Positivity preserving chemical Langevin equations

Chemical kinetic equations for cellular biochemical systems generally include stochastic contributions which arise as a consequence of Brownian buffeting of the small numbers of participating molecules. The precise structure of these kinetic equations is not known with complete certainty, but at present some arguments favor equations of chemical Langevin form. Unfortunately, these equations sometimes predict negative concentrations. Here we explore a way of modifying the chemical Langevin equations such that they preserve positivity. To test the validity of this approach we apply the original and modified equations to two representative biochemical problems. Numerical solutions are obtained using a recently developed algorithm for stochastic differential equations. We find that positivity is indeed obtained for the modified equations without distortion of the interesting qualitative aspects of the original solutions.