r-ReDirection

Biologically relevant, yet mathematically sound constraints are used to compute the propensity and thence infer the dominant direction of reactions of a generic biochemical network. The reactions must be unique and their number must exceed that of the reactants,i.e., reactions >= reactants + 2. 'ReDirection', computes the null space of a user-defined stoichiometry matrix. The spanning non-zero and unique reaction vectors (RVs) are combinatorially summed to generate one or more subspaces recursively. Every reaction is represented as a sequence of identical components across all RVs of a particular subspace. The terms are evaluated with (biologically relevant bounds, linear maps, tests of convergence, descriptive statistics, vector norms) and the terms are classified into forward-, reverse- and equivalent-subsets. Since, these are mutually exclusive the probability of occurrence is binary (all, 1; none, 0). The combined propensity of a reaction is the p1-norm of the sub-propensities, i.e., sum of the products of the probability and maximum numeric value of a subset (least upper bound, greatest lower bound). This, if strictly positive is the probable rate constant, is used to infer dominant direction and annotate a reaction as "Forward (f)", "Reverse (b)" or "Equivalent (e)". The inherent computational complexity (NP-hard) per iteration suggests that a suitable value for the number of reactions is around 20. Three functions comprise ReDirection. These are check_matrix() and reaction_vector() which are internal, and calculate_reaction_vector() which is external.