Boolean Models of Biological Processes Explain Cascade-Like Behavior

Hao Chen,Chen Zeng,Rahul Simha,Chenghang Du,Guanyu Wang

doi:10.1038/srep20067

Abstract

Biological networks play a key role in determining biological function and therefore, an understanding of their structure and dynamics is of central interest in systems biology. In Boolean models of such networks, the status of each molecule is either “on” or “off” and along with the molecules interact with each other, their individual status changes from “on” to “off” or vice-versa and the system of molecules in the network collectively go through a sequence of changes in state. This sequence of changes is termed a biological process. In this paper, we examine the common perception that events in biomolecular networks occur sequentially, in a cascade-like manner, and ask whether this is likely to be an inherent property. In further investigations of the budding and fission yeast cell-cycle, we identify two generic dynamical rules. A Boolean system that complies with these rules will automatically have a certain robustness. By considering the biological requirements in robustness and designability, we show that those Boolean dynamical systems, compared to an arbitrary dynamical system, statistically present the characteristics of cascadeness and sequentiality, as observed in the budding and fission yeast cell- cycle. These results suggest that cascade-like behavior might be an intrinsic property of biological processes.

Highlights

To answer this question, we model biological system with Boolean methods
Observing the budding and fission yeast cell-cycle, we find that: beyond dominant inhibition rule, both of them obey two additional dynamical rules which are robustness-related:
We ask the question: how likely is it that an arbitrary Boolean process has a network solution? We examined this question for both the case with robustness constraints (Eqs [2,3,4,5,6,7]) and without (only Eq [1])

Summary

Introduction

Boolean models have been applied widely in systems biology1,2 In these models, time is discrete and the whole dynamical process is divided into several time steps, the status of a particular molecule i at any given time step is either “on” (active, or in high concentration) or “off ” (inactive, or in low concentration), and in the time step the status of i is determined by the statuses of the molecules interacting with i in the present time step. Looking at the diagonal in the table, one can see that most of the “1” elements in the table are clustered along the diagonal, except for molecules Cdh and Sic (which are active in off-diagonal entries) This is a typical example of the striking cascade-like sequence of events. Observing the budding and fission yeast cell-cycle, we find that: beyond dominant inhibition rule, both of them obey two additional dynamical rules which are robustness-related:

Methods

Results

Conclusion