Abstract
Predicting crystallographic B-factors of a protein from a conventional molecular dynamics simulation is challenging, in part because the B-factors calculated through sampling the atomic positional fluctuations in a picosecond molecular dynamics simulation are unreliable, and the sampling of a longer simulation yields overly large root mean square deviations between calculated and experimental B-factors. This article reports improved B-factor prediction achieved by sampling the atomic positional fluctuations in multiple picosecond molecular dynamics simulations that use uniformly increased atomic masses by 100-fold to increase time resolution. Using the third immunoglobulin-binding domain of protein G, bovine pancreatic trypsin inhibitor, ubiquitin, and lysozyme as model systems, the B-factor root mean square deviations (mean ± standard error) of these proteins were 3.1 ± 0.2–9 ± 1 Å2 for Cα and 7.3 ± 0.9–9.6 ± 0.2 Å2 for Cγ, when the sampling was done for each of these proteins over 20 distinct, independent, and 50-picosecond high-mass molecular dynamics simulations with AMBER forcefield FF12MC or FF14SB. These results suggest that sampling the atomic positional fluctuations in multiple picosecond high-mass molecular dynamics simulations may be conducive to a priori prediction of crystallographic B-factors of a folded globular protein.
Highlights
The B-factor of a given atom in a crystal structure is defined as 8 π2 〈 u2〉 that is used in refining the crystal structure to reflect the displacement u of the atom from its mean position in the crystal structure [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
Low-mass molecular dynamics (MD) simulations at Δt = 1.00 fssmt are theoretically equivalent to standard-mass MD simulations at Δt = 10 fssmt, as long as both standard-mass and low-mass simulations are carried out for the same number of timesteps and there are no precision issues in performing these simulations. This equivalence of mass downscaling and timestep-size upscaling explains why uniform mass reduction can compress the MD simulation time and why low-mass NPT MD simulations at Δt = 1.00 fssmt can offer better configurational sampling efficacy than conventional standard-mass NPT MD simulations at Δt = 1.00 fssmt or Δt = 2.00 fssmt
20 highmass MD simulations of a folded globular protein were carried out to investigate whether combining the sampling of the atomic positional fluctuations of the protein on a timescale of tens or hundreds of pssmt with the sampling of such fluctuations
Summary
The B-factor ( known as the Debye-Waller factor or B-value) of a given atom in a crystal structure is defined as 8 π2 〈 u2〉 that is used in refining the crystal structure to reflect the displacement u of the atom from its mean position in the crystal structure (viz., the uncertainty of the atomic mean position) [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]. Knowledge-based methods can predict main-chain B-factor distribution of a protein from either its sequence using statistical methods [15, 17, 18, 19, 43, 44, 45, 46] or its structure using a single-parameter harmonic potential [47, 48] with Pearson correlation coefficients (PCCs) up to 0.71 for the predicted B-factors relative to the experimental values These methods do not require intense computation and can rapidly predict B-factors of large numbers of protein sequences to facilitate the use of these sequences in drug-target identification. This article reports an evaluation study of a physics-based method that samples the atomic positional fluctuations in 20 distinct, independent, unrestricted, unbiased, picosecond, and classical isobaric–isothermal (NPT) MD simulations with uniformly scaled atomic masses to predict a priori main-chain and side-chain B-factors of a folded globular protein for target-structure–based drug design. All B-factors are unscaled, and all simulations are multiple, distinct, independent, unrestricted, unbiased, and classical NPT MD simulations
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