Reverse engineering of biochemical equations from time-course data by means of genetic programming

Increased research aimed at simulating biological systems requires sophisticated parameter estimation methods. All current approaches, including genetic algorithms, need pre-existing equations to be functional. A generalized approach to predict not only parameters but also biochemical equations from only observable time-course information must be developed and a computational method to generate arbitrary equations without knowledge of biochemical reaction mechanisms must be developed. We present a technique to predict an equation using genetic programming. Our technique can search topology and numerical parameters of mathematical expression simultaneously. To improve the search ability of numeric constants, we added numeric mutation to the conventional procedure. As case studies, we predicted two equations of enzyme-catalyzed reactions regarding adenylate kinase and phosphofructokinase. Our numerical experimental results showed that our approach could obtain correct topology and parameters that were close to the originals. The mean errors between given and simulation-predicted time-courses were 1.6 × 10−5% and 2.0 × 10−3%, respectively. Our equation prediction approach can be applied to identify metabolic reactions from observable time-courses.