Fast Parallel Algorithm for Large Fractal Kinetic Models with Diffusion

Chemical kinetic simulations are usually based on the law of mass action that applies to behavior of particles in solution. Molecular interactions in a crowded medium as in a cell, however, are not easily described by such conventional mathematical treatment. Fractal kinetics is emerging as a novel method for simulating kinetic reactions in such an environment. To date, there has not been a fast, efficient, and, more importantly, parallel algorithm for such computations. Here, we present an algorithm with several novel features for simulating large (with respect to size and time scale) fractal kinetic models. We applied the fractal kinetic technique and our algorithm to a canonical substrate-enzyme model with explicit phase-separation in the product, and achieved a speed-up of up to 8 times over previous results with reasonably tight bounds on the accuracy of the simulation. We anticipate that this technique and algorithm will have important applications to simulation of intra-cell biochemical reactions with complex dynamic behavior.