Role of Self-Loop in Cell-Cycle Network of Budding Yeast

Shu-Ichi Kinoshita,Hiroaki Yamada

doi:10.4236/ojbiphy.2019.91002

Abstract

Study of network dynamics is very active area in biological and social sciences. However, the relationship between the network structure and the attractors of the dynamics has not been fully understood yet. In this study, we numerically investigated the role of degenerate self-loops on the attractors and its basin size using the budding yeast cell-cycle network model. In the network, all self-loops negatively surpress the node (self-inhibition loops) and the attractors are only fixed points, i.e. point attractors. It is found that there is a simple division rule of the state space by removing the self-loops when the attractors consist only of point attractors. The point attractor with largest basin size is robust against the change of the self-inhibition loop. Furthermore, some limit cycles of period 2 appear as new attractor when a self-activation loop is added to the original network. It is also shown that even in that case, the point attractor with largest basin size is robust.

Highlights

Some networks representing metabolic reactions in the cell and gene regulatory responses through transcription factors have been elucidated along with progress of experimental systems and accumulation technology in the database [1]
Li et al discovered that in the model of the gene regulatory network related to the cell-cycle, there is a fixed point with a very large basin size, and the transition process to the fixed point corresponds to the expression pattern of the gene in each process of the cell-cycle [10]
We investigated the influence of the degenerate self-loop on attractor of the gene regulatory network model of the cell-cycle of budding yeast

Summary

Introduction

Some networks representing metabolic reactions in the cell and gene regulatory responses through transcription factors have been elucidated along with progress of experimental systems and accumulation technology in the database [1]. Yamada with such network structures have been widely studied on the properties of the attractors that represent cellular activity states. In this study, using the same gene regulatory network as Li et al for the budding yeast, we clarify the relationship between the fixed points (point attractors) with large basin size and the presence of the self-loops in the network. The budding yeast cell-cycle network model (denoted by G ( 0) ) by Li et al is a special one in a sense that all nodes of the existing self-loops are given as aii = −1. Note that for fission yeast cell-cycle model with similar network structure some limit cycles of period two appear as the attractor because some of the threshold value are not zero [15] [16]. Notice that when an active self-loop is attached to the node the state update rule becomes different from those of Tran et al due to the existence of rule (3)

Numerical Result

Case of Removing Degenerate Self-Loop

Case of Adding Active Self-Loop

Findings

Summary and Discussion