Interpretable exact linear reductions via positivity
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 selfconsistent lowerdimensional 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 zeroone 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, reparametrizes 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.
 Publication:

arXiv eprints
 Pub Date:
 April 2021
 arXiv:
 arXiv:2104.14180
 Bibcode:
 2021arXiv210414180P
 Keywords:

 Quantitative Biology  Molecular Networks;
 Electrical Engineering and Systems Science  Systems and Control