A checkpoint-oriented cell cycle simulation model

Modeling and in silico simulations are of major conceptual and applicative interest in studying the cell cycle and proliferation in eukaryotic cells. In this paper, we present a cell cycle checkpoint-oriented simulator that uses agent-based simulation modeling to reproduce the dynamics of a cancer cell population in exponential growth. Our in silico simulations were successfully validated by experimental in vitro supporting data obtained with HCT116 colon cancer cells. We demonstrated that this model can simulate cell confluence and the associated elongation of the G1 phase. Using nocodazole to synchronize cancer cells at mitosis, we confirmed the model predictivity and provided evidence of an additional and unexpected effect of nocodazole on the overall cell cycle progression. We anticipate that this cell cycle simulator will be a potential source of new insights and research perspectives.     

A model with 'growth retardation' for the kinetic heterogeneity of tumour cell populations

In the present paper we propose a continuous cell population model based on Shackney's idea of growth retardation. Cells are characterized by two state variables: the cell maturity x, 0 < or = x < or = 1, and a state variable T that identifies the rate of maturation along cell cycle. During their life span, cells can change T at random by jump transitions to T values corresponding to slower maturation rates, while at each jump the maturity x is conserved. Both the time evolution of the population and the exponential stationary solution are numerically computed. The distribution of the cell cycle transit time in asynchronous exponential growth is investigated by Monte Carlo simulation. An approximated formula for the distribution of cell cycle time is also provided.     

A stochastic model of a cell population with quiescence

A cell population in which cells are allowed to enter a quiescent (nonproliferating) phase is analyzed using a stochastic approach. A general branching process is used to model the population which, under very mild conditions, exhibits balanced exponential growth. A formula is given for the asymptotic fraction of quiescent cells, and a numerical example illustrates how convergence toward the asymptotic fraction exhibits a typical oscillatory pattern. The model is compared with deterministic models based on semigroup analysis of systems of differential equations.     

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.     

The cell cycle and development: redundant roles of cell cycle regulators

The existence of families of cell cycle regulators reflects the need by a developing organism to precisely control proliferation of its cells and also suggests that family members may play redundant roles. Recent advances have shown redundancy to be a theme in development.     

Linking cell division to cell growth in a spatiotemporal model of the cell cycle

Cell division must be tightly coupled to cell growth in order to maintain cell size, yet the mechanisms linking these two processes are unclear. It is known that almost all proteins involved in cell division shuttle between cytoplasm and nucleus during the cell cycle; however, the implications of this process for cell cycle dynamics and its coupling to cell growth remains to be elucidated. We developed mathematical models of the cell cycle which incorporate protein translocation between cytoplasm and nucleus. We show that protein translocation between cytoplasm and nucleus not only modulates temporal cell cycle dynamics, but also provides a natural mechanism coupling cell division to cell growth. This coupling is mediated by the effect of cytoplasmic-to-nuclear size ratio on the activation threshold of critical cell cycle proteins, leading to the size-sensing checkpoint (sizer) and the size-independent clock (timer) observed in many cell cycle experiments.     

Globally asymptotic properties of proliferating cell populations

This paper presents a general model for the cell division cycle in a population of cells. Three hypotheses are used: (1) There is a substance (mitogen) produced by cells which is necessary for mitosis; (2) The probability of mitosis is a function of mitogen levels; and (3) At mitosis each daughter cell receives exactly one-half of the mitogen present in the mother cell. With these hypotheses we derive expressions for the and curves, the distributions of mitogen and cell cycle times, and the correlation coefficients between mother-daughter (_md) and sister-sister (_ss) cell cycle times.The distribution of mitogen levels is shown to be given by the solution to an integral equation, and under very mild assumptions we prove that this distribution is globally asymptotically stable. We further show that the limiting logarithmic slopes of (t) and (t) are equal and constant, and that _md0 while _ss0. These results are in accord with the experimental results in many different cell lines. Further, the transition probability model of the cell cycle is shown to be a simple special case of the model presented here.     

Changes of Escherichia coli cell cycle parameters during fast growth and throughout growth with limiting amounts of thymine

It is generally accepted that during fast growth of Escherichia coli, the time (D) between the end of a round of DNA replication and cell division is constant. This concept is not consistent with the fact that average cell mass of a culture is an exponential function of the growth rate, if it is also accepted that average cell mass per origin of DNA replication (M_i) changes with growth rate and negative exponential cell age distribution is taken into account. Data obtained from cell composition analysis of E. coli OV-2 have shown that not only (M_i) but also D varied with growth rate at generation times () between 54 and 30 min. E. coli OV-2 is a thymine auxotroph in which the replication time (C) can be lengthened, without inducing changes in , by growth with limiting amounts of thymine. This property has been used to study the relationship between cell size and division from cell composition measurements during growth with different amounts of thymine. When C increased, average cell mass at the end of a round of DNA replication also increased while D decreased, but only the time lapse (d) between the end of a replication round and cell constriction initiation appeared to be affected because the constriction period remained fairly constant. We propose that the rate at which cells proceed to constriction initiation from the end of replication is regulated by cell mass at this event, big cells having shorter d times than small cells.Abbreviations OD₄₅₀ and OD₆₃₀ Optical density at a given wavelength in nm Dedicated to Dr. John Ingraham to honor him for his many contributions to Science     

Importance of polyamines in cell cycle kinetics as studied in a transgenic system

Polyamines are organic cations, which are considered essential for normal cell cycle progression. This view is based on results from numerous studies using a variety of enzyme inhibitors or polyamine analogues interfering with either the metabolism or the physiological functions of the polyamines. However, the presence of non-specific effects may be hard to rule out in such studies. In the present study, we have for the first time used a transgenic cell system to analyze the importance of polyamines in cell growth. We have earlier shown that expression of trypanosomal ODC in an ODC-deficient variant of CHO cells (C55.7) supported growth of these otherwise polyamine auxotrophic cells. However, one of the transgenic cell lines grew much slower than the others. As shown in the present study, the level of ODC activity was much lower in these cells, and that was reflected in a reduction of cellular polyamine levels. Analysis of cell cycle kinetics revealed that reduction of growth was correlated to prolongation of the G₁, S, and G₂ + M phases in the cells. Providing exogenous putrescine to the cells resulted in a normalization of polyamine levels as well as cell cycle kinetics indicating a causal relationship.     

A simple time delay model for eukaryotic cell cycle

We propose a seven variable model with time delay in one of the variables for the cell cycle in higher eukaryotes. The model consists of four important phosphorylation-dephosphorylation (P-D) cycles that govern the cell cycle, namely Pre-MPF-MPF, Cdc25P-Cdc25, Wee1P-Wee1 and APCP-APC. Other variables are cyclin, free cyclin dependent kinase (Cdk) and mass. The mass acts as a G2/M checkpoint and the checkpoint is represented by a saddle node loop bifurcation. The key feature of the model is that a time lag has been introduced in the activation of anaphase promoting complex (APC) by maturation promoting factor (MPF). This is effected by treating MPF as a time-delayed variable in the activation step of APC. The time lag acts as a spindle checkpoint. Absence of time delay induces a bistability in our model. Time delay also brings about variability in G1 phase timings. The model also reproduces the mutant phenotype experiments on wee1 cells. Stochasticity has been introduced in the model to simulate the dependence of the cycle time on cell birth length. Mutant phenotypes in the stochastic model reproduce the experimental observations better than the deterministic model.     

Asymptotic behavior of nonlinear semigroup describing a model of selective cell growth regulation

A new scheme of regulation of cell population growth is considered, called the selective growth regulation. The principle is that cells are withdrawn from proliferation depending on their contents of certain biochemical species. The dynamics of the cell population structured by the contents of this species is described by the functional integral equation model, previously introduced by the authors. The solutions of the model equations generate a semigroup of nonlinear positive operators. The main problem solved in this paper concerns stability of the equilibria of the model. This requires stating and proving of an original abstract result on the spectral radius of a perturbation of a semigroup of positive linear operators. Biological applications are discussed.     

On a two-phase size-structured population model with infinite states-at-birth and distributed delay in birth process

In this paper we study the two-phase size-structured population model with infinite states-at-birth and distributed delay in birth process. The model distinguishes individuals by two different status: the ‘reproductive’ stage and the ‘nonreproductive’ stage. We establish the well-posedness for this model and show that the solution of this model exhibits asynchronous exponential growth by means of semigroups. We also consider a special case in which the individuals in the ‘reproductive’ stage and the ‘nonreproductive’ stage have the same growth rates and give a comparison between this two-phase model with the classical one-phase model.     

Stochastic Petri Net extension of a yeast cell cycle model

This paper presents the definition, solution and validation of a stochastic model of the budding yeast cell cycle, based on Stochastic Petri Nets (SPN). A specific family of SPNs is selected for building a stochastic version of a well-established deterministic model. We describe the procedure followed in defining the SPN model from the deterministic ODE model, a procedure that can be largely automated. The validation of the SPN model is conducted with respect to both the results provided by the deterministic one and the experimental results available from literature. The SPN model catches the behavior of the wild type budding yeast cells and a variety of mutants. We show that the stochastic model matches some characteristics of budding yeast cells that cannot be found with the deterministic model. The SPN model fine-tunes the simulation results, enriching the breadth and the quality of its outcome.     

病毒感染对细胞周期调控影响的研究进展

大量研究表明,病毒感染细胞时,病毒编码的蛋白或DNA可以扰乱细胞周期通路:促进细胞向S期转化或者使细胞静息于G2/M期。在细胞内,细胞周期的调控机制十分复杂,其包含了由DNA损伤导致的细胞通路活化及其他方式。关于病毒对细胞周期的调控方式及细胞周期的改变对于病毒感染的研究已取得一定进展。对于病毒的此类研究可以揭示细胞活动中的关键调控因子及细胞周期检查点的具体分子机理。对病毒调控宿主细胞周期以达到自身最大化复制的机理进行综述。     

Asymptotic stability in a generalized probabilistic/deterministic model of the cell cycle

A new mathematical model of the cell cycle is presented which generalizes the probabilistic/deterministic model of Lasota-Mackey [1] and the tandem model of Tyson and Hannsgen [7]. By the use of a multiplicative (exponential) Lyapunov function a stability theorem is proved, parallel to the results of Lasota-Mackey. Some open problems related to the tandem model are also solved.     

Stimulation of quiescent cells by individual polypeptide growth factors is limited to one cell cycle

Since little is known about the function of polypeptide growth factors as regulators of multiple cell cycles, we compared the ability of FGF1, PDGF-AB and serum to induce a second round of DNA synthesis in Swiss 3T3 cells previously exposed to either FGF1, PDGF-AB or serum during the first cell cycle using [14C]- and [3H]thymidine in a double labeling system to distinguish between the first and second cell cycles. Surprisingly, we observed that cells exposed to either FGF1 or PDGF-AB in the first cell cycle were unable to synthesize DNA in response to FGF1 or PDGF-AB in the second cell cycle; yet these cells responded well to serum as a second cycle mitogen. Interestingly, while cells exposed to either FGF1 or PDGF-AB in the second cycle displayed normal receptor-mediated signaling and expressed cyclin D and E, they, like senescent fibroblasts and endothelial cells, failed to express cyclin A, and the continuous exposure of cells to either FGF1 or PDGF-AB resulted in a decrease in the kinase activity of the cyclin E/cdk2 complex. In addition, an increased association of this complex was observed with p21 CIP in an FGF1-dependent manner as well as with p27 KIP in a PDGF-AB-dependent manner. Lastly, the downregulation of p21 expression using an antisense strategy was able to partially rescue the replicative response of Swiss 3T3 cells to FGF1 in the second cycle. These data suggest that (i) FGF1 and PDGF-AB may limit their mitogenic effect to a single cell cycle, (ii) entry into the second round of replication is serum dependent and (iii) the self-limiting nature of FGF1 and PDGF-AB correlates with the accumulation of the cdk inhibitors, p21 and p27, respectively.     

Cell growth and division: a deterministic/probabilistic model of the cell cycle

A model of the cell cycle, incorporating a deterministic cell-size monitor and a probabilistic component, is investigated. Steady-state distributions for cell size and generation time are calculated and shown to be globally asymptotically stable. These distributions are used to calculate various statistical quantities, which are then compared to known experimental data. Finally, the results are compared to distributions calculated from a Monte-Carlo simulation of the model.     

The cell cycle—A cautionary note

Abstract Cell-cycle studies, largely conducted unsystematically in undefined conditions for growth in batch synchrony cultures, generally assume a fixed intrinsic pattern of behavior for the cell cycle that ignores the variable phenotypic activity of cells experienced in practice. However, cell-cycle studies conducted systematically in continuous cultures under defined growth conditions reveal a flexibility in cell performance. It is suggested that batch-synchrony studies should be conducted under several different growth conditions to establish the variability of their presently assumed fixed cell-cycle behaviors.     

Weak cell cycle dependency but strong distortive effects of transfection with Lipofectamine 2000 in near‐physiologically synchronized cell culture

Previously, we reported a method to generate and validate cell cycle‐synchronized cultures of multiple mammalian suspension cell lines under near‐physiological conditions. This method was applied to elucidate the putative interdependencies of the cell cycle and recombinant protein expression in the human producer cell line HEK293s using Lipofectamine 2000 and the reporter plasmid pcDNA3.3 enhanced green fluorescent protein, destabilized using PEST sequence. A population‐resolved modeling approach was applied to quantitatively assess putative variations of cell cycle dependent expression rates based on the obtained experimental data. We could not confirm results published earlier by other groups, based on nonphysiological synchronization attempts, reporting transfection efficiency being strongly dependent on the cell cycle phase at transfection time point. On the other hand, it is demonstrated that transfection and protein expression distort the progression of the cell cycle.