  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.
