Optimally Adjusted Mixture Sampling and Locally Weighted Histogram Analysis

<p>Consider the two problems of simulating observations and estimating expectations and normalizing constants for multiple distributions. First, we present a self-adjusted mixture sampling method, which accommodates both adaptive serial tempering and a generalized Wang–Landau algorithm. The set of distributions are combined into a labeled mixture, with the mixture weights depending on the initial estimates of log normalizing constants (or free energies). Then, observations are generated by Markov transitions, and free energy estimates are adjusted online by stochastic approximation. We propose two stochastic approximation schemes by Rao–Blackwellization of the scheme commonly used, and derive the optimal choice of a gain matrix, resulting in the minimum asymptotic variance for free energy estimation, in a simple and feasible form. Second, we develop an offline method, locally weighted histogram analysis, for estimating free energies and expectations, using all the simulated data from multiple distributions by either self-adjusted mixture sampling or other sampling algorithms. This method can be computationally much faster, with little sacrifice of statistical efficiency, than a global method currently used, especially when a large number of distributions are involved. We provide both theoretical results and numerical studies to demonstrate the advantages of the proposed methods.</p

Resampling Markov Chain Monte Carlo Algorithms: Basic Analysis and Empirical Comparisons

<div><p>Sampling from complex distributions is an important but challenging topic in scientific and statistical computation. We synthesize three ideas, tempering, resampling, and Markov moving, and propose a general framework of resampling Markov chain Monte Carlo (MCMC). This framework not only accommodates various existing algorithms, including resample-move, importance resampling MCMC, and equi-energy sampling, but also leads to a generalized resample-move algorithm. We provide some basic analysis of these algorithms within the general framework, and present three simulation studies to compare these algorithms together with parallel tempering in the difficult situation where new modes emerge in the tails of previous tempering distributions. Our analysis and empirical results suggest that generalized resample-move tends to perform the best among all the algorithms studied when the Markov kernels lead to fast mixing or even locally so toward restricted distributions, whereas parallel tempering tends to perform the best when the Markov kernels lead to slow mixing, without even converging fast to restricted distributions. Moreover, importance resampling MCMC and equi-energy sampling perform similarly to each other, often worse than independence Metropolis resampling MCMC. Therefore, different algorithms seem to have advantages in different settings.</p></div

Environmentally Relevant Freeze–Thaw Cycles Enhance the Redox-Mediated Morphological Changes of Silver Nanoparticles

Silver nanoparticles (AgNPs) are inevitably released into natural systems, particularly into aquatic environments, where they are oxidized and release Ag⁺, which is reduced back to AgNPs. Environmental freeze–thaw cycles or freezing may accelerate the dynamic transformation between AgNPs and Ag⁺. Herein, the significant morphological changes caused by freezing treatments were assessed by UV–vis spectroscopy and high-resolution transmission electron microscopy, which revealed that reductive regeneration, particle fusion, and coalescence of the AgNPs occurred. In addition, a stable Ag isotope was used to track the AgNP redox reaction, which was found to be accelerated under freezing and freeze–thaw cycles relative to the reaction of particles stored at a normal temperature (4 °C, 25 °C). Furthermore, natural organic matter was found to stabilize the particle morphology. Ca²⁺ and Cl^– intensified the morphological changes and redox reaction through Ca²⁺-induced particle coalescence and Cl^–-enhanced reduction of Ag⁺ during the freeze–thaw treatment. These physicochemical changes also occurred for an environmentally relevant concentration of AgNPs (50 ng L^–1) in simulated environmental conditions and natural water samples after freeze–thaw cycles. Since the morphological changes and redox acceleration induced by environmental freezing conditions could dramatically influence the mobility, bioavailability, toxicity, and environmental fate of AgNPs, the freeze–thaw-induced effects should be considered in the environmental risk assessment of AgNPs

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 × 10⁷ 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

Stratified UWHAM and Its Stochastic Approximation for Multicanonical Simulations Which Are Far from Equilibrium

We describe a new analysis tool called Stratified unbinned Weighted Histogram Analysis Method (Stratified-UWHAM), which can be used to compute free energies and expectations from a multicanonical ensemble when a subset of the parallel simulations is far from being equilibrated because of barriers between free energy basins which are only rarely (or never) crossed at some states. The Stratified-UWHAM equations can be obtained in the form of UWHAM equations but with an expanded set of states. We also provide a stochastic solver, Stratified RE-SWHAM, for Stratified-UWHAM to remove its computational bottleneck. Stratified-UWHAM and Stratified RE-SWHAM are applied to study three test topics: the free energy landscape of alanine dipeptide, the binding affinity of a host–guest binding complex, and path sampling for a two-dimensional double well potential. The examples show that when some of the parallel simulations are only locally equilibrated, the estimates of free energies and equilibrium distributions provided by the conventional UWHAM (or MBAR) solutions exhibit considerable biases, but the estimates provided by Stratified-UWHAM and Stratified RE-SWHAM agree with the benchmark very well. Lastly, we discuss features of the Stratified-UWHAM approach which is based on coarse-graining in relation to two other maximum likelihood-based methods which were proposed recently, that also coarse-grain the multicanonical data

Significant Enrichment of Engineered Nanoparticles in Water Surface Microlayer

Water surface microlayer (SML), as the interface between water and the atmosphere, shows distinct physicochemical properties that differ from those of underlying water. Herein, for the first time, we demonstrate the SML enrichment of nanoparticles (NPs) by using silver nanoparticles (AgNPs) as a model via indoor experiments. The occurrence of SML enrichment of AgNPs was confirmed by the increased concentration of NPs in the SML relative to that in the bulk phase, and the <i>in situ</i> recording of the enhanced Raman spectroscopy intensity of a probe adsorbed on AgNPs in the SML. The significant enrichment of NPs is strongly influenced by environmentally relevant factors such as the solution pH, ionic strength, and natural organic matter. Additionally, the SML enrichment factor was estimated to be 14.6–26.5 for AgNPs in natural waters. Our findings indicate that NPs are inclined to accumulate in the SML, which could cause environmental effects that are differential to the bulk phase

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

Superoxide-Mediated Extracellular Biosynthesis of Silver Nanoparticles by the Fungus <i>Fusarium oxysporum</i>

The biosynthesis of silver nanoparticles (AgNPs) by microorganisms has become a hot topic in recent years, although its mechanism is still not well understood. Here we report the extracellular biosynthesis of AgNPs by the fungus <i>Fusarium oxysporum</i> through a superoxide-dependent mechanism. Reduction of Ag⁺ to AgNPs in the extracellular region of <i>F. oxysporum</i> was verified by transmission electron microscopy, while the superoxide produced extracellularly by <i>F. oxysporum</i> was evidenced by chemiluminescence. We further demonstrated that the biosynthesis of AgNPs was inhibited by a superoxide scavenger or the inhibitor of NADH oxidases, and the addition of NADH significantly improved the formation of AgNPs. These results demonstrated that, for the first time, the fungus <i>F. oxysporum</i> can mediate the synthesis of AgNPs through the enzymatic generation of extracellular superoxide, which is helpful in understanding the biosynthesis of AgNPs and the biomineralization and transformation of silver and other metals or metalloids

Samples with variants vs sequence position over Gag.

<p>Bar charts representing the number of samples in which amino acid variants are observed at each position in Gag derived from deep sequencing (top) and from 2378 drug-naive Gag sequences from LANL HIV sequence database (bottom). Variants shown from deep sequencing occur at frequencies above 1% in 5 or more patients and variants shown from LANL are present in at least 1% of sequences. The height of each vertical bar shows the number of patient samples with variants at Gag polyprotein positions. The different Gag proteins are indicated along the horizontal axis. Variants which have been documented in the literature as having associations with PI-exposure/resistance are shown in red. Positions at which the variation between the two datasets is small (|<i>f</i>_DS-<i>f</i>_LANL|<10%) are faded.</p

Mutations that are contribute to therapy failure.

<p>Bar charts showing the number of patients in which specific mutations occur during PI-based regimens including indinavir (IDV), saquinavir (SQV), and nelfinavir (NFV). Shown are the mutations with the largest differences between the successfully and unsuccessfully treated patient populations. Patients who failed therapy are shown in red and patients who had successful therapy are shown in green. The percentage above each bar denotes the percentage of all patients treated with that regimen which experience that mutation. Mutations with a */** are found to be statistically significant after Holm-Bonferroni correction with family-wise error rates 0.1 and 0.01 respectively among 140 mutations.</p