RAPID NUMERICAL-INTEGRATION ALGORITHM FOR FINDING THE EQUILIBRIUM STATE OF A SYSTEM OF COUPLED BINDING REACTIONS

We have adapted a simple method of numerical integration to predict th e equilibrium state of a population of components under going reversib le association according to the Law of Mass Action. Its particular app lication is to populations of protein molecules in aqueous solution. T he method is based on Euler integration but employs an adaptive step s ize: the time increment being reduced if it would make the concentrati on of any component negative and increased while the concentration of any component changes at greater than a specified rate. Parameters of the algorithm have been optimized empirically using a model set of bin ding equilibria with dissociation constants ranging from 10(-5) M to 1 0(-9) M. The method obtains the solution to a set of binding equilibri a more rapidly than the conventional initial value methods (simple Eul er, 4th order Runge-Kutta and variable-step Runge-Kutta methods were t ested) fbi the same accuracy. A computer code in standard C is present ed.