Modelling complex populations formed by proliferating,quiescent and quasi-quiescent cells: application to plant root meristems

A proliferating population of cells may be considered complex when its proliferative or growth fraction P is lower than 1 and/or when it is formed by subpopulations with different mean cycle times. The present paper shows that in such complex populations exponential growth is consistent with a steady-state distribution of cells. Obviously, when P=1 then cell distribution is only a function of cell age. An analytical model has been developed to study complex populations including both quiescent fractions formed by cells with unreplicated genome (G(0) cells) and cells with fully duplicated chromosomes (Q(2) cells). The model also considers those quasi-quiescent cells in their last transit through G(1) and S (Q(1) and Q(s) cells) before becoming quiescent. In order to solve the difficulties of a direct analysis of the whole population, its kinetic parameters have been obtained by studying the negative exponential distribution of two subpopulations: one formed by the proliferating cells and another formed by the quasi-quiescent cells. Additionally, the model could be applied when quiescence is initiated at any other cycle phase different from G(1) and G(2), for instance, cells in the process of replicating their DNA or being at any other mitotic phases. The utility of the method was illustrated in populations which constitute the root meristems of both Allium cepa L. and Pisum sativum L. Three facts should be stressed: (1) the method seems to be rather powerful because it can be carried out from different sets of experimentally measured parameters; (2) the rate of division and, therefore, the population doubling time can be easily estimated by this method; and (3) it also allows the determination of the amount of cells that had become quiescent either before they had replicated their DNA (G(0)) or after having completed their replication (Q(2)), as well as those quasi-quiescent cells which are progressing throughout their last pre-replicative and replicative periods (thus Q(1) and Q(s), respectively).     

Family tree analysis of a transformed cell line and the transition probability model for the cell cycle

Variation in intermitotic time between individual cells in culture can be ascribed to the occurrence of random transitions in the cell cycle. We have analysed a family tree of mouse neuroblastoma cells, and observed that variation in difference in intermitotic time between sister cells is smaller than between cousin cells, and this difference is again smaller than between second-cousin and unrelated cells. This observation is incompatible with all transition probability models presented so far. We propose a model for the cell cycle with a single random transition, but with the additional assumption that the (two) system parameters may show variability within the population such that the closer cells are in their relation to each other, the closer their values of the system parameters will be. This model describes correctly the behaviour of the family tree of the cell line and in addition is able to explain why differences in intermitotic time between sister cells are exponentially distributed, while intermitotic times themselves are more or less normally distributed. Methods have been described to quantify the various system parameters.     

Increased voltage-gated potassium conductance during interleukin 2- stimulated proliferation of a mouse helper T lymphocyte clone

Recent work has demonstrated the presence of voltage-gated potassium channels in human peripheral blood T lymphocytes (Matteson, R., and C. Deutsch, 1984, Nature (Lond.), 307:468-471; DeCoursey T. E., T. G. Chandy, S. Gupta, and M. D. Cahalan, 1984, Nature (Lond.), 307:465-468) and a murine cytolytic T-cell clone (Fukushima, Y., S. Hagiwara, and M. Henkart, 1984, J. Physiol., 351:645-656). Using the whole cell patch clamp, we have found a potassium conductance with similar properties in a murine noncytolytic T lymphocyte clone, L2. Under voltage clamp, a step from a holding potential of -70 mV to +50 mV produces an average outward current of 100-150 pA in "quiescent" L2 cells at the end of their weekly maintenance cycle. When these cells are stimulated with human recombinant interleukin 2 (rIL2, 100 U/ml), they grow in size and initiate DNA synthesis at approximately 24 h. Potassium conductance is increased as early as 8 h after stimulation with rIL2 and rises to a level 3-4 times that of excipient controls by 24 h. The level remains elevated through 72 h, but as the cells begin to leave the cell cycle at 72-96 h, the conductance decreases quickly to a value only slightly higher than the initial one. Quinine, a blocker of this conductance, markedly reduces the rate at which L2 cells traverse the cell cycle, while also reducing the rate of stimulated protein synthesis. The regulation of potassium conductance in L2 cells during rIL2-stimulated proliferation suggests that potassium channel function may play a role in support of the proliferative response.     

Is G1 normally distributed?

The normal distribution parameters were calculated for seven sets of cell cycle data of animal cells in culture. These include two sets of intermitotic times (rat S6/1 cells and mouse fibroblast L 929) and five sets of DNA synthesis (two of mouse fibroblast line L 929, two Chinese hamster CHO lines and Syrian hamster line BHK 21/613).It is demonstrated that within the errors involved the experimental data fit the normal distribution adequately. The Smith-Martin model and the normal distribution are briefly discussed in relationship to the initial curvature observed in a semilogarithmic presentation of such data.     

Murine mammary tumour cells in vitro. I. The development of a quiescent state

Three mouse mammary tumour lines (66, 67, and 68H) derived from a single mouse mammary tumour were investigated for their growth kinetics and development of quiescent cells in unfed monolayer cultures. All three lines develop pure quiescent populations when grown in unfed plateau cultures. A dramatic cell-cycle redistribution accompanied the proliferating (P) to quiescent (Q) transition, with the percentage of cells having a G1 DNA content increasing from 50% in the P state to greater than 97% in the Q state. As the cultures progressed from exponential to plateau growth, a decrease of greater than or equal to 50% in cellular RNA was observed in all three lines. This property enables the clear identification of P v. Q cells by flow cytometry using the two-step acridine orange assay. Autoradiographic data verified that these plateau cells were quiescent since less than 2.5% of the cells incorporated [3H]TdR when labelled for approximately two doubling times. Further comparison of the P and Q cells showed that: (a) the Coulter volume of Q cells was approximately half that of P cells in all three lines; (b) viability, as measured by dye exclusion was greater than 95% in all cultures regardless of their proliferative state; and (c) colony-forming ability decreased as the cells entered the quiescent state. In each of these cell lines the development of Q-cell populations was marked by similar changes in all measured parameters. These quiescent tumour cells provide a relatively simple model to evaluate what, if any, important differences exist between the response of P v. Q cells to various therapeutic agents.     

THE CELL CYCLE IN TUMOURS: AN EXAMINATION OF DATA GAINED BY THE TECHNIQUE OF LABELLED MITOSES

Published data from a large series of investigations by the technique of labelled mitoses have been analysed using a process of computer simulation. The results of the analyses of tumour data are discussed, first from the point of view of the quality of simulation that can be achieved and secondly as a review of the extent of our knowledge of the intermitotic time of cells in tumours. Particularly in primary tumors the data are often consistent with a broad distribution of intermitotic times within a tumour and the use of the term 'cell cycle time'may be misleading.     

Murine Mammary Tumour Cells In Vitro. I. the Development of A Quiescent State

Abstract Three mouse mammary tumour lines (66, 67, and 68H) derived from a single mouse mammary tumour were investigated for their growth kinetics and development of quiescent cells in unfed monolayer cultures. All three lines develop pure quiescent populations when grown in unfed plateau cultures. A dramatic cell-cycle redistribution accompanied the proliferating (P) to quiescent (Q) transition, with the percentage of cells having a G₁ DNA content increasing from 50% in the P state to <97% in the Q state. As the cultures progressed from exponential to plateau growth, a decrease of 50% in cellular RNA was observed in all three lines. This property enables the clear identification of P v. Q cells by flow cytometry using the two-step acridine orange assay. Autoradiographic data verified that these plateau cells were quiescent since >2.5% of the cells incorporated [³H]TdR when labelled for approximately two doubling times. Further comparison of the P and Q cells showed that: (a) the Coulter volume of Q cells was approximately half that of P cells in all three lines; (b) viability, as measured by dye exclusion was >95% in all cultures regardless of their proliferative state; and (c) colony-forming ability decreased as the cells entered the quiescent state. In each of these cell lines the development of Q-cell populations was marked by similar changes in all measured parameters. These quiescent tumour cells provide a relatively simple model to evaluate what, if any, important differences exist between the response of P v. Q cells to various therapeutic agents.     

Analysis of the growth factor requirements for stimulation of WI-38 cells after extended periods of density-dependent growth arrest

When cultures of WI-38 human diploid fibroblasts reach high cell densities, they cease to proliferate and enter a viable state of quiescence. WI-38 cells can remain in this quiescent state for long periods of time; however, the longer the cells remain growth arrested, the more time they require to leave G0, progress through G1, and enter S after stimulation with fresh serum. The experiments presented here compare the response of long-term quiescent WI-38 cells (stimulated 26 days after plating) and short-term quiescent WI-38 cells (stimulated 12 days after plating) to treatment with a variety of individual purified growth factors instead of whole serum. Our results show that the qualitative and quantitative growth factor requirements necessary to stimulate G1 progression and entry into S were the same for both short- and long-term quiescent WI-38 cells, in that the same defined medium (supplemented with epidermal growth factor [EGF], recombinant human insulin-like growth factor 1 [IGF-1], and dexamethasone [DEX]) stimulated both populations of cells to proliferate with the same kinetics and to the same extent as serum. However, the long-term quiescent WI-38 cells were found to exhibit a difference in the time during which either serum or these individual growth factors were required to be present during the prereplicative period. We believe that this difference may be the cause of the prolongation of the prereplicative phase after stimulation of long-term density-arrested WI-38 cells.     

Cells regulate their proliferation through alterations in transition probability

The proliferation of 3T3, 3T6 and SV3T3 cells was examined by time lapse cinephotography under a number of different growth conditions. It was found that the frequency distributions of intermitotic times of cells with widely different proliferation rates are qualitatively and quantitatively explained by the transition probability model of the cell cycle (Smith and Martin, '73). The behaviour of quiescent cells was characterized by very low values of the transition probability. No "out of cycle" or GO compartment of cells was detectable. From a consideration of these results and those in the literature it appears that the rate of cell proliferation is determined by the value of the "transition probability" (P), and that it is the biochemical manifestation of this parameter that regulates cell growth in vitro and in vivo.     

Time of c-fos and c-myc expression in human diploid fibroblasts stimulated to proliferate after prolonged periods in quiescence

When human diploid fibroblasts such as WI-38 cells become crowded, they enter a viable state of quiescence (G0) in which they can remain for prolonged periods of time. These quiescent cells can be induced to re-enter the cell cycle by addition of fresh serum. However, cells held in G0 for long periods before stimulation require more time to enter DNA synthesis as compared to cells held in a quiescent state for short periods. We have used this model system to determine if a close temporal coupling exists between the time of expression of two proto-oncogenes associated with cell growth, c-fos and c-myc, and the time of entry into DNA synthesis. WI-38 cells were stimulated to enter DNA synthesis by the addition of fresh culture medium and serum at various lengths of time after plating, ranging from 7 to 34 days. At hourly intervals thereafter, cells were harvested and total RNA was isolated. These samples were then analyzed by RNase protection assay to determine the levels of c-fos and c-myc mRNA. Our results show that the time and pattern of c-fos and c-myc mRNA accumulation after stimulation is determined only by the time which the cells are treated with serum even when they exhibit a 19-h delay in the entry into DNA synthesis. In all of our experiments, c-fos could be detected 0.5 h after stimulation and remained detectable for approximately 2 h. Likewise, the peak of c-myc accumulation occurred at about 3 h after serum addition, regardless of how long it took to initiate DNA synthesis. These results suggest that the time of c-fos and c-myc induction clearly is not the only factor which determines the length of the prereplicative period and thus the ultimate time of initiation of DNA synthesis.     

Contact-inhibition-induced quiescent state is marked by intense nuclear expression of statin

Statin, a nuclear protein of 57,000 daltons, is found in in vitro aged, nonproliferating human fibroblasts but not in their young, replicating counterparts or transformed derivatives; it is also found in the nuclei of young fibroblasts when their growth is arrested but rapidly disappears from the cells once the restriction to growth is removed. We reported earlier that as cells leave the quiescent state, the loss of statin from the nucleus precedes the initiation of DNA synthesis; here we report that in a confluent culture, as cells leave the traverse of the replicative cycle and assume the quiescent phenotype, statin is not expressed maximally until total contact inhibition of growth is achieved. This full manifestation of statin occurs in monolayer culture with cells forming the typical swirling pattern and fibronectin organized into large intercellular cables. The late expression of statin in cells approaching the quiescent state is also verified biochemically by immunoblotting assays. The present results, taken together with those reported earlier, indicate that the nuclear appearance of statin occurs only after the complete cessation of DNA synthesis and that the full manifestation of this protein can be used as a marker for the G0 quiescent state.     

Antigen-driven T-cell turnover

A mathematical model is developed to characterize the distribution of cell turnover rates within a population of T lymphocytes. Previous models of T-cell dynamics have assumed a constant uniform turnover rate; here we consider turnover in a cell pool subject to clonal proliferation in response to diverse and repeated antigenic stimulation. A basic framework is defined for T-cell proliferation in response to antigen, which explicitly describes the cell cycle during antigenic stimulation and subsequent cell division. The distribution of T-cell turnover rates is then calculated based on the history of random exposures to antigens. This distribution is found to be bimodal, with peaks in cell frequencies in the slow turnover (quiescent) and rapid turnover (activated) states. This distribution can be used to calculate the overall turnover for the cell pool, as well as individual contributions to turnover from quiescent and activated cells. The impact of heterogeneous turnover on the dynamics of CD4(+) T-cell infection by HIV is explored. We show that our model can resolve the paradox of high levels of viral replication occurring while only a small fraction of cells are infected.     

Expression of c-fos in NIH3T3 cells is very low but inducible throughout the cell cycle.

It has previously been shown that the c-fos proto-oncogene is rapidly and transiently induced following growth factor stimulation of quiescent NIH3T3 mouse fibroblasts. To investigate a possible role of c-fos in growth control mechanisms we have studied its expression and inducibility during the NIH3T3 cell cycle. Two major conclusions can be drawn from this analysis. First, expression of c-fos is not cell cycle-regulated, and is barely detectable in all phases of the cycle. Second, cells at different stages of the cell cycle (except for mitosis) are as sensitive to c-fos induction by growth factors as quiescent cells. These observations suggest that induction of the c-fos gene does not play a role during the continuous cycling of NIH3T3 cells, but they are fully compatible with the hypothesis that a function of c-fos may be associated with the induction of competence in fibroblasts. Through such a function c-fos may contribute to moving cells out of the quiescent state.     

Matrix simulation of duodenal crypt cell kinetics. I. The steady state.

Steady state crypt cell kinetics have been simulated using matrix algebra. The model crypt cell population is distributed through two proliferation compartments (P1 and P2) and a quiescent state (Q). Under steady state conditions half the daughter cells produced on completion of P1 enter G1 of P2 and half enter G1 of P1. Both P2 daughter cells enter Q. Cells in Q are non-dividing but retain the potential to divide. On completion of Q, cells lose the potential to divide and move up onto the villi. The model has been developed by simultaneously simulating the following biological data: (1) the per cent labeled mitosis (PML) curve, (2) the number of labeled cells per crypt as a function of time following an injection of 3H-thymidine, and (3) the total number of cells per crypt.     

DURATION OF CELL CYCLES IN CULTURED ROOTS OF CONVOLVULUS

The durations of the cell cycle in physiologically different regions of the meristem of cultured roots of Convolvulus arvensis were determined by the metaphase-accumulation technique involving colchicine. The cell cycle in the root cap increases from 13 hr in the actively dividing initials of the first tier to 155 hr in the slowly dividing initials of tiers 2–4 to an indeterminate value for derivatives of the initials in the root cap columella. The cycle times for the cells of the central cylinder and cortex are 21 and 27 hr, respectively. The cells of the quiescent center have a cycle of an estimated 420 hr. The duration of the cell cycle in these different regions is discussed in relation to the increased duration of G₁ in slowly or non-dividing cells. The possible regulation of cell division by the synthesis of a cell-division factor in the quiescent center is also discussed.     

Selective synchrony of cells of differing cycle times

If a growth inhibiting agent is applied periodically to a system of proliferating cells, travelling density waves in maturity space appear. These are synchrony waves; their group velocity depends on the average cycle time of the cells. If the cycle times of two types of cells differ significantly, only the type whose intermitotic period is close to the period at which the growth inhibitor is being applied comes into synchrony. A mathematical model is solved numerically to show the effect.     

Murine mammary tumour cells in vitro. II. Recruitment of quiescent cells

The development of a pure quiescent (Q) tumour cell population can be induced in three mouse mammary tumour lines (66, 67 and 68H) by nutrient deprivation. When these Q cells were removed from nutrient-deprived cultures and replated in fresh medium at a lower cell concentration within 72 hr of entering quiescence virtually all of the Q cells could re-enter the proliferating (P) state. This recruitment was characterized by an increase in cell volume, an increase in total cellular RNA, and a resumption of cell division. The length of the Q to P transition varied among the three cell lines and the depth of the quiescent state depended on the amount of time the cells had been quiescent. Once re-entry into the P compartment was completed, cell-cycle times, as estimated by the culture doubling time, were the same as the cells that had not entered the Q state, however, after 72 hr in quiescence, not all of the 66 cells could reattach after trypsinization and of those that could reattach approximately equal to 50% were incapable of either increasing their RNA levels to that of proliferating G1 cells or entering S. Clonogenicity of the nutrient-deprived Q cells in these lines decreases exponentially from time the cells enter quiescence with approximate half-times of 32, 34, and 96 hr for the 66, 68H and 67 cells, respectively. Since clonogenicity was already declining at a time when all the Q cells could re-enter the P compartment, the ability of a Q cell to form a colony is not determined solely by its capacity to re-enter the proliferating compartment.