Simple estimation of absolute free energies for biomolecules

One reason that free energy difference calculations are notoriously difficult in molecular systems is due to insufficient conformational overlap, or similarity, between the two states or systems of interest. The degree of overlap is irrelevant, however, if the absolute free energy of each state can be computed. We present a method for calculating the absolute free energy that employs a simple construction of an exactly computable reference system which possesses high overlap with the state of interest. The approach requires only a physical ensemble of conformations generated via simulation, and an auxiliary calculation of approximately equal central-processing-unit (CPU) cost. Moreover, the calculations can converge to the correct free energy value even when the physical ensemble is incomplete or improperly distributed. As a "proof of principle," we use the approach to correctly predict free energies for test systems where the absolute values can be calculated exactly, and also to predict the conformational equilibrium for leucine dipeptide in implicit solvent.Comment: To appear in J. Chem. Phys., 10 pages, 6 figure

Coupling hydrophobic, dispersion, and electrostatic contributions in continuum solvent models

Recent studies of the hydration of micro- and nanoscale solutes have demonstrated a strong {\it coupling} between hydrophobic, dispersion and electrostatic contributions, a fact not accounted for in current implicit solvent models. We present a theoretical formalism which accounts for coupling by minimizing the Gibbs free energy with respect to a solvent volume exclusion function. The solvent accessible surface is output of our theory. Our method is illustrated with the hydration of alkane-assembled solutes on different length scales, and captures the strong sensitivity to the particular form of the solute-solvent interactions in agreement with recent computer simulations.Comment: 11 pages, 2 figure

Substrate concentration dependence of the diffusion-controlled steady-state rate constant

The Smoluchowski approach to diffusion-controlled reactions is generalized to interacting substrate particles by including the osmotic pressure and hydrodynamic interactions of the nonideal particles in the Smoluchoswki equation within a local-density approximation. By solving the strictly linearized equation for the time-independent case with absorbing boundary conditions, we present an analytic expression for the diffusion-limited steady-state rate constant for small substrate concentrations in terms of an effective second virial coefficient B_2*. Comparisons to Brownian dynamics simulations excluding HI show excellent agreement up to bulk number densities of B_2* rho_0 < 0.4 for hard sphere and repulsive Yukawa-like interactions between the substrates. Our study provides an alternative way to determine the second virial coefficient of interacting macromolecules experimentally by measuring their steady-state rate constant in diffusion-controlled reactions at low densities.Comment: 7 pages, 3 figure

Application of the level-set method to the implicit solvation of nonpolar molecules

A level-set method is developed for numerically capturing the equilibrium solute-solvent interface that is defined by the recently proposed variational implicit solvent model (Dzubiella, Swanson, and McCammon, Phys. Rev. Lett. {\bf 104}, 527 (2006) and J. Chem.\Phys. {\bf 124}, 084905 (2006)). In the level-set method, a possible solute-solvent interface is represented by the zero level-set (i.e., the zero level surface) of a level-set function and is eventually evolved into the equilibrium solute-solvent interface. The evolution law is determined by minimization of a solvation free energy {\it functional} that couples both the interfacial energy and the van der Waals type solute-solvent interaction energy. The surface evolution is thus an energy minimizing process, and the equilibrium solute-solvent interface is an output of this process. The method is implemented and applied to the solvation of nonpolar molecules such as two xenon atoms, two parallel paraffin plates, helical alkane chains, and a single fullerene $C_{60}$. The level-set solutions show good agreement for the solvation energies when compared to available molecular dynamics simulations. In particular, the method captures solvent dewetting (nanobubble formation) and quantitatively describes the interaction in the strongly hydrophobic plate system

Dewetting-controlled binding of ligands to hydrophobic pockets

We report on a combined atomistic molecular dynamics simulation and implicit solvent analysis of a generic hydrophobic pocket-ligand (host-guest) system. The approaching ligand induces complex wetting/dewetting transitions in the weakly solvated pocket. The transitions lead to bimodal solvent fluctuations which govern magnitude and range of the pocket-ligand attraction. A recently developed implicit water model, based on the minimization of a geometric functional, captures the sensitive aqueous interface response to the concave-convex pocket-ligand configuration semi-quantitatively

Coupling nonpolar and polar solvation free energies in implicit solvent models

Recent studies on the solvation of atomistic and nanoscale solutes indicate that a strong coupling exists between the hydrophobic, dispersion, and electrostatic contributions to the solvation free energy, a facet not considered in current implicit solvent models. We suggest a theoretical formalism which accounts for coupling by minimizing the Gibbs free energy of the solvent with respect to a solvent volume exclusion function. The resulting differential equation is similar to the Laplace-Young equation for the geometrical description of capillary interfaces, but is extended to microscopic scales by explicitly considering curvature corrections as well as dispersion and electrostatic contributions. Unlike existing implicit solvent approaches, the solvent accessible surface is an output of our model. The presented formalism is illustrated on spherically or cylindrically symmetrical systems of neutral or charged solutes on different length scales. The results are in agreement with computer simulations and, most importantly, demonstrate that our method captures the strong sensitivity of solvent expulsion and dewetting to the particular form of the solvent-solute interactions.Comment: accpted in J. Chem. Phy

Slow relaxation of conductance of amorphous hopping insulators

We discuss memory effects in the conductance of hopping insulators due to slow rearrangements of structural defects leading to formation of polarons close to the electron hopping states. An abrupt change in the gate voltage and corresponding shift of the chemical potential change populations of the hopping sites, which then slowly relax due to rearrangements of structural defects. As a result, the density of hopping states becomes time dependent on a scale relevant to rearrangement of the structural defects leading to the excess time dependent conductivity.Comment: 6 pages, 1 figur

Observed Limits on Charge Exchange Contributions to the Diffuse X-ray Background

We present a high resolution spectrum of the diffuse X-ray background from 0.1 to 1 keV for a ~1 region of the sky centered at l=90, b=+60 using a 36-pixel array of microcalorimeters flown on a sounding rocket. With an energy resolution of 11 eV FWHM below 1 keV, the spectrum's observed line ratios help separate charge exchange contributions originating within the heliosphere from thermal emission of hot gas in the interstellar medium. The X-ray sensitivity below 1 keV was reduced by about a factor of four from contamination that occurred early in the flight, limiting the significance of the results. The observed centroid of helium-like O VII is 568+2-3 eV at 90% confidence. Since the centroid expected for thermal emission is 568.4 eV while for charge exchange is 564.2 eV, thermal emission appears to dominate for this line complex, consistent with much of the high-latitude O VII emission originating in 2-3 x 10^6 K gas in the Galactic halo. On the other hand, the observed ratio of C VI Ly gamma to Ly alpha is 0.3+-0.2. The expected ratios are 0.04 for thermal emission and 0.24 for charge exchange, indicating that charge exchange must contribute strongly to this line and therefore potentially to the rest of the ROSAT R12 band usually associated with 10^6 K emission from the Local Hot Bubble. The limited statistics of this experiment and systematic uncertainties due to the contamination require only >32% thermal emission for O VII and >20% from charge exchange for C VI at the 90% confidence level. An experimental gold coating on the silicon substrate of the array greatly reduced extraneous signals induced on nearby pixels from cosmic rays passing through the substrate, reducing the triggered event rate by a factor of 15 from a previous flight of the instrument.Comment: 14 pages, 7 figures, to be published in Ap

The thermal equation of state of FeTiO_3 ilmenite based on in situ X-ray diffraction at high pressures and temperatures

We present in situ measurements of the unit-cell volume of a natural terrestrial ilmenite (Jagersfontein mine, South Africa) and a synthetic reduced ilmenite (FeTiO_3) at simultaneous high pressure and high temperature up to 16 GPa and 1273 K. Unit-cell volumes were determined using energy-dispersive synchrotron X-ray diffraction in a multi-anvil press. Mössbauer analyses show that the synthetic sample contained insignificant amounts of Fe^(3+) both before and after the experiment. Results were fit to Birch-Murnaghan thermal equations of state, which reproduce the experimental data to within 0.5 and 0.7 GPa for the synthetic and natural samples, respectively. At ambient conditions, the unit-cell volume of the natural sample [V_0 = 314.75 ± 0.23 (1 ) Å^3] is significantly smaller than that of the synthetic sample [V_0 = 319.12 ± 0.26 Å^3]. The difference can be attributed to the presence of impurities and Fe^(3+) in the natural sample. The 1 bar isothermal bulk moduli K_(T0) for the reduced ilmenite is slightly larger than for the natural ilmenite (181 ± 7 and 165 ± 6 GPa, respectively), with pressure derivatives K_0' = 3 ± 1. Our results, combined with literature data, suggest that the unit-cell volume of reduced ilmenite is significantly larger than that of oxidized ilmenite, whereas their thermoelastic parameters are similar. Our data provide more appropriate input parameters for thermo-chemical models of lunar interior evolution, in which reduced ilmenite plays a critical role

Searching for keV Sterile Neutrino Dark Matter with X-ray Microcalorimeter Sounding Rockets

High-resolution X-ray spectrometers onboard suborbital sounding rockets can search for dark matter candidates that produce X-ray lines, such as decaying keV-scale sterile neutrinos. Even with exposure times and effective areas far smaller than XMM-Newton and Chandra observations, high-resolution, wide field-of-view observations with sounding rockets have competitive sensitivity to decaying sterile neutrinos. We analyze a subset of the 2011 observation by the X-ray Quantum Calorimeter instrument centered on Galactic coordinates l = 165, b = -5 with an effective exposure of 106 seconds, obtaining a limit on the sterile neutrino mixing angle of sin^2(2 theta) < 7.2e-10 at 95% CL for a 7 keV neutrino. Better sensitivity at the level of sin^2(2 theta) ~ 2.1e-11 at 95\% CL for a 7 keV neutrino is achievable with future 300-second observations of the galactic center by the Micro-X instrument, providing a definitive test of the sterile neutrino interpretation of the reported 3.56 keV excess from galaxy clusters.Comment: 13 pages, 13 figures, submitted to Ap