Coarse-grained brownian dynamics simulation of rule-based models

International audienceStudying spatial effects in signal transduction, such as co-localization along scaffold molecules, comes at a cost of complexity. In this paper, we propose a coarse-grained, particle-based spatial simulator, suited for large signal transduction models. Our approach is to combine the particle-based reaction and diffusion method, and (non-spatial) rule-based modeling: the location of each molecular complex is abstracted by a spheric particle, while its internal structure in terms of a site-graph is maintained explicit. The particles diffuse inside the cellular compartment and the colliding complexes stochastically interact according to a rule-based scheme. Since rules operate over molecular motifs (instead of full complexes), the rule set compactly describes a combinatorial or even infinite number of reactions. The method is tested on a model of Mitogen Activated Protein Kinase (MAPK) cascade of yeast pheromone response signaling. Results demonstrate that the molecules of the MAPK cascade co-localize along scaffold molecules, while the scaffold binds to a plasma membrane bound upstream component, localizing the whole signaling complex to the plasma membrane. Especially we show, how rings stabilize the resulting molecular complexes and derive the effective dissociation rate constant for it

Exact solution for anisotropic diffusion-controlled reactions with partially reflecting conditions

We investigate a generalization of the model of Solc and Stockmayer to describe the diffusion-controlled reactions between chemically anisotropic reactants taking into account the partially reflecting conditions on two parts of the reaction surface. The exact solution of the relevant mixed boundary-value problem was found for different ratios of the intrinsic rate constants. The results obtained may be used to test numerical programs that describe diffusion-controlled reactions in real systems of particles with anisotropic reactivity

Point-particle method to compute diffusion-limited cellular uptake

International audienceWe present an efficient point-particle approach to simulate reaction-diffusion processes of spherical absorbing particles in the diffusion-limited regime, as simple models of cellular uptake. The exact solution for a single absorber is used to calibrate themethod, linking the numerical parameters to the physical particle radius and uptake rate. We study the configurations of multiple absorbers of increasing complexity to examine the performance of themethod by comparing our simulations with available exact analytical or numerical results. We demonstrate the potential of the method to resolve the complex diffusive interactions, here quantified by the Sherwood number, measuring the uptake rate in terms of that of isolated absorbers. We implement the method in a pseudospectral solver that can be generalized to include fluid motion and fluid-particle interactions. As a test case of the presence of a flow, we consider the uptake rate by a particle in a linear shear flow. Overall, our method represents a powerful and flexible computational tool that can be employed to investigate many complex situations in biology, chemistry, and related sciences

Diffusion coefficient of cucurbit[n]urils (n = 6 or 7) at different concentrations, temperatures and pH

The diffusion coefficient of cucurbit[6]uril (CB[6]) and cucurbit[7]uril (CB[7]) was determined using pulsed gradient spin−echo nuclear magnetic resonance spectroscopy. Both CB[6] and CB[7] diffuse faster through H2O than D2O with increasing temperature, consistent with the Stokes−Einstein equation where diffusion is proportional to temperature divided by viscosity. The activation energy (EA) was also determined and is larger for CB[n] in 90 % H2O/10 % D2O v/v than in D2O. Both compounds aggregate with increasing concentration between (0.25 and 2)·10−3 mol·L−1. The pH of the solution does not significantly affect the diffusion coefficient of CB[6] and CB[7], except at very low pH where protonation of the carbonyl groups induces aggregation, which slows their rate of diffusion