Computing sparse and dense realizations of reaction kinetic systems

A numerical procedure for finding the sparsest and densest realization of a given reaction network is proposed in this paper. The problem is formulated and solved in the framework of mixed integer linear programming (MILP) where the continuous optimization variables are the nonnegative reaction rate coefficients, and the corresponding integer variables ensure the finding of the realization with the minimal or maximal number of reactions. The mass-action kinetics is expressed in the form of linear constraints adjoining the optimization problem. More complex realization problems can also be solved using the proposed framework by modifying the objective function and/or the constraints appropriately.