Mathematical Modeling of Biomolecular Surfaces

分子表面对蛋白质、DNA和RNA等大分子的稳定性和溶解性至关重要，因为它们的特征决定了其他分子如何与它们相互作用以产生所需的功能。分子表面的重要应用包括蛋白质折叠、蛋白质-蛋白质界面、蛋白质-膜相互作用、DNA结合和弯曲、大分子对接、酶催化、溶剂化能和分子动力学。尽管在过去的三十年里做了大量的工作，但分子表面的产生和分析仍然是生物分子结构预测的瓶颈。为了克服这一困难，研究人员引入了一种基于偏微分方程(PDE)的分子表面建模方法。设计了一套曲率控制的偏微分方程组，用于分子表面的生成。将分子多分辨表面和最小分子表面这两个新概念引入分子生物学领域，这两个概念是在所提出的偏微分方程模型中自然产生的。所提出的分子多分辨表面提供了范德华表面、溶剂可及表面和溶剂排除表面的统一描述。所提出的最小分子表面也与表面自由能最小化相一致。将研究包括偏微分方程求解算法和等值面提取方案在内的数值技术。将进行数值测试以验证所提出的想法。该项目将为生物分子结构预测提供可靠的方法。结构信息对于特别针对蛋白质和/或膜的合理药物设计工作特别重要。可以预期，更多蛋白质/膜结构的出现将导致药物开发工作的加速。这个项目中提出的数学分析也将影响图像处理、模式识别和计算机视觉。建议项目的结果可用于根据工业和科学的需要和目标对PDE表面进行详细控制。特别地，所提出的方程中的非线性扩散系数可用于根据PDE曲面的曲率来局部控制其形状。这项拟议的研究具有很强的教育性。该项目将支持数学生物学博士生研究人员的培训。基于PDE的分子表面建模是一个适合于研究生论文和本科生项目的主题。项目成果将被纳入生物建模和模拟的研究生课程。

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.