Robust Regulatory Networks

TL;DR

This paper formalizes the concept of robustness in gene regulatory networks using boolean network models, exploring their structures and conditions under which they maintain functionality despite mutations.

Contribution

It introduces a rigorous mathematical framework for understanding robustness in regulatory networks and provides explicit constructions and impossibility results for such networks.

Findings

Explicit constructions of robust networks

Negative results on the existence of certain robust networks

Insights into the structure of robust regulatory networks

Abstract

One of the characteristic features of genetic networks is their inherent robustness, that is, their ability to retain functionality in spite of the introduction of random errors. In this paper, we seek to better understand how robustness is achieved and what functionalities can be maintained robustly. Our goal is to formalize some of the language used in biological discussions in a reasonable mathematical framework, where questions can be answered in a rigorous fashion. These results provide basic conceptual understanding of robust regulatory networks that should be valuable independent of the details of the formalism. We model the gene regulatory network as a boolean network, a general and well-established model introduced by Stuart Kauffman. A boolean network is said to be in a viable configuration if the node states of the network at its fixpoint satisfy some given constraint. We specify how mutations affect the behavior of the boolean network. A network is then said to be robust if most random mutations to the network reach a viable configuration. The main question investigated in our study is: given a constraint on the fixpoint configuration, does there exist a network that is robust with respect to it and, if so, what is its structure? We demonstrate both explicit constructions of robust networks as well as negative results disproving their existence.