Stochastic Dynamic Modeling of Cellular Protein Interactions

Mark Kon, Julio Castrillon, Dmitri Beglov, and Sandor Vajda

Supported by:
NIH R01GM131409 “Stochastic Dynamic Modeling of Cellular Protein Interactions” (PI: Mark Kon)
NIH R35 GM118078 “Analysis and Prediction of Molecular Interactions” (PI: Sandor Vajda)

Stochastic methods for modeling molecular-protein interactions form an entirely new set of ap-proaches to the important biological goal of simulating cellular biology in silico. Though great progress has been made in this direction by computational biologists over the past 15 years, the goal of “siliconizing” cellular molecular interactions still remains remote. More precisely, the current level of model realism has led to a plateau in the prediction accuracy of molecular interactions. This motivates the development of some novel dynamic models that incorporate biological dynamic uncertainty, adding a significant layer to the realism of the biological processes. However, such models are computationally daunting, thus motivating the development of efficient and accurate computational methods to solve them.

Receptor-ligand interactions (docking) consists of two primary selections. One is the choice of goodness of fit measure (called the scoring function) while the other is the choice of the search algorithm. Both of these decisions are based on an assumed molecular model. The scoring function includes consideration of molecular properties, which includes electron density representations of the molecular shape. Another important property involves the electrostatic fields generated by the proteins, which are numerically computed using the nonlinear Poisson Boltzmann (PB) Partial Differential Equation (PDE). Prof. Castrillo, at the Department of Mathematics and Statistics from Boston University, has significant experience in the area of stochastic PDEs with probabilistic domains and high dimensional computational statistics. Prof. Mark Kon has a PhD from MIT in Applied Mathematics. He has an extensive background in high dimensional probability theory and statistics, and machine learning (ML). Prof. Vajda has been successful in developing rigid body docking algorithms, such as ClusPro, which is extensively used and cited by the computational biology community. Prof. Beglov was one of the key developers of protein docking program PIPER used in ClusPro. The major shortcoming of ClusPro and all global docking algorithms is the rigid body assumption. Although docking algorithms have been developed to account for backbone flexibility, these are inherently local, and for the difficult targets in the CAPRI benchmark datasets have not performed better than rigid methods. The main goal of this collaboration is to introduce probabilistic modeling of protein structures into the interactions; this is posed as a stochastic optimization. However, for many cases the stochastic scoring function will become a high dimensional, non-Gaussian, non-linear random field that will be computationally very challenging to optimize with reasonable accuracy. This is a hard problem that we plan to address in this project by developing novel mathematical theory and numerical analysis for non-linear partial differential equations.