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2021 | OriginalPaper | Chapter

Interpretable Exact Linear Reductions via Positivity

Authors : Gleb Pogudin, Xingjian Zhang

Published in: Computational Methods in Systems Biology

Publisher: Springer International Publishing

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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 [16] 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.

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previous chapter Compiling Elementary Mathematical Functions into Finite Chemical Reaction Networks via a Polynomialization Algorithm for ODEs

next chapter Explainable Artificial Neural Network for Recurrent Venous Thromboembolism Based on Plasma Proteomics

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Title: Interpretable Exact Linear Reductions via Positivity
Authors: Gleb Pogudin
Xingjian Zhang
Publisher: Springer International Publishing
Book: Computational Methods in Systems Biology
Print ISBN: 978-3-030-85632-8

Electronic ISBN: 978-3-030-85633-5

Copyright Year: 2021
DOI: https://doi.org/10.1007/978-3-030-85633-5_6

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