The yeast cell-cycle network is robustly designed

Abstract

The interactions between proteins, DNA, and RNA in living cells constitute molecular networks that govern various cellular functions. To investigate the global dynamical properties and stabilities of such networks, we studied the cell-cycle regulatory network of the budding yeast. With the use of a simple dynamical model, it was demonstrated that the cell-cycle network is extremely stable and robust for its function. The biological stationary state, the G1 state, is a global attractor of the dynamics. The biological pathway, the cell-cycle sequence of protein states, is a globally attracting trajectory of the dynamics. These properties are largely preserved with respect to small perturbations to the network. These results suggest that cellular regulatory networks are robustly designed for their functions. Despite the complex environment in and outside of the cell, various cellular functions are carried out reliably by the underlying biomolecular networks. How is the stability of a cell state achieved? How can a biological pathway take the cell from one state to another reliably? Evolution must have played a crucial role in the selection of the architectures of these networks for them to have such a remarkable property. Much attention has recently been focused on the ''topological'' properties of largescale networks (1-5). It was argued that a power-law distribution of connectivity, which is apparent for some bionetworks (2, 4), is more tolerable against random failure (1). Here we address this question from a dynamic systems point of view. We study the network regulating the cell cycle of the budding yeast, investigating its global dynamical property and stability. We find that the stationary states of the cell, or states at the checkpoints in general, correspond to global attractors of the dynamics: almost all initial protein states flow to these biological stationary states. Furthermore, the biological pathway of the cell-cycle sequence, which is a particular trajectory in the state space, is a globally stable and attracting trajectory of the dynamics. These dynamic properties, arising from the underlying network connection, are also robust against small perturbations to the network. They are directly responsible for the robustness of the cellular process. The Yeast Cell-Cycle NetworkThe cell-cycle process, by which one cell grows and divides into two daughter cells, is a vital biological process the regulation of which is highly conserved among the eukaryotes (6). The process consists of four phases: G 1 (in which the cell grows and, under appropriate conditions, commits to division), S (in which the DNA is synthesized and chromosomes replicated), G 2 (a ''gap'' between S and M), and M (in which chromosomes are separated and the cell is divided into two). After the M phase, the cell enters the G 1 phase, hence completing a ''cycle.'' The process has been studied in great detail in the budding yeast Saccharomyces cerevisiae, a single-cell model eukaryotic organism (see supporting information, which is publishe...

Biochemical and statistical network models for systems biology

“…Boolean networks have also been used to model the yeast and mammalian cell cycle [33,34]. Li et al demonstrated that the cell cycle sequence of protein states, which is a globally attracting trajectory of the dynamics, is extremely robust with respect to small perturbations to the network.…”

Modelling gene and protein regulatory networks with Answer Set Programming

“…This setup already allows to model fairly complex interaction networks, such as the Budding Yeast network described in Li et al (2004). We describe the model of this network in Fayruzov (2009).…”

“…We have applied our tool to model the Budding Yeast network presented in Li et al (2004) and the Fission Yeast network described in Davidich & Bornholdt (2008). The details and complete answer set programs can be found in the technical report Fayruzov (2009).…”

Niflumic acid disrupts marine spermatozoan chemotaxis without impairing the spatiotemporal detection of chemoattractant gradients

“…The model consists of 22 nodes representing the principal components involved, or likely participating, in the signaling cascade: ion channel activities, intracellular ion and molecular concentrations and the membrane potential, amongst others. To analyze the dynamics of the network, we implemented a discrete formulation that is a generalization of the Boolean approach and that has proven to be revealing for the gene regulation dynamics of many systems (Kauffman, 1969;Espinosa-Soto et al, 2004;Albert and Othmer, 2003;Huang and Ingber, 2000;Li et al, 2004), as well as other cell signaling networks (Morris et al, 2010). In this approach, the dynamic state of the network consists of a set of N discrete variables {s 1 , s 2 ,... s n }, each representing the state of a node.…”