Coarse-Grained Molecular Simulation of Diffusion and Reaction Kinetics in a Crowded Virtual Cytoplasm

Abstract

We present a general-purpose model for biomolecular simulations at the molecular level that incorporates stochasticity, spatial dependence, and volume exclusion, using diffusing and reacting particles with physical dimensions. To validate the model, we first established the formal relationship between the microscopic model parameters (timestep, move length, and reaction probabilities) and the macroscopic coefficients for diffusion and reaction rate. We then compared simulation results with Smoluchowski theory for diffusion-limited irreversible reactions and the best available approximation for diffusion-influenced reversible reactions. To simulate the volumetric effects of a crowded intracellular environment, we created a virtual cytoplasm composed of a heterogeneous population of particles diffusing at rates appropriate to their size. The particle-size distribution was estimated from the relative abundance, mass, and stoichiometries of protein complexes using an experimentally derived proteome catalog from Escherichia coli K12. Simulated diffusion constants exhibited anomalous behavior as a function of time and crowding. Although significant, the volumetric impact of crowding on diffusion cannot fully account for retarded protein mobility in vivo, suggesting that other biophysical factors are at play. The simulated effect of crowding on barnase-barstar dimerization, an experimentally characterized example of a bimolecular association reaction, reveals a biphasic time course, indicating that crowding exerts different effects over different timescales. These observations illustrate that quantitative realism in biosimulation will depend to some extent on mesoscale phenomena that are not currently well understood.

Modeling Three-Dimensional Spatial Regulation of Bacterial Cell Division (Dissertation)

“…In addition, as previously reported in (Ridgway et al, 2008), mass action fails to correctly reproduce the predicted survival probability of A for volume reversible reactions (Figure 2.5A) because it assumes A, B and C to be HD species. Figure 2.5B…”

“…Instead, we use a time-driven, lattice-based method to skip two costly operations -molecule search and distance calculation -required by off-lattice methods (Andrews and Bray, 2004;van Zon and ten Wolde, 2005b;Ridgway et al, 2008) to resolve collisions. Diffusion-independent reactions, however, are event driven to further reduce the computational cost.…”

Molecular simulations of cellular processes

“…Ridgway et al (2008) represented the E. coli cytoplasm with 12 types of inert spherical crowders, whose sizes and abundances reflected the ones measured in the bacterium. They used a continuous reaction-diffusion equation, solved for discrete particle jumps, to efficiently simulate particle motion and also binding.…”

Modeling Three-Dimensional Spatial Regulation of Bacterial Cell Division (Dissertation)

“…To verify the diffusion-influenced reactions of our method we employ a similar approach as in (Ridgway et al, 2008) by comparing the simulation results with the predicted survival probability of reacting species in irreversible (S irr ) and reversible (S rev ) reactions. Here, we describe the analytical and numerical methods to obtain S irr and S rev since they have not been previously described for surface reactions.…”

“…The anomalous diffusion, defined as sub-linear scaling of meansquared displacement of the molecule over time, is used as a measure for cytoplasmic crowding (Weiss et al, 2004). Molecular crowding can also alter protein activities and reaction kinetics (Ridgway et al, 2008). For reviews about the influence of molecular crowding on thermodynamics and volume exclusion, including experimental findings and biochemical reactions in physiological media, see (Minton, 2001) and (Hall and Minton, 2003).…”