  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.
