Development of a lattice-sum method emulating nonperiodic boundary conditions for the treatment of electrostatic interactions in molecular simulations: A continuum-electrostatics study

Quantifying Fluctuations of Average Solvent Environments for Embedding Calculations

The viability and effectiveness of replacing an ensemble of embedded solute calculations by a single calculation using an average description of the solvent environment are evaluated. This work explores the fluctuations of the average description of the system obtained in two ways: from calculations on an ensemble of geometries and from an average environment constructed from the same ensemble. To this end, classical molecular dynamics simulations of a rigid acetone solute in SPCE water are performed in order to generate an ensemble of solvent environments. From this ensemble of solvent configurations, a number of different approaches for constructing an average solvent environment are employed. We perform a thorough numerical analysis of the fluctuations of the electrostatic potential experienced by the solute, as well as the resulting fluctuations of the solute's electronic density, measured through its dipole moment and fitted atomic point charges. At the same time, we inspect the accuracy of the methods used to construct average environments. Finally, the proposed method for generating the embedding potential from an average environment density is applied to estimate the solvatochromic shift of the first excitation of acetone. In order to account for quantum confinement effects, which may be important in certain cases, the fluctuations in the shift due to the interaction with the solvent are evaluated using frozen-density-embedding theory. Our results demonstrate that, for normally distributed environments, the constructed average environment is a reasonably good representation of a fluctuating molecular solvent environment. We then provide guidance for future comparisons between these theoretical treatments of solute/solvent systems to experimental measurements.

On the Effect of the Various Assumptions and Approximations used in Molecular Simulations on the Properties of Bio-Molecular Systems: Overview and Perspective on Issues

Computer simulations of molecular systems enable structure-energy-function relationships of molecular processes to be described at the sub-atomic, atomic, supra-atomic or supra-molecular level and plays an increasingly important role in chemistry, biology and physics. To interpret the results of such simulations appropriately, the degree of uncertainty and potential errors affecting the calculated properties must be considered. Uncertainty and errors arise from (1) assumptions underlying the molecular model, force field and simulation algorithms, (2) approximations implicit in the interatomic interaction function (force field), or when integrating the equations of motion, (3) the chosen values of the parameters that determine the accuracy of the approximations used, and (4) the nature of the system and the property of interest. In this overview, advantages and shortcomings of assumptions and approximations commonly used when simulating bio-molecular systems are considered. What the developers of bio-molecular force fields and simulation software can do to facilitate and broaden research involving bio-molecular simulations is also discussed.

Toward the correction of effective electrostatic forces in explicit-solvent molecular dynamics simulations: restraints on solvent-generated electrostatic potential and solvent polarization

Despite considerable advances in computing power, atomistic simulations under nonperiodic boundary conditions, with Coulombic electrostatic interactions and in systems large enough to reduce finite-size associated errors in thermodynamic quantities to within the thermal energy, are still not affordable. As a result, periodic boundary conditions, systems of microscopic size and effective electrostatic interaction functions are frequently resorted to. Ensuing artifacts in thermodynamic quantities are nowadays routinely corrected a posteriori, but the underlying configurational sampling still descends from spurious forces. The present study addresses this problem through the introduction of on-the-fly corrections to the physical forces during an atomistic molecular dynamics simulation. Two different approaches are suggested, where the force corrections are derived from special potential energy terms. In the first approach, the solvent-generated electrostatic potential sampled at a given atom site is restrained to a target value involving corrections for electrostatic artifacts. In the second approach, the long-range regime of the solvent polarization around a given atom site is restrained to the Born polarization, i.e., the solvent polarization corresponding to the ideal situation of a macroscopic system under nonperiodic boundary conditions and governed by Coulombic electrostatic interactions. The restraints are applied to the explicit-water simulation of a hydrated sodium ion, and the effect of the restraints on the structural and energetic properties of the solvent is illustrated. Furthermore, by means of the calculation of the charging free energy of a hydrated sodium ion, it is shown how the electrostatic potential restraint translates into the on-the-fly consideration of the corresponding free-energy correction terms. It is discussed how the restraints can be generalized to situations involving several solute particles. Although the present study considers a very simple system only, it is an important step toward the on-the-fly elimination of finite-size and approximate-electrostatic artifacts during atomistic molecular dynamics simulations.

Bulk simulation of polar liquids in spherical symmetry

Molecular simulations of strongly coupled dipolar systems of varying size have been carried out, using particles confined inside a dielectric cavity and an image charge approach to treat the dielectric response from the surroundings. A simple method using penalty functions was employed to create an isotropic and homogeneous distribution of particles inside the cavity. The dielectric response of the molecular system was found to increase as the number of particles N was increased. Nevertheless, a significant surface effect remained even for the largest systems (N=10,000), manifesting itself through a decrease in the dielectric constant of the system as the confining surface was approached. The surface effect was significantly reduced by using a negative dielectric constant of the surrounding dielectric medium, although accomplishing a full dielectric solvation of the molecular system was not possible.

Roles of boundary conditions in DNA simulations: analysis of ion distributions with the finite-difference Poisson-Boltzmann method

The wide use of lattice-sum strategies in biomolecular simulations has raised many questions on potential artifacts in these strategies. One interesting question is the artifacts in the counterion distributions of highly charged systems. As one would anticipate, Coulombic interactions under the periodic boundary condition may deviate noticeably from those under the free boundary condition in the highly charged systems, significantly influencing their counterion distributions. On the other hand, the electrostatic screening due to water molecules and mobile ions may effectively damp the possible periodic distortions in Coulombic interactions. Therefore, the magnitude of periodicity-induced artifacts in counterion distributions is not straightforward to dissect without detailed analyses. In this study, we have developed a hybrid explicit counterion/implicit salt representation of mobile ions to address this question. We have chosen a well-studied DNA for easy validation of the minimal hybrid ion representation. Our detailed analysis of continuum ion distributions, explicit ion distributions, radial counterion distribution functions, and sequence-dependent counterion distributions, however, indicates that periodicity artifacts are not apparent at the surface of the tested DNA. Nevertheless, influence of boundary conditions does show up starting at the second solvation shell and becomes apparent at the cell boundary.

Structural flexibility of the nucleosome core particle at atomic resolution studied by molecular dynamics simulation

Comparative explicit solvent molecular dynamics (MD) simulations have been performed on a complete nucleosome core particle with and without N-terminal histone tails for more than 20 ns. Main purpose of the simulations was to study the dynamics of mobile elements such as histone N-terminal tails and how packing and DNA-bending influences the fine structure and dynamics of DNA. Except for the tails, histone and DNA molecules stayed on average close to the crystallographic start structure supporting the quality of the current force field approach. Despite the packing strain, no increase of transitions to noncanonical nucleic acid backbone conformations compared to regular B-DNA was observed. The pattern of kinks and bends along the DNA remained close to the experiment overall. In addition to the local dynamics, the simulations allowed the analysis of the superhelical mobility indicating a limited relative mobility of DNA segments separated by one superhelical turn (mean relative displacement of approximately +/-0.2 nm, mainly along the superhelical axis). An even higher rigidity was found for relative motions (distance fluctuations) of segments separated by half a superhelical turn (approximately +/-0.1 nm). The N-terminal tails underwent dramatic conformational rearrangements on the nanosecond time scale toward partially and transiently wrapped states around the DNA. Many of the histone tail changes corresponded to coupled association and folding events from fully solvent-exposed states toward complexes with the major and minor grooves of DNA. The simulations indicate that the rapid conformational changes of the tails can modulate the DNA accessibility within a few nanoseconds.