Enhancing Biomolecular Simulations with Hybrid Potentials Incorporating NMR Data

Abstract

Some recent advances in biomolecular simulation and global optimization have used hybrid restraint potentials, where harmonic restraints that penalize conformations inconsistent with experimental data are combined with molecular mechanics force fields. These hybrid potentials can be used to improve the performance of molecular dynamics, structure prediction, energy landscape sampling, and other computational methods that rely on the accuracy of the underlying force field. Here, we develop a hybrid restraint potential based on NapShift, an artificial neural network trained to predict protein nuclear magnetic resonance (NMR) chemical shifts from sequence and structure. In addition to providing accurate predictions of experimental chemical shifts, NapShift is fully differentiable with respect to atomic coordinates, which allows us to use it for structural refinement. By employing NapShift to predict chemical shifts from the protein conformation at each simulation step, we can compute an energy penalty and the corresponding hybrid restraint forces based on the difference between the predicted values and the experimental chemical shifts. The performance of the hybrid restraint potential was benchmarked using both basin-hopping global optimization and molecular dynamics simulations. In each case, the NapShift hybrid potential improved the accuracy, leading to better structure prediction via basin-hopping and increased local stability in molecular dynamics simulations. Our results suggest that neural network hybrid potentials based on NMR observables can enhance a broad range of molecular simulation methods, and the prediction accuracy will improve as more experimental training data become available.

Thermal tuning of protein hydration in a hyperthermophilic enzyme

“…The CS-restrained MD trajectories of mt AcP at 37°C and Sso AcP at 80°C showed a significant agreement with experimental chemical shifts ( Supplementary Figures S1, S2 ), as calculated using the SPARTA+ program ( Shen and Bax, 2010 ), which is different from the NapShift method employed for the CS restraints in our MD samplings ( Qi et al, 2022 ). The backbone dynamics of the two proteins in the trajectories showed similar patterns of rigid and dynamical regions, with the strongest fluctuations found in the loops connecting secondary structure elements (S1-H1, S2-S3 and H2-S4) as probed by root mean square fluctuations (RMSF, Figures 1A,B ; Supplementary Figures S3A,B ).…”

“…In this study, we employed CS to restrain MD simulations using our previously developed method NapShift ( https://github.com/vrettasm/NapShift ), which is based on artificial neuronal networks to model CS from structure and enable derivatives to apply experimental restraints in MD simulations ( Qi et al, 2022 ). The CS restraints of NapShift are based on experimental CS of six protein atoms (Cα, Cβ, C’, N, HN, and Hα) and act on dihedral angles of the main chain (φ, ψ) and of the side chains (χ 1 , χ 2 ) ( Qi et al, 2022 ). NapShift restraints were implemented in the GROMACS package for MD simulations ( Páll et al, 2020 ) and imposed by adding an experimentally driven energy term to the standard force field ( Eq.…”

The αC-β4 loop controls the allosteric cooperativity between nucleotide and substrate in the catalytic subunit of protein kinase A

“…Using four replicas restrained with backbone chemical shifts (CS), we simulated the apo, binary (PKA-C/ATP), and ternary (PKA-C/ATP/PKI 5-24 ) complexes of PKA-C. Incorporating the CS restrains in the simulations ensures a close agreement with the conformational space explored by the kinase under our NMR experimental conditions ( Robustelli et al, 2010 ; Qi et al, 2022 ), whereas the enhanced sampling through metadynamics simulations boosts the conformational plasticity of the enzyme along different degrees of freedom (i.e., collective variables, CVs, see Methods) ( Figure 2—figure supplement 1 ; Piana and Laio, 2007 ). In our case, back-calculations of the CS values with Sparta+ ( Shen and Bax, 2010 ) show that the restrained simulations improved the agreement between theoretical and experimental CS values of ~0.2 ppm for the amide N atoms and ~0.1 ppm for the remainder backbone atoms ( Figure 2—figure supplement 2 ).…”

The αC-β4 loop controls the allosteric cooperativity between nucleotide and substrate in the catalytic subunit of protein kinase A

“…24,25 Using four replicas restrained with backbone chemical shifts (CS), we simulated the apo, binary (PKA-C/ATP), and ternary (PKA-C/ATP/PKI5-24) complexes of PKA-C. Incorporating the CS restrains in the simulations ensures a close agreement with the conformational space explored by the kinase under our NMR experimental conditions, 31,32 whereas the enhanced sampling through metadynamics simulations boosts the conformational plasticity of the enzyme along different degrees of freedom (i.e., collective variables, CVs. See Methods) (Figure 2 -figure supplement 1).…”