Statistical Inference for Big Data Problems in Molecular Biophysics

We highlight the role of statistical inference techniques in providing biological insights from analyzing long time-scale molecular simulation data. Technological and algorithmic improvements in computation have brought molecular simulations to the forefront of techniques applied to investigating the basis of living systems. These longer, increasingly complex simulations are reaching petabyte scales. While these simulations promise important insights into the mechanisms of bio-molecular function, teasing out the important information that provide insights into the atomistic-scale behavior, has now become a true challenge on its own. Mining this data for important and biologically relevant patterns is critical to automating therapeutic intervention discovery, improving protein design, and fundamentally understanding the mechanistic basis of cellular homeostasis. 1 Molecular Biophysics Biological macromolecules such as proteins, de-oxy/ribose nucleic acid (DNA/RNA), carbohydrates and lipids play a diverse role in regulating cellular functions, and thus are easential to sustain life. In order to investigate and understand the mechanistic basis of biomolecular function, biophysicists, over the last 30 years, have taken advantage of the advances in computing power to run increasingly detailed simulations of these biomolecules. In particular, much attention has been paid to the simulation of proteins, which are often considered the workhorses of a cell, and made up of long polymers of amino-acid residues, and fold into three-dimensional structures to perform their function. Biological functions are controlled by the dynamical interactions between various biomolecules and can occur at multiple time-scales from femto-seconds up to micro-, milli-, seconds and beyond, spanning more than 15 orders of magnitude between them. In this paper, we focus on fully-atomistic simulations of proteins/biomolecules in solution as they best represent the cellular environment. Molecular dynamics (MD) simulations provide insights into the dependence of biological function on interactions at multiple length and time scales. MD simulations are governed by a potential energy function that includes both bonded and non-bonded interaction terms. The gradient of the energy function defines a force-field which is then applied to every atom in the molecule. At each time step, Newton’s laws of motion are integrated to generate a trajectory. A time-step on the order of a femtosecond (10−15s) is necessary for capturing the smallest vibrations of interest and to ensure numerical stability for integrating the equations of motions as simulations progress. However, biologically interesting events (related to bimolecular function) typically occur at microsecond (10−6s) and higher time scales. With improvements in sampling