Collaborative Proposal: CDI-Type I: A multidisciplinary, multiscale approach to discover organizing principles in macromolecular dynamics and functions

生物分子系统中的协同过程（如蛋白质动力学、折叠和自组装）的理解对理论和实验都提出了突出的挑战。所涉及的大量自由度和存在的异质性程度，乍一看可能表明缺乏一般原则。正如弗朗西斯·克里克20年前在评论大分子动力学时所写的那样，“在物理学家看来极其复杂的过程，可能正是大自然发现的最简单的过程”。大分子体系的行为显得异常复杂。生物学上相关的大分子系统是数十亿年进化的结果，在此期间，由于功能原因，细节和例外被选择。尽管复杂，但在大分子系统中出现了集体现象，例如在蛋白质折叠和自组装过程中，这表明存在组织原则，实际上可能利用复杂性来获得简单性。（即复制、量化和预测）生物分子系统中单自由度的相互作用如何产生组织，在一个广泛的长度和时间范围内？经验和理论证据支持的想法，大多数大分子的过程中，只有一小部分的构象空间被访问，并为中/长时间尺度的参数是非常少的数量足以描述一个大的大分子系统的粗动力学。以前在这个方向上的工作并不是自动的或系统的，并且主要是由物理直觉驱动的，很少或没有成功的保证。这项工作的目标是开发和应用一种完全不同的方法，将生物学和生物化学方法与物理和数学观点相协调。进化用于调节生物分子过程行为的一般“规则”的制定的关键一步在于对忠实再现感兴趣的大分子过程所需的最小有效参数集的数学上严格的识别和物理上合理的解释。为此，将开发的方法是基于多尺度几何测量理论，谐波分析和降维。这些想法的核心将被广泛应用于大型高维数据集的几何分析，跨越和超越生物物理学，从而导致新的一般范式降维和回归等数据集。

AbstractThe understanding of cooperative processes in biomolecular systems (such as protein dynamics, folding, and self-assembly) poses outstanding challenges both for theory and experiment. The large number of degrees of freedom involved, and the degree of heterogeneity present, may at a first glance suggest the lack of general principles. As Francis Crick wrote twenty years ago, commenting on macromolecular dynamics, "what seems to physicists a hopelessly complicated process may have been what Nature found simplest". The behavior of a macro-molecular system appears overwhelmingly complicated. Biologically relevant macro-molecular systems are the result of billions of years of evolution, during which details and exceptions have been selected for functional reasons. In spite of the complexity, collective phenomena emerge in macromolecular systems, as for instance in protein folding and self-assembly processes, suggesting the existence of organizing principles that may actually exploit the complexity to obtain simplicity.Is it possible to understand (that is, reproduce, quantify, and predict) how organization emerges from the interactions of the single degrees of freedom in a biomolecular system, over a broad spectrum of length and timescales? Empirical and theoretical evidence supports the idea that for most macromolecular processes only a small portion of the conformational space is visited, and that for medium/long time scales a very small number of parameters are enough to describe the coarse dynamics of a large macromolecular system. Previous work in this direction has not been automatic or systematic, and has been driven mostly by physical intuition, with little or no guarantee of success.It is the goal of this work to develop and apply a radically different approach, that reconciles biological and biochemical approaches with a physical and mathematical perspective. A key step towards the formulation of the general "rules" that evolution has employed for regulating the behavior of biomolecular processes resides in the mathematically rigorous identification and the physically sound interpretation of the minimal set of effective parameters needed to faithful reproduce the macromolecular process of interest. The methods that will be developed to this end are based on multiscale geometric measure theory, harmonic analysis, and dimensionality reduction. The core of these ideas will be widely applicable to the analysis of the geometry of large high dimensional data sets, across and beyond biophysics, leading to novel general paradigms for dimensionality reduction and regression on such data sets.