Statistical Inference for Molecular Landscapes

生物分子建模和模拟的进展已经产生了大量的生物分子数据，暴露了生物分子所假设和利用的无数形式/结构，以调节其在细胞中的生物活性。这些结构嵌入在能量景观中，能量景观通过能量学组织结构，并强调生物分子作为具有不同能量的结构之间相互转换的动态系统的固有性质。原则上，景观包含了揭示和表征生物分子动力学所需的所有信息，并将其与（dys）功能，分子机制和我们的生物学联系起来。本项目的目标是推进蛋白质能量景观几何特征的统计推断研究，作为理解和预测蛋白质序列变异对动力学和功能的表型/功能影响的重要手段。为了科普几何特征的灵活形状，在所提出的推断框架中采用非参数方法，其中的挑战是解决协同整合统计与微分几何和莫尔斯理论。将研究新的方法来测试稳定结构状态（反模式）对分子景观的统计意义，并研究稳定状态之间的最佳路径（积分曲线）估计的渐近行为，以支持构建分子景观的随机优化研究。一个计算上可行的拟合优度测试将开发盆地（水平集）的景观。该项目还将建立盆地边界表面积分的渐近分布结果，这些结果是景观拓扑和几何信息的定量描述符，支持对蛋白质序列变异的功能影响的计算机发现。拟议的活动将通过将能量景观的统计推断与（改变的）分子动力学和（dys）功能联系起来，对现代统计学，分子生物学和分子建模做出直接贡献。这些活动还将支持空间数据中的几何特征感兴趣的领域，如地质学、宇宙学、神经科学、遥感和大气科学。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Advances in biomolecular modeling and simulation have yielded massive amounts of biomolecular data, exposing the myriad of forms/structures assumed and leveraged by a biomolecule to modulate its biological activities in the cell. These structures are embedded in the energy landscape, which organizes structures by their energetics and underscores the inherent nature of biomolecules as dynamic systems interconverting between structures with varying energies. In principle, the landscape contains all the information needed to expose and characterize biomolecular dynamics and link it to (dys)function, molecular mechanisms, and our biology. The objective of this project is to advance research on statistical inference of geometric features of protein energy landscapes as an essential means of understanding and predicting the phenotypic/functional impact of protein sequence variations on dynamics and function.To cope with the flexible shape of geometric features, nonparametric approaches are adopted in the proposed inferential framework, where challenges are tackled by synergistically integrating statistics with differential geometry and Morse theory. Novel methodology will be investigated to test the statistical significance of stable structural states (anti-modes) on molecular landscapes, and study asymptotic behaviors in the estimation of optimal paths (integral curves) between stable states to support stochastic optimization research on constructing molecular landscapes. A computationally-feasible goodness-of-fit test will be developed for basins (level sets) on landscapes. The project will also establish asymptotic distributional results of surface integrals on the boundary of basins, which are quantitative descriptors of the topological and geometric information of the landscapes that support in-silico discoveries on the functional impact of protein sequence variations. The proposed activities will make a direct contribution to modern statistics, molecular biology and molecular modeling by linking the statistical inference of energy landscapes to (altered) molecular dynamics and (dys)function. The activities will additionally support fields where geometric features in spatial data are of interest, such as geology, cosmology, neuroscience, remote sensing, and atmospheric science.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.