It is now well accepted that structured governed dynamics modulate function, yet we still don’t know how a few changes (e.g., mutations) in sequence modify dynamics to alter function. Understanding this interplay is a key step to engineering proteins with desired function to address disease, and viral evolution to fight with endemics or future pandemics, as well as many other bioengineering applications. Despite the work of many researchers, the connection between sequence, structure and dynamics remains elusive. This is partly because there is no powerful methods that can accurately quantify each amino-acid position’s contribution to structure and dynamics. We propose to fill this gap by using an innovative, interdisciplinary method based on mathematical topology and physics based protein dynamics modeling. The guiding hypothesis is that the topological landscape of proteins governs conformational dynamics and that it can be modified with sitespecific mutations. To test this hypothesis, we will create the mathematical framework upon which the local and global topology of proteins and conformational dynamics can be rigorously associated and the evolution of the topological landscape can be quantified. This work is particularly timely for two reasons: (1) conformational dynamics have established a connection between structure and function and evolution at the proteotome scale and (2) methods from mathematical topology have shown evidence of being able to characterize protein structure. This research advances knowledge in mathematics and biology and breaks existing barriers in: (1) topology and geometry, (2) quantitative characterizations of protein structure, (3) connecting microscopic effects to the macroscopic properties of proteins and (4) providing a novel framework that enables not only to uncover the molecular mechanism of protein function and evolution based on fundamental mathematical and physical concepts, but also enables to design novel proteins with desired function. This is achieved by (1) creating novel measures of topological complexity and a mathematical topological framework for characterizing multiscale protein structure, by (2) coarse-grained modeling and dynamical analysis of proteins and (3) by combining the two to establish the connection between conformational dynamics and the topological landscape of proteins. This integrated novel framework will be tested on different protein systems with available deep scanning mutational experimental data. The successful completion of this work could lead to a breakthrough that would enable to predict and modulate protein function based on structural dynamics.

The mechanisms by which certain mutations can lead to the same apparent native fold but can cause differences in function is of fundamental biological relevance, whose understanding could lead to new drug discoveries. It also speaks to broader issues in molecular self-assembly, protein folding in general, biological and biology-inspired materials, bioengineering, human health and disease. Our proposed work, at the interface of biology and mathematical topology, will provide the rigorous framework upon which the relation between structure and function of biomolecules can be understood and controlled to address these questions.