Exact linear reduction for rational dynamical systems

TL;DR

This paper extends the CLUE algorithm to enable exact linear reduction of dynamical systems with rational dynamics, facilitating model simplification in life sciences.

Contribution

We developed an extension of the CLUE algorithm to handle rational dynamics, broadening its applicability to more realistic biological models.

Findings

Successfully applied to literature examples

Preserves key variables in reduced models

Available implementation in CLUE v1.5

Abstract

Detailed dynamical systems models used in life sciences may include dozens or even hundreds of state variables. Models of large dimension are not only harder from the numerical perspective (e.g., for parameter estimation or simulation), but it is also becoming challenging to derive mechanistic insights from such models. Exact model reduction is a way to address this issue by finding a self-consistent lower-dimensional projection of the corresponding dynamical system. A recent algorithm CLUE allows one to construct an exact linear reduction of the smallest possible dimension such that the fixed variables of interest are preserved. However, CLUE is restricted to systems with polynomial dynamics. Since rational dynamics occurs frequently in the life sciences (e.g., Michaelis-Menten or Hill kinetics), it is desirable to extend CLUE to the models with rational dynamics. In this paper, we present an extension of CLUE to the case of rational dynamics and demonstrate its applicability on examples from literature. Our implementation is available in version 1.5 of CLUE at https://github.com/pogudingleb/CLUE.