Analysis of biochemical networks using linear programming

The application of mathematical programming methodologies to biochemical systems is demonstrated with the presentation of a linear programming (LP) algorithm for calculating minimal pathway distances in biochemical networks. Minimal pathway distances are identified as the smallest number of steps separating two nodes in the network. Two case studies are examined: 1) the minimal distances for Escherichia coli Small Molecule Metabolism (SMM) enzymes are calculated and their correlations with genome distance and enzyme function are considered; 2) a study of the p53 cell cycle and apoptosis control network is performed in order to assess the survivability of the network to both random node failures and a directed assault, by studying the modification of the network’s diameter for successive protein knockouts. The results verify the applicability of the algorithm to problems of biochemical nature.