Learning dynamical information from static protein and sequencing data

Abstract

Many complex processes, from protein folding and virus evolution to brain activity and neuronal network dynamics, can be described as stochastic exploration of a high-dimensional energy landscape. While efficient algorithms for cluster detection and data completion in high-dimensional spaces have been developed and applied over the last two decades, considerably less is known about the reliable inference of state transition dynamics in such settings. Here, we introduce a flexible and robust numerical framework to infer Markovian transition networks directly from time-independent data sampled from stationary equilibrium distributions. Our approach combines Gaussian mixture approximations and self-consistent dimensionality reduction with minimal-energy path estimation and multi-dimensional transition-state theory. We demonstrate the practical potential of the inference scheme by reconstructing the network dynamics for several protein folding transitions, gene regulatory network motifs and HIV evolution pathways. The predicted network topologies and relative transition time scales agree well with direct estimates from time-dependent molecular dynamics data, stochastic simulations and phylogenetic trees, respectively. The underlying numerical protocol thus allows the recovery of relevant dynamical information from instantaneous ensemble measurements, effectively alleviating the need for time-dependent data in many situations. Owing to its generic structure, the framework introduced here will be applicable to high-throughput RNA and protein sequencing datasets and future cryo-electron-microscopy data, and can guide the design of new experimental approaches towards studying complex multiphase phenomena.