Molecular mechanisms from reaction coordinate graph enabled multidimensional free energies illustrated on water dimer hydrogen bonding

Computing the free energies of molecular mechanisms in multidimensional space relies on combinations of geometrically complex reaction coordinates. We show how a graph theory implementation reduces complexity, and illustrate this on the arrangements of hydrogen bonding of a water dimer. The reaction coordinates and forces are computed using graphs that define the dependencies on the atoms in the Free Energy from Adaptive Reaction Coordinate Forces (FEARCF) library. The library can be interfaced with classical molecular dynamics as well as quantum molecular dynamics packages. Multidimensional interdependent reaction coordinates are constructed to produce complex free energy hypersurfaces. The reaction coordinates are graphed from atomic and molecular components to define points, distances, vectors, angles, planes and combinations thereof. The resultant free energy surfaces that are a function of the distance, angles, planes, and so on, can represent molecular mechanisms in reduced dimensions from the component atomic Cartesian coordinate degrees of freedom. The FEARCF library can be interfaced with any molecular package. Here, we demonstrate the link to NWChem to compute a hyperdimensional DFT (aug‐cc‐pVDZ basis set and X3LYP exchange correlation functionals) free energy space of a water dimer. Analysis of the water dimer free energy hypervolume reveals that while the chain and cyclic hydrogen bonding configurations are located in stable minimum energy wells, the bifurcated hydrogen bond configuration is a gateway to instability and dimer dissociation.

Pseudo-Improper-Dihedral Model for Intrinsically Disordered Proteins

We present a new coarse-grained C_α-based protein model with a nonradial multibody pseudo-improper-dihedral potential that is transferable, time-independent, and suitable for molecular dynamics. It captures the nature of backbone and side-chain interactions between amino acid residues by adapting a simple improper dihedral term for a one-bead-per-residue model. It is parameterized for intrinsically disordered proteins and applicable to simulations of such proteins and their assemblies on millisecond time scales.

Improved Sugar Puckering Profiles for Nicotinamide Ribonucleoside for Hybrid QM/MM Simulations

The coenzyme nicotinamide adenine dinucleotide (NAD⁺) and its reduced form (NADH) play ubiquitous roles as oxidizing and reducing agents in nature. The binding, and possibly the chemical redox step, of NAD⁺/NADH may be influenced by the cofactor conformational distribution and, in particular, by the ribose puckering of its nicotinamide-ribonucleoside (NR) moiety. In many hybrid quantum mechanics-molecular mechanics (QM/MM) studies of NAD⁺/NADH dependent enzymes, the QM region is treated by semiempirical (SE) methods. Recent work suggests that SE methods do not adequately describe the ring puckering in sugar molecules. In the present work we adopt an efficient and practical strategy to correct for this deficiency for NAD⁺/NADH. We have implemented a cost-effective correction to a SE Hamiltonian by adding a correction potential, which is defined as the difference between an accurate benchmark density functional theory (DFT) potential energy surface (PES) and the SE PES. In practice, this is implemented via a B-spline interpolation scheme for the grid-based potential energy difference surface. We find that the puckering population distributions obtained from free energy QM(SE)/MM simulations are in good agreement with DFT and in fair accord with experimental results. The corrected PES should facilitate a more accurate description of the ribose puckering in the NAD⁺/NADH cofactor in simulations of biological systems.

Thermodynamics of coupled protein adsorption and stability using hybrid Monte Carlo simulations

A better understanding of changes in protein stability upon adsorption can improve the design of protein separation processes. In this study, we examine the coupling of the folding and the adsorption of a model protein, the B1 domain of streptococcal protein G, as a function of surface attraction using a hybrid Monte Carlo (HMC) approach with temperature replica exchange and umbrella sampling. In our HMC implementation, we are able to use a molecular dynamics (MD) time step that is an order of magnitude larger than in a traditional MD simulation protocol and observe a factor of 2 enhancement in the folding and unfolding rate. To demonstrate the convergence of our systems, we measure the travel of our order parameter the fraction of native contacts between folded and unfolded states throughout the length of our simulations. Thermodynamic quantities are extracted with minimum statistical variance using multistate reweighting between simulations at different temperatures and harmonic distance restraints from the surface. The resultant free energies, enthalpies, and entropies of the coupled unfolding and absorption processes are in qualitative agreement with previous experimental and computational observations, including entropic stabilization of the adsorbed, folded state relative to the bulk on surfaces with low attraction.

Atomic forces for geometry-dependent point multipole and gaussian multipole models

In standard treatments of atomic multipole models, interaction energies, total molecular forces, and total molecular torques are given for multipolar interactions between rigid molecules. However, if the molecules are assumed to be flexible, two additional multipolar atomic forces arise because of (1) the transfer of torque between neighboring atoms and (2) the dependence of multipole moment on internal geometry (bond lengths, bond angles, etc.) for geometry-dependent multipole models. In this study, atomic force expressions for geometry-dependent multipoles are presented for use in simulations of flexible molecules. The atomic forces are derived by first proposing a new general expression for Wigner function derivatives partial derivative D(m'm)(l)/partial derivative Omega. The force equations can be applied to electrostatic models based on atomic point multipoles or gaussian multipole charge density. Hydrogen-bonded dimers are used to test the intermolecular electrostatic energies and atomic forces calculated by geometry-dependent multipoles fit to the ab initio electrostatic potential. The electrostatic energies and forces are compared with their reference ab initio values. It is shown that both static and geometry-dependent multipole models are able to reproduce total molecular forces and torques with respect to ab initio, whereas geometry-dependent multipoles are needed to reproduce ab initio atomic forces. The expressions for atomic force can be used in simulations of flexible molecules with atomic multipoles. In addition, the results presented in this work should lead to further development of next generation force fields composed of geometry-dependent multipole models.

Computational chemistry and molecular modeling of electron-transfer proteins

The methods of computational chemistry and molecular modeling are becoming more and more accessible to biochemists with the advent of fast, inexpensive graphics workstations and well-tested computer programs. The state of the art in small molecules allows chemists to use these programs as "black boxes" and be confident of the results at an amazingly high level of precision. This is not the case, however, for biological macro-molecules at this time. Therefore, it is necessary before using the programs listed in Section I that we familiarize ourselves with their theoretical basis and limitations. It is also important that they be used in the context of the accumulated literature on their use. The survey given in this chapter is intended as an introduction to these tools and as a source for initiating the discovery process with the literature cited.