A.3.2. Monte Carlo Simulations of Microphysiological Processes

Computational tools for modeling biological processes, at the microphysiological level, using realistic spatial representation: MCell

Numerous theoretical studies have analyzed physiological processes such as cell cycle control, chemotaxis, and viral infection using ODEs for reaction kinetics (Table A.2). These assume continuous chemical concentration and deterministic dynamics, which are usually violated in vivo, because most of the examined processes occur at low concentrations, are isolated spatially, and can involve slow reactions (96).

One numerical approach to complex systems of discrete, coupled stochastic reactions is the Monte Carlo (MC) algorithm described by Gillespie (97). This algorithm uses a random number generator to generate the probabilistic time-evolution of chemical reactions, and timesteps of variable length. While this method takes explicit account of the number of interacting molecules and the stochastic nature of their interactions, it becomes inefficient for large numbers of reactions, and does not consider the different substates associated with a given molecule. The simulator StochSim developed by Bray and coworkers (21;22;98), on the other hand, takes account of the different (complexed, chemically modified or conformationally distinct) forms of the same molecule, and reaction probabilities are assigned using rate constants known from experiments. While these simulations provide a more realistic description of the stochastic aspects of reaction systems, they do not take account of the spatially heterogeneous distribution of reactants. The implementation of detailed, spatially realistic models was a main motivation underlying the development of MCell, originally for neurotransmitter-mediated synaptic transmission (99) (http://www.mcell.psc.edu/). For space-independent unimolecular transitions such as unbinding and conformation changes, MCell computes time-evolved probabilities and makes decisions in a fashion similar to Gillespie method. For space-dependent associations, on the other hand, MCell's algorithm is a unique and highly optimized integration of probabilistic diffusion methods and testing for binding transitions.

In brief, MCell uses high-resolution 3-D polygon meshes to represent curved cell and organelle membranes, and the defined structure and diffusion space is then populated with molecules that interact probabilistically (Fig. A.2, color version in Appendix). Molecules move by random walk (BD), and test for all possible transitions (binding, unbinding, conformation changes) using MC probabilities derived from bulk solution rate constants. Details about individual molecular structures are ignored (making computation feasible), but the functional impact of individual molecular positions and density fluctuations within realistic subcellular topologies are included explicitly. During the past year, we have rigorously tested and described our methods for use with simple and complex biochemical reaction networks superimposed on increasingly complex spatial arrangements of participating molecules(16).

During the Center's planning phase, adaptation of MCell simulations to projects such as DP1-3 will begin with proof-of-principle steps and bi-directional education between the computational and experimental collaborators. The relevant chemical reaction pathways (e.g., NO signaling or DNA damage recognition) will be translated into modular MCell input files that can be used piecemeal or in combination. In addition, modular cell structure input files will be designed at variable levels of complexity, ranging from simple uniform organization to realistic architectures for the cells under study (see § A.4.4). Thereafter, different static or dynamic signaling paradigms will be used with the reaction and structural modules in different combinations, and the results will be used in two primary ways: (1) for direct comparison with experimental measurements of reactant time courses and, where available, spatial distributions; and (2) to parameterize stochastic variability and other kinetic factors for higher-level mathematical models (see § A.3.3 and A.4.4). Output from these proof-of-principle (and beyond) studies will be novel and critical preliminary results for later submission of a full Center grant proposal.