Accurately predicting absolute binding free energies of protein-ligand complexes is important as a fundamental problem in both computational biophysics and pharmaceutical discovery. Calculating binding free energies for charged ligands is generally considered to be challenging because of the strong electrostatic interactions between the ligand and its environment in aqueous solution. In this work, we compare the performance of the potential of mean force (PMF) method and the double decoupling method (DDM) for computing absolute binding free energies for charged ligands. We first clarify an unresolved issue concerning the explicit use of the binding site volume to define the complexed state in DDM together with the use of harmonic restraints. We also provide an alternative derivation for the formula for absolute binding free energy using the PMF approach. We use these formulas to compute the binding free energy of charged ligands at an allosteric site of HIV-1 integrase, which has emerged in recent years as a promising target for developing antiviral therapy. As compared with the experimental results, the absolute binding free energies obtained by using the PMF approach show unsigned errors of 1.5-3.4 kcal mol-1, which are somewhat better than the results from DDM (unsigned errors of 1.6-4.3 kcal mol-1) using the same amount of CPU time. According to the DDM decomposition of the binding free energy, the ligand binding appears to be dominated by nonpolar interactions despite the presence of very large and favorable intermolecular ligand-receptor electrostatic interactions, which are almost completely cancelled out by the equally large free energy cost of desolvation of the charged moiety of the ligands in solution. We discuss the relative strengths of computing absolute binding free energies using the alchemical and physical pathway methods.
Bioelectrical impedance equations are frequently used by food and nutrition professionals to estimate percent fat mass in overweight and obese children. However, it is not known whether they are accurate for such children, as they have been primarily developed for children of varying body weights. The aim of this cross-sectional study was to evaluate the predictive validity of four previously published prediction equations developed for the pediatric population, among a sample of overweight and obese children. Thirty overweight or obese children (mean age=7.57+/-1.28 years) underwent measurement of fat mass, percent fat mass, and fat-free mass using dual-energy x-ray absorptiometry (DEXA) and bioelectrical impedance analysis (BIA). Impedance values from the BIA were entered into the four prediction equations and Pearson correlations used to determine the significance of associations between each of the BIA prediction equations and DEXA for percent fat mass, fat mass, and fat-free mass. For percent fat mass, paired t tests were used to assess differences between the methods and the technique of Bland and Altman was used to determine bias and error. Results showed that the mean percent fat mass as determined by DEXA for this age group was 40.79%. In comparison with other BIA prediction equations, the Schaefer equation had the closest mean value of 41.98%, and was the only equation not to significantly differ from the DEXA (P=0.121). This study suggests that the Schaefer equation is the only accurate BIA prediction equation for assessing percent fat mass in this sample of overweight and obese children from primarily white backgrounds.
The advent of modern solar energy technologies can improve the costs of energy consumption on a global, national, and regional level, ultimately spanning stakeholders from governmental entities to utility companies, corporations, and residential homeowners. For those stakeholders experiencing the four seasons, accurately accounting for snow-related energy losses is important for effectively predicting photovoltaic performance energy generation and valuation. This paper provides an examination of a new, simplified approach to decrease snow-related forecasting error, in comparison to current solar energy performance models. A new method is proposed to allow model designers, and ultimately users, the opportunity to better understand the return on investment for solar energy systems located in snowy environments. The new method is validated using two different sets of solar energy systems located near Green Bay, WI, USA: a 3.0-kW micro inverter system and a 13.2-kW central inverter system. Both systems were unobstructed, facing south, and set at a tilt of 26.56°. Data were collected beginning in May 2014 (micro inverter system) and October 2014 (central inverter system), through January 2018. In comparison to reference industry standard solar energy prediction applications (PVWatts and PVsyst), the new method results in lower mean absolute percent errors per kilowatt hour of 0.039 and 0.055%, respectively, for the micro inverter system and central inverter system. The statistical analysis provides support for incorporating this new method into freely available, online, up-to-date prediction applications, such as PVWatts and PVsyst.
In finite element methods that are based on position and slope coordinates, a representation of axial and bending deformation by means of an elastic line approach has become popular. Such beam and plate formulations based on the so-called absolute nodal coordinate formulation have not yet been verified sufficiently enough with respect to analytical results or classical nonlinear rod theories. Examining the existing planar absolute nodal coordinate element, which uses a curvature proportional bending strain expression, it turns out that the deformation does not fully agree with the solution of the geometrically exact theory and, even more serious, the normal force is incorrect. A correction based on the classical ideas of the extensible elastica and geometrically exact theories is applied and a consistent strain energy and bending moment relations are derived. The strain energy of the solid finite element formulation of the absolute nodal coordinate beam is based on the St. Venant-Kirchhoff material: therefore, the strain energy is derived for the latter case and compared to classical nonlinear rod theories. The error in the original absolute nodal coordinate formulation is documented by numerical examples. The numerical example of a large deformation cantilever beam shows that the normal force is incorrect when using the previous approach, while a perfect agreement between the absolute nodal coordinate formulation and the extensible elastica can be gained when applying the proposed modifications. The numerical examples show a very good agreement of reference analytical and numerical solutions with the solutions of the proposed beam formulation for the case of large deformation pre-curved static and dynamic problems, including buckling and eigenvalue analysis. The resulting beam formulation does not employ rotational degrees of freedom and therefore has advantages compared to classical beam elements regarding energy-momentum conservation.
Hubble's Next Generation Spectral Library (NGSL) consists of R-l000 spectra of 374 stars of assorted temperature, gravity, and metallicity. Each spectrum covers the wavelength range, 0.18-1.00 microns. The library can be viewed and/or downloaded from the website, Stars in the NGSL are now being used as absolute flux standards at ground-based observatories. However, the uncertainty in the absolute flux is about 2%, which does not meet the requirements of dark-energy surveys. We are therefore developing an observing procedure that should yield fluxes with uncertainties less than 1 % and will take part in an HST proposal to observe up to 15 stars using this new procedure. 2b1af7f3a8