# Markov chain aggregation and its application to rule-based modelling

## TL;DR

This paper presents a method to efficiently aggregate Markov chains derived from rule-based molecular models, reducing complexity while preserving key properties, thus enabling analysis of large biochemical systems.

## Contribution

It introduces algorithms based on formal lumpability concepts to automatically construct smaller, equivalent Markov chains without enumerating all states, applicable to complex biological models.

## Key findings

- Successfully applied to a signaling pathway example
- Reduces computational complexity of Markov chain analysis
- Preserves essential properties of the original chain

## Abstract

Rule-based modelling allows to represent molecular interactions in a compact and natural way. The underlying molecular dynamics, by the laws of stochastic chemical kinetics, behaves as a continuous-time Markov chain. However, this Markov chain enumerates all possible reaction mixtures, rendering the analysis of the chain computationally demanding and often prohibitive in practice. We here describe how it is possible to efficiently find a smaller, aggregate chain, which preserves certain properties of the original one. Formal methods and lumpability notions are used to define algorithms for automated and efficient construction of such smaller chains (without ever constructing the original ones). We here illustrate the method on an example and we discuss the applicability of the method in the context of modelling large signalling pathways.