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Abstract

Accurately describing the conformational ensembles of proteins in solution has been a long-standing challenge in protein biophysics. The first difficulty is the necessity of evaluating the large and competing sources of energy and entropy that determine the thermodynamics and conformation of the protein. The second is the intensive sampling required to obtain the Boltzmann ensemble of conformations. We address the sampling challenge by defining a method to obtain an approximate free energy of the side chains for a given backbone configuration. This allows us to obtain backbone dynamics in a much smoother energy surface by greatly reducing the steric rattling and side chain repacking that exist on a variety of timescales in atomic molecular dynamics. Using only three backbone atoms per residue, we have developed a coarse-grained model for Langevin dynamics simulations that is capable of rapidly folding some small proteins with near-angstrom accuracy in hours on a home computer. Specifically, the location of the backbone atoms defines the positions of groups not explicitly represented in the model, enabling computation of the forces on these inferred positions and the distribution of these forces onto the backbone atoms. Importantly, the reconstructed protein is associated with detailed Ramachandran maps, backbone H-bonding, and side chain packing potentials, features absent in many coarse-grained folding models. This reconstruction allows the forces from a more detailed model to act directly on the fundamental backbone degrees of freedom despite using only 3 explicit atoms per amino acid. This algorithm is implemented in a novel simulation framework, Upside, that is highly configurable and efficient. Parameter training is accomplished using contrastive divergence to maximize the population of native-like structures for a set of 400 proteins. Contrastive divergence creates its own low energy decoys using molecular simulations at every optimization step. While Upside is designed to describe protein folding, we are also applying it to study intrinsically disordered and membrane proteins, as well as conformational change. Upside's extreme speed makes it a powerful method for studies requiring extensive conformational sampling.

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