[Paper Review] Maximum-likelihood, self-consistent side chain free energies with applications to protein molecular dynamics

John Jumper, Karl F. Freed+1 more|arXiv (Cornell University)|Oct 24, 2016

Protein Structure and Dynamics3 citations

TL;DR

This paper proposes a maximum-likelihood, self-consistent method to compute side chain free energies on the fly during protein molecular dynamics simulations, using a reduced single-bead side chain model. By treating side chain free energy as instantaneously equilibrated, the method smooths the energetic landscape, enabling rapid sampling of the Boltzmann distribution and achieving state-of-the-art accuracy in predicting $χ_1$ rotamer states in milliseconds of CPU time, with sufficient accuracy for de novo folding of small proteins.

ABSTRACT

To address the large gap between time scales that can be easily reached by molecular simulations and those required to understand protein dynamics, we propose a new methodology that computes a self-consistent approximation of the side chain free energy at every integration step. In analogy with the adiabatic Born-Oppenheimer approximation in which the nuclear dynamics are governed by the energy of the instantaneously-equilibrated electronic degrees of freedom, the protein backbone dynamics are simulated as preceding according to the dictates of the free energy of an instantaneously-equilibrated side chain potential. The side chain free energy is computed on the fly; hence, the protein backbone dynamics traverse a greatly smoothed energetic landscape, resulting in extremely rapid equilibration and sampling of the Boltzmann distribution. Because our method employs a reduced model involving single-bead side chains, we also provide a novel, maximum-likelihood method to parameterize the side chain model using input data from high resolution protein crystal structures. We demonstrate state-of-the-art accuracy for predicting $\chi_1$ rotamer states while consuming only milliseconds of CPU time. We also show that the resulting free energies of side chains is sufficiently accurate for de novo folding of some small proteins.

Motivation & Objective

• To bridge the gap between accessible simulation time scales and biologically relevant dynamics in protein molecular dynamics.
• To develop a computationally efficient method that accelerates equilibration by smoothing the free energy landscape using instantaneously equilibrated side chain free energies.
• To create a maximum-likelihood parameterization scheme for side chain models using high-resolution crystal structures.
• To enable accurate prediction of $χ_1$ rotamer states and de novo folding of small proteins with minimal computational cost.

Proposed method

• The method computes side chain free energy on the fly at each integration step, treating it as instantaneously equilibrated, analogous to the Born-Oppenheimer approximation.
• A reduced single-bead model is used to represent side chains, significantly lowering computational cost.
• A maximum-likelihood approach is employed to parameterize the side chain model using input data from high-resolution protein crystal structures.
• The backbone dynamics are propagated according to the free energy of the instantaneously equilibrated side chain potential, leading to a smoothed effective potential energy surface.
• The method enables rapid equilibration and sampling of the Boltzmann distribution by minimizing energy barriers associated with side chain reorganization.
• The self-consistent approximation ensures that the side chain free energy is updated dynamically in response to backbone conformational changes.

Experimental results

Research questions

• RQ1 Can on-the-fly computation of side chain free energy significantly accelerate equilibration in protein molecular dynamics simulations?
• RQ2 How accurately can a single-bead side chain model, parameterized via maximum-likelihood from crystal structures, predict $χ_1$ rotamer states?
• RQ3 To what extent can the computed side chain free energies support de novo folding of small proteins?
• RQ4 Can the self-consistent approximation of side chain free energy lead to a smoother, more efficient sampling of conformational space?
• RQ5 What is the computational efficiency of the method in terms of CPU time for accurate side chain prediction?

Key findings

• The method achieves state-of-the-art accuracy in predicting $χ_1$ rotamer states while consuming only milliseconds of CPU time per simulation.
• The on-the-fly computation of side chain free energy results in a greatly smoothed energetic landscape, enabling extremely rapid equilibration of the protein backbone.
• The maximum-likelihood parameterization of the single-bead side chain model yields free energies that are sufficiently accurate for de novo folding of some small proteins.
• The self-consistent approximation effectively reduces the computational barrier to sampling, allowing efficient traversal of the conformational landscape.
• The method demonstrates high efficiency and accuracy, combining fast sampling with reliable side chain state prediction.