State vector models of the cell cycle. III: Continuous time cell cycle models

In this paper the elements of the matrix of the Hahn cell-cycle model are identified with the infinitesimal transition probabilities of a Markov process, and as a limiting process a differential equation analogue is derived. The probability density function of the discrete time model is derived and used to obtain the density function for transit times of the continuous time model. It is shown that the mean transit time remains constant and that the variances of the discrete and continuous time models are the same to the order of the time increment. Finally, it is shown how to derive the Takahashi model from the continuous time Hahn model.     

Age-dependent cell cycle models.

This paper presents age-dependent cell cycle models i.e., models where cell generation time is a random variable given by some distribution function, and the probability of cell division per unit time is a function only of cell age (not, for example, of cell mass). It is shown that there does not exist a stable mass distribution if the cells grow exponentially. In the case of linear growth, conditions for stability of the mass distribution are derived. To show these, the methods different from those considered up till now in the literature, are used. It is also shown that one can consider the cell mass growth as a linear dynamical system with a stochastic perturbation. The sister cell model as an improvement of the Transition Probability Model is derived. Statistical data are obtained for that model, and comparisons are made with some experimental data. As a verification tool, alpha and beta curves, are used.     

Mathematical models of cell cycle regulation

The cell division cycle is a fundamental process of cell biology and a detailed understanding of its function, regulation and other underlying mechanisms is critical to many applications in biotechnology and medicine. Since a comprehensive analysis of the molecular mechanisms involved is too complex to be performed intuitively, mathematical and computational modelling techniques are essential. This paper is a review and analysis of recent approaches attempting to model cell cycle regulation by means of protein-protein interaction networks.     

Evolutionary aspects and sensitivity studies of some major gene models

Extensive biometrical and statistically oriented studies in segregation and pedigree analyses reflect current efforts to demonstrate major gene factors playing a significant role for a whole hierarchy of multifactorial diseases and related risk factors exhibiting continuous variation. The evolutionary aspects of the changes in gene frequencies of some major gene one locus models admitting a broad range of genotype-phenotype associations and different forms of selection functions are investigated. The flexibility of differences among the genotypic-phenotypic distribution can take account of variable penetrance expressivity, complex multifarious heterogeneous background effects, or partial dominance concepts. The phenotype distribution and selection function are assumed to be time invariant such that the environments with which the population interacts do not depend on either the phenotypes or the genotypes present in the population of any particular generation. Viability selection optimizing or directional acts on the phenotypic level. We consider random mating, and concentrate mostly on evaluating the nature of the equilibrium structure for the cases of “strong” and “weak” selection. For weak stabilizing selection the determinants of superior genotypic fitness in the class of phenotypic symmetric distributions reside in minimizing a combination of the phenotypic variance and the deviation of the phenotypic mean from the optimal phenotype. With equal means of central phenotype values, a canalizing selection effect signifying fitness superiority for the genotype with minimal variance is in force. For strong stabilizing selection the genotype-phenotype density at the optimal value determines the relative genotype fitness value. For directional selection the determinants of the selection realizations depend on a “standardized” deviation of the mean phenotype distributional value relative to its total variance. The effects of symmetry as against asymmetry in the genotype distributions with prescribed means and variances were investigated by numerical computations.     

Unstable activator models for size control of the cell cycle

The unstable activator model of Wheals & Silverman (1982) is extended to account for the delay of nuclear division in the acellular slime mold, Physarum polycephalum, that is caused by pulse treatments with inhibitors of protein synthesis. The model is solved exactly to predict the delay as a function of the half-life of the activator. The Wheals-Silverman model is found to give results comparable, but not superior, to other unstable activator models of the cell cycle.     

Effect of FMdC on the cell cycle of some leukemia cell lines.

BACKGROUND: (E)-2'-deoxy-2'-(fluoromethylene)-cytidine (FMdC), an irreversible inhibitor of ribonucleotide reductase, displays a strong toxicity towards many cell lines derived from human solid tumors, while its activity on leukemia lines is less well-known. The aim of this study was to assess the effect of FMdC on the cell cycle and cell death of human leukemia lines HL-60 and MOLT-4, and murine leukemia L-1210 in vitro. It has been assumed that a prerequisite of FMdC cytotoxicity is intracellular phosphorylation by deoxycytidine kinase (dCK). METHODS:Cell cultures in the exponential phase of growth were exposed to different concentrations of FMdC (10 nM to 10 microM) for 6 and 24 hours. In a parallel set of experiments 1 mM deoxycytidine was added to prevent phosphorylation of the drug by dCK. The DNA and protein content in the cells, as well as Annexin V/PI binding were assessed by flow cytometry. The cell cycle was analyzed by the MacCycle software. RESULTS: The cytotoxic effects of FMdC, i.e., G(1)/S block and cell death were observed, associated with pronounced changes in the protein content. These effects were of variable intensity among the cell lines studied (HL-60 being the most susceptible), and in some cases, were not completely reversed by deoxycytidine excess. CONCLUSIONS: FMdC is a potent cytotoxic/cytostatic agent against human leukemia cell lines in vitro. It also changes the cellular protein content. Unphosphorylated FMdC may slightly influence the cell cycle of some leukemic lines.     

Insights into regulation of the mammalian cell cycle from studies on spermatogenesis using genetic approaches in animal models

The genetic hierarchy controlling mitosis and especially meiosis during gamete formation is not well understood, even in less complicated systems such as the yeasts. Meiotic divisions are obviously restricted to germ line cells and as such likely require mechanisms of cell cycle control that do not function and may not exist in somatic cells. While male and female germ cells have stages of cell cycle regulation in common, the timing of these events and the stage of development at which these events occur differ in the two sexes. Understanding the genetic program controlling the mitotic and meiotic divisions of the germ line represents a unique opportunity for providing insight into cell cycle control in vivo. Elucidating the key control points and proteins may also enhance our understanding of the etiology of infertility and provide new directions for contraception.     

Time-lapse cinematography studies of cell cycle and mitosis duration

The progenies of 44 cells (EMT6 cell line) have been studied in vitro by time-lapse cinematography for up to eight generations. It has been found that the mean mitotic and intermitotic times vary significantly with the age of the culture and that they are positively correlated. There are correlations between mother and daughter parameters and between sister cells. All these correlations are higher when the age of the culture is greater.     

Genetic mouse models to investigate cell cycle regulation

Early studies on cell cycle regulation were based on experiments in model systems (Yeast, Xenopus, Starfish, Drosophila) and have shaped the way we understand many events that control the cell cycle. Although these model systems are of great value, the last decade was highlighted by studies done in human cells and using in vivo mouse models. Mouse models are irreplaceable tools for understanding the genetics, development, and survival strategies of mammals. New developments in generating targeting vectors and mutant mice have improved our approaches to study cell cycle regulation and cancer. Here we summarize the most recent advances of mouse model approaches in dissecting the mechanisms of cell cycle regulation and the relevance to human disease. W. Li and S. Kotoshiba contributed equally.     

Identification of age-structured models: cell cycle phase transitions

A methodology is developed that determines age-specific transition rates between cell cycle phases during balanced growth by utilizing age-structured population balance equations. Age-distributed models are the simplest way to account for varied behavior of individual cells. However, this simplicity is offset by difficulties in making observations of age distributions, so age-distributed models are difficult to fit to experimental data. Herein, the proposed methodology is implemented to identify an age-structured model for human leukemia cells (Jurkat) based only on measurements of the total number density after the addition of bromodeoxyuridine partitions the total cell population into two subpopulations. Each of the subpopulations will temporarily undergo a period of unbalanced growth, which provides sufficient information to extract age-dependent transition rates, while the total cell population remains in balanced growth. The stipulation of initial balanced growth permits the derivation of age densities based on only age-dependent transition rates. In fitting the experimental data, a flexible transition rate representation, utilizing a series of cubic spline nodes, finds a bimodal G(0)/G(1) transition age probability distribution best fits the experimental data. This resolution may be unnecessary as convex combinations of more restricted transition rates derived from normalized Gaussian, lognormal, or skewed lognormal transition-age probability distributions corroborate the spline predictions, but require fewer parameters. The fit of data with a single log normal distribution is somewhat inferior suggesting the bimodal result as more likely. Regardless of the choice of basis functions, this methodology can identify age distributions, age-specific transition rates, and transition-age distributions during balanced growth conditions.     

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.