Extending rule-based methods to model molecular geometry

Computational modeling is an important tool for the study of complex biochemical processes associated with cell signaling networks. However, it is challenging to simulate processes that involve hundreds of large molecules due to the high computational cost of such simulations. Rule-based modeling is a computational method that can be used to model these processes with reasonably low computational cost, but traditional rule-based modeling approaches do not include details of molecular geometry. The incorporation of molecular geometry into biochemical models can more accurately capture details of these processes, and may lead to insights into how geometry affects the products that form. Furthermore, geometric rule-based modeling can be used to complement other computational methods that explicitly represent molecular geometry in order to quantify binding site accessibility and steric effects. In this work, we propose a novel implementation of rulebased modeling that encodes details of molecular geometry into the rules and the binding rate constant associated with each rule. We demonstrate how the set of rules is constructed according to the curvature of the molecule. We then perform a study of antigen-antibody aggregation using our proposed method. We first simulate the binding of IgE antibodies bound to cell surface receptors Fc RI to various binding regions of the shrimp allergen Pen a 1 using a previously developed 3D rigid-body Monte Carlo simulation, and we analyze the distribution of the sizes of the aggregates that form during the simulation. Then, using our novel rule-based approach, we optimize a rule-based model according to the geometry of the Pen a 1 molecule and the data from the Monte Carlo simulation. In particular, we use the distances between the binding regions of the Pen a 1 molecule to optimize the rules and associated binding rate constants. We perform this procedure for three molecular conformations of Pen a 1 and analyze the impact of conformation on the aggregate size distribution and the optimal rule-based model. We find that the optimized rule-based models provide information about the average steric hindrance between binding regions and the probability that IgE-Fc RI receptor complexes will bind to these regions. In addition, the optimized rule-based models provide a means of quantifying the variation in aggregate size distribution that results from differences in molecular geometry.