Models of cell cycle control in eukaryotes.

The molecular mechanisms of cell cycle control are now known in enough detail to warrant mathematical modeling by kinetic equations. Despite the repetitive nature of the cell division cycle, the most appropriate models emphasize steady-state solutions rather than limit cycle oscillations, because cells progress toward division by passing a series of checkpoints (steady states).     

Derepression as a model for control of the DNA-division cycle in eukaryotes

A mechanism is presented whereby synthesis of a gene product can be switched on and off during the cell cycle as a result of gene replication events. We suggest that such a mechanism may be operative in controlling the production of putative mitotic activator, whose synthesis appears to be shut off at the beginning of S phase and turned on again at the end of S. Furthermore, a mechanism of this sort could account for the synthesis of certain inducible enzymes during restricted periods of the cell cycle.     

Cell cycle control of replication initiation in eukaryotes

Studies on the initiation of DNA replication in eukaryotes have progressed recently through different approaches that promise to converge. Proteins interacting with the origin recognition complex form a prereplicative complex early in the cell cycle. The regulation of the binding of MCM/P1 proteins to chromatin plays a key role in the replication licensing system which prevents re-replication in a single cell cycle. Cyclin-dependent kinases provide an overall control of the cell cycle by stimulating S-phase entry and possibly by preventing re-establishment of prereplicative complexes in G₂ phase.     

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.     

A mathematical model of the cell cycle of a hybridoma cell line

A one-dimensional age-based population balance model of the cell cycle is proposed for a mouse-mouse hybridoma cell line (mm321) producing immunoglobulin G antibody to paraquat. It includes the four conventional cell cycle phases, however, G1 is divided into two parts (G1a and G1b). Two additional phases have been added, a non-cycling state G1', and a pre-death phase D. The duration of these additional phases is determined by cumulative glutamine content and ammonia concentration, respectively. It is assumed that glutamine is only consumed during G1 and antibody is only produced during G1b and S, the kinetics are assumed to be zero-order. Glucose is consumed throughout the cell cycle at a rate that is dependent upon its prevalent concentration. Ammonia and lactate are produced in direct proportion to glutamine and glucose consumption, respectively. Parameters in the model have been determined from experimental data or from fitting the model to post-synchronisation data. The model thus fitted has been used to successfully predict this cell lines behaviour in conventional batch culture at different initial glutamine concentrations, and in chemostat culture at steady-state and in response to a glutamine pulse. The model predicts viable cell, glutamine, glucose and lactate kinetics well, but there are some discrepancies in the prediction for ammonia and antibody. Overall, the results obtained support the assumptions made in the model relating to the regulation of cell cycle progression. It is concluded that this approach has the potential to be exploited with other cell lines and used in a model-based control scheme.     

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.     

Triggering cell mitosis in higher eukaryotes

Dramatic changes of cell organisation occur at onset of mitosis. Genetic analysis of fission yeast and physiological studies of vertebrate and invertebrate oocytes showed that activation of cyclin B-cdc2 kinase triggers mitosis. Nevertheless, upstream mechanisms responsible for this activation remain largely unknown in somatic cells of higher eukaryotes. This review discusses possible pathways and mechanisms involved in triggering onset of mitosis in such cells, including inhibitory checkpoint mechanisms that detect defects in structural organisation of the cell.     

Negative control of cell proliferation in eukaryotes

Abstract. Control over cell growth in eukaryotes is predominantly achieved by regular transition of cells from proliferation to rest and vice versa as a result of a co-ordinated inter-relationship between intracellular growth inhibitors and extracellular growth stimulators (mitogens). The ability to cease and resume growth on demand implies the existence of a refined intracellular regulatory network including both positive and negative control elements. We review here evidence that resting cells are able to produce molecules with antiproliferative activity, some of which behave as short-lived repressor proteins. A number of genes coding for growth inhibitory molecules have been identified. However, it is not yet certain whether the same molecules ensure the maintenance of a resting state. It has become apparent that immediate growth arrest or growth resumption require not only a rapid production of inhibitors and stimulators but also their biochemical transformation (e.g. phosphorylation or dephosphorylation) and/ or translocation within the cell, whereby one and the same molecule can be a growth inhibitor or fulfil some other function in the cell cycle, according to circumstances or context. At present, three levels of negative cell growth control can be tentatively outlined: 1 rapid appearance of growth inhibitory molecules to bring about temporary arrest at critical checkpoints of the proliferative cycle; 2 transition of a cell to proliferative rest with continuous production of growth inhibitor(s); 3 long-lasting maintenance of the resting state provided for by complex intracellular changes not connected with production of growth inhibitor(s).     

Simulations of the contractile cycle in cell migration using a bio-chemical-mechanical model

Cell migration relies on traction forces in order to propel a cell. Several computational models have been developed that help explain the trajectory that cells take during migration, but little attention has been placed on traction forces during this process. Here, we investigated the spatiotemporal dynamics of cell migration by using a bio-chemical-mechanical contractility model that incorporates the first steps of cell migration on an array of posts. In the model, formation of a new adhesion causes a reactivation of stress fibre assembly within a cell. The model was able to predict the spatial distribution of traction forces observed with previous experiments. Moreover, the model found that the strain energy exerted by the traction forces of a migrating cell underwent a cyclic relationship that rose with the formation of a new adhesion and fell with the release of an adhesion at its rear.     

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.     

Tuning the cell cycle: a model based on averaging

Abstract. The ability of intercellular communication and the basement membrane to revert the phenotypic behaviour of malignant cells suggests that such cells can be tuned to behave more benignly. In addition, the large variation in cell doubling times observed in tumour cells poses the question of whether or not cell doubling times, and hence, patient survival, can be lengthened by therapeutic intervention. In both cases, the understanding may be enhanced by obtaining a parsimonious and tractable model of the cell cycle which behaves appropriately and suggests a philosophical framework for addressing these complex issues. We introduce a simple two-dimensional model based on averaging cyclin and maturation promotion factor over a fast oscillating subsystem that exhibits the basic features of cellular division, and discuss the ramifications of the model.     

A stochastic model of cell cycle desynchronization

A general branching process model is suggested to describe cell cycle desynchronization. Cell cycle phase times are modeled as random variables and a formula for the expected fraction of cells in S phase as a function of time is established. The model is compared to data from the literature and is also compared to previously suggested deterministic and stochastic models.     

A deterministic model of the cell cycle

The variability of the duration of the cell cycle is explained by the phenomenon of sensitive dependence upon initial conditions; as may occur in deterministic non-linear systems. Chaotic dynamics of a system is the result of this sensitive dependence. First a deterministic system is formulated that is equivalent to the Smith-Martin transition probability model of the cell cycle. Next the model is extended to a dynamic process that ranges over the cell generations. A deterministic non-linear relationship between the cycle time of the mother and daughter cell is established. It clarifies the variability of mother-daughter correlation for the different cell types. The model is fitted to two different cell cultures; it shows that the graph of the non-linear relation has the same shape for different cell types.     

Analysis of cell cycle in root meristems

We have analyzed the cell proliferation in a meristem assuming a single file model for root architecture. The meristem file appears to be built up by two clearly separated zones: the first going from the initial cell to the middle of the meristem and the second from the middle to the meristem boundary. The first half of the meristem shows an exponential age distribution for the cell population. In contrast, in the second half of the meristem, the cell kinetics of cycling cells strongly disagree with exponential kinetics and due to the compensation between the observed deviations in both halves, cell supply in the file meristem is in line with linear kinetics. However, we proposed that exponential kinetic equations offer a suitable approach to problems of cell cycle compartments and population age distributions in real meristems, where non-cycling cells cannot be identified inside the meristem, whether we consider the meristem as a whole or study a “window” inside it. Nevertheless, for more exact kinetic analysis, when estimating the proliferative fraction, the width of the “window” and its location along the axis must carefully be taken into account.