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.     

Modelling cell population growth with applications to cancer therapy in human tumour cell lines

In this paper we present an overview of the work undertaken to model a population of cells and the effects of cancer therapy. We began with a theoretical one compartment size structured cell population model and investigated its asymptotic steady size distributions (SSDs) (On a cell growth model for plankton, MMB JIMA 21 (2004) 49). However these size distributions are not similar to the DNA (size) distributions obtained experimentally via the flow cytometric analysis of human tumour cell lines (data obtained from the Auckland Cancer Society Research Centre, New Zealand). In our one compartment model, size was a generic term, but in order to obtain realistic steady size distributions we chose size to be DNA content and devised a multi-compartment mathematical model for the cell division cycle where each compartment corresponds to a distinct phase of the cell cycle (J. Math. Biol. 47 (2003) 295). We then incorporated another compartment describing the possible induction of apoptosis (cell death) from mitosis phase (Modelling cell death in human tumour cell lines exposed to anticancer drug paclitaxel, J. Math. Biol. 2004, in press). This enabled us to compare our model to flow cytometric data of a melanoma cell line where the anticancer drug, paclitaxel, had been added. The model gives a dynamic picture of the effects of paclitaxel on the cell cycle. We hope to use the model to describe the effects of other cancer therapies on a number of different cell lines.     

Using a stem cell and progeny model to illustrate the relationship between cell cycle times of in vivo human tumour cell tissue populations, in vitro primary cultures and the cell lines derived from them

There is increasing evidence that the growth of human tumours is driven by a small proportion of tumour stem cells with self-renewal properties. Multiplication of these cells leads to loss of self-renewal and after division for a finite number of times the cells undergo programmed cell death. Cell cycle times of human cancers have been measured in vivo and shown to vary in the range from two days to several weeks, depending on the individual. Cells cultured directly from tumours removed at surgery initially grow at a rate comparable to the in vivo rate but continued culture leads to the generation of cell lines that have shorter cycle times (1–3 days). It has been postulated that the more rapidly growing sub-population exhibits some of the properties of tumour stem cells and are the precursors of a slower growing sub-population that comprise the bulk of the tumour. We have previously developed a mathematical model to describe the behaviour of cell lines and we extend this model here to describe the behaviour of a system with two cell populations with different kinetic characteristics and a precursor–product relationship. The aim is to provide a framework for understanding the behaviour of cancer tissue that is sustained by a minor population of proliferating stem cells.     

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.     

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.     

Global asymptotic stability of the size distribution in probabilistic models of the cell cycle

Probabilistic models of the cell cycle maintain that cell generation time is a random variable given by some distribution function, and that the probability of cell division per unit time is a function only of cell age (and not, for instance, of cell size). Given the probability density, f(t), for time spent in the random compartment of the cell cycle, we derive a recursion relation for _n(x), the probability density for cell size at birth in a sample of cells in generation n. For the case of exponential growth of cells, the recursion relation has no steady-state solution. For the case of linear cell growth, we show that there exists a unique, globally asymptotically stable, steady-state birth size distribution, _*(x). For the special case of the transition probability model, we display _*(x) explicitly.This work was supported by the National Science Foundation under grants MCS8301104 (to J.J.T.) and MCS8300559 (to K.B.H.), and by the National Institutes of Health under grant GM27629 (to J.J.T.).     

Chromosomes and their relationship to nuclear components during the cell cycle in Chinese hamster cells

Summary Chromosomes and their relationship to nuclear components during various phases of the cell cycle were studied with different fixation, embedding, and enzyme techniques. The results showed that interphase chromosomes may have oriented in such a way that a given locus became associated with the nuclear membrane. Some chromosomes also appeared to interact with the nucleolus. The nuclear matrix materials, however, were distributed between the chromosomes and formed a delineating boundary for the chromosomes. These matrix materials, furthermore, formed channel-like structures within the nucleus and towards the cytoplasm through their interaction with nuclear pore complexes. During mitosis, chromosomes were encapsulated with material that appeared to be derived from the matrix, disintegrated residues and fragments of the nuclear envelope, the lamina, and nucleolar material. These chromosome-associated materials seen in mitosis appeared to serve as foci for formation of new nuclear components in subsequent interphase.     

Cell orientation response to cyclically deformed substrates: Experimental validation of a cell model

We have developed a stochastic model that describes the orientation response of bipolar cells grown on a cyclically deformed substrate. The model was based on the following hypotheses regarding the behavior of individual cells: (a) the mechanical signal responsible for cell reorientation is the peak to peak surface strain along the cell's major axis (p-p axial strain); (b) each cell has an axial strain threshold and the threshold is normally distributed in the cell population; (c) the cell will avoid any direction where the p-p axial strain is above its threshold; and (d) the cell will randomly orient within the range of directions where the p-p axial strains are less than the cell's threshold. These hypotheses were tested by comparing model predictions with experimental observations from stretch experiments conducted with human melanocytes. The cells were grown on elastic rectangular culture dishes subjected to unidirectional cyclic (1 Hz) stretching with amplitudes of 0, 4, 8, and 12%. After 24 h of stimulation, the distribution of cell orientations was determined by measuring the orientations of 300–400 randomly selected cells. The 12% stretch experiment was used to determine the mean, 3.5%, and the standard deviation, 1.0%, of the strain threshold for the cell population. The Kolmogorov-Smirnov test was then used to determine if the orientation distributions predicted by the model were different from experimentally measured distributions for the 4 and 8% stretches. No significant differences were found between the predicted and experimental distributions (4%: p = 0.70; and 8%: p = 0.71). These results support the hypothesis that cells randomly orient, but avoid directions where the p-p axial strains are above their thresholds.     

Stability of the steady-state size distribution in a model of cell growth and division

The approach to steady-state size distribution is studied for a growing population of cells. The model incorporates cell growth at a linear rate and division into two equal daughters after a random time composed of an exponentially distributed phase and a constant deterministic phase.This work was supported by the National Science Foundation under Grant No. MCS 8300559This work was supported by the National Science Foundation under Grant No. MCS 8301104     

Microarrays and the relationship of mRNA variation to protein variation during the cell cycle

Microarray analyses have led to the postulated existence and identification of numerous genes that are believed to be expressed and presumably to act in a cell-cycle-specific manner because their expression varies during the cell cycle. It is important to see how protein variation can be produced from mRNA variation. We have calculated the protein content throughout the cell cycle resulting from cell-cycle-specific mRNA expression, and compared the result to protein content resulting from constant, cell-cycle independent, mRNA expression. For stable proteins, cell-cycle-specific mRNA expression leads to a maximum 2-fold change in protein content compared to proteins synthesized from constantly expressed mRNA. More realistic sinusoidal patterns of mRNA expression exhibit much smaller ratios of 1.25 or lower, even for extremely large amplitudes in mRNA expression. For unstable proteins that have a cycle-independent half-life, only at extremely short protein half-lives does mRNA variation have a significant impact on variation of protein content during the division cycle. We also apply these findings to proteins with a cycle-specific decay pattern. mRNA variations during the eukaryotic division cycle variation of mRNA during the cell cycle can have only a minimal affect on the variation of protein content during the cell cycle. We conclude that mRNA variations during the division cycle, as measured by microarrays, cannot by themselves, identify cycle-specific functions related to protein variations.     

DEPDC1 is a novel cell cycle related gene that regulates mitotic progression

DEPDC1 is a recently identified novel tumor-related gene that is upregulated in several types of cancer and contributes to tumorigenesis. In this study, we have investigated the expression pattern and functional implications of DEPDC1 during cell cycle progression. Expression studies using synchronized cells demonstrated that DEPDC1 is highly expressed in the mitotic phase of the cell cycle. Immunofluorescence assays showed that DEPDC1 is predominantly localized in the nucleus during interphase and is redistributed into the whole cell upon nuclear membrane breakdown in metaphase. Subsequently, siRNA-mediated knockdown of DEPDC1 caused a significant mitotic arrest. Moreover, knockdown of DEPDC1 resulted in remarkable mitotic defects such as abnormal multiple nuclei and multipolar spindle structures accompanied by the upregulation of the A20 gene as well as several cell cycle-related genes such as CCNB1 and CCNB2. Taken together, our current observations strongly suggest that this novel cancerous gene, DEPDC1, plays a pivotal role in the regulation of proper mitotic progression. [BMB Reports 2015; 48(7): 413-418]     

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.     

Mechanokinetic model of cell membrane: theoretical analysis of plasmalemma homeostasis, growth and division

A theoretical model dealing with endocytosis, exocytosis and caveolae invagination, describing plasmalemma homeostasis during cell growth and division, is proposed. It considers transmembrane pressure, membrane tension and mechanosensitivity of membrane processes. Membrane hydraulic conductivity and the flux of transmembrane nonvesicular transport are taken into account. The developed mathematical analysis operates with a formulated set of constitutive equations describing the mechanical state and kinetics of changes in an open dynamic membrane system. The standard version of a model with adjusted parameters was implemented, and predictions including a discussion on the effect of possible parameter modifications were presented. Computer simulations indicate big changes in the magnitude of membrane tension and elasticity, and in the number of membrane buddings in young cells and during mitosis. They also show the extent of cell growth inhibition resulting from a decrease in transmembrane transport or an increase in the exerted difference in osmotic pressure. Moreover, the simulations reveal that exocytosis regulated during mitosis may not be as important for cell growth, as sometimes presumed. Finally, practical application and possible extension of the model are discussed.     

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.     

Interdependence of cell cycle events inSchizosaccharomyces pombe. Terminal phenotypes of cell division cycle mutants arrested during dna synthesis and nuclear division

Summary Temperature-sensitive cell division cycle (cdc) mutants of the fission yeastSchizosaccharomyces pombe, previously characterized as defective in nuclear division were examined by thin section electron microscopy. All of the mutants failed to enter mitosis, rather they accumulated at one of four distinct terminal phenotypes. Class one were arrested with a nucleus rectangular in cross-section and a laterally situated spindle pole body (SPB). The second group had spherical or rectangular nuclei with a single SPB. The sole member of the third group wascdc 27. K 3, which had a spherical crenated nucleus with a single SPB from which microtubules emerged and extended into the cytoplasm. Allelic variants ofcdc 25 comprised the fourth group all of which displayed aberrant nuclear morphologies. Utilizing this ultrastructural data together with a knowledge of the transition points of these mutants a model for the interdependence of certain cell cycle event is proposed in which the initiation of DNA synthesis is uncoupled from the replication and separation of the SPB. This paper also provides new information on SPB structure inS. pombe. This is discussed in connection with the transient assembly of both spindle and cytoplasmic microtubules.     

Actin filament branching and protrusion velocity in a simple 1D model of a motile cell

We formulate and analyse a 1D model for the spatial distribution of actin density at the leading edge of a motile cell. The model incorporates nucleation, capping, growth and decay of actin filaments, as well as retrograde flow of the actin meshwork and known parameter values based on the literature. Using a simplified geometry, and reasonable assumptions about the biochemical processes, we derive PDEs for the density of actin filaments and their tips. Analytic travelling wave solutions are used to predict how the speed of the cell depends on rates of nucleation, capping, polymerization and membrane resistance. Analysis and simulations agree with experimental profiles for measured actin distributions. Extended versions of the model are studied numerically. We find that our model produces stable travelling wave solutions with reasonable cell speeds. Increasing the rate of nucleation of filaments (by the actin related protein Arp2/3) or the rate of actin polymerization leads to faster cell speed, whereas increasing the rate of capping or the membrane resistance reduces cell speed. We consider several variants of nucleation (spontaneous, tip, and side branching) and find best agreement with experimentally measured spatial profiles of filament and tip density in the side branching case.     

Eukaryotic checkpoints are absent in the cell division cycle ofEntamoeba histolytica

Fidelity in transmission of genetic characters is ensured by the faithful duplication of the genome, followed by equal segregation of the genetic material in the progeny. Thus, alternation of DNA duplication (S-phase) and chromosome segregation during the M-phase are hallmarks of most well studied eukaryotes. Several rounds of genome reduplication before chromosome segregation upsets this cycle and leads to polyploidy. Polyploidy is often witnessed in cells prior to differentiation, in embryonic cells or in diseases such as cancer. Studies on the protozoan parasite,Entamoeba histolytica suggest that in its proliferative phase, this organism may accumulate polyploid cells. It has also been shown that although this organism contains sequence homologs of genes which are known to control the cell cycle of most eukaryotes, these genes may be structurally altered and their equivalent function yet to be demonstrated in amoeba. The available information suggests that surveillance mechanisms or ‘checkpoints’ which are known to regulate the eukaryotic cell cycle may be absent or altered inE. histolytica.