Anharmonic Vibrational Calculations Based on Group-Localized Coordinates: Applications to Internal Water Molecules in Bacteriorhodopsin

GENESIS 2.1: High-Performance Molecular Dynamics Software for Enhanced Sampling and Free-Energy Calculations for Atomistic, Coarse-Grained, and Quantum Mechanics/Molecular Mechanics Models

GENeralized-Ensemble SImulation System (GENESIS) is a molecular dynamics (MD) software developed to simulate the conformational dynamics of a single biomolecule, as well as molecular interactions in large biomolecular assemblies and between multiple biomolecules in cellular environments. To achieve the latter purpose, the earlier versions of GENESIS emphasized high performance in atomistic MD simulations on massively parallel supercomputers, with or without graphics processing units (GPUs). Here, we implemented multiscale MD simulations that include atomistic, coarse-grained, and hybrid quantum mechanics/molecular mechanics (QM/MM) calculations. They demonstrate high performance and are integrated with enhanced conformational sampling algorithms and free-energy calculations without using external programs except for the QM programs. In this article, we review new functions, molecular models, and other essential features in GENESIS version 2.1 and discuss ongoing developments for future releases.

Retinal photoisomerization versus counterion protonation in light and dark-adapted bacteriorhodopsin and its primary photoproduct

Discovered over 50 years ago, bacteriorhodopsin is the first recognized and most widely studied microbial retinal protein. Serving as a light-activated proton pump, it represents the archetypal ion-pumping system. Here we compare the photochemical dynamics of bacteriorhodopsin light and dark-adapted forms with that of the first metastable photocycle intermediate known as "K". We observe that following thermal double isomerization of retinal in the dark from bio-active all-trans 15-anti to 13-cis, 15-syn, photochemistry proceeds even faster than the ~0.5 ps decay of the former, exhibiting ballistic wave packet curve crossing to the ground state. In contrast, photoexcitation of K containing a 13-cis, 15-anti chromophore leads to markedly multi-exponential excited state decay including much slower stages. QM/MM calculations, aimed to interpret these results, highlight the crucial role of protonation, showing that the classic quadrupole counterion model poorly reproduces spectral data and dynamics. Single protonation of ASP212 rectifies discrepancies and predicts triple ground state structural heterogeneity aligning with experimental observations. These findings prompt a reevaluation of counter ion protonation in bacteriorhodopsin and contribute to the broader understanding of its photochemical dynamics.

Hydroxide Ion Mechanism for Long-Range Proton Pumping in the Third Proton Transfer of Bacteriorhodopsin

In bacteriorhodopsin, representative light-driven proton pump, five proton transfers yield vectorial active proton translocation, resulting in a proton gradient in microbes. Third proton transfer occurs from Asp96 to the Schiff base on the photocycle, which is expected to be a long-range proton transfer via the Grotthuss mechanism through internal water molecules. Here, large-scale quantum molecular dynamics simulations are performed for the third proton transfer, where all the atoms (~50000 atoms) are treated quantum-mechanically. The simulations demonstrate that two reaction paths exist along the water wire, namely, via hydronium and via hydroxide ions. The free energy analysis confirms that the path via hydroxide ions is considerably favorable and consistent with the observed lifetime of the transient water wire. Therefore, the proposed hydroxide ion mechanism, as in the first proton transfer, is responsible for the third long-range proton transfer.

Matrix Product State Formulation of the MCTDH Theory in Local Mode Representations for Anharmonic Potentials

The matrix product state formulation of the multiconfiguration time-dependent Hartree theory, MPS-MCTDH, reported previously [Kurashige, J. Chem. Phys. 2018, 19, 194114] is extended to realistic anharmonic potentials with n-mode representations beyond the linear vibronic coupling model. For realistic vibrational potentials, the local mode representation should give a more compact representation of the potentials, i.e., lowering the dimensionality of the entanglements, than the normal coordinates, and the MPS-MCTDH formulation should work more efficiently and maintain the accuracy with a small bond dimension of the MPS ansatz. In fact, it was confirmed that the use of the local coordinates made the interaction matrices diagonal dominant and the number of terms in the n-body expansion of the potentials was significantly reduced. The method was applied to the IR spectrum of the CH₂O molecule, the zero-point energies, and the vibrational energy redistribution dynamics of polyenes C_2nH_2n+2. The results showed that the efficiency of the MPS-MCTDH method is significantly accelerated by the use of local coordinates even if the long-range interactions are included in the potential.

Towards complete assignment of the infrared spectrum of the protonated water cluster H+(H2O)21

The spectroscopic features of protonated water species in dilute acid solutions have been long sought after for understanding the microscopic behavior of the proton in water with gas-phase water clusters H⁺(H₂O)_n extensively studied as bottom-up model systems. We present a new protocol for the calculation of the infrared (IR) spectra of complex systems, which combines the fragment-based Coupled Cluster method and anharmonic vibrational quasi-degenerate perturbation theory, and demonstrate its accuracy towards the complete and accurate assignment of the IR spectrum of the H⁺(H₂O)₂₁ cluster. The site-specific IR spectral signatures reveal two distinct structures for the internal and surface four-coordinated water molecules, which are ice-like and liquid-like, respectively. The effect of inter-molecular interaction between water molecules is addressed, and the vibrational resonance is found between the O-H stretching fundamental and the bending overtone of the nearest neighboring water molecule. The revelation of the spectral signature of the excess proton offers deeper insight into the nature of charge accommodation in the extended hydrogen-bonding network underpinning this aqueous cluster.

Protonated water species have been the subject of numerous experimental and computational studies. Here the authors provide a nearly complete assignment of the experimental IR spectrum of the H⁺(H₂O)₂₁ water cluster based on high-level wavefunction theory and anharmonic vibrational quasi-degenerate perturbation theory.

Weight average approaches for predicting dynamical properties of biomolecules

Recent advances in atomistic molecular dynamics (MD) simulations of biomolecules allow us to explore their conformational spaces widely, observing large-scale conformational fluctuations or transitions between distinct structures. To reproduce or refine experimental data using MD simulations, structure ensembles, which are characterized by multiple structures and their statistical weights on the rugged free-energy landscapes, are often used. Here, we summarize weight average approaches for various experimental measurements. Weight average approaches are now applied to hybrid quantum mechanics/molecular mechanics MD simulations to predict fast vibrational motions in a protein with a high accuracy for better understanding of molecular functions from atomic structures.