Specification, Construction, and Exact Reduction of State Transition System Models of Biochemical Processes

TL;DR

This paper presents a high-level modeling approach for biochemical systems using hypergraphs, enabling automated generation and exact reduction of large state transition models through symmetry and invariant manifold techniques.

Contribution

It introduces a novel method combining high-level hypergraph specification with automated exact reduction techniques for biochemical state transition models.

Findings

Successfully reduced complex biochemical models to manageable sizes

Automated symmetry and invariant manifold reduction techniques are effective

Application to ion-channel models demonstrates practical utility

Abstract

Biochemical reaction systems may be viewed as discrete event processes characterized by a number of states and state transitions. These systems may be modeled as state transition systems with transitions representing individual reaction events. Since they often involve a large number of interactions, it can be difficult to construct such a model for a system, and since the resulting state-level model can involve a huge number of states, model analysis can be difficult or impossible. Here, we describe methods for the high-level specification of a system using hypergraphs, for the automated generation of a state-level model from a high-level model, and for the exact reduction of a state-level model using information from the high-level model. Exact reduction is achieved through the automated application of symmetry reduction and invariant manifold reduction techniques to the high-level model, allowing potentially significant reductions without the need to generate a full model. The application of the method to biochemical reaction systems is illustrated by models describing a hypothetical ion-channel at several levels of complexity. The method allows for the reduction of the otherwise intractable example models to a manageable size.