Lumpability Abstractions of Rule-based Systems

TL;DR

This paper introduces a mathematical framework for reducing the complexity of rule-based biological systems by lumping states, ensuring the preservation of stochastic semantics and enabling more efficient analysis of signaling pathways.

Contribution

It proves that a specific quotienting method guarantees weak lumpability and establishes a backward Markov bisimulation, advancing the modeling of complex biological systems.

Findings

Framework applied to EGF/insulin receptor crosstalk case study

Proves quotienting preserves stochastic semantics

Establishes conditions for lumpability and bisimulation

Abstract

The induction of a signaling pathway is characterized by transient complex formation and mutual posttranslational modification of proteins. To faithfully capture this combinatorial process in a mathematical model is an important challenge in systems biology. Exploiting the limited context on which most binding and modification events are conditioned, attempts have been made to reduce the combinatorial complexity by quotienting the reachable set of molecular species, into species aggregates while preserving the deterministic semantics of the thermodynamic limit. Recently we proposed a quotienting that also preserves the stochastic semantics and that is complete in the sense that the semantics of individual species can be recovered from the aggregate semantics. In this paper we prove that this quotienting yields a sufficient condition for weak lumpability and that it gives rise to a backward Markov bisimulation between the original and aggregated transition system. We illustrate the framework on a case study of the EGF/insulin receptor crosstalk.