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Protein design has focused primarily on the design of ground states, ensuring they are sufficiently low energy to be highly populated 1 . Designing the kinetics and dynamics of a system requires, in addition, the design of excited states that are traversed in transitions from one low-lying state to another 2,3 . This is a challenging task as such states must be sufficiently strained to be poorly populated, but not so strained that they are not populated at all, and because protein design methods have generally focused on creating near-ideal structures 4-7 . Here we describe a general approach for designing systems which use an induced-fit power stroke 8 to generate a structurally frustrated 9 and strained excited state, allosterically driving protein complex dissociation. X-ray crystallography, double electron-electron resonance spectroscopy, and kinetic binding measurements demonstrate that incorporating excited states enables design of effector-induced increases in dissociation rates as high as 6000-fold. We highlight the power of this approach by designing cytokine mimics which can be dissociated within seconds from their receptors.

Extracellular signals induce changes to molecular programs that modulate multiple cellular phenotypes, including proliferation, motility, and differentiation status. The connection between dynamically adapting phenotypic states and the molecular programs that define them is not well understood. Here we develop data-driven models of single-cell phenotypic responses to extracellular stimuli by linking gene transcription levels to "morphodynamics" - changes in cell morphology and motility observable in time-lapse image data. We adopt a dynamics-first view of cell state by grouping single-cell trajectories into states with shared morphodynamic responses. The single-cell trajectories enable development of a first-of-its-kind computational approach to map live-cell dynamics to snapshot gene transcript levels, which we term MMIST, Molecular and Morphodynamics-Integrated Single-cell Trajectories. The key conceptual advance of MMIST is that cell behavior can be quantified based on dynamically defined states and that extracellular signals alter the overall distribution of cell states by altering rates of switching between states. We find a cell state landscape that is bound by epithelial and mesenchymal endpoints, with distinct sequences of epithelial to mesenchymal transition (EMT) and mesenchymal to epithelial transition (MET) intermediates. The analysis yields predictions for gene expression changes consistent with curated EMT gene sets and provides a prediction of thousands of RNA transcripts through extracellular signal-induced EMT and MET with near-continuous time resolution. The MMIST framework leverages true single-cell dynamical behavior to generate molecular-level omics inferences and is broadly applicable to other biological domains, time-lapse imaging approaches and molecular snapshot data., Competing Interests: Competing Interest The authors declare no competing interests.

On the one hand, much of computational chemistry is concerned with "bottom-up" calculations which elucidate observable behavior starting from exact or approximated physical laws, a paradigm exemplified by typical quantum mechanical calculations and molecular dynamics simulations. On the other hand, "top down" computations aiming to formulate mathematical models consistent with observed data, e.g., parametrizing force fields, binding or kinetic models, have been of interest for decades but recently have grown in sophistication with the use of Bayesian inference (BI). Standard BI provides an estimation of parameter values, uncertainties, and correlations among parameters. Used for "model selection," BI can also distinguish between model structures such as the presence or absence of individual states and transitions. Fortunately for physical scientists, BI can be formulated within a statistical mechanics framework, and indeed, BI has led to a resurgence of interest in Monte Carlo (MC) algorithms, many of which have been directly adapted from or inspired by physical strategies. Certain MC algorithms─notably procedures using an "infinite temperature" reference state─can be successful in a 5-20 parameter BI context which would be unworkable in molecular spaces of 10 3 coordinates and more. This Review provides a pedagogical introduction to BI and reviews key aspects of BI through a physical lens, setting the computations in terms of energy landscapes and free energy calculations and describing promising sampling algorithms. Statistical mechanics and basic probability theory also provide a reference for understanding intrinsic limitations of Bayesian inference with regard to model selection and the choice of priors.

Electrophysiology studies of secondary active transporters have revealed quantitative mechanistic insights over many decades of research. However, the emergence of new experimental and analytical approaches calls for investigation of the capabilities and limitations of the newer methods. We examine the ability of solid-supported membrane electrophysiology (SSME) to characterize discrete-state kinetic models with >10 rate constants. We use a Bayesian framework applied to synthetic data for three tasks: to quantify and check (i) the precision of parameter estimates under different assumptions, (ii) the ability of computation to guide the selection of experimental conditions, and (iii) the ability of our approach to distinguish among mechanisms based on SSME data. When the general mechanism, i.e., event order, is known in advance, we show that a subset of kinetic parameters can be "practically identified" within ∼1 order of magnitude, based on SSME current traces that visually appear to exhibit simple exponential behavior. This remains true even when accounting for systematic measurement bias and realistic uncertainties in experimental inputs (concentrations) are incorporated into the analysis. When experimental conditions are optimized or different experiments are combined, the number of practically identifiable parameters can be increased substantially. Some parameters remain intrinsically difficult to estimate through SSME data alone, suggesting that additional experiments are required to fully characterize parameters. We also demonstrate the ability to perform model selection and determine the order of events when that is not known in advance, comparing Bayesian and maximum-likelihood approaches. Finally, our studies elucidate good practices for the increasingly popular but subtly challenging Bayesian calculations for structural and systems biology.

The U.S. Food and Drug Administration (FDA) approved eteplirsen (Exondys 51) for Duchenne muscular dystrophy in 2016 via its accelerated approval program on the basis of a study of 12 boys. After a contentious review process and a high-profile meeting of an external advisory committee, FDA leaders concluded that very small increases in treated patients' levels of dystrophin, a muscle protein, were reasonably likely to predict clinical benefit. The eteplirsen approval, which was followed by approvals of other drugs in the same class via the same pathway, has been controversial because of the questionable evidence underlying these decisions, delays in mandated postapproval testing, and high U.S. prices. Questions remain about the effectiveness and long-term safety of these products. Although the FDA initially set a November 2020 deadline for eteplirsen's manufacturer to complete a clinical trial determining whether the drug has clinical benefit, the company will not complete the trial until 2024 or later. The relationship between levels of truncated dystrophin, the muscle protein studied in eteplirsen's pivotal trial, and clinical outcomes remains uncertain. Despite recent legislative and regulatory changes to the FDA's accelerated approval pathway, the history of eteplirsen and similar drugs points to the need for additional reforms to better balance evidence generation with patient safety and access to promising medications. Lawmakers and regulators should take further action to limit excessive spending on unproven therapies and ensure that drug sponsors conduct robust and timely confirmatory trials after receiving accelerated approval., Competing Interests: Disclosures: Disclosures can be viewed at www.acponline.org/authors/icmje/ConflictOfInterestForms.do?msNum=M23-1073.

Time-lapse imaging is a powerful approach to gain insight into the dynamic responses of cells, but the quantitative analysis of morphological changes over time remains challenging. Here, we exploit the concept of "trajectory embedding" to analyze cellular behavior using morphological feature trajectory histories-that is, multiple time points simultaneously, rather than the more common practice of examining morphological feature time courses in single timepoint (snapshot) morphological features. We apply this approach to analyze live-cell images of MCF10A mammary epithelial cells after treatment with a panel of microenvironmental perturbagens that strongly modulate cell motility, morphology, and cell cycle behavior. Our morphodynamical trajectory embedding analysis constructs a shared cell state landscape revealing ligand-specific regulation of cell state transitions and enables quantitative and descriptive models of single-cell trajectories. Additionally, we show that incorporation of trajectories into single-cell morphological analysis enables (i) systematic characterization of cell state trajectories, (ii) better separation of phenotypes, and (iii) more descriptive models of ligand-induced differences as compared to snapshot-based analysis. This morphodynamical trajectory embedding is broadly applicable to the quantitative analysis of cell responses via live-cell imaging across many biological and biomedical applications., (© 2023. The Author(s).)

Multistep protein-protein interactions underlie most biological processes, but their characterization through methods such as isothermal titration calorimetry (ITC) is largely confined to simple models that provide little information on the intermediate, individual steps. In this study, we primarily examine the essential hub protein LC8, a small dimer that binds disordered regions of 100+ client proteins in two symmetrical grooves at the dimer interface. Mechanistic details of LC8 binding have remained elusive, hampered in part by ITC data analyses employing simple models that treat bivalent binding as a single event with a single binding affinity. We build on existing Bayesian ITC approaches to quantify thermodynamic parameters for multi-site binding interactions impacted by significant uncertainty in protein concentration. Using a two-site binding model, we identify positive cooperativity with high confidence for LC8 binding to multiple client peptides. In contrast, application of an identical model to the two-site binding between the coiled-coil NudE dimer and the intermediate chain of dynein reveals little evidence of cooperativity. We propose that cooperativity in the LC8 system drives the formation of saturated induced-dimer structures, the functional units of most LC8 complexes. In addition to these system-specific findings, our work advances general ITC analysis in two ways. First, we describe a previously unrecognized mathematical ambiguity in concentrations in standard binding models and clarify how it impacts the precision with which binding parameters are determinable in cases of high uncertainty in analyte concentrations. Second, building on observations in the LC8 system, we develop a system-agnostic heat map of practical parameter identifiability calculated from synthetic data which demonstrates that the ability to determine microscopic binding parameters is strongly dependent on both the parameters themselves and experimental conditions. The work serves as a foundation for determination of multi-step binding interactions, and we outline best practices for Bayesian analysis of ITC experiments., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2023 Estelle et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

Weighted ensemble (WE) is an enhanced sampling method based on periodically replicating and pruning trajectories generated in parallel. WE has grown increasingly popular for computational biochemistry problems due, in part, to improved hardware and accessible software implementations. Algorithmic and analytical improvements have played an important role, and progress has accelerated in recent years. Here, we discuss and elaborate on the WE method from a mathematical perspective, highlighting recent results that enhance the computational efficiency. The mathematical theory reveals a new strategy for optimizing trajectory management that approaches the best possible variance while generalizing to systems of arbitrary dimension.

We seek to completely revise current models of airborne transmission of respiratory viruses by providing never-before-seen atomic-level views of the SARS-CoV-2 virus within a respiratory aerosol. Our work dramatically extends the capabilities of multiscale computational microscopy to address the significant gaps that exist in current experimental methods, which are limited in their ability to interrogate aerosols at the atomic/molecular level and thus obscure our understanding of airborne transmission. We demonstrate how our integrated data-driven platform provides a new way of exploring the composition, structure, and dynamics of aerosols and aerosolized viruses, while driving simulation method development along several important axes. We present a series of initial scientific discoveries for the SARS-CoV-2 Delta variant, noting that the full scientific impact of this work has yet to be realized., Competing Interests: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article., (© The Author(s) 2022.)

The weighted ensemble (WE) strategy has been demonstrated to be highly efficient in generating pathways and rate constants for rare events such as protein folding and protein binding using atomistic molecular dynamics simulations. Here we present two sets of tutorials instructing users in the best practices for preparing, carrying out, and analyzing WE simulations for various applications using the WESTPA software. The first set of more basic tutorials describes a range of simulation types, from a molecular association process in explicit solvent to more complex processes such as host-guest association, peptide conformational sampling, and protein folding. The second set ecompasses six advanced tutorials instructing users in the best practices of using key new features and plugins/extensions of the WESTPA 2.0 software package, which consists of major upgrades for larger systems and/or slower processes. The advanced tutorials demonstrate the use of the following key features: (i) a generalized resampler module for the creation of "binless" schemes, (ii) a minimal adaptive binning scheme for more efficient surmounting of free energy barriers, (iii) streamlined handling of large simulation datasets using an HDF5 framework, (iv) two different schemes for more efficient rate-constant estimation, (v) a Python API for simplified analysis of WE simulations, and (vi) plugins/extensions for Markovian Weighted Ensemble Milestoning and WE rule-based modeling for systems biology models. Applications of the advanced tutorials include atomistic and non-spatial models, and consist of complex processes such as protein folding and the membrane permeability of a drug-like molecule. Users are expected to already have significant experience with running conventional molecular dynamics or systems biology simulations., Competing Interests: 10Potentially Conflicting Interests The authors declare the following competing financial interests): L.T.C. is a current member of the Scientific Advisory Board of OpenEye Scientific and an Open Science Fellow with Psivant Sciences. S Zhang, JP Thompson, and DN LeBard are employees of OpenEye Scientific.

Regulation of pancreatic K ATP channels involves orchestrated interactions of their subunits, Kir6.2 and SUR1, and ligands. Previously we reported K ATP channel cryo-EM structures in the presence and absence of pharmacological inhibitors and ATP, focusing on the mechanisms by which inhibitors act as pharmacological chaperones of K ATP channels (Martin et al., 2019). Here we analyzed the same cryo-EM datasets with a focus on channel conformational dynamics to elucidate structural correlates pertinent to ligand interactions and channel gating. We found pharmacological inhibitors and ATP enrich a channel conformation in which the Kir6.2 cytoplasmic domain is closely associated with the transmembrane domain, while depleting one where the Kir6.2 cytoplasmic domain is extended away into the cytoplasm. This conformational change remodels a network of intra- and inter-subunit interactions as well as the ATP and PIP 2 binding pockets. The structures resolved key contacts between the distal N-terminus of Kir6.2 and SUR1's ABC module involving residues implicated in channel function and showed a SUR1 residue, K134, participates in PIP 2 binding. Molecular dynamics simulations revealed two Kir6.2 residues, K39 and R54, that mediate both ATP and PIP 2 binding, suggesting a mechanism for competitive gating by ATP and PIP 2 ., Competing Interests: Competing interests The authors declare that they have no competing financial or non-financial interests with the contents of this article., (Copyright © 2022 The Author(s). Published by Elsevier Ltd.. All rights reserved.)

Multivalent intrinsically disordered protein (IDP) complexes are prevalent in biology and act in regulation of diverse processes, including transcription, signaling events, and the assembly and disassembly of complex macromolecular architectures. These systems pose significant challenges to structural investigation, due to continuum dynamics imparted by the IDP and compositional heterogeneity resulting from characteristic low-affinity interactions. Here, we developed a modular pipeline for automated single-particle electron microscopy (EM) distribution analysis of common but relatively understudied semi-ordered systems: 'beads-on-a-string' assemblies, composed of IDPs bound at multivalent sites to the ubiquitous ∼20 kDa cross-linking hub protein LC8. This approach quantifies conformational geometries and compositional heterogeneity on a single-particle basis, and statistically corrects spurious observations arising from random proximity of bound and unbound LC8. The statistical correction is generically applicable to oligomer characterization and not specific to our pipeline. Following validation, the approach was applied to the nuclear pore IDP Nup159 and the transcription factor ASCIZ. This analysis unveiled significant compositional and conformational diversity in both systems that could not be obtained from ensemble single particle EM class-averaging strategies, and new insights for exploring how these architectural properties might contribute to their physiological roles in supramolecular assembly and transcriptional regulation. We expect that this approach may be adopted to many other intrinsically disordered systems that have evaded traditional methods of structural characterization., Competing Interests: Competing Interest Statement The authors have no competing interests., (Copyright © 2022 Elsevier Ltd. All rights reserved.)

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.

Vascular tone is dependent on smooth muscle K ATP channels comprising pore-forming Kir6.1 and regulatory SUR2B subunits, in which mutations cause Cantú syndrome. Unique among K ATP isoforms, they lack spontaneous activity and require Mg-nucleotides for activation. Structural mechanisms underlying these properties are unknown. Here, we determined cryogenic electron microscopy structures of vascular K ATP channels bound to inhibitory ATP and glibenclamide, which differ informatively from similarly determined pancreatic K ATP channel isoform (Kir6.2/SUR1). Unlike SUR1, SUR2B subunits adopt distinct rotational "propeller" and "quatrefoil" geometries surrounding their Kir6.1 core. The glutamate/aspartate-rich linker connecting the two halves of the SUR-ABC core is observed in a quatrefoil-like conformation. Molecular dynamics simulations reveal MgADP-dependent dynamic tripartite interactions between this linker, SUR2B, and Kir6.1. The structures captured implicate a progression of intermediate states between MgADP-free inactivated, and MgADP-bound activated conformations wherein the glutamate/aspartate-rich linker participates as mobile autoinhibitory domain, suggesting a conformational pathway toward K ATP channel activation., Competing Interests: The authors declare no competing interest., (Copyright © 2021 the Author(s). Published by PNAS.)

Despite the importance of non-equilibrium statistical mechanics in modern physics and related fields, the topic is often omitted from undergraduate and core-graduate curricula. Key aspects of non-equilibrium physics, however, can be understood with a minimum of formalism based on a rigorous trajectory picture. The fundamental object is the ensemble of trajectories, a set of independent time-evolving systems, which easily can be visualized or simulated (e.g., for protein folding) and which can be analyzed rigorously in analogy to an ensemble of static system configurations. The trajectory picture provides a straightforward basis for understanding first-passage times, "mechanisms" in complex systems, and fundamental constraints on the apparent reversibility of complex processes. Trajectories make concrete the physics underlying the diffusion and Fokker-Planck partial differential equations. Last but not least, trajectory ensembles underpin some of the most important algorithms that have provided significant advances in biomolecular studies of protein conformational and binding processes.

Key Points: Gap junctions formed by different connexins are expressed throughout the body and harbour unique channel properties that have not been fully defined mechanistically. Recent structural studies by cryo-electron microscopy have produced high-resolution models of the related but functionally distinct lens connexins (Cx50 and Cx46) captured in a stable open state, opening the door for structure-function comparison. Here, we conducted comparative molecular dynamics simulation and electrophysiology studies to dissect the isoform-specific differences in Cx46 and Cx50 intercellular channel function. We show that key determinants Cx46 and Cx50 gap junction channel open stability and unitary conductance are shaped by structural and dynamic features of their N-terminal domains, in particular the residue at the 9th position and differences in hydrophobic anchoring sites. The results of this study establish the open state Cx46/50 structural models as archetypes for structure-function studies targeted at elucidating the mechanism of gap junction channels and the molecular basis of disease-causing variants., Abstract: Connexins form intercellular communication channels, known as gap junctions (GJs), that facilitate diverse physiological roles, from long-range electrical and chemical coupling to coordinating development and nutrient exchange. GJs formed by different connexin isoforms harbour unique channel properties that have not been fully defined mechanistically. Recent structural studies on Cx46 and Cx50 defined a novel and stable open state and implicated the amino-terminal (NT) domain as a major contributor for isoform-specific functional differences between these closely related lens connexins. To better understand these differences, we constructed models corresponding to wildtype Cx50 and Cx46 GJs, NT domain swapped chimeras, and point variants at the 9th residue for comparative molecular dynamics (MD) simulation and electrophysiology studies. All constructs formed functional GJ channels, except the chimeric Cx46-50NT variant, which correlated with an introduced steric clash and increased dynamical behaviour (instability) of the NT domain observed by MD simulation. Single channel conductance correlated well with free-energy landscapes predicted by MD, but resulted in a surprisingly greater degree of effect. Additionally, we observed significant effects on transjunctional voltage-dependent gating (V j gating) and/or open state dwell times induced by the designed NT domain variants. Together, these studies indicate intra- and inter-subunit interactions involving both hydrophobic and charged residues within the NT domains of Cx46 and Cx50 play important roles in defining GJ open state stability and single channel conductance, and establish the open state Cx46/50 structural models as archetypes for structure-function studies targeted at elucidating GJ channel mechanisms and the molecular basis of cataract-linked connexin variants., (© 2021 The Authors. The Journal of Physiology © 2021 The Physiological Society.)

Markov state models (MSMs) have been widely applied to study the kinetics and pathways of protein conformational dynamics based on statistical analysis of molecular dynamics (MD) simulations. These MSMs coarse-grain both configuration space and time in ways that limit what kinds of observables they can reproduce with high fidelity over different spatial and temporal resolutions. Despite their popularity, there is still limited understanding of which biophysical observables can be computed from these MSMs in a robust and unbiased manner, and which suffer from the space-time coarse-graining intrinsic in the MSM model. Most theoretical arguments and practical validity tests for MSMs rely on long-time equilibrium kinetics, such as the slowest relaxation time scales and experimentally observable time-correlation functions. Here, we perform an extensive assessment of the ability of well-validated protein folding MSMs to accurately reproduce path-based observable such as mean first-passage times (MFPTs) and transition path mechanisms compared to a direct trajectory analysis. We also assess a recently proposed class of history-augmented MSMs (haMSMs) that exploit additional information not accounted for in standard MSMs. We conclude with some practical guidance on the use of MSMs to study various problems in conformational dynamics of biomolecules. In brief, MSMs can accurately reproduce correlation functions slower than the lag time, but path-based observables can only be reliably reproduced if the lifetimes of states exceed the lag time, which is a much stricter requirement. Even in the presence of short-lived states, we find that haMSMs reproduce path-based observables more reliably.

Background: Current and future pandemics will require informatics solutions to assess the risks, resources and policies to guide better public health decision-making., Methods: Cross-sectional study of all COVID-19 cases and deaths in the USA on a population- and resource-adjusted basis (as of 24 April 2020) by applying biomedical informatics and data visualization tools to several public and federal government datasets, including analysis of the impact of statewide stay-at-home orders., Results: There were 2753.2 cases and 158.0 deaths per million residents, respectively, in the USA with variable distributions throughout divisions, regions and states. Forty-two states and Washington, DC, (84.3%) had statewide stay-at-home orders, with the remaining states having population-adjusted characteristics in the highest risk quartile., Conclusions: Effective national preparedness requires clearly understanding states' ability to predict, manage and balance public health needs through all stages of a pandemic. This will require leveraging data quickly, correctly and responsibly into sound public health policies., (© The Author(s) 2020. Published by Oxford University Press on behalf of Faculty of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

The weighted ensemble (WE) simulation strategy provides unbiased sampling of nonequilibrium processes, such as molecular folding or binding, but the extraction of rate constants relies on characterizing steady-state behavior. Unfortunately, WE simulations of sufficiently complex systems will not relax to steady state on observed simulation times. Here, we show that a postsimulation clustering of molecular configurations into "microbins" using methods developed in the Markov State Model (MSM) community can yield unbiased kinetics from WE data before steady-state convergence of the WE simulation itself. Because WE trajectories are directional and not equilibrium distributed, the history-augmented MSM (haMSM) formulation can be used, which yields the mean first-passage time (MFPT) without bias for arbitrarily small lag times. Accurate kinetics can be obtained while bypassing the often prohibitive convergence requirements of the nonequilibrium weighted ensemble. We validate the method in a simple diffusive process on a two-dimensional (2D) random energy landscape and then analyze atomistic protein folding simulations using WE molecular dynamics. We report significant progress toward the unbiased estimation of protein folding times and pathways, though key challenges remain.

Although published structural models of viral capsids generally exhibit a high degree of regularity or symmetry, structural defects might be expected because of the fluctuating environment in which capsids assemble and the requirement of some capsids for disassembly before genome delivery. Defective structures are observed in computer simulations, and are evident in single-particle cryoelectron microscopy studies. Here, we quantify the conditions under which defects might be expected, using a statistical mechanics model allowing for ideal, defective, and vacant sites. The model displays a threshold in affinity parameters below which there is an appreciable population of defective capsids. Even when defective sites are not allowed, there is generally some population of vacancies. Analysis of single particles in cryoelectron microscopy micrographs yields a confirmatory ≳15% of defective particles. Our findings suggest structural heterogeneity in virus capsids may be under-appreciated, and also points to a nontraditional strategy for assembly inhibition., (Copyright © 2020 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Gap junctions establish direct pathways for cells to transfer metabolic and electrical messages. The local lipid environment is known to affect the structure, stability and intercellular channel activity of gap junctions; however, the molecular basis for these effects remains unknown. Here, we incorporate native connexin-46/50 (Cx46/50) intercellular channels into a dual lipid nanodisc system, mimicking a native cell-to-cell junction. Structural characterization by CryoEM reveals a lipid-induced stabilization to the channel, resulting in a 3D reconstruction at 1.9 Å resolution. Together with all-atom molecular dynamics simulations, it is shown that Cx46/50 in turn imparts long-range stabilization to the dynamic local lipid environment that is specific to the extracellular lipid leaflet. In addition, ~400 water molecules are resolved in the CryoEM map, localized throughout the intercellular permeation pathway and contributing to the channel architecture. These results illustrate how the aqueous-lipid environment is integrated with the architectural stability, structure and function of gap junction communication channels.

Motivated by growing evidence for pathway heterogeneity and alternative functions of molecular machines, we demonstrate a computational approach for investigating two questions: (1) Are there multiple mechanisms (state-space pathways) by which a machine can perform a given function, such as cotransport across a membrane? (2) How can additional functionality, such as proofreading/error-correction, be built into machine function using standard biochemical processes? Answers to these questions will aid both the understanding of molecular-scale cell biology and the design of synthetic machines. Focusing on transport in this initial study, we sample a variety of mechanisms by employing Metropolis Markov chain Monte Carlo. Trial moves adjust transition rates among an automatically generated set of conformational and binding states while maintaining fidelity to thermodynamic principles and a user-supplied fitness/functionality goal. Each accepted move generates a new model. The simulations yield both single and mixed reaction pathways for cotransport in a simple environment with a single substrate along with a driving ion. In a "competitive" environment including an additional decoy substrate, several qualitatively distinct reaction pathways are found which are capable of extremely high discrimination coupled to a leak of the driving ion, akin to proofreading. The array of functional models would be difficult to find by intuition alone in the complex state-spaces of interest., Competing Interests: The authors have declared that no competing interests exist.

Membrane transport is generally thought to occur via an alternating access mechanism in which the transporter adopts at least two states, accessible from two different sides of the membrane to exchange substrates from the extracellular environment and the cytoplasm or from the cytoplasm and the intracellular matrix of the organelles (only in eukaryotes). In recent years, a number of high resolution structures have supported this general framework for a wide class of transport molecules, although additional states along the transport pathway are emerging as critically important. Given that substrate binding is often weak in order to enhance overall transport rates, there exists the distinct possibility that transporters may transport the incorrect substrate. This is certainly the case for many pharmaceutical compounds that are absorbed in the gut or cross the blood brain barrier through endogenous transporters. Docking studies on the bacterial sugar transporter vSGLT reveal that many highly toxic compounds are compatible with binding to the orthosteric site, further motivating the selective pressure for additional modes of selectivity. Motivated by recent work in which we observed failed substrate delivery in a molecular dynamics simulation where the energized ion still goes down its concentration gradient, we hypothesize that some transporters evolved to harness this 'slip' mechanism to increase substrate selectivity and reduce the uptake of toxic molecules. Here, we test this idea by constructing and exploring a kinetic transport model that includes a slip pathway. While slip reduces the overall productive flux, when coupled with a second toxic molecule that is more prone to slippage, the overall substrate selectivity dramatically increases, suppressing the accumulation of the incorrect compound. We show that the mathematical framework for increased substrate selectivity in our model is analogous to the classic proofreading mechanism originally proposed for tRNA synthase; however, because the transport cycle is reversible we identified conditions in which the selectivity is essentially infinite and incorrect substrates are exported from the cell in a 'detoxification' mode. The cellular consequences of proofreading and membrane slippage are discussed as well as the impact on future drug development., Competing Interests: The authors have declared that no competing interests exist.

We propose parameter optimization techniques for weighted ensemble sampling of Markov chains in the steady-state regime. Weighted ensemble consists of replicas of a Markov chain, each carrying a weight, that are periodically resampled according to their weights inside of each of a number of bins that partition state space. We derive, from first principles, strategies for optimizing the choices of weighted ensemble parameters, in particular the choice of bins and the number of replicas to maintain in each bin. In a simple numerical example, we compare our new strategies with more traditional ones and with direct Monte Carlo.

Probability currents are fundamental in characterizing the kinetics of nonequilibrium processes. Notably, the steady-state current J ss for a source-sink system can provide the exact mean-first-passage time (MFPT) for the transition from the source to sink. Because transient nonequilibrium behavior is quantified in some modern path sampling approaches, such as the "weighted ensemble" strategy, there is strong motivation to determine bounds on J ss -and hence on the MFPT-as the system evolves in time. Here, we show that J ss is bounded from above and below by the maximum and minimum, respectively, of the current as a function of the spatial coordinate at any time t for one-dimensional systems undergoing overdamped Langevin (i.e., Smoluchowski) dynamics and for higher-dimensional Smoluchowski systems satisfying certain assumptions when projected onto a single dimension. These bounds become tighter with time, making them of potential practical utility in a scheme for estimating J ss and the long time scale kinetics of complex systems. Conceptually, the bounds result from the fact that extrema of the transient currents relax toward the steady-state current.

Membrane nanodomains have been implicated in Ras signaling, but what these domains are and how they interact with Ras remain obscure. Here, using single particle tracking with photoactivated localization microscopy (spt-PALM) and detailed trajectory analysis, we show that distinct membrane domains dictate KRas G12D (an active KRas mutant) diffusion and trafficking in U2OS cells. KRas G12D exhibits an immobile state in ~70 nm domains, each embedded in a larger domain (~200 nm) that confers intermediate mobility, while the rest of the membrane supports fast diffusion. Moreover, KRas G12D is continuously removed from the membrane via the immobile state and replenished to the fast state, reminiscent of Ras internalization and recycling. Importantly, both the diffusion and trafficking properties of KRas G12D remain invariant over a broad range of protein expression levels. Our results reveal how membrane organization dictates membrane diffusion and trafficking of Ras and offer new insight into the spatial regulation of Ras signaling., Competing Interests: YL, CP, TH, BM, LW, YZ, KT, YC, PS, JG, DZ, XN No competing interests declared, (© 2019, Lee et al.)

Recent advances in molecular simulations allow the evaluation of previously unattainable observables, such as rate constants for protein folding. However, these calculations are usually computationally expensive, and even significant computing resources may result in a small number of independent estimates spread over many orders of magnitude. Such small-sample, high "log-variance" data are not readily amenable to analysis using the standard uncertainty (i.e., "standard error of the mean") because unphysical negative limits of confidence intervals result. Bootstrapping, a natural alternative guaranteed to yield a confidence interval within the minimum and maximum values, also exhibits a striking systematic bias of the lower confidence limit in log space. As we show, bootstrapping artifactually assigns high probability to improbably low mean values. A second alternative, the Bayesian bootstrap strategy, does not suffer from the same deficit and is more logically consistent with the type of confidence interval desired. The Bayesian bootstrap provides uncertainty intervals that are more reliable than those from the standard bootstrap method but must be used with caution nevertheless. Neither standard nor Bayesian bootstrapping can overcome the intrinsic challenge of underestimating the mean from small-size, high log-variance samples. Our conclusions are based on extensive analysis of model distributions and reanalysis of multiple independent atomistic simulations. Although we only analyze rate constants, similar considerations will apply to related calculations, potentially including highly nonlinear averages like the Jarzynski relation.

Despite the development of massively parallel computing hardware including inexpensive graphics processing units (GPUs), it has remained infeasible to simulate the folding of atomistic proteins at room temperature using conventional molecular dynamics (MD) beyond the microsecond scale. Here, we report the folding of atomistic, implicitly solvated protein systems with folding times τ ranging from ∼10 μs to ∼100 ms using the weighted ensemble (WE) strategy in combination with GPU computing. Starting from an initial structure or set of structures, WE organizes an ensemble of GPU-accelerated MD trajectory segments via intermittent pruning and replication events to generate statistically unbiased estimates of rate constants for rare events such as folding; no biasing forces are used. Although the variance among atomistic WE folding runs is significant, multiple independent runs are used to reduce and quantify statistical uncertainty. Folding times are estimated directly from WE probability flux and from history-augmented Markov analysis of the WE data. Three systems were examined: NTL9 at low solvent viscosity (yielding τ f = 0.8-9 μs), NTL9 at water-like viscosity (τ f = 0.2-2 ms), and Protein G at low viscosity (τ f = 3-200 ms). In all cases, the folding time, uncertainty, and ensemble properties could be estimated from WE simulation; for Protein G, this characterization required significantly less overall computing than would be required to observe a single folding event with conventional MD simulations. Our results suggest that the use and calibration of force fields and solvent models for precise estimation of kinetic quantities is becoming feasible.

There is a vast gulf between the two primary strategies for simulating protein-ligand interactions. Docking methods significantly limit or eliminate protein flexibility to gain great speed at the price of uncontrolled inaccuracy, whereas fully flexible atomistic molecular dynamics simulations are expensive and often suffer from limited sampling. We have developed a flexible docking approach geared especially for highly flexible or poorly resolved targets based on mixed-resolution Monte Carlo (MRMC), which is intended to offer a balance among speed, protein flexibility, and sampling power. The binding region of the protein is treated with a standard atomistic force field, while the remainder of the protein is modeled at the residue level with a Gō model that permits protein flexibility while saving computational cost. Implicit solvation is used. Here we assess three facets of the MRMC approach with implications for other docking studies: (i) the role of receptor flexibility in cross-docking pose prediction; (ii) the use of non-equilibrium candidate Monte Carlo (NCMC) and (iii) the use of pose-clustering in scoring. We examine 61 co-crystallized ligands of estrogen receptor α, an important cancer target known for its flexibility. We also compare the performance of the MRMC approach with Autodock smina. Adding protein flexibility, not surprisingly, leads to significantly lower total energies and stronger interactions between protein and ligand, but notably we document the important role of backbone flexibility in the improvement. The improved backbone flexibility also leads to improved performance relative to smina. Somewhat unexpectedly, our implementation of NCMC leads to only modestly improved sampling of ligand poses. Overall, the addition of protein flexibility improves the performance of docking, as measured by energy-ranked poses, but we do not find significant improvements based on cluster information or the use of NCMC. We discuss possible improvements for the model including alternative coarse-grained force fields, improvements to the treatment of solvation, and adding additional types of NCMC moves., Competing Interests: The authors have declared that no competing interests exist.

The weighted ensemble (WE) strategy has been demonstrated to be highly efficient in generating pathways and rate constants for rare events such as protein folding and protein binding using atomistic molecular dynamics simulations. Here we present five tutorials instructing users in the best practices for preparing, carrying out, and analyzing WE simulations for various applications using the WESTPA software. Users are expected to already have significant experience with running standard molecular dynamics simulations using the underlying dynamics engine of interest (e.g. Amber, Gromacs, OpenMM). The tutorials range from a molecular association process in explicit solvent to more complex processes such as host-guest association, peptide conformational sampling, and protein folding., Competing Interests: 9Potentially Conflicting Interests The authors declare no conflicting interests.

This document provides a starting point for approaching molecular simulations, guiding beginning practitioners to what issues they need to know about before and while starting their first simulations, and why those issues are so critical. This document makes no claims to provide an adequate introduction to the subject on its own. Instead, our goal is to help people know what issues are critical before beginning, and to provide references to good resources on those topics. We also provide a checklist of key issues to consider before and while setting up molecular simulations which may serve as a foundation for other best practices documents.

Gap junctions establish direct pathways for cell-to-cell communication through the assembly of twelve connexin subunits that form intercellular channels connecting neighbouring cells. Co-assembly of different connexin isoforms produces channels with unique properties and enables communication across cell types. Here we used single-particle cryo-electron microscopy to investigate the structural basis of connexin co-assembly in native lens gap junction channels composed of connexin 46 and connexin 50 (Cx46/50). We provide the first comparative analysis to connexin 26 (Cx26), which-together with computational studies-elucidates key energetic features governing gap junction permselectivity. Cx46/50 adopts an open-state conformation that is distinct from the Cx26 crystal structure, yet it appears to be stabilized by a conserved set of hydrophobic anchoring residues. 'Hot spots' of genetic mutations linked to hereditary cataract formation map to the core structural-functional elements identified in Cx46/50, suggesting explanations for many of the disease-causing effects.

Policy Points: A 1993 law required the National Institutes of Health to include women and racial and ethnic minorities in relevant research studies. Most federal health agencies adopted the same policy, but the US Food and Drug Administration (FDA) did not. A 2012 law encouraged the FDA to ensure that new medical products be analyzed for safety and effectiveness for key demographic patient groups. Our study of high-risk medical devices reviewed by the FDA in 2014-2017 found that due to lack of patient diversity and publicly available data, clinicians and patients often cannot determine which devices are safe and effective for specific demographic groups., Context: Demographic differences can influence the safety and effectiveness of medical devices; however, clinical trials of devices for adults have historically underrepresented women, people of color, and patients over age 65. The US Food and Drug Administration (FDA) Safety and Innovation Act became law in 2012, encouraging greater diversity and subgroup analyses. In 2013, the FDA reported that there was diversity in clinical trials considered "pivotal" for approval decisions and that subgroup analyses were conducted for most applications for the highest-risk medical devices. However, the FDA's report did not specify whether analyses included sufficient numbers to be meaningful, whether analyses were conducted for most major subgroups, or whether analyses included safety, effectiveness, or accuracy., Methods: We examined publicly available documents for all 22 medical devices that the FDA designated "highest risk" or "novel," were reviewed through the premarket approval pathway, and were scrutinized at FDA public meetings from 2014 to 2017. We evaluated patient demographics and subgroup analyses for all pivotal trials., Findings: Only 3 (14%) of the devices provided subgroup analyses for both effectiveness and safety or both sensitivity and selectivity for gender, race, and age. However, 55% of the devices reported both of those subgroup analyses for at least 1 of the 3 subgroups. Whether analyses were reported or not, the number of patients in most subgroups was too small to draw meaningful conclusions. Subgroup analyses were more likely to be reported to the FDA's Advisory Committees than in the FDA's public reviews or labeling., Conclusions: Despite a law encouraging more diversity and subgroup analyses in pivotal trials used as the basis for FDA approval, the results of our study indicate relatively few subgroup analyses are publicly available for the highest-risk and novel medical devices. The lack of subgroup analyses makes it impossible to inform patients or physicians as to whether many newly approved medical devices are safe and effective for specific demographic subgroups defined by gender, race, and age., (© 2018 Milbank Memorial Fund.)

This special topic highlights recent developments in enhanced sampling methods for molecular-level simulations of chemical and biological systems. These methods are designed to enable more efficient exploration of phase space and extend the time scales that can be explored by simulations.

Despite recent advances in the supramolecular assembly of cell-penetrating peptide (CPP) nanostructures, the tuning of size, shape, morphology and packaging of drugs in these materials still remain unexplored. Herein, through sequential ligation of peptide building blocks, we create cell-penetrating self-assembling peptide nanomaterials (CSPNs) with the capability to translocate inside cells. We devised a triblock array of Tat 48-59 [HIV-1 derived transactivator of transcription 48-59 ] based CPPs, conjugated to up to four Phenylalanine (Phe) residues through an amphiphilic linker, (RADA) 2 . We observed that the sequential addition of Phe leads to the transition of CSPN secondary structures from a random coil, to a distorted α-helix, a β-sheet, or a pure α-helix. This transition occurs due to formation of a heptad by virtue of even number of Phe. Atomic force microscopy revealed that CSPNs form distinct shapes reminiscent of a "drill-bit". CSPNs containing two, three or four Phe, self-assemble into "nanodrill-like structures" with a coarse-twisted, non-twisted or fine-twisted morphology, respectively. These nanodrills had a high capacity to encapsulate hydrophobic guest molecules. In particular, the coarse-twisted nanodrills demonstrate higher internalization and are able to deliver rapamycin, a hydrophobic small molecule that induced autophagy and are capable of in vivo delivery. Molecular dynamics studies provide microscopic insights into the structure of the nanodrills that can contribute to its morphology and ability to interact with cellular membrane. CSPNs represent a new modular drug delivery platform that can be programmed into exquisite structures through sequence-specific fine tuning of amino acids., (Copyright © 2018 Elsevier B.V. All rights reserved.)

The T4 lysozyme L99A mutant is often used as a model system to study small-molecule binding to proteins, but pathways for ligand entry and exit from the buried binding site and the associated protein conformational changes have not been fully resolved. Here, molecular dynamics simulations were employed to model benzene exit from its binding cavity using the weighted ensemble (WE) approach to enhance sampling of low-probability unbinding trajectories. Independent WE simulations revealed four pathways for benzene exit, which correspond to transient tunnels spontaneously formed in previous simulations of apo T4 lysozyme. Thus, benzene unbinding occurs through multiple pathways partially created by intrinsic protein structural fluctuations. Motions of several α-helices and side chains were involved in ligand escape from metastable microstates. WE simulations also provided preliminary estimates of rate constants for each exit pathway. These results complement previous works and provide a semiquantitative characterization of pathway heterogeneity for binding of small molecules to proteins., (Copyright © 2018 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Motivated by the extremely high computing costs associated with estimates of free energies for biological systems using molecular simulations, we further the exploration of existing "belief propagation" (BP) algorithms for fixed-backbone peptide and protein systems. The precalculation of pairwise interactions among discretized libraries of side-chain conformations, along with representation of protein side chains as nodes in a graphical model, enables direct application of the BP approach, which requires only ∼1 s of single-processor run time after the precalculation stage. We use a "loopy BP" algorithm, which can be seen as an approximate generalization of the transfer-matrix approach to highly connected (i.e., loopy) graphs, and it has previously been applied to protein calculations. We examine the application of loopy BP to several peptides as well as the binding site of the T4 lysozyme L99A mutant. The present study reports on (i) the comparison of the approximate BP results with estimates from unbiased estimators based on the Amber99SB force field; (ii) investigation of the effects of varying library size on BP predictions; and (iii) a theoretical discussion of the discretization effects that can arise in BP calculations. The data suggest that, despite their approximate nature, BP free-energy estimates are highly accurate-indeed, they never fall outside confidence intervals from unbiased estimators for the systems where independent results could be obtained. Furthermore, we find that libraries of sufficiently fine discretization (which diminish library-size sensitivity) can be obtained with standard computing resources in most cases. Altogether, the extremely low computing times and accurate results suggest the BP approach warrants further study.

Objective: Twenty to fifty percent of estrogen receptor-positive (ER+) metastatic breast cancers express mutations within the ER ligand-binding domain. While most studies focused on the constitutive ER signaling activity commonly engendered by these mutations selected during estrogen deprivation therapy, our study was aimed at investigating distinctive phenotypes conferred by different mutations within this class., Methods: We examined the two most prevalent mutations, D538G and Y537S, employing corroborative genome-edited and lentiviral-transduced ER+ T47D cell models. We used a luciferase-based reporter and endogenous phospho-ER immunoblot analysis to characterize the estrogen response of ER mutants and determined their resistance to known ER antagonists., Results: Consistent with their selection during estrogen deprivation therapy, these mutants conferred constitutive ER activity. While Y537S mutants showed no estrogen dependence, D538G mutants demonstrated an enhanced estrogen-dependent response. Both mutations conferred resistance to ER antagonists that was overcome at higher doses acting specifically through their ER target., Conclusions: These observations provide a tenable hypothesis for how D538G ESR1-expressing clones can contribute to shorter progression-free survival observed in the exemestane arm of the BOLERO-2 study. Thus, in those patients with dominant D538G-expressing clones, longitudinal analysis for this mutation in circulating free DNA may prove beneficial for informing more optimal therapeutic regimens., (© 2018 S. Karger AG, Basel.)

The quantitative assessment of uncertainty and sampling quality is essential in molecular simulation. Many systems of interest are highly complex, often at the edge of current computational capabilities. Modelers must therefore analyze and communicate statistical uncertainties so that "consumers" of simulated data understand its significance and limitations. This article covers key analyses appropriate for trajectory data generated by conventional simulation methods such as molecular dynamics and (single Markov chain) Monte Carlo. It also provides guidance for analyzing some 'enhanced' sampling approaches. We do not discuss systematic errors arising, e.g., from inaccuracy in the chosen model or force field.

Policy Points: Medical software has become an increasingly critical component of health care, yet the regulation of these devices is inconsistent and controversial. No studies of medical devices and software assess the impact on patient safety of the FDA's current regulatory safeguards and new legislative changes to those standards. Our analysis quantifies the impact of software problems in regulated medical devices and indicates that current regulations are necessary but not sufficient for ensuring patient safety by identifying and eliminating dangerous defects in software currently on the market. New legislative changes will further deregulate health IT, reducing safeguards that facilitate the reporting and timely recall of flawed medical software that could harm patients., Context: Medical software has become an increasingly critical component of health care, yet the regulatory landscape for digital health is inconsistent and controversial. To understand which policies might best protect patients, we examined the impact of the US Food and Drug Administration's (FDA's) regulatory safeguards on software-related technologies in recent years and the implications for newly passed legislative changes in regulatory policy., Methods: Using FDA databases, we identified all medical devices that were recalled from 2011 through 2015 primarily because of software defects. We counted all software-related recalls for each FDA risk category and evaluated each high-risk and moderate-risk recall of electronic medical records to determine the manufacturer, device classification, submission type, number of units, and product details., Findings: A total of 627 software devices (1.4 million units) were subject to recalls, with 12 of these devices (190,596 units) subject to the highest-risk recalls. Eleven of the devices recalled as high risk had entered the market through the FDA review process that does not require evidence of safety or effectiveness, and one device was completely exempt from regulatory review. The largest high-risk recall categories were anesthesiology and general hospital, with one each in cardiovascular and neurology. Five electronic medical record systems (9,347 units) were recalled for software defects classified as posing a moderate risk to patient safety., Conclusions: Software problems in medical devices are not rare and have the potential to negatively influence medical care. Premarket regulation has not captured all the software issues that could harm patients, evidenced by the potentially large number of patients exposed to software products later subject to high-risk and moderate-risk recalls. Provisions of the 21st Century Cures Act that became law in late 2016 will reduce safeguards further. Absent stronger regulations and implementation to create robust risk assessment and adverse event reporting, physicians and their patients are likely to be at risk from medical errors caused by software-related problems in medical devices., (© 2017 Milbank Memorial Fund.)

The weighted ensemble (WE) methodology orchestrates quasi-independent parallel simulations run with intermittent communication that can enhance sampling of rare events such as protein conformational changes, folding, and binding. The WE strategy can achieve superlinear scaling-the unbiased estimation of key observables such as rate constants and equilibrium state populations to greater precision than would be possible with ordinary parallel simulation. WE software can be used to control any dynamics engine, such as standard molecular dynamics and cell-modeling packages. This article reviews the theoretical basis of WE and goes on to describe successful applications to a number of complex biological processes-protein conformational transitions, (un)binding, and assembly processes, as well as cell-scale processes in systems biology. We furthermore discuss the challenges that need to be overcome in the next phase of WE methodological development. Overall, the combined advances in WE methodology and software have enabled the simulation of long-timescale processes that would otherwise not be practical on typical computing resources using standard simulation.