Fast Monte Carlo Simulation Methods for Biological Reaction-Diffusion Systems in Solution and on Surfaces

Abstract

Many important physiological processes operate at time and space scales far beyond those accessible to atom-realistic simulations, and yet discrete stochastic rather than continuum methods may best represent finite numbers of molecules interacting in complex cellular spaces. We describe and validate new tools and algorithms developed for a new version of the MCell simulation program (MCell3), which supports generalized Monte Carlo modeling of diffusion and chemical reaction in solution, on surfaces representing membranes, and combinations thereof. A new syntax for describing the spatial directionality of surface reactions is introduced, along with optimizations and algorithms that can substantially reduce computational costs (e.g., event scheduling, variable time and space steps). Examples for simple reactions in simple spaces are validated by comparison to analytic solutions. Thus we show how spatially realistic Monte Carlo simulations of biological systems can be far more cost-effective than often is assumed, and provide a level of accuracy and insight beyond that of continuum methods.

New insights into short-term synaptic facilitation at the frog neuromuscular junction

“…788) using a custom binary output format to allow for efficient storage and compression of simulation results. The algorithms underlying MCell have been described in detail in the past (Kerr et al 2008;Stiles and Bartol 2001). For each distinct simulation condition (different numbers of Ca 2ϩ sensor sites on vesicles, varying external Ca 2ϩ concentration, etc.)…”

“…1A). Using stochastic reaction-diffusion simulation via MCell (Kerr et al 2008;Stiles and Bartol 2001), we were able to show that a model of the frog NMJ with eight synaptotagmin molecules on each synaptic vesicle (corresponding to 40 Ca 2ϩ binding sites) without any ad hoc Ca 2ϩ binding site cooperativity could predict experimentally known properties of single-action potential-triggered vesicle fusion ). In the current study we found that our previous model was not able to predict the experimentally observed facilitation during multiple stimuli at high frequency.…”

Coupled Mesoscopic and Microscopic Simulation of Stochastic Reaction-Diffusion Processes in Mixed Dimensions

“…In the microscopic model, individual molecules move by Brownian motion and when they are close they can react with each other. The molecules diffuse in the simulation either by taking small time steps in a solution of a Langevin equation [5,32] or by sampling a probability distribution for the new position [29,40,52]. Such microscopic models are much more computationally demanding than a corresponding mesoscopic simulation, at least for reasonable mesh resolutions.…”

“…[2,22,28,50] and for microscopic simulation e.g. [4,32,48,52] of cell biochemistry and diffusion. Some of them are compared in [14], but only a few integrate single molecule models with a meso or macro level model [6,42].…”

“…In this way, the randomness of the motion and reactions of single molecules bound to a membrane is modeled. Other software packages for microscopic simulations on membranes, such as Smoldyn [3][4][5] and MCell [32] are available. They are also based on the Smoluchowski model but differ from our approach.…”