentally observable is E(t). Ideally, desynchronization would not occur and the age distribution would be infinitely narrow; S(t, a) would then be the delta function d ( t - a).? If this was the case then A ( t ) = E(t). so that the desired function would be experimentally observable and the ambiguity referred to above would no longer exist. The ambiguity in interpreting synchrony experiments stems from the fact that S(t, a) is not a 6 function and that this age distribution broadens with time. The analysis required to obtain A(a) is rarely performed due to the difficulties involved. However, computer simulation of the broadening physiological age distribution of mitotically collected cells with time has been used to analyse the experimental age response for cell lethality following exposure to various drugs (Steward & Hahn, 1971). We report here a similar analysis of the age response for pyruvate kinase activity, and we show that the activity of this enzyme is not likely to be a function of physiological age alone. MATERIALS A N D METHODS Cell line WI-38 human embryonic lung fibroblasts were obtained from Dr L. Hayflick at the thirteenth passage. These were maintained as a monolayer culture in McCoy's 5a medium with 15% foetal calf serum, neomycin and 10 mM HEPES. Synchrony Cells were grown in roller bottles and maintained at 0.5 rev/min. To select mitotic cells, the roller speed was increased to 200 rev/min for 5 min and the medium plus mitotic cells were then pumped out of the rollers and into Falcon T C flasks. This process was repeated hourly until the necessary number of samples had been collected (Klevecz & Kapp, 1973). Synchronized cells were collected at passages 20 to 25. * Chronological age is defined as the time elapsed since the previous mitosis. Physiological age is defined as the extent of biochemical progression towards the next mitosis. 6(x) dx = 1.O. 'f A 6 function is defined such that 6(x) = 0 for x # 0 and Pyruvate kinase activity in WI-38 cells E nzvme activity Pyruvate kinase activity was measured as described by Shonk & Boxer (1964). Cells were washed, trypsinized and sonicated for 30 sec (Sonifier, Heat Systems Inc.). An aliquot of the sonicate was then incubated in a reaction mixture containing 0.05 M Tris-HC1, 0.01 M MgCI,, 0.2 m M NADH, 3.0 mM phosphoenolpyruvic acid and 1 u/ml L D H at p H 7.5. The optical density change of the reaction mixture was followed at 340 nm with a Gilford model 2400 spectrophotometer. The slope of a line which was optical density plotted as a function of time was proportional to the enzyme activity. Computer simulation o the synchrony f The mathematical technique used to simulate the progression of cells about the cell cycle is a slight modification of that developed by Hahn ( 1 966. 1970). Slight variations of this model have also been used by Young & Fowler ( I 969) to study repair of sublethal damage following X-irradiation: by Roti Roti & Okada (1971) to analyse cell cycle synchrony produced by exposure to excess thymidine and to colcemid: by Niederer & Cunningham (1976) to study the effect on cell populations of sequential X-ray doses: by Gray (1976) to anaiyse D N A histograms: and Kim. Bahrami & Woo ( 1974) have proposed this model to study cell size. age and DNA distributions. The cell cycle is divided into 17 physiological age intervals and the physiological age distribution is represented as a n dimensional vector called the state vector. For example, the initial physiological age distriubtion, So (0). is represented as: mi where m , is the number of cells in the first physiological age interval of G , phase, i n , is the cell number in the ith age interval, and m, is the number of cells in the nth age interval which, by our convention, are the mitotic cells, all at time t = 0. The ageing of the population represented in equation 2 is simulated by advancing cells down the state vector into mitosis, doubling the number of mitotic cells which are then entered into the first age interval. This rotation process occurs in discrete steps. the implementation of each simulates the passage of one time interval A t . Since all cells do not age physiologically at the same rate, following each time interval At, the cell fraction q,, a'? a,, and a,are advanced by 0, 1, 2. and 3 physiological age intervals respectively. The probability of a cell's progressing by more than 3 physiological age intervals in the time A t is presumed to be negligible for the simulations described below. For the number of cells in a population to neither increase nor decrease as they pass through an age interval, a,, + a,+ cr, -I- a, = 1 for that interval. The distribution of cell generation times is determined by the number of age intervals and the values chosen for the as. In order to permit cell kinetic behaviour t o vary from one phase of the cell cycle to the next. one set of as can be chosen for all of the age P. G. Steward, L. N . Kapp and R . R. Klevecz intervals of the G I phase, another set for all of the age intervals of the S phase and a third set for the age intervals of the G2phase and mitosis. Formally, the ageing process is incorporated into the model by means of a matrix operator H. such that the physiological age distribution at the time t = At is S,(A t ) = HSJO), and at time iAt the age distribution is S,(iAt) = H”S,(O). (3) The matrix operator H,for the special case when two age intervals are assigned to each of the G,, S and G2phases and one interval is assigned to mitosis, is: ‘OG, rCC3G,M ‘OG, “2G,M “3G,M raIG,M “2G,M ‘lG, H= (4) ax a2s a3S ~IG,M a2GZM ~OG,M ‘lG,M ‘OG,M where r - 1 is the number of cells added to the population per mitotic event and the (IS are defined as above. Equation 4 differs slightly from the operator developed by Hahn (1970) for the state vector model, but is similar to the one used by Steward (1975). RESULTS The age distribution of a cycling cell population as a function of time can be computed by means of the state vector model described above. Three characteristics ofthe population must be known, however: firstly, the initial age distribution, i.e. the ms of equation 2; secondly, the rate at which cells enter and exit from the population or, in our case, the r of equation 4: and thirdly. the probability density distribution for the cell transit times through each phase of the cell cycle, i.e. the as and the number of age intervals for each phase as utilized in equation 4. With these parameters known, the age distribution can be found by means of equation 3 for any integral number of time intervals A t . Since, immediately following mitotic collection, the mitotic index of the WI-38 cells used in these experiments was found to be 85%, we assume that the initial age distribution is characterized by 85% of the cells being in mitosis and the other 15% being distributed uniformly throughout the cell cycle. When we placed these 15% in the first age interval of the G I phase, the conclusions of this study were unchanged, indicating that the disposition of this 15% is not critical. We assume that cells enter or exit the cell cycle only at mitosis. For the case where r of equation 4 is 2, two cells enter G, phase for each cell passing through mitosis. If r = 1, then the cycling population is just self-maintaining and one cell exists from this population for each cell passing through mitosis. For 1 < r < 2, the population is expanding and cell loss (from the cycling population) is occurring. The continuous labelling index curve of Fig. 1 indicates Pyruvate kinase activity in WI-38 cells that only about 70% of the mitotically collected cells enter S phase. The viability of cells in the population was determined by taking samples at various times following collection and staining with 0.5% eosin. In each sample only 2-3% of the cells were stained (data not shown), implying that although 97-98% of the cells were alive by this assay (Watanabe & Okada, 1967), only about 70% entered DNA synthesis. On the basis of these experiments we chose an r of either 1.46 or 1-5, which is 73 or 75% respectively of the r value corresponding to no cell loss. The final characteristics of the cycling population required in order t o compute the age density distribution as a function of time following mitotic collection are the transit time I2 Time after collection ihri FIG. 1. Labelling index as a function of time after mitotic collection. WI-38 cells at passage 25 were exposed continuously to ['HITdR (5.0 pCi/ml, 6.0 Ci/mmol) from the time of collection until they were fixed for autoradiography. Points were taken from Kapp & Klevecz (1976). The line is computed for the cell population characterized in Table 1. distributions for segments of the cell cycle. These are estimated from the continuous labelling index data and the mitotic index data of Figs 1 and 2b respectively. The slope of the labelling index curve (Fig. 1) yields the rate of entry into S phase of mitotically collected cells, i.e. it is a measure primarily of the G I phase transit time distribution. The mitotic index data (Fig. 2b) determine the distribution of transit times for the cell cycle in the first generation following mitotic coliection. The data of Figs 1 and 2b were analysed by computer to yield the required transit time distributions. This was accomplished by simulating, by means of the computer model, the experiments which produced these data. For the continuous labelling experiment, 85% of the cells were placed in mitosis, the remainder were distributed equally among the other age intervals, and r was set to 1.5. The cells were accumulated in the first age interval of S phase. The cell fraction accumulated, presented as the line in Fig. 1, represents the labelling index. Since most of the cells transited only the G I phase before being accumulated, it was primarily the CIS and nG,for G, phase (i.e. the G , phase transit time distribution) which were determined by this simulation. The parameters found for the G,phase are given in line l'of Table 1. The resulting mean transit time and its standard deviation and coefficient of variation are also given. T o simulate the experiment producing the mitotic index data, again 85% of the cells were initially placed in mitosis and the remaining 15% distributed equally among the other age intervals. In the experiment, a 2 hr colcemid block preceded the determination of each P. G. Steward, L . N . Kapp and R. R. Klevecz 0. I .c 0. I 0.0: 0.1: o.oe Time after collection (hr) Time ( h r ) FIG.2. FIG.3. Flti. 2. Mitotic index as a function of time after mitotic collection. (a) Computed for the population characterized in Table 1 as described in the text. For this computer simulation, r = 1.2 (see equation 4), implying that 60% of the collected cells were observed to enter the subsequent mitosis. (b) WI-38 cells at passage 25 were exposed to colcemid for the 2 hr indicated by the bars before determining the mitotic index (redrawn from Kapp & Klevecz, 1976). FIG.3. Probability density distributions for cell transit times computed for the population characterized in Table 1. (a) G , phase; (b) S plus G, plus M phases; (c) cell cycle. mitotic index. For purposes of the simulation, cells in mitosis when the drug is administered are not blocked and thus, in effect, we assume a 0.5 hr delay in the blocking action of the drug, such as has been reported for colchicine (Bertalanffy, 1964). With this assumption the TABLE Characteristics of cell population 1 1. ~ ~~ ~~~~ ~~ ~~ ~~ ~~ ~~ ~ Cell cycle interval GI S plus G, plus M Entire cycle Mean transit time (hr) Standard deviation (hr) Coefficient ofvariation a, 0.59 0 - a, 0.31 1 - a, 0.05 0 - a, 0.05 0 - Pyruvate kinase activity in WI-38 cells experimental mitotic index data indicates that only about 55% of the collected cells were experimentally observed at the subsequent mitosis. Thus, to simulate the mitotic index experiments, it was necessary to reduce the value of r to about 1.0 in order to match the peak heights of the simulated mitotic index curves with the peak height of the experimental curve. This reduction in r from 1.5 to about 1.O for simulation of this mitotic index experiment does not necessarily mean that cells are lost from cycle in the S or G, phase since it is likely, due to their reduced adhesion and increased mechanical fragility, that mitotic cells were selectively lost during the preparation of the slides analysed. Since the shapes of our mitotic index curves have been reproducible, we believe that the frequency of mitotic cell loss is approximately constant for all preparations, so the distribution, although not the amplitude, of these curves is accurate. Thus the reduction in r is artificial and does not affect our computation of the age distribution of cycling cells. The exact value of r for each mitotic index simulation is given in the corresponding figure. The narrowest possible mitotic index curve would be simulated by assuming a deterministic progression of cells through the S phase, the G, phase and mitosis, i.e. by assuming that cells in these phases age physiologically and chronologically at the same rate. This assumption, although biologically unreasonable, does represent a limiting case with respect to the dispersion of a synchronous age cohort traversing these phases. Even with this assumption the simulated mitotic index curve, presented as Fig. 2a, apears to be at least as broad as the experimental curve of Fig. 2b. On this basis we accept for now a deterministic progression through these phases as indicated in line 2 of Table 1. Characteristics of the resulting cell cycle are presented in line 3. Since the mean generation time that we derived from the experimental mitotic index data was about 18.4 hr, we have restricted our simulated populations also to this mean. Transit time distributions computed using the parameters of Table 1 are presented in Fig. 3. Age density distributions have been computed by means of the state vector model incorporating the parameters of Table 1. Selected examples of these distributions are illustrated in Fig. 4.The initial age distribution is presented as the one at 0.25 hr, since it is presumed to exist over the first 0.5 hr time interval. The age distribution, although initially narrow, is seen to broaden significantly as it penetrates the G, phase; it broadens no further as it transits the rest of the cell cycle. At 17.25 hr some cells have passed through mitosis and are seen to be re-entering the G, phase. The physiological age unit used as the abscissa scale is defined such that 10 units are awarded t o GI phase, 28 to the S and G, phases and 1 to mitosis. The physiological age intervals as utilized by the state vector model are indicated at their corresponding age unit. If the activity of a particular enzyme in an individual cell varies as a function of its physiological age, then this enzyme activity, when measured in a population of a large number of cells, is a function of the distribution of cell ages. As an example, take the case illustrated in Fig. 5. In Fig. 5 a the age distribution of cells is a 6 function, i.e. cells of only one age are present and this age increases with time. The enzyme activity as a function of time for the population accurately reflects the enzyme activity as a function of age for the cells. If, however, as illustrated in Fig. 5b, only cells of age a, manifest any enzyme activity and the cell population is somewhat distributed in ages, then the measured activity as a function of time reflects the age distribution of cells within the population rather than the age distribution of the enzyme activity. If both the cell population and enzyme activity are distributed in age then. of course, the enzyme activity for the population measured as a function of time must necessarily be broader than if one or the other was a 6 function. Explicitly, the enzyme p;w P. G. Steward, L . N. Kapp and R . R . Klevecz Physiological oge inlervol (4.25 hr; NC.025) (9.25 hr;NC=0.26) (13.25 h r ; N C = 0 . 2 6 ) Physiologicol oge unit FIG. 4. FIG. 5 FIG.4. Age density distributions computed for the cell population characterized in Table 1 at the indicated times after mitotic collection. Illustrated are the critical distributions corresponding to the times of peak enzyme activity (Fig. 6 ) . The fraction of cells not cycling (NC), due to the fact that r < 2, is indicated for each distribution. The ‘physiological age unit’ is defined in order to permit direct visual comparison between these distributions and those of Fig. 10. The corresponding physiological age intervals are indicated. FIG. 5. Representations of the experimentally determinable enzyme activities under two extreme conditions. (a) The cell population maintains perfect synchrony as it ages with increasing time, while the enzyme activity is distributed. (b) The cell population is distributed in age. while only cells of a single age have any enzyme activity. Pyruvate kinase activity in WI-38 cells activity E ( t ) is given by equation 1, where A ( a ) is the enzyme activity per cell as a function of physiological age. The enzyme activity as a function of time following mitotic collection was determined experimentally for the WI-38 cell population and is given as the solid line in Fig. 6a.* Using for E ( t ) these experimental data of Fig. 6 a and for the function S(t, a) the computed age distributions which were sampled for Fig. 4, equation 1 was solved indirectly for A(a) as " 0 a, Ln Tlme after collection (hr) Physiological age interval FIG. 6. (a) Pyruvate kinase activity. E(r) (nmol substrate utilized/min/106 cells) as a function of or time after mitotic collection determined experimentally (0) computed (----). (b) Pyruvate kinase, A ( a ) (nmol substrate utilized/min/106 cells in the indicated age interval) as a function of the physiological age intervals as incorporated by the state vector model. outlined below. A program was written for the PC 12/7 computer which solved equation 1 for E(t). The enzyme activity as a function of the physiological age interval, A (a), was adjusted by the operator ysing the computer analogue inputs until the computed E(t), which was continuously flashed onto the display scope, followed as closely as possible the experimental data points which were simultaneously imaged on the screen. In all simulations reported here it was found advantageous to give the cells in only four age intervals a non-zero enzyme activity, one interval corresponding to each of the prominent peaks mapped by the data points of Fig. 6a. The value of A ( a )chosen as yielding the E(t)most closely approximating the * Although the data presented in Fig. 6a are from a single experiment, the shape and relative position of the peaks were found to be reproducible in two other experiments. Due to slight temporal shifts in the maxima from experiment to experiment. averaging data for more than one experiment changes the shape of these peaks. This has been found for other enzymes and has been discussed previously (Klevecz & Kapp, 1973). Therefore, for purposes of the computer analysis presented here. it was thought best to work with data from a single, representative experiment. P. G. Steward, L . N . Kapp and R. R. Klevecz data is presented in Fig. 6b, and the resulting E(t) is plotted as the dashed line in Fig. 6a. Clearly the age distribution at the times of peak enzyme activities (illustrated in Fig. 4) are too broad to permit simulation of the experimental data, even though it was assumed that after leaving the G, phase no further dispersion of the synchronous age cohort occurs. It was a matter of some concern to us that the mitotic index data and the corresponding simulation presented in Fig. 2 do not match well. The data indicates that the distribution of generation times for this population is skewed to the left. The simulation by the state vector model skews this distribution to the right, in agreement with what is generally thought to be Time ofter collection lhr) FIG.7. Continuous labelling index. Points are the same as in Fig. 1. The line is computed for the cell populations characterized in Tables 2 and 3. the case for most cell populations. Also, the main part of the peak for the mitotic index data (Fig. 2b) is narrower than that of the simulation (Fig. 2a), indicating that the age cohort as it reaches mitosis may not be distributed as broadly as that of our simulated population. Therefore, since our simulated cell population is compatible with the labelling index data of Fig. 1, and the deterministic progression through S and G , phases permits no further desynchrony, an incompatibility between the labelling index data and the mitotic index data could be indicated unless, of course, the population becomes more synchronous after entering S phase. In an attempt to resolve these inconsistencies, we examined the characteristics of a simulated cell population which are compatible with our state vector model and which TABLE Characteristics of cell population 2 2. Mean transit time (hr) Cell cycle interval Standard deviation (hr) Coefficient ofvariation a . a, a, 0.2 0 - a, 0.2 0 - tl G, S plus G, plus M Entire cycle 0.2 1 - Pyruvate kinase activity in WI-38 cells minimize the incompatibility of all of the experimental data. The computer-generated labelling index of this population is compared with the corresponding experimental data points in Fig. 7. Other characteristics of the population are tabulated in Table 2 . Note that again no dispersion of the age cohort is permitted as it traverses the S and G, phases. With this unrealistic assumption, the mitotic index data are computed and presented in Fig. 8a; the Time after collection (hr) Time (hr) FIG. 8. FIG. 9. FIG.8. Mitotic index as a function of time after mitotic collection. (a) Computed for the population characterized in Table 2. Here r = 0.8, implying that 40% of the collected cells were observed to enter the subsequent mitosis. (b) Experimental (the same as Fig. 2b). (c) Computed for the population characterized in Table 3. Here r = 1.1, implying that 55% of the collected cells were observed in the subsequent mitosis. FIG. 9. Probability density distributions for cell transit times computed for the populations and 3 (-----). (a) G, phase: (b) S plus G , plus M phases: (c) cell characterized in Tables 2 () cycle. experimental data are presented for comparison in Fig. 8b. The probability density functions for transit times and physiological ages are given as the solid lines in Figs 9 and 10 respectively. Since the age distributions of Fig. 10 are much narrower than those of Fig. 4, the computer program described above can approximate the experimental enzyme activity data much more closely than before. Age distributions of the present cell population, of which the solid curves P. G. Steward, L. N. Kapp and R. R. Klevecz + x z .+ Time after " 0 collection ( h r ) W + 2. 2 a (17.25 hr; NC: 0.301 Physiological age interval 10 20 30 40 Physiological age interval FIG. 10. FIG. 1 1 FIG.10. Age density distributions computed for the cell populations characterized in Tables 2 () and 3 (----) at the indicated times after mitotic collection. Illustrated are the critical distributions corresponding to the times of peak enzyme activity (Fig. 11). The fraction of cells not cycling (NC) is indicated for each distribution. The abscissa scale is the physiological age intervals incorporated into the state vector model. FIG.11. (a) Pyruvate kinase activity, E ( t ) (nmol substrate utilized/min/106 cells) as a function of (same as in Fig. 6 ) . or computed for time after mitotic collection determined experimentally (0) the cell population characterized in Tables 2 (----) and 3 (.....), (b) Pyruvate kinase activity, A ( a ) (nmol substrate utilized/min/106 cells in the indicated age interval) as a function of the physiological age intervals as incorporated into the state vector model. This function was used for computing each of the two functions E ( t ) presented in Fig. 1 la. Pyruvate kinase activity in WI-38 cells TABLE Characteristics of cell population 3 3. Mean transit time (hr) 4.2 14.3 18.4 Cell cycle interval G, S plus G, plus M Entire cycle Standard deviation (hr) Coefficient of variation a,, al 0.2 0.8 - a 2 1.5 1.2 I .9 0 - of Fig. 10 are examples, were used to compute the enzyme activities indicated by the dashed line in Fig. 1 l a . This is a reasonably close approximation, particularly for the activity peaks at 13 and 17 hr, to the experimental data (solid line of Fig. l l a ) . The corresponding enzyme activity as a function of physiological age is shown in Fig. 1 lb. Since we believe that deterministic progression of cells through S and G , phases is biologically unrealistic, we re-examined this cell population after introducing a slight dispersion of the age cohort as it transversed these phases. Characteristics of this revised cell population are tabulated in Table 3 and the corresponding computed mitotic index curve is presented in Fig. 8c. This curve appears somewhat broader than the experimental curve (Fig. 8b). The resulting probability density functions for transit times and physiological ages are given as dashed lines in Figs 9 and 10 respectively. Even though the age distributions are only slightly broader than before, the computed enzyme activities as a function of time after mitotic collection, presented as the dotted line in Fig. 1la, fit the experimental data poorly. The enzyme activity as a function of physiological age is again that illustrated in Fig. 1 1b. In order to compare the kinetics of the WI-38 cell populations used in our simulations with the kinetics of this cell line as reported by others, we have analysed, by means of the state vector model, the PLM curve for passage 18 WI-38 cells reported by Macieira-Coelho, Ponten & Philipson (1 966). The results of this analysis are presented in Table 4 and can be compared with the characteristics of our three cell populations tabulated in Tables 1, 2 and 3. Note that for each phase of the cell cycle the coefficient of variation, which is here a measure of the rate at which a synchronous subpopulation will disperse, is greater for the asynchronous population of Macieira-Coelho et al. (1966) than for our synchronized populations. This reinforces our impression that we have not over-estimated the rate of desynchronization for the population characterized in Table 3, and that our experimental enzyme activity data and our theoretical model are prclbably incompatible. TABLE Characteristics of a WI-38 cell population obtained by 4. analysis of a pulse-labelled mitoses curve (see text) Mean transit time (hr) Cell cycle interval G, S plus G, plus M Entire cycle Standard deviation (hr) Coefficient of variation P. G. Steward, L . N . Kapp and R. R. Klevecz DISCUSSION We have described a theoretical analysis of the desynchronization of a mitotically collected WI-38 cell population. It is shown that a hypothetical population which traverses the G, phase in a manner maximally consistent with continuous labelling index data (Fig. 1) is probably incompatible with the mitotic index data (Fig. 2). Presuming pyruvate kinase activity to be a function of physiological age alone, there is no question that the age distributions of this cell population are too broad to be compatible with the experimental pyruvate kinase activity data (Fig. 6). We then identified a hypothetical cell population which is consistent with our pyruvate kinase activity data, and also with our presumption that this activity is a function of only a cell’s physiological age. This was done by reducing the rate of desynchronization through G I barely enough t o provide age distributions which were sufficiently narrow, in the absence of any further desynchronization in S and G, phases, so that enzyme activities of the theoretical and actual populations could agree (Fig. 11, dashed line). Although the experimental mitotic index data (Fig. 8a) is not seriously incompatible with that of this hypothetical population (Table 2 and Fig. 8b), the continuous labelling index for this population appears to increase somewhat more abruptly than the experimental data (Fig. 7). It may seem encouraging that we were nearly successful in identifying a cell population tor which our computer simulations agree with the experimental labelling and mitotic indexes and with the enzyme activity data. However, these simulations incorporate two improbable assumptions. Firstly, it is unlikely that the enzyme activity as a function of cell age, A(a), changes as abruptly as indicated in Fig. 1 Ib. Secondly, it is biologically unrealistic to presume that no stochastic processes to occur in S and G, phases. Unfortunately, introducing even a slight further dispersion of the age cohort as it traverses these phases causes the age distributions to be so broad that they are incompatible with the experimental pyruvate kinase activity data (Fig. 11, dotted line). We conclude that a cell population which is compatible with the pyruvate kinase activity data and is also biologically realistic would have a continuous labelling index curve which rises even more abruptly than that shown in Fig. 7, and is thus inconsistent with the experimental labelling index data. It is not clear, though, that this enzyme activity is also incompatible with the mitotic index data. Our analysis of the PLM curve of Macieira-Coelho et al. (1966), presented in Table 4, indicates that a synchronous subpopulation of her asynchronous WI-38 cells would desynchronize much faster than our hypothetical populations, which yield age distributions already too broad to be consistent with the enzyme activity data. For example, from Tables 3 and 4 it is seen that the population. which in Fig. 1 l a is shown to be incompatible with the enzyme data, has coefficients of variation of 0.35 and 0 . 1 for the G, phase and the cell cycle respectively, compared to 0.59 and 0.18 for the asynchronous population of MacieiraCoelho et al. (1 966). It appears that either our presumption that pyruvate kinase activity is a function only of cell age, or our presumption that cells age in a manner consistent with the state vector model, or both of these, is incompatible with our experimental data as well as with this PLM curve. We believe our experimental techniques and our data t o be valid. The automated synchrony system used here has been previously described (Klevecz & Kapp, 1973). Such a system avoids use of drugs or inhibitors, lowered temperatures and centrifugation, and thus minimizes manipulation of the cells during the synchronizing process. In addition, oscillatory Pyruvate kinase activity in WI-38 cells or multiple peak enzyme patterns, similar t o those reported here for pyruvate kinase. have been reported for lactate dehydrogenase in Chinese hamster cells (Klevecz & Ruddle, 1968). acid phosphatase in mouse cells (Kapp & Okada, 1972), serine dehydratase in hamster cells (Kapp, Remington & Klevecz, 1973), lactate dehydrogenase in human cells (Klevecz & Kapp, 1973) and for other enzymes in other cell lines (Klevecz & Forrest, 1977). In view of this it appears that it may be necessary t o examine the cell cycle concepts incorporated into the theoretical model in order t o explain the discrepancies between the experimental results and the theoretically predicted results. For example, the experimental generation time distribution (Fig. 2b) appears skewed to the left. However, our theoretical model is adapted to the more usual finding that cell transit time distributions are skewed to the right, presumably because a minimum time is required for the biochemical synthesis necessary t o advance to the next cell cycle stage, but a few cells may take much more time than this minimum. Detailed inspection of Fig. 2b reveals what could be bursts of mitoses at about 12, 17 and 20 hr after collection with the overall envelope, resulting in the appearance of a single distribution skewed to the left. Klevecz (1976) has collected some evidence to support his suggestion that cells can enter the S phase only after residing in the G, phase for an integral number of 4 hr intervals. Thus the age distribution late in the cell cycle for a population synchronized in mitosis could appear to be a series of age distributions with cells clustered about modes spaced 4 hr apart. Were this the case, these three bursts of mitoses could be three of these subpopulations passing through mitosis, and this would identify a departure of the behaviour of these cells from the concepts incorporated into the model. Consider our concept of physiological age. We have assumed that physiological age can be defined in terms of a sequence of biochemical activities which progress systematically and irreversibly from one mitosis towards the next. Furthermore, we have assumed that the onset and decline of D N A synthesis, pyruvate kinase activity and mitosis all have discrete positions within this sequence. Alternatively, within each cell there may be more than one sequence of biochemical activities, and progression along these toward mitosis may occur somewhat independently of one another (Kapp & Okada, 1972). Such a possibility identifies a potential ambiguity in the definition of physiological age. If DNA synthesis were in one sequence and pyruvate kinase in another, a cell population could be quite synchronous with respect to pyruvate kinase activity and less so with respect to D N A synthesis. A second possibility is that pyruvate kinase is not a part of any biochemical sequence determining physiological age. It may be a part of a sequence which can be initiated anywhere within a set of physiological age intervals and, once initiated, progression along the sequence toward a pyruvate kinase activity peak may not be tied to progression in physiological age. Essentially, it is assumed in our modelling that a cohort of cells, synchronized with respect to physiological age, will desynchronize at a uniform rate from one physiological age marker t o the next. If there were some factor responsible for communicating, throughout a cell culture, information resulting in a peak of pyruvate kinase activity, then the activiy peak or peaks would not be a function of only the cell’s physiological age. Some evidence indicating something of this nature t o exist for the initiation of D N A synthesis in synchronous cultures has been reported by Dewey, Miller & Nagasawa (1 973), who have shown that conditioned medium from synchronized cells entering the S phase, or the proximity of S phase cells, can cause a synchronized G, population to enter S phase as much as 1.5 t o 2.5 hr earlier than would be expected for an isolated G, population. Similarly, Rao & Johnson (1970) have P. G. Steward, L. N . Kapp and R. R. Klevecz reported that a G, nucleus fused t o an S phase nucleus enters S phase earlier than either two fused G, nuclei or an isolated G, cell. Hormonally regulated enzyme synthesis has been reported which permits the intracellular enzyme activity to be somewhat independent of cell age. Consider, for example, the model for control of tyrosine aminotransferase (TAT) synthesis in cultured hepatoma cells proposed by Tomkins et al. (1972).* Here, translation of the T A T message is suppressed by a labile repressor. The enzyme inducer in this case inactivates the repressor, permitting translation of the already present message. Conversely, the enzyme synthesis is suppressed by withdrawing the inducer, thus reactivating the repressor. If the enzyme itself were sufficiently labile or actively degraded, such a post-transcriptional control mechanism could provide, as a function of time, very sharp peaks in enzyme activity. One way of adapting such concepts to our culture conditions could be the following. Suppose the concentration of a humoral inducer for pyruvate kinase in a synchronized culture increases in an age-dependent fashion. As the synchronized culture ages, the cohort desynchronizes yet, as the inducer concentration in the nutrient medium reaches sufficient levels, the cells begin translating the pyruvate kinase message in synchrony. If feedback exists such that a repressor is activated by a sufficient enzyme concentration, repeating synchronous bursts of enzyme translation could occur. Thus short bursts of enzyme activity could be assayed which would be independent of the culture’s physiological age distribution as defined by D N A synthetic and morphological age markers. We d o not claim that the above outline actually represents the control for pyruvate kinase in synchronous cultures. However, in the context of such post-transcriptional control mechanisms, it is not surprising that the bursts of enzyme activity observed by us d o not represent only age-dependent changes in individual cells. We conclude that pyruvate kinase activity is not a function of physiological cell age alone. Furthermore, we conclude that there exists no unique and non-trivial definition of physiological age. This is true because no matter what sequence of age markers one adopts in order to define physiological age, individuals of the same age can exhibit different biochemical activities and can, therefore, be heterogeneous in their response to some chemical or physical probes. In contrast to this, the usual concept of physiological age is defined in terms of mitosis and the initiation and completion of D N A synthesis, because these markers can be conveniently measured morphologically o r biochemically, and any other physiological function or status must fit as a sequence with these markers. Age cohorts would be expected to desynchronize uniformly and irreversibly from one marker to the next. It is this latter concept of physiological age which is incorporated into our model and most other theoretical models which are currently used to describe the progression of cells through the cell cycle. Although this may be an acceptable concept when applied to some cellular processes, clearly it may be a deceptive oversimplification when applied to others. One common application of theoretical models incorporating the concept of physiological age is in the field of cancer biology. Here one simulates the response of a cell population t o sequential administrations of physical agents (e.g. radiation) or chemical agents (e.g. phasespecific drugs). In this case the problems of applying the concept of physiological age are compounded, since these agents have the sub-lethal effect of altering the ageing rate, and it is likely that this perturbation is greater for some biochemical processes than for others. Physiological age then becomes little more than a construct of the theoretical model since the * By citing this well-known model, we are making no assertion regarding how strictly it conforms to reality. Pyruvate kinase activity in WI-38 cells relationship between cell age (however defined) and cell response to further administrations of cytotoxic agents may well be lost. ACKNOWLEDGMENT This investigation was supported by grant No. 5POlCA13053-05, awarded by the National Cancer Institute, DHEW, and by grant No. H004699, awarded by the National Institutes for Child Health and Human Development, DHEW.

Journal

Cell ProliferationWiley

Published: Nov 1, 1978

There are no references for this article.