Minimization and Equivalence in Multi-valued Logical Models of Regulatory Networks

TL;DR

This paper investigates conditions under which different multi-valued logical models of biological regulatory networks exhibit equivalent dynamics, and introduces an algorithm to find minimal models within these equivalence classes.

Contribution

It provides a theoretical analysis of dynamic equivalence in multi-valued models and offers an efficient algorithm for constructing minimal representatives of model classes.

Findings

Identifies conditions for dynamic equivalence between models

Characterizes structurally maximal and minimal models

Develops an algorithm for minimal model construction

Abstract

Multi-valued logical models can be used to describe biological networks on a high level of abstraction based on the network structure and logical parameters capturing regulatory effects. Interestingly, the dynamics of two distinct models need not necessarily be different, which might hint at either only non-functional characteristics distinguishing the models or at different possible implementations for the same behaviour. Here, we study the conditions allowing for such effects by analysing classes of dynamically equivalent models and both structurally maximal and minimal representatives of such classes. Finally, we present an efficient algorithm that constructs a minimal representative of the respective class of a given multi-valued model.