Integrative Analysis of Cell Cycle Control in Budding Yeast

Abstract

The adaptive responses of a living cell to internal and external signals are controlled by networks of proteins whose interactions are so complex that the functional integration of the network cannot be comprehended by intuitive reasoning alone. Mathematical modeling, based on biochemical rate equations, provides a rigorous and reliable tool for unraveling the complexities of molecular regulatory networks. The budding yeast cell cycle is a challenging test case for this approach, because the control system is known in exquisite detail and its function is constrained by the phenotypic properties of >100 genetically engineered strains. We show that a mathematical model built on a consensus picture of this control system is largely successful in explaining the phenotypes of mutants described so far. A few inconsistencies between the model and experiments indicate aspects of the mechanism that require revision. In addition, the model allows one to frame and critique hypotheses about how the division cycle is regulated in wild-type and mutant cells, to predict the phenotypes of new mutant combinations, and to estimate the effective values of biochemical rate constants that are difficult to measure directly in vivo.

Hybrid modeling and simulation of stochastic effects on progression through the eukaryotic cell cycle

“…These large costs make Kar et al's method hard to generalize to more complicated cell cycle models, such as Chen et al's budding yeast cell cycle model. 9 In this paper, we have proposed to accelerate the stochastic simulation using Haseltine and Rawlings' hybrid method with a more efficient partitioning strategy. Through numerical experiments, we explored different partitioning strategies and concluded that, for certain classes of models, a reaction should be put into the SSA regime only when both of the following conditions are met: (1) the reaction has a relatively low average propensity; (2) at least one of its limiting species has a very low molecule number on average.…”

“…However, the cost is a much larger system of variables and reactions. If a more detailed deterministic model, such as Chen et al, 9 were to be unpacked for stochastic simulation, the complexity of the model would quickly increase as well as the central processing unit (CPU) time for simulation by Gillespie's SSA.…”

Systems biology towards life in silico: mathematics of the control of living cells

“…This is still an aspect of many models of cell biology such as models of the cell cycle [7]. And it becomes an ever increasing problem as the model and the total experimental dataset gets larger, making it more and more difficult to find the best fit.…”

Model reduction using a posteriori analysis

“…Many biological and physiological systems are modelled by large systems of ordinary differential equations (ODEs), for example cellular electrophysiology (Noble et al 1998;Iyer et al 2004), cell cycle dynamics (Chen et al 2004), gene regulation (Vilar et al 2002), metabolism (Beard, 2005) and coupled mechano-electrophysiology (Hunter et al 1998). When solving a (possibly non-linear) system of ODEs such as these, our main interest is often a linear functional of the solution, for example: (i) the solution of a given component at a specific time t * , u i (t * ); (ii) the weighted average of some component of the solution over a given time interval; (iii) a linear functional of the derivative of a specific component of the solution; or (iv) a combination of these simple linear functionals.…”