Abstract

In biology, intracellular molecular systems are elaborate. Systems biology and bioinformatics are examples of whole areas of research which exist to make sense of these types of complex systems. As technology inevitably marches forward it has offered a tool for which complex systems may be investigated; simulation. Simulating a whole human cell at the level of individual molecules and proteins is an ambitious goal for mathematicians and computer scientists. There are multiple approaches to simulating stochastic intracellular molecular systems with spatial resolution. One of the most common approaches, due to its relative conceptual simplicity, utilises Smoluchowski reaction kinetics. The primary characteristic of these approaches is the abstract reduction of the chemical reaction to a rule that states that reactions may occur when two reactants are within a particular distance of each other. The critical distance that is used in the simulation is a parameter which controls the macroscopic reaction rate. One of the greatest problems with these types of approaches is that they are only applicable to bimolecular reactions. In this presentation, I hope to demonstrate that overcoming this limitation is critical to accurate Smoluchowski-like simulation of diffusion-limited chemical systems which contain catalytic reactions. Often exploited in mathematics, catalytic reactions may usually be approximated by high order reactions (reactions that involve three or more reactants). I will present a generalised Smoluchowski theory for diffusion-limited reaction kinetics of any order, N.