ReDirection: Predict Dominant Direction of Reactions of a Biochemical Network
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.
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