CLUE: Exact maximal reduction of kinetic models by constrained lumping of differential equations

TL;DR

CLUE is an algorithm that performs exact reduction of complex biological models by linear lumping, preserving key dynamics and enabling easier analysis of high-dimensional polynomial differential systems.

Contribution

It introduces a novel linear lumping method for exact reduction of polynomial differential equations, applicable to high-dimensional biological models.

Findings

Significantly reduces model dimensionality.

Preserves dynamics of specified linear combinations.

Facilitates biological insight extraction.

Abstract

Motivation: Detailed mechanistic models of biological processes can pose significant challenges for analysis and parameter estimations due to the large number of equations used to track the dynamics of all distinct configurations in which each involved biochemical species can be found. Model reduction can help tame such complexity by providing a lower-dimensional model in which each macro-variable can be directly related to the original variables. Results: We present CLUE, an algorithm for exact model reduction of systems of polynomial differential equations by constrained linear lumping. It computes the smallest dimensional reduction as a linear mapping of the state space such that the reduced model preserves the dynamics of user-specified linear combinations of the original variables. Even though CLUE works with nonlinear differential equations, it is based on linear algebra tools, which makes it applicable to high-dimensional models. Using case studies from the literature, we show how CLUE can substantially lower model dimensionality and help extract biologically intelligible insights from the reduction. Availability: An implementation of the algorithm and relevant resources to replicate the experiments herein reported are freely available for download at https://github.com/pogudingleb/CLUE. Supplementary information: enclosed.