Models in biology: lessons from modeling regulation of the eukaryotic cell cycle (original) (raw)

Mathematical and Computational Models of Cell Cycle in Higher Eukaryotes

CMBEBIH 2017, 2017

The cell cycle is an ordered sequence of coordinated biological processes that enable cells to grow and divide, to check for certain abnormalities whenever it is appropriate, to regulate the different stages of growth and division in the predefined order, and to respond to DNA damage and other dysfunctions by arresting progression through the cell cycle so that to allow the regulators to repair DNA damage and recover from dysfunction before DNA is completely replicated. Understanding the detailed structure of cell cycle regulation is of practical importance in biotechnology, medicine, and pharmacology. Since a detailed analysis of cellular mechanisms behind of cell cycle regulation is too complex to be preformed intuitively, mathematical and computational modeling of involved processes is essential part of the research in this field. The main idea behind this approach is to create the closest approximation of a biological system based on wet lab results, and predict its dynamic behavior through measuring the amounts of biological components. Mathematical and computational approaches implemented to cell cycle regulation have the following benefits. Firstly, it makes possible to provide a detailed qualitative and quantitative structure of the biological system describing the cell cycle regulation. Secondly, modeling allows us to conjecture a hypothesis regarding the biological system and then check consistency of the hypothesis to desired deep by extrapolating the parameters involved into the model.

Modeling Controls and Variability of the Cell Cycle

Cell cycle events (initiation of DNA replication, length of the G2 phase, occurrence of mitosis and of cell division) follow temporal patterns which are characteristic of each cell type and growth condition, thus suggesting the existence of complex control mechanisms /1,2/. While considerable progress as been made in the description of macromolecular syntheses which characterize different growth conditions, our knowledge on the regulatory mechanisms that coordinate growth with nuclear and cell division is still poor. Clearly the reductionistic approach, which has been so useful for the description of the molecular components of a cell and of the more simple regulatory systems (regulation of enzymatic pathways, control of gene expression in bacteria), is not adequate for the study of highly integrated systems, such those controlling growth and cell division, for which it seems necessary to develop an integrated approach. Mathematical models may well be useful for this undertaking. In fact, they allow quantitative description of both the interrelations among the relevant variables of the phenomenon and the dynamics of the events under consideration. Many mathematical models have been developed in order to describe the dynamics of the cycle events, and their analytical solutions and the simulations, which are often required for a more accurate analysis of their predictions, may help to better understand the regulatory mechanisms of cell proliferation. Comparison of the predictions of the model with experimental results allows verification of the validity of the assumed functional or causal links.

Mathematical analysis of the Tyson model of the regulation of the cell division cycle

Nonlinear Analysis: Theory, Methods & Applications, 2005

In this paper, we study the mathematical properties of a family of models of Eukaryotic cell cycle, which extend the qualitative model proposed by Tyson [Proc. Natl. Acad. Sci. 88 (1991) 7328-7332]. By means of some recent results in the theory of Lienard's systems, conditions for the uniqueness of the limit cycle and on the global asymptotic stability of the unique equilibrium (idest of the arrest of the cell division) are given.

Analysis of a Generic Model of Eukaryotic Cell-Cycle Regulation

Biophysical Journal, 2006

We propose a protein interaction network for the regulation of DNA synthesis and mitosis that emphasizes the universality of the regulatory system among eukaryotic cells. The idiosyncrasies of cell cycle regulation in particular organisms can be attributed, we claim, to specific settings of rate constants in the dynamic network of chemical reactions. The values of these rate constants are determined ultimately by the genetic makeup of an organism. To support these claims, we convert the reaction mechanism into a set of governing kinetic equations and provide parameter values (specific to budding yeast, fission yeast, frog eggs, and mammalian cells) that account for many curious features of cell cycle regulation in these organisms. Using one-parameter bifurcation diagrams, we show how overall cell growth drives progression through the cell cycle, how cell-size homeostasis can be achieved by two different strategies, and how mutations remodel bifurcation diagrams and create unusual cell-division phenotypes. The relation between gene dosage and phenotype can be summarized compactly in two-parameter bifurcation diagrams. Our approach provides a theoretical framework in which to understand both the universality and particularity of cell cycle regulation, and to construct, in modular fashion, increasingly complex models of the networks controlling cell growth and division.

Mathematical modeling as a tool for investigating cell cycle control networks

Methods, 2007

Although not a traditional experimental ''method,'' mathematical modeling can provide a powerful approach for investigating complex cell signaling networks, such as those that regulate the eukaryotic cell division cycle. We describe here one modeling approach based on expressing the rates of biochemical reactions in terms of nonlinear ordinary differential equations. We discuss the steps and challenges in assigning numerical values to model parameters and the importance of experimental testing of a mathematical model. We illustrate this approach throughout with the simple and well-characterized example of mitotic cell cycles in frog egg extracts. To facilitate new modeling efforts, we describe several publicly available modeling environments, each with a collection of integrated programs for mathematical modeling. This review is intended to justify the place of mathematical modeling as a standard method for studying molecular regulatory networks and to guide the non-expert to initiate modeling projects in order to gain a systems-level perspective for complex control systems.

An autonomous mathematical model for the mammalian cell cycle

A mathematical model for the mammalian cell cycle is developed as a system of 13 coupled nonlinear ordinary differential equations. The variables and interactions included in the model are based on detailed consideration of available experimental data. Key features are that the model is autonomous, except for dependence on external growth factors; variables are continuous in time, without instantaneous resets at phase boundaries; cell cycle controllers and completion of tasks associated with cell cycle progression are represented; mechanisms to prevent rereplication are included; and cycle progression is independent of cell size. Eight variables represent cell cycle controllers: Cyclin D1 in complex with Cdk4/6, APCCdh1, SCFβTrcp, Cdc25A, MPF, NUMA, securin-separase complex, and separase. Five variables represent task completion, with four for the status of origins and one for kinetochore attachment. The model predicts distinct behaviors consistent with each main phase of the cell c...

A review of computational models of mammalian cell cycle

Weber, T., McPhee, M.J. and Anderssen, R.S. (eds) MODSIM2015, 21st International Congress on Modelling and Simulation, 2015

Cell cycle, which comprises an ordered sequence of phases (G1, S, G2, and M) that leads to growth and division of a cell, is an essential part of life and its malfunction may cause formation of tumors and cancer. Therefore, study of cell cycle system has been the topic of many computational modelling research studies. In this paper, a thorough review of all modelling methods for mammalian cell cycle and corresponding models are presented. Due to its high complexity, mammalian cell cycle system has been less modelled than other organisms, such as yeast. Majority of models have investigated various parts of mammalian cell cycle, with few covering the whole system including all the phases. There are four main modelling types (discrete, deterministic continuous, stochastic continuous, and hybrid) that enable researchers to explore and understand system properties, such as dynamics of key regulators, oscillation behaviors, feedback loops, etc. Discrete models provide an abstract view of the system where different nodes interact with each other based on discrete logic. On the other hand, continuous models usually utilize Ordinary Differential Equations (ODEs) to incorporate continuous dynamics of the system elements (i.e., protein concentrations). The effect of noise in biological systems has been modelled through stochastic models. Hybrid models combine aforementioned modelling methods to overcome limitations of individual methods. The paper covers all the above methods highlighting their strengths and weaknesses and presents some open questions as promising future prospects for modelling cell cycle.

Mathematical Modelling of Cell Growth and Proliferation

IFAC Proceedings Volumes, 1988

Models able to describe the events of cellular growth and divi sion and the dyn ami cs of cell populations are useful for the understanding of control mechanisms and for theoretical support for the automated analysis of flow cytometric data and of cell volume distributions. This paper reports on models that have been developed by the Authors with this aim, describing in a rather unitary frame the cell cycle of eukaryotic cells, like mammalian cells and yeast, and of prokaryotic cells. The model is based on the assumption that the progression of the nuclear divi sion cycle is regulated by a sequential attainment of two threshold protein levels.lt accounts for a number of features of cell growth and division in population of actively growing cells, it explains all the different patterns of cell cycle which are experimentally found and yields quantitative relations between timing of the cell cycle and macromolecular composition of the cells. The model is also used to study the effect of various sources of variability on the statistical properties of cell populations and the main source of variability appears to be an inaccuracy of the molecular mechanism that monitors the cell size. Besides in normal mammalian cells a second source of variability is apparent, which depends upon the interaction with growth factors which give competence. An extended version of the model, which comprises also this additional variability, is also considered and used to describe properties of normal and transformed cell growth. Keywords Mathematical models; cell growth and proliferation; cell populations; normal and transformed cells.

A Hybrid Model of Mammalian Cell Cycle Regulation

PLoS Computational Biology, 2011

The timing of DNA synthesis, mitosis and cell division is regulated by a complex network of biochemical reactions that control the activities of a family of cyclin-dependent kinases. The temporal dynamics of this reaction network is typically modeled by nonlinear differential equations describing the rates of the component reactions. This approach provides exquisite details about molecular regulatory processes but is hampered by the need to estimate realistic values for the many kinetic constants that determine the reaction rates. It is difficult to estimate these kinetic constants from available experimental data. To avoid this problem, modelers often resort to 'qualitative' modeling strategies, such as Boolean switching networks, but these models describe only the coarsest features of cell cycle regulation. In this paper we describe a hybrid approach that combines the best features of continuous differential equations and discrete Boolean networks. Cyclin abundances are tracked by piecewise linear differential equations for cyclin synthesis and degradation. Cyclin synthesis is regulated by transcription factors whose activities are represented by discrete variables (0 or 1) and likewise for the activities of the ubiquitin-ligating enzyme complexes that govern cyclin degradation. The discrete variables change according to a predetermined sequence, with the times between transitions determined in part by cyclin accumulation and degradation and as well by exponentially distributed random variables. The model is evaluated in terms of flow cytometry measurements of cyclin proteins in asynchronous populations of human cell lines. The few kinetic constants in the model are easily estimated from the experimental data. Using this hybrid approach, modelers can quickly create quantitatively accurate, computational models of protein regulatory networks in cells.

Some Properties of a ‘G 0 ’-Model of the Cell Cycle

Cell Proliferation, 1977

The two-phase (G and C phases) model first proposed by Burns & Tannock (1970) to describe the cell cycle kinetics has the major advantage of requiring only two parameters for a complete description of the kinetic behaviour of populations that are in a steady-state, or that grow exponentially (with no cell loss from the population). Steady-state populations were examined in paper I of this series. Exponential populaticns with no cell loss are investigated here. The model assumes two basic kinetic states-a 'C' phase which includes S, G 2 , M and perhaps part of G,, and a 'G' phase which cells enter after completing the C-phase and from which either are lost or return to C-phase randomly. The model assumes that transit time through C-phase is constant for all cells in the population. An original method isdescribed whichallows the determination of two independent parameters ofthe model from the experimental 'fraction of labelled mitoses' (FLM) curve. From those two parameters, the ratio of G-cells among the total number of cells (N G / N) has been calculated for each cell population studied. The range of the N , / N values thus obtained is fairly restricted, and the mean N,/N value for exponential growths is not statistically different from that found in steady-states considering in that case the only sub-population of cycling cells (i.e. the cells that will undergo a further mitosis). I. I N T R O D U C T I O N Burns & Tannock (1970) have elaborated a mathematical model of the cell cycle. Its basic concepts were already set out in an earlier paper by Lajtha (1966). In this model, the cell cycle is divided into two phases (see Fig.