Bayesian nonparametrics for biophysics

As theorists, we draw trends and make predictions on protein function and interactions from models of protein dynamics. One route to modeling protein dynamics involves the bottom-up, molecular simulation, approach. Here we take a different route. Instead we present a top-bottom approach to building models of protein dynamics. The approach we present exploits a novel branch of Statistics -- called Bayesian nonparametrics (BNPs) -- first proposed in 1973 and now widely used in data science as the important conceptual advances of BNPs have become computational feasible in the last decade. BNPs are new to the physical sciences and use flexible (nonparametric) model structures to efficiently learn models from complex data sets. Here we will show how BNPs can be adapted to address important questions in protein biophysics directly from the data often limited by factors such as finite photon budgets as well as other data collection artifacts (e.g. aliasing, drift). More specifically, we will show that BNPs hold promise by allowing complex time traces (e.g. smFRET, photon arrivals) or images (e.g. single particle tracking) to be analyzed and turned into principled models of protein motion -- from diffusion to conformational dynamics and beyond.