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Raman spectra of the orientationally disordered phase II of solid ammonia in the intramolecular and lattice regions are reported for the first time. The spectrum of the intramolecular region contains one line for each vibrational mode, broadened by the orientational disorder. The lattice region contains two broad lines near 50 and 280 cm-1, assigned to translational modes, and two central peaks ascribed to rotational relaxation. [ABSTRACT FROM AUTHOR]

Our previous article has established the theory of molecular dynamics (MD) simulations for systems modeled with the polarizable Gaussian multipole (pGM) electrostatics [Wei et al., J. Chem. Phys. 153(11), 114116 (2020)]. Specifically, we proposed the covalent basis vector framework to define the permanent multipoles and derived closed-form energy and force expressions to facilitate an efficient implementation of pGM electrostatics. In this study, we move forward to derive the pGM internal stress tensor for constant pressure MD simulations with the pGM electrostatics. Three different formulations are presented for the flexible, rigid, and short-range screened systems, respectively. The analytical formulations were implemented in the SANDER program in the Amber package and were first validated with the finite-difference method for two different boxes of pGM water molecules. This is followed by a constant temperature and constant pressure MD simulation for a box of 512 pGM water molecules. Our results show that the simulation system stabilized at a physically reasonable state and maintained the balance with the externally applied pressure. In addition, several fundamental differences were observed between the pGM and classic point charge models in terms of the simulation behaviors, indicating more extensive parameterization is necessary to utilize the pGM electrostatics.

Molecular dynamics (MD) is a powerful (and the most viable) tool to compute the thermal conductivities of solid disordered materials. However, conventional classical MD fails to describe the nuclear quantum effects (NQEs), so it may give inaccurate results for light materials at low temperatures. While the importance of NQE has been widely acknowledged, yet we do not have a fully reliable method to account for NQE in the MD thermal conductivity calculations. In this work, we will investigate and analyze the performances of a number of path-integral-based quantum MD methods, using ordered ice as a test case. To establish the validity of these methods, we will compare the MD results with the lattice dynamics results, in both classical and quantum limits. Through such a comparison, we will show that methods such as ring polymer MD stand as a good approach for a complex solid with short phonon lifetimes but could be problematic when describing long-living acoustic phonons. In addition, we will show that the rigid water model, which is the state-of-the-art model in the studies of ice/water systems, fails to capture most of the NQEs in ice thermal conductivity. Neglecting librational and translational NQEs leads to essential errors, which clearly demonstrates the importance of a true quantum simulation method that treats all modes at a consistent quantum level.

Molecular dynamics simulations of biomolecules have been widely adopted in biomedical studies. As classical point-charge models continue to be used in routine biomolecular applications, there have been growing demands on developing polarizable force fields for handling more complicated biomolecular processes. Here, we focus on a recently proposed polarizable Gaussian Multipole (pGM) model for biomolecular simulations. A key benefit of pGM is its screening of all short-range electrostatic interactions in a physically consistent manner, which is critical for stable charge-fitting and is needed to reproduce molecular anisotropy. Another advantage of pGM is that each atom's multipoles are represented by a single Gaussian function or its derivatives, allowing for more efficient electrostatics than other Gaussian-based models. In this study, we present an efficient formulation for the pGM model defined with respect to a local frame formed with a set of covalent basis vectors. The covalent basis vectors are chosen to be along each atom's covalent bonding directions. The new local frame can better accommodate the fact that permanent dipoles are primarily aligned along covalent bonds due to the differences in electronegativity of bonded atoms. It also allows molecular flexibility during molecular simulations and facilitates an efficient formulation of analytical electrostatic forces without explicit torque computation. Subsequent numerical tests show that analytical atomic forces agree excellently with numerical finite-difference forces for the tested system. Finally, the new pGM electrostatics algorithm is interfaced with the particle mesh Ewald (PME) implementation in Amber for molecular simulations under the periodic boundary conditions. To validate the overall pGM/PME electrostatics, we conducted an NVE simulation for a small water box of 512 water molecules. Our results show that to achieve energy conservation in the polarizable model, it is important to ensure enough accuracy on both PME and induction iteration. It is hoped that the reformulated pGM model will facilitate the development of future force fields based on the pGM electrostatics for applications in biomolecular systems and processes where polarization plays crucial roles.

Transcription factor cyclic Adenosine monophosphate response-element binding protein plays a critical role in the cyclic AMP response pathway via its intrinsically disordered kinase inducible transactivation domain (KID). KID is one of the most studied intrinsically disordered proteins (IDPs), although most previous studies focus on characterizing its disordered state structures. An interesting question that remains to be answered is how the order-disorder transition occurs at experimental conditions. Thanks to the newly developed IDP-specific force field ff14IDPSFF, the quality of conformer sampling for IDPs has been dramatically improved. In this study, molecular dynamics (MD) simulations were used to study the order-to-disorder transition kinetics of KID based on the good agreement with the experiment on its disordered-state properties. Specifically, we tested four force fields, ff99SBildn, ff99IDPs, ff14IDPSFF, and ff14IDPs in the simulations of KID and found that ff14IDPSFF can generate more diversified disordered conformers and also reproduce more accurate experimental secondary chemical shifts. Kinetics analysis of MD simulations demonstrates that the order-disorder transition of KID obeys the first-order kinetics, and the transition nucleus is I127/L128/L141. The possible transition pathways from the nucleus to the last folded residues were identified as I127-R125-L138-L141-S143-A145 and L128-R125-L138-L141-S143-A145 based on a residue-level dynamical network analysis. These computational studies not only provide testable prediction/hypothesis on the order-disorder transition of KID but also confirm that the ff14IDPSFF force field can be used to explore the correlation between the structure and function of IDPs.

We explored a multi-scale algorithm for the Poisson-Boltzmann continuum solvent model for more robust simulations of biomolecules. In this method, the continuum solvent/solute interface is explicitly simulated with a numerical fluid dynamics procedure, which is tightly coupled to the solute molecular dynamics simulation. There are multiple benefits to adopt such a strategy as presented below. At this stage of the development, only nonelectrostatic interactions, i.e., van der Waals and hydrophobic interactions, are included in the algorithm to assess the quality of the solvent-solute interface generated by the new method. Nevertheless, numerical challenges exist in accurately interpolating the highly nonlinear van der Waals term when solving the finite-difference fluid dynamics equations. We were able to bypass the challenge rigorously by merging the van der Waals potential and pressure together when solving the fluid dynamics equations and by considering its contribution in the free-boundary condition analytically. The multi-scale simulation method was first validated by reproducing the solute-solvent interface of a single atom with analytical solution. Next, we performed the relaxation simulation of a restrained symmetrical monomer and observed a symmetrical solvent interface at equilibrium with detailed surface features resembling those found on the solvent excluded surface. Four typical small molecular complexes were then tested, both volume and force balancing analyses showing that these simple complexes can reach equilibrium within the simulation time window. Finally, we studied the quality of the multi-scale solute-solvent interfaces for the four tested dimer complexes and found that they agree well with the boundaries as sampled in the explicit water simulations.

Continuum modeling of electrostatic interactions based upon numerical solutions of the Poisson-Boltzmann equation has been widely used in structural and functional analyses of biomolecules. A limitation of the numerical strategies is that it is conceptually difficult to incorporate these types of models into molecular mechanics simulations, mainly because of the issue in assigning atomic forces. In this theoretical study, we first derived the Maxwell stress tensor for molecular systems obeying the full nonlinear Poisson-Boltzmann equation. We further derived formulations of analytical electrostatic forces given the Maxwell stress tensor and discussed the relations of the formulations with those published in the literature. We showed that the formulations derived from the Maxwell stress tensor require a weaker condition for its validity, applicable to nonlinear Poisson-Boltzmann systems with a finite number of singularities such as atomic point charges and the existence of discontinuous dielectric as in the widely used classical piece-wise constant dielectric models.

The Poisson-Boltzmann theory has become widely accepted in modeling electrostatic solvation interactions in biomolecular calculations. However the standard practice of atomic point charges in molecular mechanics force fields introduces singularity into the Poisson-Boltzmann equation. The finite-difference/finite-volume discretization approach to the Poisson-Boltzmann equation alleviates the numerical difficulty associated with the charge singularity but introduces discretization error into the electrostatic potential. Decomposition of the electrostatic potential has been explored to remove the charge singularity explicitly to achieve higher numerical accuracy in the solution of the electrostatic potential. In this study, we propose an efficient method to overcome the charge singularity problem. In our framework, two separate equations for two different potentials in two different regions are solved simultaneously, i.e., the reaction field potential in the solute region and the total potential in the solvent region. The proposed method can be readily implemented with typical finite-difference Poisson-Boltzmann solvers and return the singularity-free reaction field potential with a single run. Test runs on 42 small molecules and 4 large proteins show a very high agreement between the reaction field energies computed by the proposed method and those by the classical finite-difference Poisson-Boltzmann method. It is also interesting to note that the proposed method converges faster than the classical method, though additional time is needed to compute Coulombic potential on the dielectric boundary. The higher precision, accuracy, and efficiency of the proposed method will allow for more robust electrostatic calculations in molecular mechanics simulations of complex biomolecular systems.

A continuum treatment of electronic polarization has been explored for in molecular mechanics simulations in implicit solvents. The dielectric constant for molecule interior is the only parameter in the continuum polarizable model. A value of 4 is found to yield optimal agreement with high-level ab initio quantum mechanical calculations for the tested molecular systems. Interestingly, its performance is not sensitive to the definition of molecular volume, in which the continuum electronic polarization is defined. In this model, quantum mechanical electrostatic field in different dielectric environments from vacuum, low-dielectric organic solvent, and water can be used simultaneously in atomic charge fitting to achieve consistent treatment of electrostatic interactions. The tests show that a single set of atomic charges can be used consistently in different dielectric environments and different molecular conformations, and the atomic charges transfer well from training monomers to tested dimers. The preliminary study gives us the hope of developing a continuum polarizable force field for more consistent simulations of proteins and nucleic acids in implicit solvents.

The Poisson-Boltzmann theory has been widely used in the studies of energetics and conformations of biological macromolecules. Recently, introduction of the efficient generalized Born approximation has greatly extended its applicability to areas such as protein folding simulations where highly efficient computation is crucial. However, limitations have been found in the folding simulations of a well-studied beta hairpin with several generalized Born implementations and different force fields. These studies have raised the question whether the underlining Poisson-Boltzmann theory, on which the generalized Born model is calibrated, is adequate in the treatment of polar interactions for the challenging protein folding simulations. To address the question whether the Poisson-Boltzmann theory in the current formalism might be insufficient, we directly tested our efficient numerical Poisson-Boltzmann implementation in the beta-hairpin folding simulation. Good agreement between simulation and experiment was found for the beta-hairpin equilibrium structures when the numerical Poisson-Boltzmann solvent and a recently improved generalized Born solvent were used. In addition simulated thermodynamic properties also agree well with experiment in both solvents. Finally, an overall agreement on the beta-hairpin folding mechanism was found between the current and previous studies. Thus, our simulations indicate that previously observed limitations are most likely due to imperfect calibration in previous generalized Born models but not due to the limitation of the Poisson-Boltzmann theory.

An enhanced sampling method is proposed for ab initio protein folding simulations. The new method couples a high-resolution model for accuracy and a low-resolution model for efficiency. It aims to overcome the entropic barrier found in the exponentially large protein conformational space when a high-resolution model, such as an all-atom molecular mechanics force field, is used. The proposed method is designed to satisfy the detailed balance condition so that the Boltzmann distribution can be generated in all sampling trajectories in both high and low resolutions. The method was tested on model analytical energy functions and ab initio folding simulations of a beta-hairpin peptide. It was found to be more efficient than replica-exchange method that is used as its building block. Analysis with the analytical energy functions shows that the number of energy calculations required to find global minima and to converge mean potential energies is much fewer with the new method. Ergodic measure shows that the new method explores the conformational space more rapidly. We also studied imperfect low-resolution energy models and found that the introduction of errors in low-resolution models does decrease its sampling efficiency. However, a reasonable increase in efficiency is still observed when the global minima of the low-resolution models are in the vicinity of the global minimum basin of the high-resolution model. Finally, our ab initio folding simulation of the tested peptide shows that the new method is able to fold the peptide in a very short simulation time. The structural distribution generated by the new method at the equilibrium portion of the trajectory resembles that in the equilibrium simulation starting from the crystal structure.

The denatured state of a miniprotein BBA1 is studied under the native condition with the AMBER/Poisson-Boltzmann energy model and with the self-guided enhanced sampling technique. Forty independent trajectories are collected to sample the highly diversified denatured structures. Our simulation data show that the denatured BBA1 contains high percentage of native helix and native turn, but low percentage of native hairpin. Conditional population analysis indicates that the native helix formation and the native hairpin formation are not cooperative in the denatured state. Side-chain analysis shows that the native hydrophobic contacts are more preferred than the non-native hydrophobic contacts in the denatured BBA1. In contrast, the salt-bridge contacts are more or less nonspecific even if their populations are higher than those of hydrophobic contacts. Analysis of the trajectories shows that the native helix mostly initiates near the N terminus and propagates to the C terminus, and mostly forms from 3(10)-helix/turn to alpha helix. The same analysis shows that the native turn is important but not necessary in its formation in the denatured BBA1. In addition, the formations of the two strands in the native hairpin are rather asymmetric, demonstrating the likely influence of the protein environment. Energetic analysis shows that the native helix formation is largely driven by electrostatic interactions in denatured BBA1. Further, the native helix formation is associated with the breakup of non-native salt-bridge contacts and the accumulation of native salt-bridge contacts. However, the native hydrophobic contacts only show a small increase upon the native helix formation while the non-native hydrophobic contacts stay essentially the same, different from the evolution of hydrophobic contacts observed in an isolated helix folding., ((c) 2004 American Institute of Physics.)