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.     

A Dynamic Gene Regulatory Network Model That Recovers the Cyclic Behavior of Arabidopsis thaliana Cell Cycle

Cell cycle control is fundamental in eukaryotic development. Several modeling efforts have been used to integrate the complex network of interacting molecular components involved in cell cycle dynamics. In this paper, we aimed at recovering the regulatory logic upstream of previously known components of cell cycle control, with the aim of understanding the mechanisms underlying the emergence of the cyclic behavior of such components. We focus on Arabidopsis thaliana, but given that many components of cell cycle regulation are conserved among eukaryotes, when experimental data for this system was not available, we considered experimental results from yeast and animal systems. We are proposing a Boolean gene regulatory network (GRN) that converges into only one robust limit cycle attractor that closely resembles the cyclic behavior of the key cell-cycle molecular components and other regulators considered here. We validate the model by comparing our in silico configurations with data from loss- and gain-of-function mutants, where the endocyclic behavior also was recovered. Additionally, we approximate a continuous model and recovered the temporal periodic expression profiles of the cell-cycle molecular components involved, thus suggesting that the single limit cycle attractor recovered with the Boolean model is not an artifact of its discrete and synchronous nature, but rather an emergent consequence of the inherent characteristics of the regulatory logic proposed here. This dynamical model, hence provides a novel theoretical framework to address cell cycle regulation in plants, and it can also be used to propose novel predictions regarding cell cycle regulation in other eukaryotes.     

A novel model for studying Baculovirus infection process

In this paper, a new Ansatz for modelling the Baculovirus infection cycle is presented. The base of this model is the cell cycle distribution at the time of infection. It is possible to calculate the growth of the culture and the initiation of virus processing by considering cell cycle distribution. By taking into account the length of the viral genome and the polymerase activity, it is possible to calculate the virus production rate, which underlies a logistic growth. In the present work, a new hypothesis explaining the accelerated death rates of infected cells has been introduced. This assumption provides the possibilities of performing calculation without any fixed time intervals. The simulation was tested by comparing experimental data with the model prediction. Therefore, cell cycle distributions over the culture time and the growth behaviour of infected and non-infected insect cells were measured. A model, Baculovirus coding for GFP was employed for the present investigation, as it allows tracking the infection and determining the effectiveness of the infection, which is highly dependent on the cell density at the time of infection (TOI). Furthermore, the new model is is taken to simulate data gained from literature about virus release and adsorption. The new assumptions make the model more independent to fit into different cultivation systems.     

Embryonic cell commitment by a simultaneous alteration in nucleo/cytoplasmic ratio in sibling cells between subsequent cell cycles

Studies on murine embryonal carcinoma (EC) cell lines have revealed a mechanism for commitment of early embryonic cells. By means of a particular intraclonal cell surface glycoprotein and intermitotic time heterogeneity found in the EC lines used, we have devised a cell cycle model and written a computer program for cell cycle stimulation. In the present investigation experimental tissue culture data obtained from the EC lines were inserted into the computer program and the simulations represent a good fit to experimental data. It is shown that the dynamics of the driving forces in the 'cell growth cycle' and the 'DNA-division cycle', when assumed to be loosely coupled and analyzed in subsequent cell cycles, reveal a mechanism that can commit the mother cell to impel her daughter cells into the next stage in embryonic development by altering the relationship between those two uncoupled subcycles. Thereby the nucleo/cytoplasmic ratio (DNA/mass) is altered in a similar way in the two daughter cells. The simulations increase the reliability of the model and open up possibilities to test other embryonic cell systems.     

The growth kinetics ofB. subtilis

There has been considerable discussion by Kubitschek and Cooper concerning the growth rate of cells ofE. coli throughout the cell cycle. Consequently, it is relevant to test Kubitschek's linear model against the exponential model espoused by Cooper (and many others) with another organism and another technique.Burdett et al. measured, by electron microscopy and computer analysis of the microphotographs, the distribution of lengths of a population of cells ofBacillus subtilis grown in 0.4% succinate in a minimal medium. The data were fitted to the extended Collins-Richmond method of Kirkwood & Burdett which subdivided the cell cycle into several phases. I have taken their results and compared them with the linear and exponential growth models for the entire cell cycle after applying correction to the data for the shape of completed and forming poles; i.e., to put the data on a cell-volume basis instead of a cell-length basis. Most of the correction involves no arbitrary assumptions. The conclusion is that global volume growth rate is nearly proportional to cell volume; i.e. growth ofBacillus subtilis is nearly exponential for almost every cell in the growing culture.     

Protein kinase C signaling mediates a program of cell cycle withdrawal in the intestinal epithelium

Members of the protein kinase C (PKC) family of signal transduction molecules have been widely implicated in regulation of cell growth and differentiation, although the underlying molecular mechanisms involved remain poorly defined. Using combined in vitro and in vivo intestinal epithelial model systems, we demonstrate that PKC signaling can trigger a coordinated program of molecular events leading to cell cycle withdrawal into G(0). PKC activation in the IEC-18 intestinal crypt cell line resulted in rapid downregulation of D-type cyclins and differential induction of p21(waf1/cip1) and p27(kip1), thus targeting all of the major G(1)/S cyclin-dependent kinase complexes. These events were associated with coordinated alterations in expression and phosphorylation of the pocket proteins p107, pRb, and p130 that drive cells to exit the cell cycle into G(0) as indicated by concomitant downregulation of the DNA licensing factor cdc6. Manipulation of PKC isozyme levels in IEC-18 cells demonstrated that PKCalpha alone can trigger hallmark events of cell cycle withdrawal in intestinal epithelial cells. Notably, analysis of the developmental control of cell cycle regulatory molecules along the crypt-villus axis revealed that PKCalpha activation is appropriately positioned within intestinal crypts to trigger this program of cell cycle exit-specific events in situ. Together, these data point to PKCalpha as a key regulator of cell cycle withdrawal in the intestinal epithelium.     

An elementary approach to cell cycle analysis

An elementary semistochastic model for cell cycle analysis is presented. Various independently generated experimental data sets are compared with the theory in which for the first time, a consistent consideration of non-proliferating cells has also been taken into account.     

An elementary approach to cell cycle analysis

An elementary semistochastic model for cell cycle analysis is presented. Various independently generated experimental data sets are compared with the theory in which for the first time, a consistent consideration of non-proliferating cells has also been taken into account.     

Cell cycle progression

In this paper we consider cell cycle models for which the transition operator for the evolution of birth mass density is a simple, linear dynamical system with a stochastic perturbation. The convolution model for a birth mass distribution is presented. Density functions of birth mass and tail probabilities in n-th generation are calculated by a saddle-point approximation method. With these probabilities, representing the probability of exceeding an acceptable mass value, we have more control over pathological growth. A computer simulation is presented for cell proliferation in the age-dependent cell cycle model. The simulation takes into account the fact that the age-dependent model with a linear growth is a simple linear dynamical system with an additive stochastic perturbation. The simulated data as well as the experimental data (generation times for mouse L) are fitted by the proposed convolution model.     

Cell size at S phase initiation: an emergent property of the G1/S network

The eukaryotic cell cycle is the repeated sequence of events that enable the division of a cell into two daughter cells. It is divided into four phases: G₁, S, G₂, and M. Passage through the cell cycle is strictly regulated by a molecular interaction network, which involves the periodic synthesis and destruction of cyclins that bind and activate cyclin-dependent kinases that are present in nonlimiting amounts. Cyclin-dependent kinase inhibitors contribute to cell cycle control. Budding yeast is an established model organism for cell cycle studies, and several mathematical models have been proposed for its cell cycle. An area of major relevance in cell cycle control is the G₁ to S transition. In any given growth condition, it is characterized by the requirement of a specific, critical cell size, P_S, to enter S phase. The molecular basis of this control is still under discussion. The authors report a mathematical model of the G₁ to S network that newly takes into account nucleo/cytoplasmic localization, the role of the cyclin-dependent kinase Sic1 in facilitating nuclear import of its cognate Cdk1-Clb5, Whi5 control, and carbon source regulation of Sic1 and Sic1-containing complexes. The model was implemented by a set of ordinary differential equations that describe the temporal change of the concentration of the involved proteins and protein complexes. The model was tested by simulation in several genetic and nutritional setups and was found to be neatly consistent with experimental data. To estimate P_S, the authors developed a hybrid model including a probabilistic component for firing of DNA replication origins. Sensitivity analysis of P_S provides a novel relevant conclusion: P_S is an emergent property of the G₁ to S network that strongly depends on growth rate.     

Parametric analysis of volume distributions of Schizosaccharomyces pombe and other cells

Time-lapse photomicrographic data have been obtained on mating strains of the yeast Schizosaccharomyces pombe to evaluate the effect of the variability of the patterns of cell cycle behavior on population structure. These have been used to design a computer model which accepts volume distribution data from exponential cultures of a cell and yields estimates of the mean and standard deviation of daughter cell volume and telophase cell volume, as well as a stop-grow point, and the degree of cell volume doubling. Given a cell population's volume distribution and a volume distribution from a subpopulation, the program will estimate the mean age and display how the age is distributed in the subpopulation. Several cell types have been examined.     

Cell population dynamics during the differentiative phase of tissue development

The dynamics of a cell population whose numbers are growing exponentially have been described well by a mathematical model based on the theory of age-dependent branching processes. Such a model, however, does not cover the period following exponential growth when cell differentiation curtails population size. This paper offers an extension to the branching process model to remedy this deficiency. The extended model is ideal for describing embryonic growth; its use is illustrated with data from embryonic retina. The model offers a better computational framework for the interpretation of a variety of data (growth curves of cell numbers, DNA histograms, thymidine labelling indices, FLM curves, BUdR-labelled mitoses curves) because age-distributions can be calculated at any stage of development, not just during exponential growth. Proportions of cells in the various phases of the cell cycle can be computed as growth slows. Such calculations show the gradual transition from a population dominated by cells which are young with respect to cell cycle age to one dominated by those which are old, and the effects such biases have on the proportions of cells in each phase.     

Cell cycle model for growth rate and death rate in continuous suspension hybridoma cultures

As a result of recent advances in flow cytometry, renewed interest is shown in modeling the kinetic behavior of cells in culture on the basis of cell cycle parameters. An important but often overlooked kinetic variable in hybridoma cultures is the cell death rate. Not only the overall cell growth but also the kinetics of nutrient metabolism and monoclonal antibody production have been shown to depend on the cell death rate in continuous suspension hybridoma cultures. The present study shows that the death rate in hybridoma cultures is proportional to the fraction of cells arrested in the G(1) phase of the cell cycle. The steady-state cell age distributions in the various phases of the division cycle have been calculated analytically. A simple mathematical model has been used to produce the profiles of the cycling and arrested cell fractions with respect to the dilution rate. The calculated steady-state growth rate, death rate, and viability profiles are shown to be in agreement with recently published experimental data from continuous suspension hybridoma cultures. (c) 1992 John Wiley & Sons, Inc.     

Morphologically-structured models of growing budding yeast populations

It has been well recognized that many key aspects of cell cycle regulation are encoded into the size distributions of growing budding yeast populations due to the tight coupling between cell growth and cell division present in this organism. Several attempts have been made to model the cell size distribution of growing yeast populations in order to obtain insight on the underlying control mechanisms, but most were based on the age structure of asymmetrically dividing populations. Here we propose a new framework that couples a morphologically-structured representation of the population with population balance theory to formulate a dynamic model for the size distribution of growing yeast populations. An advantage of the presented framework is that it allows derivation of simpler models that are directly identifiable from experiments. We show how such models can be derived from the general framework and demonstrate their utility in analyzing yeast population data. Finally, by employing a recently proposed numerical scheme, we proceed to integrate numerically the full distributed model to provide predictions of dynamics of the cell size structure of growing yeast populations.     

A stochastic model to analyze clonal data on multi-type cell populations

This article presents a stochastic model designed to analyze experimental data on the development of cell clones composed of two (or more) distinct types of cells. The proposed model is an extension of the traditional multi-type Bellman-Harris branching stochastic process allowing for nonidentical time-to-transformation distributions defined for different cell types. A simulated pseudo likelihood method has been developed for the parametric statistical inference from experimental data on cell clones under the proposed model. The method uses simulation-based approximations of the means and the variance-covariance matrices of cell counts. The proposed estimator for the vector of unknown parameters is strongly consistent and asymptotically normal under mild regularity conditions, while its variance-covariance matrix is estimated by the parametric bootstrap. A Monte Carlo Wald test is proposed for the test of hypotheses. Finite sample properties of the estimator have been studied by computer simulations. The model and associated methods of parametric inference have been applied to the analysis of proliferation and differentiation of cultured O-2A progenitor cells that play a key role in the development of the central nervous system. It follows from this analysis that the time to division of the progenitor cell and the time to its differentiation (into an oligodendrocyte) are not identically distributed. This biological finding suggests that a molecular event determining the type of cell transformation is more likely to occur at the start rather than at the end of the mitotic cycle.     

Model of cap‐dependent translation initiation in sea urchin: A step towards the eukaryotic translation regulation network

The large and rapid increase in the rate of protein synthesis following fertilization of the sea urchin egg has long been a paradigm of translational control, an important component of the regulation of gene expression in cells. This translational up‐regulation is linked to physiological changes that occur upon fertilization and is necessary for entry into first cell division cycle. Accumulated knowledge on cap‐dependent initiation of translation makes it suited and timely to start integrating the data into a system view of biological functions. Using a programming environment for system biology coupled with model validation (named Biocham), we have built an integrative model for cap‐dependent initiation of translation. The model is described by abstract rules. It contains 51 reactions involved in 74 molecular complexes. The model proved to be coherent with existing knowledge by using queries based on computational tree logic (CTL) as well as Boolean simulations. The model could simulate the change in translation occurring at fertilization in the sea urchin model. It could also be coupled with an existing model designed for cell‐cycle control. Therefore, the cap‐dependent translation initiation model can be considered a first step towards the eukaryotic translation regulation network. Mol. Reprod. Dev. 77: 257–264, 2010. © 2009 Wiley‐Liss, Inc.