Mathematical Modeling of Biomolecular Surfaces

点击翻译按钮获取中文摘要

Molecular surfaces are paramount to the stability and solubility of macromolecules, such as proteins, DNAs and RNAs, because their features determine how other molecules interact with them to produce the desired function. Important applications of molecular surfaces include protein folding, protein-protein interfaces, protein-membrane interaction, DNA binding and bending, macromolecular docking, enzyme catalysis, solvation energy and molecular dynamics. Despite extensive effort in the past three decades, the generation and analysis of molecular surfaces remain a bottleneck in the structure prediction of biomolecules. To overcome this difficulty, investigators introduce a partial differential equation (PDE) based approach of molecular surface modeling. A set of curvature-controlled PDEs is designed for molecular surface generation. Two new concepts, molecular multiresolution surfaces and minimal molecular surfaces, which naturally arise in the proposed PDE modeling, are introduced to the field of molecular biology. The proposed molecular multiresolution surfaces provide a unified description of the van der Waals surface, solvent accessible surface, and solvent excluded surface. The proposed minimal molecular surface is also consistent with surface free energy minimization. Numerical techniques, including PDE solution algorithms and isosurface extraction schemes will be investigated. Numerical tests will be carried out to validate the proposed ideas.This project will lead to reliable methods in the structure prediction of biomolecules. Structural information is particularly important for rational drug design efforts specifically targeting proteins and/or membranes. It can be expected that the availability of more protein/membrane structures will lead to accelerated drug development efforts. The mathematical analysis proposed in this project will also impact image processing, pattern recognition, and computer vision. The results of the proposed project can be used for detailed control of PDE surfaces according to industrial and scientific needs and objectives. In particular, nonlinear diffusivities in the proposed equations can be used to control the shape of a PDE surface locally according to its curvature. The proposed research has a strong educational component. The project will support the training of a Ph.D. student researcher in mathematical biology. PDE-based molecular surface modeling is a suitable topic for graduate theses and undergraduate projects. Project results will be incorporated in graduate courses in biological modeling and simulation.