Bifurcation analysis of a model of the budding yeast cell cycle

We study the bifurcations of a set of nine nonlinear ordinary differential equations that describe the regulation of the cyclin-dependent kinase that triggers DNA synthesis and mitosis in the budding yeast, Saccharomyces cerevisiae. We show that Clb2-dependent kinase exhibits bistability (stable steady states of high or low kinase activity). The transition from low to high Clb2-dependent kinase activity is driven by transient activation of Cln2-dependent kinase, and the reverse transition is driven by transient activation of the Clb2 degradation machinery. We show that a four-variable model retains the main features of the nine-variable model. In a three-variable model exhibiting birhythmicity (two stable oscillatory states), we explore possible effects of extrinsic fluctuations on cell cycle progression.Comment: 31 pages,13 figure

Globally Optimized Parameters for a Model of Mitotic Control in Frog Egg Extracts

DNA synthesis and nuclear division in the developing frog egg are controlled by fluctuations in the activity of M-phase promoting factor (MPF). The biochemical mechanism of MPF regulation is most easily studied in cytoplasmic extracts of frog eggs, for which careful experimental studies of the kinetics of phosphorylation and dephosphorylation of MPF and its regulators have been made. In 1998 Marlovits et al. used these data sets to estimate the kinetic rate constants in a mathematical model of the control system originally proposed by Novak and Tyson. In a recent publication, we showed that a gradient-based optimization algorithm finds a locally optimal parameter set quite close to the Marlovits estimates. In this paper, we combine global and local optimization strategies to show that the refined Marlovits parameter set, with one minor but significant modification to the Novak-Tyson equations, is the unique, best-fitting solution to the parameter estimation problem

Simulation as a method for asymptotic system behavior identification (e.g. water frog hemiclonal population systems)

Studying any system requires development of ways to describe the variety of its conditions. Such development includes three steps. The first one is to identify groups of similar systems (associative typology). The second one is to identify groups of objects which are similar in characteristics important for their description (analytic typology). The third one is to arrange systems into groups based on their predicted common future (dynamic typology). We propose a method to build such a dynamic topology for a system. The first step is to build a simulation model of studied systems. The model must be undetermined and simulate stochastic processes. The model generates distribution of the studied systems output parameters with the same initial parameters. We prove the correctness of the model by aligning the parameters sets generated by the model with the set of the original systems conditions evaluated empirically. In case of a close match between the two, we can presume that the model is adequately describing the dynamics of the studied systems. On the next stage, we should determine the probability distribution of the systems transformation outcome. Such outcomes should be defined based on the simulation of the transformation of the systems during the time sufficient to determine its fate. If the systems demonstrate asymptotic behavior, its phase space can be divided into pools corresponding to its different future state prediction. A dynamic typology is determined by which of these pools each system falls into. We implemented the pipeline described above to study water frog hemiclonal population systems. Water frogs (Pelophylax esculentus complex) is an animal group displaying interspecific hybridization and non-mendelian inheritance

When the optimal is not the best: parameter estimation in complex biological models

Background: The vast computational resources that became available during the past decade enabled the development and simulation of increasingly complex mathematical models of cancer growth. These models typically involve many free parameters whose determination is a substantial obstacle to model development. Direct measurement of biochemical parameters in vivo is often difficult and sometimes impracticable, while fitting them under data-poor conditions may result in biologically implausible values. Results: We discuss different methodological approaches to estimate parameters in complex biological models. We make use of the high computational power of the Blue Gene technology to perform an extensive study of the parameter space in a model of avascular tumor growth. We explicitly show that the landscape of the cost function used to optimize the model to the data has a very rugged surface in parameter space. This cost function has many local minima with unrealistic solutions, including the global minimum corresponding to the best fit. Conclusions: The case studied in this paper shows one example in which model parameters that optimally fit the data are not necessarily the best ones from a biological point of view. To avoid force-fitting a model to a dataset, we propose that the best model parameters should be found by choosing, among suboptimal parameters, those that match criteria other than the ones used to fit the model. We also conclude that the model, data and optimization approach form a new complex system, and point to the need of a theory that addresses this problem more generally

Dynamical modeling of syncytial mitotic cycles in Drosophila embryos

Immediately following fertilization, the fruit fly embryo undergoes 13 rapid, synchronous, syncytial nuclear division cycles driven by maternal genes and proteins. During these mitotic cycles, there are barely detectable oscillations in the total level of B-type cyclins. In this paper, we propose a dynamical model for the molecular events underlying these early nuclear division cycles in Drosophila. The model distinguishes nuclear and cytoplasmic compartments of the embryo and permits exploration of a variety of rules for protein transport between the compartments. Numerical simulations reproduce the main features of wild-type mitotic cycles: patterns of protein accumulation and degradation, lengthening of later cycles, and arrest in interphase 14. The model is consistent with mutations that introduce subtle changes in the number of mitotic cycles before interphase arrest. Bifurcation analysis of the differential equations reveals the dependence of mitotic oscillations on cycle number, and how this dependence is altered by mutations. The model can be used to predict the phenotypes of novel mutations and effective ranges of the unmeasured rate constants and transport coefficients in the proposed mechanism

A Mathematical Programming Formulation for the Budding Yeast Cell Cycle

The budding yeast cell cycle can be modeled by a set of ordinary differential equations with 143 rate constant parameters. The quality of the model (and an associated vector of parameter settings) is measured by comparing simulation results to the experimental data derived from observing the cell cycles of over 100 selected mutated forms. Unfortunately, determining whether the simulated phenotype matches experimental data is difficult since the experimental data tend to be qualitative in nature (i.e., whether the mutation is viable, or which development phase it died in). Because of this, previous methods for automatically comparing simulation results to experimental data used a discontinuous penalty function, which limits the range of techniques available for automated estimation of the differential equation parameters. This paper presents a system of smooth inequality constraints that will be satisfied if and only if the model matches the experimental data. Results are presented for evaluating the mutants with the two most frequent phenotypes. This nonlinear inequality formulation is the first step toward solving a large-scale feasibility problem to determine the ordinary differential equation model parameters

HISTOLOGICAL STUDIES OF BREWERY SPENT GRAINS IN DIETARY PROTEIN FORMULATION IN DONRYU RATS

The increasing production of large tonnage of products in brewing industries continually generates lots of solid waste which includes spent grains, surplus yeast, malt sprout and cullet. The disposal of spent grains is often a problem and poses major health and environmental challenges, thereby making it imminently necessary to explore alternatives for its management. This paper focuses on investigating the effects of Brewery Spent Grain formulated diet on haematological, biochemical, histological and growth performance of Donryu rats. The rats were allocated into six dietary treatment groups and fed on a short-term study with diet containing graded levels of spent grains from 0, 3, 6, 9, 12 and 100% weight/weight. The outcome demonstrated that formulated diet had a positive effect on the growth performance of the rats up to levels of 6% inclusions, while the haematological and biochemical evaluation revealed that threshold limit should not exceed 9% of the grain. However, the histological study on the liver indicated a limit of 3% inclusion in feed without serious adverse effect. Thus invariably showing that blend between ranges 1-3% is appropriate for the utilization of the waste in human food without adverse effect on the liver organ. The economic advantage accruing from this waste conversion process not only solves problem of waste disposal but also handle issues of malnutrition in feeding ration

Simulating Quantitative Cellular Responses Using Asynchronous Threshold Boolean Network Ensembles

<p>Abstract</p> <p>Background</p> <p>With increasing knowledge about the potential mechanisms underlying cellular functions, it is becoming feasible to predict the response of biological systems to genetic and environmental perturbations. Due to the lack of homogeneity in living tissues it is difficult to estimate the physiological effect of chemicals, including potential toxicity. Here we investigate a biologically motivated model for estimating tissue level responses by aggregating the behavior of a cell population. We assume that the molecular state of individual cells is independently governed by discrete non-deterministic signaling mechanisms. This results in noisy but highly reproducible aggregate level responses that are consistent with experimental data.</p> <p>Results</p> <p>We developed an asynchronous threshold Boolean network simulation algorithm to model signal transduction in a single cell, and then used an ensemble of these models to estimate the aggregate response across a cell population. Using published data, we derived a putative crosstalk network involving growth factors and cytokines - i.e., Epidermal Growth Factor, Insulin, Insulin like Growth Factor Type 1, and Tumor Necrosis Factor α - to describe early signaling events in cell proliferation signal transduction. Reproducibility of the modeling technique across ensembles of Boolean networks representing cell populations is investigated. Furthermore, we compare our simulation results to experimental observations of hepatocytes reported in the literature.</p> <p>Conclusion</p> <p>A systematic analysis of the results following differential stimulation of this model by growth factors and cytokines suggests that: (a) using Boolean network ensembles with asynchronous updating provides biologically plausible noisy individual cellular responses with reproducible mean behavior for large cell populations, and (b) with sufficient data our model can estimate the response to different concentrations of extracellular ligands. Our results suggest that this approach is both quantitative, allowing statistical verification and calibration, and extensible, allowing modification and revision as guided by experimental evidence. The simulation methodology is part of the US EPA Virtual Liver, which is investigating the effects of everyday contaminants on living tissues. Future models will incorporate additional crosstalk surrounding proliferation as well as the putative effects of xenobiotics on these signaling cascades within hepatocytes.</p

A Quantitative Study of the Division Cycle of Caulobacter crescentus Stalked Cells

Progression of a cell through the division cycle is tightly controlled at different steps to ensure the integrity of genome replication and partitioning to daughter cells. From published experimental evidence, we propose a molecular mechanism for control of the cell division cycle in Caulobacter crescentus. The mechanism, which is based on the synthesis and degradation of three “master regulator” proteins (CtrA, GcrA, and DnaA), is converted into a quantitative model, in order to study the temporal dynamics of these and other cell cycle proteins. The model accounts for important details of the physiology, biochemistry, and genetics of cell cycle control in stalked C. crescentus cell. It reproduces protein time courses in wild-type cells, mimics correctly the phenotypes of many mutant strains, and predicts the phenotypes of currently uncharacterized mutants. Since many of the proteins involved in regulating the cell cycle of C. crescentus are conserved among many genera of α-proteobacteria, the proposed mechanism may be applicable to other species of importance in agriculture and medicine