Normal modes for large molecules with arbitrary link constraints in the mobile block Hessian approach

A revised formulation of the generalized subsystem vibrational analysis (GSVA)

In this work, a simplified formulation of our recently developed generalized subsystem vibrational analysis (GSVA) for obtaining intrinsic fragmental vibrations (J Chem Theory Comput 14:2558, 2018) is presented. In contrast to the earlier implementation, which requires the explicit definition of a non-redundant set of internal coordinate parameters to be constructed for the subsystem, the new implementation circumvents this process by employing massless Eckart conditions to the subsystem fragment paired with a Gram-Schmidt orthogonalization to span the same internal vibration space indirectly. This revised version of GSVA (rev-GSVA) can be applied to equilibrium structure as well as transition state structure, and it has been incorporated into the open-source package UniMoVib (https://github.com/zorkzou/UniMoVib).

Supplementary Information

The online version contains supplementary material available at 10.1007/s00214-021-02727-y.

Effective representation of amide III, II, I, and A modes on local vibrational modes: Analysis of ab initio quantum calculation results

The Hamiltonian matrix for the first excited vibrational states of a protein can be effectively represented by local vibrational modes constituting amide III, II, I, and A modes to simulate various vibrational spectra. Methods for obtaining the Hamiltonian matrix from ab initio quantum calculation results are discussed, where the methods consist of three steps: selection of local vibrational mode coordinates, calculation of a reduced Hessian matrix, and extraction of the Hamiltonian matrix from the Hessian matrix. We introduce several methods for each step. The methods were assessed based on the density functional theory calculation results of 24 oligopeptides with four different peptide lengths and six different secondary structures. The completeness of a Hamiltonian matrix represented in the reduced local mode space is improved by adopting a specific atom group for each amide mode and reducing the effect of ignored local modes. The calculation results are also compared to previous models using C=O stretching vibration and transition dipole couplings. We found that local electric transition dipole moments of the amide modes are mainly bound on the local peptide planes. Their direction and magnitude are well conserved except amide A modes, which show large variation. Contrary to amide I modes, the vibrational coupling constants of amide III, II, and A modes obtained by analysis of a dipeptide are not transferable to oligopeptides with the same secondary conformation because coupling constants are affected by the surrounding atomic environment.

Correcting for the free energy costs of bond or angle constraints in molecular dynamics simulations

BACKGROUND

Free energy simulations are an important tool in the arsenal of computational biophysics, allowing the calculation of thermodynamic properties of binding or enzymatic reactions. This paper introduces methods to increase the accuracy and precision of free energy calculations by calculating the free energy costs of constraints during post-processing. The primary purpose of employing constraints for these free energy methods is to increase the phase space overlap between ensembles, which is required for accuracy and convergence.

METHODS

The free energy costs of applying or removing constraints are calculated as additional explicit steps in the free energy cycle. The new techniques focus on hard degrees of freedom and use both gradients and Hessian estimation. Enthalpy, vibrational entropy, and Jacobian free energy terms are considered.

RESULTS

We demonstrate the utility of this method with simple classical systems involving harmonic and anharmonic oscillators, four-atomic benchmark systems, an alchemical mutation of ethane to methanol, and free energy simulations between alanine and serine. The errors for the analytical test cases are all below 0.0007kcal/mol, and the accuracy of the free energy results of ethane to methanol is improved from 0.15 to 0.04kcal/mol. For the alanine to serine case, the phase space overlaps of the unconstrained simulations range between 0.15 and 0.9%. The introduction of constraints increases the overlap up to 2.05%. On average, the overlap increases by 94% relative to the unconstrained value and precision is doubled.

CONCLUSIONS

The approach reduces errors arising from constraints by about an order of magnitude. Free energy simulations benefit from the use of constraints through enhanced convergence and higher precision.

GENERAL SIGNIFICANCE

The primary utility of this approach is to calculate free energies for systems with disparate energy surfaces and bonded terms, especially in multi-scale molecular mechanics/quantum mechanics simulations. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

Long Timestep Molecular Dynamics on the Graphical Processing Unit

Molecular dynamics (MD) simulations now play a key role in many areas of theoretical chemistry, biology, physics, and materials science. In many cases, such calculations are significantly limited by the massive amount of computer time needed to perform calculations of interest. Herein, we present Long Timestep Molecular Dynamics (LTMD), a method to significantly speed MD simulations. In particular, we discuss new methods to calculate the needed terms in LTMD as well as issues germane to a GPU implementation. The resulting code, implemented in the OpenMM MD library, can achieve a significant 6-fold speed increase, leading to MD simulations on the order of 5 μs/day using implicit solvent models.

Comparative study of various normal mode analysis techniques based on partial Hessians

Standard normal mode analysis becomes problematic for complex molecular systems, as a result of both the high computational cost and the excessive amount of information when the full Hessian matrix is used. Several partial Hessian methods have been proposed in the literature, yielding approximate normal modes. These methods aim at reducing the computational load and/or calculating only the relevant normal modes of interest in a specific application. Each method has its own (dis)advantages and application field but guidelines for the most suitable choice are lacking. We have investigated several partial Hessian methods, including the Partial Hessian Vibrational Analysis (PHVA), the Mobile Block Hessian (MBH), and the Vibrational Subsystem Analysis (VSA). In this article, we focus on the benefits and drawbacks of these methods, in terms of the reproduction of localized modes, collective modes, and the performance in partially optimized structures. We find that the PHVA is suitable for describing localized modes, that the MBH not only reproduces localized and global modes but also serves as an analysis tool of the spectrum, and that the VSA is mostly useful for the reproduction of the low frequency spectrum. These guidelines are illustrated with the reproduction of the localized amine-stretch, the spectrum of quinine and a bis-cinchona derivative, and the low frequency modes of the LAO binding protein.