Analysis of growth kinetics by division tracking

Cell division tracking using fluorescent dyes, such as carboxyfluorescein diacetate succinimidyl ester, provides a unique opportunity for analysis of cell growth kinetics. The present review article presents new methods for enhancing resolution of division tracking data as well as derivation of quantities that characterize growth from time-series data. These include the average time between successive divisions, the proportion of cells that survive and the proliferation per division. The physical significance of these measured quantities is interpreted by formulation of a two-compartment model of cell cycle transit characterized by stochastic and deterministic cell residence times, respectively. The model confirmed that survival is directly related to the proportion of cells that enter the next cell generation. The proportion of time that cells reside in the stochastic compartment is directly related to the proliferation per generation. This form of analysis provides a starting point for more sophisticated physical and biochemical models of cell cycle regulation.     

Growth control of normal and transformed cells

Both serum factors and protein synthesis are required for normal cell growth. Swiss 3T3 cells require the serum growth factors insulin and EGF (epidermal growth factor) during the initial part of the G₁ period, until they pass a restriction point about 2 h before the initiation of DNA synthesis. Concentration of cycloheximide that inhibit protein synthesis by as much as 70% dramatically lengthen the cell cycle before the restriction point, while the cell cycle after the restriction point remains nearly constant. These results are consistent with a model in which labile proteins are required for transit of cells past the serum-sensitive restriction point. The relation of these findings to the growth control of transformed cells is discussed.     

Regulation of the G1 phase of the mammalian cell cycle

In any multi-cellular organism,the balance between cell division and cell death maintains a constant cell number.Both cell division cycle and cell death are highly regulated events.Whether the cell will proceed through the cycle or not,depends upon whether the conditions required at the checkpoints during the cycle and fulfilled.In higher eucaryotic cells,such as mammalian cells,signals that arrest the cycle usually act at a G1 checkpoint.Cells that pass this restriction point are committed to complete the cycle.Regulation of the G1 phase of the cell cycle is extremely complex and involves many different families of proteins such as retinoblastoma family,cyclin dependent kinases,cyclins,and cyclin kinase inhibitors.     

Stochastic E2F Activation and Reconciliation of Phenomenological Cell-Cycle Models

The transition of the mammalian cell from quiescence to proliferation is a highly variable process. Over the last four decades, two lines of apparently contradictory, phenomenological models have been proposed to account for such temporal variability. These include various forms of the transition probability (TP) model and the growth control (GC) model, which lack mechanistic details. The GC model was further proposed as an alternative explanation for the concept of the restriction point, which we recently demonstrated as being controlled by a bistable Rb-E2F switch. Here, through a combination of modeling and experiments, we show that these different lines of models in essence reflect different aspects of stochastic dynamics in cell cycle entry. In particular, we show that the variable activation of E2F can be described by stochastic activation of the bistable Rb-E2F switch, which in turn may account for the temporal variability in cell cycle entry. Moreover, we show that temporal dynamics of E2F activation can be recast into the frameworks of both the TP model and the GC model via parameter mapping. This mapping suggests that the two lines of phenomenological models can be reconciled through the stochastic dynamics of the Rb-E2F switch. It also suggests a potential utility of the TP or GC models in defining concise, quantitative phenotypes of cell physiology. This may have implications in classifying cell types or states.     

细胞历经周期的随机模型

本文提出了一类细胞历经周期的随机模型。在证明此模型下细胞出生大小渐近稳定分布的存在唯一性的同时证明了Tyson(1986)的一个猜测。此外,本文还考察了稳定分布的求解问题以及细胞历经周期的特征性质,并与基于实验数据的估计进行比较,结果表明,本模型与实际情形吻合较好。     

Equilibrium Between Cell Division and Apoptosis in Immortal Cells as an Alternative to the G1 Restriction Mechanism in Mammalian Cells

Starvation arrests cultured mammalian cells in the G1 restriction point of the cell cycle, whereas cancer cells generally lose the regulatory control of the cell cycle. Human lymphocytes, infected with Epstein-Barr virus (EBV), also lose their cell cycle control and produce immortal lymphoblastoid cell lines. We show that during starvation, EBV-lymphoblasts override the cell cycle arrest in the G1 restriction point and continue cell division. Simultaneously, starvation activates apoptosis in an approximately half of the daughter cells in each cell generation. Continuos cell division and partial removal of cells by apoptosis results in stabilization of viable cell numbers, where a majority of viable cells are in the G1 phase of the cell cycle. In contrast to starvation, anticancer drug etoposide activates apoptosis indiscriminately in all EBV-lymphoblasts and convertes all the viable cells into apoptotic. We conclude that the removal of surplus cells by apoptosis may represent a survival mechanism of transformed (i.e. cancer) cell population in nutrient restricted conditions, whereas non-transformed mammalian cells are arrested in the G1 restriction point of the cell cycle.     

Equilibrium between cell division and apoptosis in immortal cells as an alternative to the G1 restriction mechanism in mammalian cells

Starvation arrests cultured mammalian cells in the G(1) restriction point of the cell cycle, whereas cancer cells generally lose the regulatory control of the cell cycle. Human lymphocytes, infected with Epstein-Barr virus (EBV), also lose their cell cycle control and produce immortal lymphoblastoid cell lines. We show that during starvation, EBV-lymphoblasts override the cell cycle arrest in the G(1) restriction point and continue cell division. Simultaneously, starvation activates apoptosis in an approximately half of the daughter cells in each cell generation. Continuos cell division and partial removal of cells by apoptosis results in stabilization of viable cell numbers, where a majority of viable cells are in the G(1) phase of the cell cycle. In contrast to starvation, anticancer drug etoposide activates apoptosis indiscriminately in all EBV-lymphoblasts and convertes all the viable cells into apoptotic. We conclude that the removal of surplus cells by apoptosis may represent a survival mechanism of transformed (i.e., cancer) cell population in nutrient restricted conditions, whereas nontransformed mammalian cells are arrested in the G(1) restriction point of the cell cycle.     

A simple model of the growth of phytoplankton populations in light/dark cycles

Phytoplankton populations have been shown to be entrained byalternating periods of light and darkness in natural watersas well as in laboratory cultures. A simple model for the growthof such populations, as reflected by cell division, is presentedhere. The model takes as its structural unit the single cell,using Spudich and Sager's transition point hypothesis for thecoupling between received light and cell cycle progression.A stochastic component is also included to account for cell-to-cellvariability. The model predicts that the characteristics ofcell division patterns in populations entrained by photocyclesdepends mainly on the position of the transition point withinthe cell cycle, rather than on the characteristics of the photocyclicregime. The model simulates successfully the major featuresof observed division patterns of several phytoplankton species.In addition, the model can be used to predict division patternsin high frequency photocycles and during transients inducedby shifts in light regime. Under these conditions, the simulatedpatterns are also consistent with the hypothesis of a circadianclock controlled cell cycle, except in the case of free runningtransients. ¹Present address: Station Biologique Roscoff, CNRS, Roscoff29211, France     

Control models of cell cycle transit, exit, and arrest

Several distinct cycles mediate the events which occur between one cell division and the next. In micro-organisms there are generally two cycles. One governs biomass growth, the other DNA synthesis and cell division. In higher eukaryotes there can be as many as four distinct cycles, with growth, DNA synthesis, cell division, and nuclear division each possessing its own functional sequence of events. These cycles are controlled and coordinated by several different regulatory mechanisms. Restriction points are specific steps in the cycle whose completion is governed by external regulatory agents. One set of restriction points requires nutrients and growth hormones for step completion. Another set serves as receptors for differentiating factors which cause cycle arrest and initiate cellular differentiation. There is currently a debate as to whether restriction point inhibition involves permanent arrest or temporary arrest with a stochastic arrested-state residence time controlled by a transition probability mechanism. Tissue sizing is a process of negative feedback inhibition mediated by intercellular communication via cell surface contact and the extracellular matrix. Sizers commonly operate throughout broad portions of the cycle and appear to cause a slowing of cycle transit velocity rather than arrest. Sizers are probably the major regulatory mechanism for cell growth under conditions of nutrient and growth factor excess. They also generate compensatory proliferation following wounding or cell death. A growing body of evidence suggests that both the transit velocity, with which cells move through their several cycles, and the coordination of the cycles are controlled by intracellular regulatory mechanisms which behave as biological oscillators. These oscillators trigger complex sequences of events such as DNA synthesis and cell division.     

A model for restriction point control of the mammalian cell cycle

Inhibition of protein synthesis by cycloheximide blocks subsequent division of a mammalian cell, but only if the cell is exposed to the drug before the "restriction point" (i.e. within the first several hours after birth). If exposed to cycloheximide after the restriction point, a cell proceeds with DNA synthesis, mitosis and cell division and halts in the next cell cycle. If cycloheximide is later removed from the culture medium, treated cells will return to the division cycle, showing a complex pattern of division times post-treatment, as first measured by Zetterberg and colleagues. We simulate these physiological responses of mammalian cells to transient inhibition of growth, using a set of nonlinear differential equations based on a realistic model of the molecular events underlying progression through the cell cycle. The model relies on our earlier work on the regulation of cyclin-dependent protein kinases during the cell division cycle of yeast. The yeast model is supplemented with equations describing the effects of retinoblastoma protein on cell growth and the synthesis of cyclins A and E, and with a primitive representation of the signaling pathway that controls synthesis of cyclin D.     

Dynamics of the cell cycle: checkpoints, sizers, and timers

We have developed a generic mathematical model of a cell cycle signaling network in higher eukaryotes that can be used to simulate both the G1/S and G2/M transitions. In our model, the positive feedback facilitated by CDC25 and wee1 causes bistability in cyclin-dependent kinase activity, whereas the negative feedback facilitated by SKP2 or anaphase-promoting-complex turns this bistable behavior into limit cycle behavior. The cell cycle checkpoint is a Hopf bifurcation point. These behaviors are coordinated by growth and division to maintain normal cell cycle and size homeostasis. This model successfully reproduces sizer, timer, and the restriction point features of the eukaryotic cell cycle, in addition to other experimental findings.     

Stochastic exit from mitosis in budding yeast

Unlike many mutants that are completely viable or inviable, the CLB2-dbΔ clb5Δ mutant of Saccharomyces cerevisiae is inviable in glucose but partially viable on slower growth media such as raffinose. On raffinose, the mutant cells can bud and divide but in each cycle there is a chance that a cell will fail to divide (telophase arrest), causing it to exit the cell cycle. This effect gives rise to a stochastic phenotype that cannot be explained by a deterministic model. We measure the inter-bud times of wild type and mutant cells growing on raffinose and compute statistics and distributions to characterize the mutant’s behavior. We convert a detailed deterministic model of the budding yeast cell cycle to a stochastic model and determine the extent to which it captures the stochastic phenotype of the mutant strain. Predictions of the mathematical model are in reasonable agreement with our experimental data and suggest directions for improving the model. Ultimately, the ability to accurately model stochastic phenotypes may prove critical to understanding disease and therapeutic interventions in higher eukaryotes.     

A mathematical model for analysis of the cell cycle in cell lines derived from human tumors

The growth of human cancers is characterised by long and variable cell cycle times that are controlled by stochastic events prior to DNA replication and cell division. Treatment with radiotherapy or chemotherapy induces a complex chain of events involving reversible cell cycle arrest and cell death. In this paper we have developed a mathematical model that has the potential to describe the growth of human tumour cells and their responses to therapy. We have used the model to predict the response of cells to mitotic arrest, and have compared the results to experimental data using a human melanoma cell line exposed to the anticancer drug paclitaxel. Cells were analysed for DNA content at multiple time points by flow cytometry. An excellent correspondence was obtained between predicted and experimental data. We discuss possible extensions to the model to describe the behaviour of cell populations in vivo.     

Estimating the variation in S phase duration from flow cytometric histograms

A stochastic model for interpreting BrdUrd DNA FCM-derived data is proposed. The model is based on branching processes and describes the progression of the DNA distribution of BrdUrd-labelled cells through the cell cycle. With the main focus on estimating the S phase duration and its variation, the DNA replication rate is modelled by a piecewise linear function, while assuming a gamma distribution for the S phase duration. Estimation of model parameters was carried out using maximum likelihood for data from two different cell lines. The results provided quite a good fit to the data, suggesting that stochastic models may be a valuable tool for analysing this kind of data.     

Stochastic exit from mitosis in budding yeast: Model predictions and experimental observations

Unlike many mutants that are completely viable or inviable, the CLB2-dbΔ clb5Δ mutant of Saccharomyces cerevisiae is inviable in glucose but partially viable on slower growth media such as raffinose. On raffinose, the mutant cells can bud and divide but in each cycle there is a chance that a cell will fail to divide (telophase arrest), causing it to exit the cell cycle. This effect gives rise to a stochastic phenotype that cannot be explained by a deterministic model. We measure the interbud times of wild-type and mutant cells growing on raffinose and compute statistics and distributions to characterize the mutant''s behavior. We convert a detailed deterministic model of the budding yeast cell cycle to a stochastic model and determine the extent to which it captures the stochastic phenotype of the mutant strain. Predictions of the mathematical model are in reasonable agreement with our experimental data and suggest directions for improving the model. Ultimately, the ability to accurately model stochastic phenotypes may prove critical to understanding disease and therapeutic interventions in higher eukaryotes.Key words: stochastic phenotype, mitotic exit, non-genetic variability, cell cycle modeling, computational biology, stochastic modeling, deterministic modeling