Building Water Models, A Different Approach

Simplified, classical models of water are an integral part of atomistic molecular simulations, especially in biology and chemistry where hydration effects are critical. Yet, despite several decades of effort, these models are still far from perfect. Presented here is an alternative approach to constructing point charge water models - currently, the most commonly used type. In contrast to the conventional approach, we do not impose any geometry constraints on the model other than symmetry. Instead, we optimize the distribution of point charges to best describe the "electrostatics" of the water molecule, which is key to many unusual properties of liquid water. The search for the optimal charge distribution is performed in 2D parameter space of key lowest multipole moments of the model, to find best fit to a small set of bulk water properties at room temperature. A virtually exhaustive search is enabled via analytical equations that relate the charge distribution to the multipole moments. The resulting "optimal" 3-charge, 4-point rigid water model (OPC) reproduces a comprehensive set of bulk water properties significantly more accurately than commonly used rigid models: average error relative to experiment is 0.76%. Close agreement with experiment holds over a wide range of temperatures, well outside the ambient conditions at which the fit to experiment was performed. The improvements in the proposed water model extend beyond bulk properties: compared to the common rigid models, predicted hydration free energies of small molecules in OPC water are uniformly closer to experiment, root-mean-square error < 1kcal/mol

Accurate Evaluation of Charge Asymmetry in Aqueous Solvation

Charge hydration asymmetry (CHA)--a characteristic dependence of hydration free energy on the sign of the solute charge--quantifies the asymmetric response of water to electric field at microscopic level. Accurate estimates of CHA are critical for understanding hydration effects ubiquitous in chemistry and biology. However, measuring hydration energies of charged species is fraught with significant difficulties, which lead to unacceptably large (up to 300%) variation in the available estimates of the CHA effect. We circumvent these difficulties by developing a framework which allows us to extract and accurately estimate the intrinsic propensity of water to exhibit CHA from accurate experimental hydration free energies of neutral polar molecules. Specifically, from a set of 504 small molecules we identify two pairs that are analogous, with respect to CHA, to the K+/F- pair--a classical probe for the effect. We use these "CHA-conjugate" molecule pairs to quantify the intrinsic charge-asymmetric response of water to the microscopic charge perturbations: the asymmetry of the response is strong, ~50% of the average hydration free energy of these molecules. The ability of widely used classical water models to predict hydration energies of small molecules correlates with their ability to predict CHA

Heat conductivity of DNA double helix

Thermal conductivity of isolated single molecule DNA fragments is of importance for nanotechnology, but has not yet been measured experimentally. Theoretical estimates based on simplified (1D) models predict anomalously high thermal conductivity. To investigate thermal properties of single molecule DNA we have developed a 3D coarse-grained (CG) model that retains the realism of the full all-atom description, but is significantly more efficient. Within the proposed model each nucleotide is represented by 6 particles or grains; the grains interact via effective potentials inferred from classical molecular dynamics (MD) trajectories based on a well-established all-atom potential function. Comparisons of 10 ns long MD trajectories between the CG and the corresponding all-atom model show similar root-mean-square deviations from the canonical B-form DNA, and similar structural fluctuations. At the same time, the CG model is 10 to 100 times faster depending on the length of the DNA fragment in the simulation. Analysis of dispersion curves derived from the CG model yields longitudinal sound velocity and torsional stiffness in close agreement with existing experiments. The computational efficiency of the CG model makes it possible to calculate thermal conductivity of a single DNA molecule not yet available experimentally. For a uniform (polyG-polyC) DNA, the estimated conductivity coefficient is 0.3 W/mK which is half the value of thermal conductivity for water. This result is in stark contrast with estimates of thermal conductivity for simplified, effectively 1D chains ("beads on a spring") that predict anomalous (infinite) thermal conductivity. Thus, full 3D character of DNA double-helix retained in the proposed model appears to be essential for describing its thermal properties at a single molecule level.Comment: 16 pages, 12 figure

Point Charges Optimally Placed to Represent the Multipole Expansion of Charge Distributions

We propose an approach for approximating electrostatic charge distributions with a small number of point charges to optimally represent the original charge distribution. By construction, the proposed optimal point charge approximation (OPCA) retains many of the useful properties of point multipole expansion, including the same far-field asymptotic behavior of the approximate potential. A general framework for numerically computing OPCA, for any given number of approximating charges, is described. We then derive a 2-charge practical point charge approximation, PPCA, which approximates the 2-charge OPCA via closed form analytical expressions, and test the PPCA on a set of charge distributions relevant to biomolecular modeling. We measure the accuracy of the new approximations as the RMS error in the electrostatic potential relative to that produced by the original charge distribution, at a distance the extent of the charge distribution–the mid-field. The error for the 2-charge PPCA is found to be on average 23% smaller than that of optimally placed point dipole approximation, and comparable to that of the point quadrupole approximation. The standard deviation in RMS error for the 2-charge PPCA is 53% lower than that of the optimal point dipole approximation, and comparable to that of the point quadrupole approximation. We also calculate the 3-charge OPCA for representing the gas phase quantum mechanical charge distribution of a water molecule. The electrostatic potential calculated by the 3-charge OPCA for water, in the mid-field (2.8 Å from the oxygen atom), is on average 33.3% more accurate than the potential due to the point multipole expansion up to the octupole order. Compared to a 3 point charge approximation in which the charges are placed on the atom centers, the 3-charge OPCA is seven times more accurate, by RMS error. The maximum error at the oxygen-Na distance (2.23 Å ) is half that of the point multipole expansion up to the octupole order