A Topological Data Analytic Approach for Discovering Biophysical Signatures in Protein Dynamics

Abstract

Identifying structural differences among proteins can be a non-trivial task. When contrasting ensembles of protein structures obtained from molecular dynamics simulations, biologically-relevant features can be easily overshadowed by spurious fluctuations. Here, we present SINATRA Pro, a computational pipeline designed to robustly identify topological differences between two sets of protein structures. Algorithmically, SINATRA Pro works by first taking in the 3D atomic coordinates for each protein snapshot and summarizing them according to their underlying topology. Statistically significant topological features are then projected back onto an user-selected representative protein structure, thus facilitating the visual identification of biophysical signatures of different protein ensembles. We assess the ability of SINATRA Pro to detect minute conformational changes in five independent protein systems of varying complexities. In all test cases, SINATRA Pro identifies known structural features that have been validated by previous experimental and computational studies, as well as novel features that are also likely to be biologically-relevant according to the literature. These results highlight SINATRA Pro as a promising method for facilitating the non-trivial task of pattern recognition in trajectories resulting from molecular dynamics simulations, with substantially increased resolution.

A Sheaf-Theoretic Construction of Shape Space

“…The ECT and PHT have two useful properties: standard statistical methods can be applied to the transformed shape and the transforms are injective [24,13], so no information about the shape is lost via the transform. The utility of the transforms for applied problems in evolutionary anthropology, biomedical applications and plant biology were demonstrated in [11,41,38,2]. The shape space we construct in this paper is a dramatic generalization of the sheaf-theoretic formulation of the PHT found in [13].…”

Topological Analysis of Molecular Dynamics Simulations using the Euler Characteristic

“…20,25 Persistent homology has been shown to provide powerful characterizations of the topology and geometry of data. [25][26][27][28][29][30] However, the outputs of these methods (e.g., persistence diagrams) can be difficult to directly integrate into data analysis and ML tasks without further transformation (e.g., vectorization and smoothing) and hyperparameter optimization. 21 The main goal of this work is to demonstrate that topology can be applied to a broad range of molecular simulation settings.…”