A mathematically rigorous algorithm to define, compute and assess relevance of the probable dissociation constant for every reaction of a constrained biochemical network

Abstract

Abstract Metabolism is a combination of enzymatic- and non-enzymatic interactions of several macro- and small-molecules and occurs via biochemical networks. Here, we present a mathematically rigorous algorithm to define, compute and assess relevance of the probable dissociation constant for every reaction of a constrained biochemical network. A reaction outcome is forward, reverse or equivalent, and is computed directly from the null space generated subspace of a stoichiometric number matrix of the reactants/products and reactions of the modelled biochemical network. This is accomplished by iteratively and recursively populating a reaction-specific sequence vector with the combinatorial sums of all unique and non-trivial vectors that span each null space generated subspace. After a finite number of iterations the terms of this reaction-specific sequence vector will diverge and belong to the open intervals \(\left(1,\infty \right)\) and/or \(\left(-\infty ,-1\right)\). Statistical and mathematical descriptors (mean, standard deviation, bounds, linear maps, vector norms, tests of convergence) are used to select and bin terms from the reaction-specific sequence vector into distinct subsets for all three predicted outcomes of a reaction. The terms of each outcome-specific subset are summed, mapped to the open interval \(\left(0,\infty \right)\) and used to populate a reaction-specific outcome vector. The p1-norm of this vector is numerically equal to the probable disassociation constant for that reaction. These steps are continued until every reaction of a modelled network is unambiguously annotated. Numerical studies to ascertain the relevance and suitability of the probable dissociation constant as a parameter are accomplished by characterizing a constrained biochemical network of aerobic glycolysis. This is implemented by the R-package “ReDirection” which is freely available and accessible at the comprehensive R archive network (CRAN) with the URL (https://cran.r-project.org/package=ReDirection).