Ergodic Sets as Cell Phenotype of Budding Yeast Cell Cycle

Robert G Todd,Tomáš Helikar,Jean Peccoud

doi:10.1371/journal.pone.0045780

Abstract

It has been suggested that irreducible sets of states in Probabilistic Boolean Networks correspond to cellular phenotype. In this study, we identify such sets of states for each phase of the budding yeast cell cycle. We find that these “ergodic sets” underly the cyclin activity levels during each phase of the cell cycle. Our results compare to the observations made in several laboratory experiments as well as the results of differential equation models. Dynamical studies of this model: (i) indicate that under stochastic external signals the continuous oscillating waves of cyclin activity and the opposing waves of CKIs emerge from the logic of a Boolean-based regulatory network without the need for specific biochemical/kinetic parameters; (ii) suggest that the yeast cell cycle network is robust to the varying behavior of cell size (e.g., cell division under nitrogen deprived conditions); (iii) suggest the irreversibility of the Start signal is a function of logic of the G1 regulon, and changing the structure of the regulatory network can render start reversible.

Highlights

Complex network structures can be found across the biological spectrum, and growing evidence indicates that these biochemical networks have evolved to perform complex information processing tasks in order for the cells to appropriately respond to the often noisy and contradictory environmental cues [1]
The logic of our network was constructed based on the descriptions of the cell cycle interaction as given in section 3.1 of [12], which is an expansion of the network found in [5]
The model used in this study has four external inputs: cell size signal (CSS) to model cell growth, the Start checkpoint (Start), the budding checkpoint (BuddingCP) and the spindle assembly checkpoint (SpindleCP)

Summary

Introduction

Complex network structures can be found across the biological spectrum, and growing evidence indicates that these biochemical networks have evolved to perform complex information processing tasks in order for the cells to appropriately respond to the often noisy and contradictory environmental cues [1]. While reductionist techniques focus on the local interactions of biological components, the systems approach aims at studying properties of biological processes as a result of all components and their local interactions working together [2]. A wide spectrum of modeling techniques ranging from continuous frameworks utilizing differential equations to discrete (e.g., Boolean) techniques based on qualitative biological relationships exist [3,4,5]. Differential equation models can depict the dynamics of biological systems in great detail, but depend on a large number of difficult-to-obtain biological (kinetic) parameters. Discrete modeling frameworks, namely Boolean networks, are qualitative and parameter-free, which makes them more suitable to study the dynamics of large-scale systems for which these parameters are not available. Probabilistic Boolean networks (PBN) enhance the discrete framework by allowing for uncertainty and stochasticity (e.g., [6,7])

Methods

Results

Conclusion