Changes of GH-IGFs and its relationship with growth retardation in children with bronchial asthma.

OBJECTIVE: To explore the relationship between Growth Hormone Insulin-like Growth Factors (GH-IGFs) and growth retardation in children with bronchial asthma. METHODS: 112 children with bronchial asthma and 50 healthy children were studied. Serum GH, IGF-1, and Insulin-like Growth Factor Binding Protein 3 (IGFBP3) were assessed by ELISA. GH-IGFs-related parameters were compared, and the correlation between the parameters and bronchial asthma severity was analyzed. The bronchial asthma group was divided into the growth retardation group and non-growth retardation group to analyze the diagnostic value of GH-IGFs in growth retardation and the relationship between GH-IGFs and growth retardation. RESULTS: GH, IGF-1, and IGFBP3 in the bronchial asthma group were lower. GH, IGF-1, and IGFBP3 levels were decreased with the severity of bronchial asthma. GH, IGF-1, and IGFBP3 in the growth retardation group were lower than those in the non-growth retardation group. The AUC of GH-IGFs combined detection was higher than that of GH and IGFBP3 alone detection. GH < 9.27 µg/L and IGF-1 < 179.53 mmoL/L were risk factors for growth retardation in patients with bronchial asthma. CONCLUSION: GH-IGFs-related parameters have diagnostic value for growth retardation in children, and decreased levels of GH and IGF-1 are risk factors for growth retardation in children.

Crystal growth engineering and origin of the weak ferromagnetism in antiferromagnetic matrix of orthochromates from t-e orbital hybridization.

We report a combined experimental and theoretical study on intriguing magnetic properties of quasiferroelectric orthochromates. Large single crystals of the family of RECrO3 (RE = Y, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu) compounds were successfully grown. Neutron Laue study indicates a good quality of the obtained single crystals. Applied magnetic field and temperature dependent magnetization measurements reveal their intrinsic magnetic properties, especially the antiferromagnetic (AFM) transition temperatures. Density functional theory studies of the electronic structures were carried out using the Perdew-Burke-Ernzerhof functional plus Hubbard U method. Crystallographic information and magnetism were theoretically optimized systematically. When RE3+ cations vary from Y3+ and Eu3+ to Lu3+ ions, the calculated t-e orbital hybridization degree and Néel temperature behave similarly to the experimentally determined AFM transition temperature with variation in cationic radius. We found that the t-e hybridization is anisotropic, causing a magnetic anisotropy of Cr3+ sublattices. This was evaluated with the nearest-neighbor J 1-J 2 model. Our research provides a picture of the electronic structures during the t-e hybridization process while changing RE ions and sheds light on the nature of the weak ferromagnetism coexisting with predominated antiferromagnetism. The available large RECrO3 single crystals build a platform for further studies of orthochromates.

Mechanistic Insights into Passive Membrane Permeability of Drug-like Molecules from a Weighted Ensemble of Trajectories.

Passive permeability of a drug-like molecule is a critical property assayed early in a drug discovery campaign that informs a medicinal chemist how well a compound can traverse biological membranes, such as gastrointestinal epithelial or restrictive organ barriers, so it can perform a specific therapeutic function. However, the challenge that remains is the development of a method, experimental or computational, which can both determine the permeation rate and provide mechanistic insights into the transport process to help with the rational design of any given molecule. Typically, one of the following three methods are used to measure the membrane permeability: (1) experimental permeation assays acting on either artificial or natural membranes; (2) quantitative structure-permeability relationship models that rely on experimental values of permeability or related pharmacokinetic properties of a range of molecules to infer those for new molecules; and (3) estimation of permeability from the Smoluchowski equation, where free energy and diffusion profiles along the membrane normal are taken as input from large-scale molecular dynamics simulations. While all these methods provide estimates of permeation coefficients, they provide very little information for guiding rational drug design. In this study, we employ a highly parallelizable weighted ensemble (WE) path sampling strategy, empowered by cloud computing techniques, to generate unbiased permeation pathways and permeability coefficients for a set of drug-like molecules across a neat 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidylcholine membrane bilayer. Our WE method predicts permeability coefficients that compare well to experimental values from an MDCK-LE cell line and PAMPA assays for a set of drug-like amines of varying size, shape, and flexibility. Our method also yields a series of continuous permeation pathways weighted and ranked by their associated probabilities. Taken together, the ensemble of reactive permeation pathways, along with the estimate of the permeability coefficient, provides a clearer picture of the microscopic underpinnings of small-molecule membrane permeation.

WESTPA 2.0: High-Performance Upgrades for Weighted Ensemble Simulations and Analysis of Longer-Timescale Applications.

The weighted ensemble (WE) family of methods is one of several statistical mechanics-based path sampling strategies that can provide estimates of key observables (rate constants and pathways) using a fraction of the time required by direct simulation methods such as molecular dynamics or discrete-state stochastic algorithms. WE methods oversee numerous parallel trajectories using intermittent overhead operations at fixed time intervals, enabling facile interoperability with any dynamics engine. Here, we report on the major upgrades to the WESTPA software package, an open-source, high-performance framework that implements both basic and recently developed WE methods. These upgrades offer substantial improvements over traditional WE methods. The key features of the new WESTPA 2.0 software enhance the efficiency and ease of use: an adaptive binning scheme for more efficient surmounting of large free energy barriers, streamlined handling of large simulation data sets, exponentially improved analysis of kinetics, and developer-friendly tools for creating new WE methods, including a Python API and resampler module for implementing both binned and "binless" WE strategies.

Super-Necking Crystal Growth and Structural and Magnetic Properties of SrTb2O4 Single Crystals.

We report on single-crystal growths of the SrTb2O4 compound by a super-necking technique with a laser-floating-zone furnace and study the stoichiometry, growth mode, and structural and magnetic properties by scanning electronic microscopy, neutron Laue, X-ray powder diffraction, and the physical property measurement system. We optimized the growth parameters, mainly the growth speed, atmosphere, and the addition of a Tb4O7 raw material. Neutron Laue diffraction displays the characteristic feature of a single crystal. Our study reveals an atomic ratio of Sr:Tb = 0.97(2):2.00(1) and a possible layer by layer crystal growth mode. Our X-ray powder diffraction study determines the crystal structure, lattice constants, and atomic positions. The paramagnetic (PM) Curie-Weiss (CW) temperature θCW = 5.00(4) K, and the effective PM moment M mea eff = 10.97(1) µB per Tb3+ ion. The data of magnetization versus temperature can be divided into three regimes, showing a coexistence of antiferromagnetic and ferromagnetic interactions. This probably leads to the magnetic frustration in the SrTb2O4 compound. The magnetization at 2 K and 14 T originates from both the Tb1 and Tb2 sites and is strongly frustrated with an expected saturation field at ∼41.5 T, displaying an intricate phase diagram with three ranges.

Ligand Selectivity in the Recognition of Protoberberine Alkaloids by Hybrid-2 Human Telomeric G-Quadruplex: Binding Free Energy Calculation, Fluorescence Binding, and NMR Experiments.

The human telomeric G-quadruplex (G4) is an attractive target for developing anticancer drugs. Natural products protoberberine alkaloids are known to bind human telomeric G4 and inhibit telomerase. Among several structurally similar protoberberine alkaloids, epiberberine (EPI) shows the greatest specificity in recognizing the human telomeric G4 over duplex DNA and other G4s. Recently, NMR study revealed that EPI recognizes specifically the hybrid-2 form human telomeric G4 by inducing large rearrangements in the 5'-flanking segment and loop regions to form a highly extensive four-layered binding pocket. Using the NMR structure of the EPI-human telomeric G4 complex, here we perform molecular dynamics free energy calculations to elucidate the ligand selectivity in the recognition of protoberberines by the human telomeric G4. The MM-PB(GB)SA (molecular mechanics-Poisson Boltzmann/Generalized Born) Surface Area) binding free energies calculated using the Amber force fields bsc0 and OL15 correlate well with the NMR titration and binding affinity measurements, with both calculations correctly identifying the EPI as the strongest binder to the hybrid-2 telomeric G4 wtTel26. The results demonstrated that accounting for the conformational flexibility of the DNA-ligand complexes is crucially important for explaining the ligand selectivity of the human telomeric G4. While the MD-simulated (molecular dynamics) structures of the G-quadruplex-alkaloid complexes help rationalize why the EPI-G4 interactions are optimal compared with the other protoberberines, structural deviations from the NMR structure near the binding site are observed in the MD simulations. We have also performed binding free energy calculation using the more rigorous double decoupling method (DDM); however, the results correlate less well with the experimental trend, likely due to the difficulty of adequately sampling the very large conformational reorganization in the G4 induced by the protoberberine binding.

Massive-Scale Binding Free Energy Simulations of HIV Integrase Complexes Using Asynchronous Replica Exchange Framework Implemented on the IBM WCG Distributed Network.

To perform massive-scale replica exchange molecular dynamics (REMD) simulations for calculating binding free energies of protein-ligand complexes, we implemented the asynchronous replica exchange (AsyncRE) framework of the binding energy distribution analysis method (BEDAM) in implicit solvent on the IBM World Community Grid (WCG) and optimized the simulation parameters to reduce the overhead and improve the prediction power of the WCG AsyncRE simulations. We also performed the first massive-scale binding free energy calculations using the WCG distributed computing grid and 301 ligands from the SAMPL4 challenge for large-scale binding free energy predictions of HIV-1 integrase complexes. In total there are ∼10000 simulated complexes, ∼1 million replicas, and ∼2000 µs of aggregated MD simulations. Running AsyncRE MD simulations on the WCG requires accepting a trade-off between the number of replicas that can be run (breadth) and the number of full RE cycles that can be completed per replica (depth). As compared with synchronous Replica Exchange (SyncRE) running on tightly coupled clusters like XSEDE, on the WCG many more replicas can be launched simultaneously on heterogeneous distributed hardware, but each full RE cycle requires more overhead. We compared the WCG results with that from AutoDock and more advanced RE simulations including the use of flattening potentials to accelerate sampling of selected degrees of freedom of ligands and/or receptors related to slow dynamics due to high energy barriers. We propose a suitable strategy of RE simulations to refine high throughput docking results which can be matched to corresponding computing resources: from HPC clusters, to small or medium-size distributed campus grids, and finally to massive-scale computing networks including millions of CPUs like the resources available on the WCG.

Comparing alchemical and physical pathway methods for computing the absolute binding free energy of charged ligands.

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.

Improving Prediction Accuracy of Binding Free Energies and Poses of HIV Integrase Complexes Using the Binding Energy Distribution Analysis Method with Flattening Potentials.

To accelerate conformation sampling of slow dynamics from receptor or ligand, we introduced flattening potentials on selected bonded and nonbonded intramolecular interactions to the binding energy distribution analysis method (BEDAM) for calculating absolute binding free energies of protein-ligand complexes using an implicit solvent model and implemented flattening BEDAM using the asynchronous replica exchange (AsyncRE) framework for performing large scale replica exchange molecular dynamics (REMD) simulations. The advantage of using the flattening feature to reduce high energy barriers was exhibited first by the p-xylene-T4 lysozyme complex, where the intramolecular interactions of a protein side chain on the binding site were flattened to accelerate the conformational transition of the side chain from the trans to the gauche state when the p-xylene ligand is present in the binding site. Much more extensive flattening BEDAM simulations were performed for 53 experimental binders and 248 nonbinders of HIV-1 integrase which formed the SAMPL4 challenge, with the total simulation time of 24.3 µs. We demonstrated that the flattening BEDAM simulations not only substantially increase the number of true positives (and reduce false negatives) but also improve the prediction accuracy of binding poses of experimental binders. Furthermore, the values of area under the curve (AUC) of receiver operating characteristic (ROC) and the enrichment factors at 20% cutoff calculated from the flattening BEDAM simulations were improved significantly in comparison with that of simulations without flattening as we previously reported for the whole SAMPL4 database. Detailed analysis found that the improved ability to discriminate the binding free energies between the binders and nonbinders is due to the fact that the flattening simulations reduce the reorganization free energy penalties of binders and decrease the overlap of binding free energy distributions of binders relative to that of nonbinders. This happens because the conformational ensemble distributions for both the ligand and protein in solution match those at the fully coupled (complex) state more closely when the systems are more fully sampled after the flattening potentials are applied to the intermediate states.

Enhanced Sampling of Interdomain Motion Using Map-Restrained Langevin Dynamics and NMR: Application to Pin1.

Many signaling proteins consist of globular domains connected by flexible linkers that allow for substantial domain motion. Because these domains often serve as complementary functional modules, the possibility of functionally important domain motions arises. To explore this possibility, we require knowledge of the ensemble of protein conformations sampled by interdomain motion. Measurements of NMR residual dipolar couplings (RDCs) of backbone HN bonds offer a per-residue characterization of interdomain dynamics, as the couplings are sensitive to domain orientation. A challenge in reaching this potential is the need to interpret the RDCs as averages over dynamic ensembles of domain conformations. Here, we address this challenge by introducing an efficient protocol for generating conformational ensembles appropriate for flexible, multi-domain proteins. The protocol uses map-restrained self-guided Langevin dynamics simulations to promote collective, interdomain motion while restraining the internal domain motion to near rigidity. Critically, the simulations retain an all-atom description for facile inclusion of site-specific NMR RDC restraints. The result is the rapid generation of conformational ensembles consistent with the RDC data. We illustrate this protocol on human Pin1, a two-domain peptidyl-prolyl isomerase relevant for cancer and Alzheimer's disease. The results include the ensemble of domain orientations sampled by Pin1, as well as those of a dysfunctional variant, I28A-Pin1. The differences between the ensembles corroborate our previous spin relaxation results that showed weakened interdomain contact in the I28A variant relative to wild type. Our protocol extends our abilities to explore the functional significance of protein domain motions.

Simultaneously determination of bisphenol A and its alternatives in sediment by ultrasound-assisted and solid phase extractions followed by derivatization using GC-MS.

Bisphenol analogues are a group of chemicals which are being widely applied in industrial and household products owing to regulations on bisphenol A (BPA) in many countries. In this study, an analytical method, including extraction from complex environmental matrices, clean-up using solid phase extraction (SPE) and following-up derivatization prior to gas chromatography coupled with mass spectrometry (GC-MS), was developed to analyze seven commonly used bisphenols in sediment. Five kinds of extraction solvents, four kinds of SPE cartridges, and four kinds of SPE eluting solvents were individually tested for their performances; and the conditions for derivatizing were also optimized. Finally, C18 cartridge was determined as the SPE cartridge and methanol was selected as extracting and eluting solvent. Acetic anhydride (AA) was used as derivatizing agent and reaction took 20 min at room temperature. The method was used successfully to measure the seven bisphenol compounds in sediment samples from Taihu Lake, China. BPA, bisphenol F and bisphenol S were detected in all sediment samples, with concentrations in the range of 3.94-33.2; 0.503-3.28 and 0.323-27.3 ng g-1 dw. Other compounds were detected at low frequencies or not detected. We provided a convenient, reliable, and sensitive method to analyze bisphenol compounds in complex environmental samples.

A combined treatment of hydration and dynamical effects for the modeling of host-guest binding thermodynamics: the SAMPL5 blinded challenge.

As part of the SAMPL5 blinded experiment, we computed the absolute binding free energies of 22 host-guest complexes employing a novel approach based on the BEDAM single-decoupling alchemical free energy protocol with parallel replica exchange conformational sampling and the AGBNP2 implicit solvation model specifically customized to treat the effect of water displacement as modeled by the Hydration Site Analysis method with explicit solvation. Initial predictions were affected by the lack of treatment of ionic charge screening, which is very significant for these highly charged hosts, and resulted in poor relative ranking of negatively versus positively charged guests. Binding free energies obtained with Debye-Hückel treatment of salt effects were in good agreement with experimental measurements. Water displacement effects contributed favorably and very significantly to the observed binding affinities; without it, the modeling predictions would have grossly underestimated binding. The work validates the implicit/explicit solvation approach employed here and it shows that comprehensive physical models can be effective at predicting binding affinities of molecular complexes requiring accurate treatment of conformational dynamics and hydration.

Impacts of Morphology, Natural Organic Matter, Cations, and Ionic Strength on Sulfidation of Silver Nanowires.

Silver nanowires (AgNWs) are being widely utilized in an increasing number of consumer products, which could release silver to aquatic environments during the use or washing process, and have received growing concerns on their potential risks to bio-organisms and humans. The present study demonstrated that AgNWs mainly experienced direct oxysulfidation by reacting with dissolved sulfide species (initial S2- concentration at 1.6 mg/L) to produce silver sulfide nanostructures under environmentally relevant conditions. Granular Ag2S nanoparticles were formed on the surface of the nanowires. The sulfidation rate constant (kAg) of AgNWs was compared with those of silver nanoparticles (AgNPs) at different particle sizes. It was found that the kAg positively correlated with the specific surface areas of the silver nanomaterials. Natural organic matter (NOM) suppressed the sulfidation of AgNWs to different extents depending on its concentration. Divalent cations (Mg2+ and Ca2+ ions) substantially accelerated the sulfidation rates of AgNWs compared to monovalent cations (Na+ and K+ ions). At the same ionic strengths, Ca2+ ions displayed the highest promoting effect among the four metallic ions.

Large scale free energy calculations for blind predictions of protein-ligand binding: the D3R Grand Challenge 2015.

We describe binding free energy calculations in the D3R Grand Challenge 2015 for blind prediction of the binding affinities of 180 ligands to Hsp90. The present D3R challenge was built around experimental datasets involving Heat shock protein (Hsp) 90, an ATP-dependent molecular chaperone which is an important anticancer drug target. The Hsp90 ATP binding site is known to be a challenging target for accurate calculations of ligand binding affinities because of the ligand-dependent conformational changes in the binding site, the presence of ordered waters and the broad chemical diversity of ligands that can bind at this site. Our primary focus here is to distinguish binders from nonbinders. Large scale absolute binding free energy calculations that cover over 3000 protein-ligand complexes were performed using the BEDAM method starting from docked structures generated by Glide docking. Although the ligand dataset in this study resembles an intermediate to late stage lead optimization project while the BEDAM method is mainly developed for early stage virtual screening of hit molecules, the BEDAM binding free energy scoring has resulted in a moderate enrichment of ligand screening against this challenging drug target. Results show that, using a statistical mechanics based free energy method like BEDAM starting from docked poses offers better enrichment than classical docking scoring functions and rescoring methods like Prime MM-GBSA for the Hsp90 data set in this blind challenge. Importantly, among the three methods tested here, only the mean value of the BEDAM binding free energy scores is able to separate the large group of binders from the small group of nonbinders with a gap of 2.4 kcal/mol. None of the three methods that we have tested provided accurate ranking of the affinities of the 147 active compounds. We discuss the possible sources of errors in the binding free energy calculations. The study suggests that BEDAM can be used strategically to discriminate binders from nonbinders in virtual screening and to more accurately predict the ligand binding modes prior to the more computationally expensive FEP calculations of binding affinity.

Binding Energy Distribution Analysis Method: Hamiltonian Replica Exchange with Torsional Flattening for Binding Mode Prediction and Binding Free Energy Estimation.

Molecular dynamics modeling of complex biological systems is limited by finite simulation time. The simulations are often trapped close to local energy minima separated by high energy barriers. Here, we introduce Hamiltonian replica exchange (H-REMD) with torsional flattening in the Binding Energy Distribution Analysis Method (BEDAM), to reduce energy barriers along torsional degrees of freedom and accelerate sampling of intramolecular degrees of freedom relevant to protein-ligand binding. The method is tested on a standard benchmark (T4 Lysozyme/L99A/p-xylene complex) and on a library of HIV-1 integrase complexes derived from the SAMPL4 blind challenge. We applied the torsional flattening strategy to 26 of the 53 known binders to the HIV Integrase LEDGF site found to have a binding energy landscape funneled toward the crystal structure. We show that our approach samples the conformational space more efficiently than the original method without flattening when starting from a poorly docked pose with incorrect ligand dihedral angle conformations. In these unfavorable cases convergence to a binding pose within 2-3 Å from the crystallographic pose is obtained within a few nanoseconds of the Hamiltonian replica exchange simulation. We found that torsional flattening is insufficient in cases where trapping is due to factors other than torsional energy, such as the formation of incorrect intramolecular hydrogen bonds and stacking. Work is in progress to generalize the approach to handle these cases and thereby make it more widely applicable.

Simulating Replica Exchange: Markov State Models, Proposal Schemes, and the Infinite Swapping Limit.

Replica exchange molecular dynamics is a multicanonical simulation technique commonly used to enhance the sampling of solvated biomolecules on rugged free energy landscapes. While replica exchange is relatively easy to implement, there are many unanswered questions about how to use this technique most efficiently, especially because it is frequently the case in practice that replica exchange simulations are not fully converged. A replica exchange cycle consists of a series of molecular dynamics steps of a set of replicas moving under different Hamiltonians or at different thermodynamic states followed by one or more replica exchange attempts to swap replicas among the different states. How the replica exchange cycle is constructed affects how rapidly the system equilibrates. We have constructed a Markov state model of replica exchange (MSMRE) using long molecular dynamics simulations of a host-guest binding system as an example, in order to study how different implementations of the replica exchange cycle can affect the sampling efficiency. We analyze how the number of replica exchange attempts per cycle, the number of MD steps per cycle, and the interaction between the two parameters affects the largest implied time scale of the MSMRE simulation. The infinite swapping limit is an important concept in replica exchange. We show how to estimate the infinite swapping limit from the diagonal elements of the exchange transition matrix constructed from MSMRE "simulations of simulations" as well as from relatively short runs of the actual replica exchange simulations.

Locally weighted histogram analysis and stochastic solution for large-scale multi-state free energy estimation.

The weighted histogram analysis method (WHAM) including its binless extension has been developed independently in several different contexts, and widely used in chemistry, physics, and statistics, for computing free energies and expectations from multiple ensembles. However, this method, while statistically efficient, is computationally costly or even infeasible when a large number, hundreds or more, of distributions are studied. We develop a locally WHAM (local WHAM) from the perspective of simulations of simulations (SOS), using generalized serial tempering (GST) to resample simulated data from multiple ensembles. The local WHAM equations based on one jump attempt per GST cycle can be solved by optimization algorithms orders of magnitude faster than standard implementations of global WHAM, but yield similarly accurate estimates of free energies to global WHAM estimates. Moreover, we propose an adaptive SOS procedure for solving local WHAM equations stochastically when multiple jump attempts are performed per GST cycle. Such a stochastic procedure can lead to more accurate estimates of equilibrium distributions than local WHAM with one jump attempt per cycle. The proposed methods are broadly applicable when the original data to be "WHAMMED" are obtained properly by any sampling algorithm including serial tempering and parallel tempering (replica exchange). To illustrate the methods, we estimated absolute binding free energies and binding energy distributions using the binding energy distribution analysis method from one and two dimensional replica exchange molecular dynamics simulations for the beta-cyclodextrin-heptanoate host-guest system. In addition to the computational advantage of handling large datasets, our two dimensional WHAM analysis also demonstrates that accurate results similar to those from well-converged data can be obtained from simulations for which sampling is limited and not fully equilibrated.

Large-scale asynchronous and distributed multidimensional replica exchange molecular simulations and efficiency analysis.

We describe methods to perform replica exchange molecular dynamics (REMD) simulations asynchronously (ASyncRE). The methods are designed to facilitate large scale REMD simulations on grid computing networks consisting of heterogeneous and distributed computing environments as well as on homogeneous high-performance clusters. We have implemented these methods on NSF (National Science Foundation) XSEDE (Extreme Science and Engineering Discovery Environment) clusters and BOINC (Berkeley Open Infrastructure for Network Computing) distributed computing networks at Temple University and Brooklyn College at CUNY (the City University of New York). They are also being implemented on the IBM World Community Grid. To illustrate the methods, we have performed extensive (more than 60 ms in aggregate) simulations for the beta-cyclodextrin-heptanoate host-guest system in the context of one- and two-dimensional ASyncRE, and we used the results to estimate absolute binding free energies using the binding energy distribution analysis method. We propose ways to improve the efficiency of REMD simulations: these include increasing the number of exchanges attempted after a specified molecular dynamics (MD) period up to the fast exchange limit and/or adjusting the MD period to allow sufficient internal relaxation within each thermodynamic state. Although ASyncRE simulations generally require long MD periods (>picoseconds) per replica exchange cycle to minimize the overhead imposed by heterogeneous computing networks, we found that it is possible to reach an efficiency similar to conventional synchronous REMD, by optimizing the combination of the MD period and the number of exchanges attempted per cycle.

A Stochastic Solution to the Unbinned WHAM Equations.

The weighted histogram analysis method (WHAM) and unbinned versions such as the multistate Bennett acceptance ratio (MBAR) and unbinned WHAM (UWHAM) are widely used to compute free energies and expectations from data generated by independent or coupled parallel simulations. Here we introduce a replica exchange-like algorithm (RE-SWHAM) that can be used to solve the UWHAM equations stochastically. This method is capable of analyzing large data sets generated by hundreds or even thousands of parallel simulations that are too large to be "WHAMMED" using standard methods. We illustrate the method by applying it to obtain free energy weights for each of the 240 states in a simulation of host-guest ligand binding containing ∼3.5 × 10(7) data elements collected from 16 parallel Hamiltonian replica exchange simulations, performed at 15 temperatures. In addition to using much less memory, RE-SWHAM showed a nearly 80-fold improvement in computational time compared with UWHAM.