Interpretable exact linear reductions via positivity

TL;DR

This paper introduces an algorithm that enhances the interpretability of exact linear reductions in biochemical kinetic models by re-parametrizing the reduced variables, making the models more meaningful without losing their accuracy.

Contribution

The authors develop a novel algorithm that re-parametrizes exact linear reductions to improve interpretability, addressing the issue of non-physical variables in prior methods.

Findings

Uninterpretable variables are eliminated in case studies.

The algorithm produces more physically meaningful reduced models.

Implementation and case studies are publicly available.

Abstract

Kinetic models of biochemical systems used in the modern literature often contain hundreds or even thousands of variables. While these models are convenient for detailed simulations, their size is often an obstacle to deriving mechanistic insights. One way to address this issue is to perform an exact model reduction by finding a self-consistent lower-dimensional projection of the corresponding dynamical system. Recently, a new algorithm CLUE has been designed and implemented, which allows one to construct an exact linear reduction of the smallest possible dimension such that the fixed variables of interest are preserved. It turned out that allowing arbitrary linear combinations (as opposed to zero-one combinations used in the prior approaches) may yield a much smaller reduction. However, there was a drawback: some of the new variables did not have clear physical meaning, thus making the reduced model harder to interpret. We design and implement an algorithm that, given an exact linear reduction, re-parametrizes it by performing an invertible transformation of the new coordinates to improve the interpretability of the new variables. We apply our algorithm to three case studies and show that "uninterpretable" variables disappear entirely in all the case studies. The implementation of the algorithm and the files for the case studies are available at https://github.com/xjzhaang/LumpingPostiviser.