Metabolic P grammars are a particular class of multiset rewriting grammars
introduced in the MP systems' theory for modelling metabolic processes. In this paper,
a new algebraic formulation of inverse dynamical problems, based on MP grammars
and Kronecker product, is given, for further motivating the correctness of the LGSS
(Log-gain Stoichiometric Stepwise) algorithm, introduced in 2010s for solving dynamical
inverse problems in the MP framework. At the end of the paper, a section is included
that introduces the problem of multicollinearity, which could arise during the execution
of LGSS, and that de nes an algorithm, based on a hierarchical clustering technique,
that solves it in a suitable way