The smallest electrochemical bubbles.

Many of the relevant electrochemical processes in the context of catalysis or energy conversion and storage, entail the production of gases. This often implicates the nucleation of bubbles at the interface, with the concomitant blockage of the electroactive area leading to overpotentials and Ohmic drop. Nanoelectrodes have been envisioned as assets to revert this effect, by inhibiting bubble formation. Experiments show, however, that nanobubbles nucleate and attach to nanoscale electrodes, imposing a limit to the current, which turns out to be independent of size and applied potential in a wide range from 3 nm to tenths of microns. Here we investigate the potential-current response for disk electrodes of diameters down to a single-atom, employing molecular simulations including electrochemical generation of gas. Our analysis reveals that nanoelectrodes of 1 nm can offer twice as much current as that delivered by electrodes with areas four orders of magnitude larger at the same bias. This boost in the extracted current is a consequence of the destabilization of the gas phase. The grand potential of surface nanobubbles shows they can not reach a thermodynamically stable state on supports below 2 nm. As a result, the electroactive area becomes accessible to the solution and the current turns out to be sensitive to the electrode radius. In this way, our simulations establish that there is an optimal size for the nanoelectrodes, in between the single-atom and ∼3 nm, that optimizes the gas production.

Spectrally refined unbiased Monte Carlo estimate of the Earth's global radiative cooling.

The Earth's radiative cooling is a key driver of climate. Determining how it is affected by greenhouse gas concentration is a core question in climate-change sciences. Due to the complexity of radiative transfer processes, current practices to estimate this cooling require the development and use of a suite of radiative transfer models whose accuracy diminishes as we move from local, instantaneous estimates to global estimates over the whole globe and over long periods of time (decades). Here, we show that recent advances in nonlinear Monte Carlo methods allow a paradigm shift: a completely unbiased estimate of the Earth's infrared cooling to space can be produced using a single model, integrating the most refined spectroscopic models of molecular gas energy transitions over a global scale and over years, all at a very low computational cost (a few seconds).

Kinetic coevolutionary models predict the temporal emergence of HIV-1 resistance mutations under drug selection pressure.

Drug resistance in HIV type 1 (HIV-1) is a pervasive problem that affects the lives of millions of people worldwide. Although records of drug-resistant mutations (DRMs) have been extensively tabulated within public repositories, our understanding of the evolutionary kinetics of DRMs and how they evolve together remains limited. Epistasis, the interaction between a DRM and other residues in HIV-1 protein sequences, is key to the temporal evolution of drug resistance. We use a Potts sequence-covariation statistical-energy model of HIV-1 protein fitness under drug selection pressure, which captures epistatic interactions between all positions, combined with kinetic Monte-Carlo simulations of sequence evolutionary trajectories, to explore the acquisition of DRMs as they arise in an ensemble of drug-naive patient protein sequences. We follow the time course of 52 DRMs in the enzymes protease, RT, and integrase, the primary targets of antiretroviral therapy. The rates at which DRMs emerge are highly correlated with their observed acquisition rates reported in the literature when drug pressure is applied. This result highlights the central role of epistasis in determining the kinetics governing DRM emergence. Whereas rapidly acquired DRMs begin to accumulate as soon as drug pressure is applied, slowly acquired DRMs are contingent on accessory mutations that appear only after prolonged drug pressure. We provide a foundation for using computational methods to determine the temporal evolution of drug resistance using Potts statistical potentials, which can be used to gain mechanistic insights into drug resistance pathways in HIV-1 and other infectious agents.

Highly parallelizable path sampling with minimal rejections using asynchronous replica exchange and infinite swaps.

Capturing rare yet pivotal events poses a significant challenge for molecular simulations. Path sampling provides a unique approach to tackle this issue without altering the potential energy landscape or dynamics, enabling recovery of both thermodynamic and kinetic information. However, despite its exponential acceleration compared to standard molecular dynamics, generating numerous trajectories can still require a long time. By harnessing our recent algorithmic innovations-particularly subtrajectory moves with high acceptance, coupled with asynchronous replica exchange featuring infinite swaps-we establish a highly parallelizable and rapidly converging path sampling protocol, compatible with diverse high-performance computing architectures. We demonstrate our approach on the liquid-vapor phase transition in superheated water, the unfolding of the chignolin protein, and water dissociation. The latter, performed at the ab initio level, achieves comparable statistical accuracy within days, in contrast to a previous study requiring over a year.

Message-Passing Monte Carlo: Generating low-discrepancy point sets via graph neural networks.

Discrepancy is a well-known measure for the irregularity of the distribution of a point set. Point sets with small discrepancy are called low discrepancy and are known to efficiently fill the space in a uniform manner. Low-discrepancy points play a central role in many problems in science and engineering, including numerical integration, computer vision, machine perception, computer graphics, machine learning, and simulation. In this work, we present a machine learning approach to generate a new class of low-discrepancy point sets named Message-Passing Monte Carlo (MPMC) points. Motivated by the geometric nature of generating low-discrepancy point sets, we leverage tools from Geometric Deep Learning and base our model on graph neural networks. We further provide an extension of our framework to higher dimensions, which flexibly allows the generation of custom-made points that emphasize the uniformity in specific dimensions that are primarily important for the particular problem at hand. Finally, we demonstrate that our proposed model achieves state-of-the-art performance superior to previous methods by a significant margin. In fact, MPMC points are empirically shown to be either optimal or near-optimal with respect to the discrepancy for low dimension and small number of points, i.e., for which the optimal discrepancy can be determined.

On the surprising effectiveness of a simple matrix exponential derivative approximation, with application to global SARS-CoV-2.

The continuous-time Markov chain (CTMC) is the mathematical workhorse of evolutionary biology. Learning CTMC model parameters using modern, gradient-based methods requires the derivative of the matrix exponential evaluated at the CTMC's infinitesimal generator (rate) matrix. Motivated by the derivative's extreme computational complexity as a function of state space cardinality, recent work demonstrates the surprising effectiveness of a naive, first-order approximation for a host of problems in computational biology. In response to this empirical success, we obtain rigorous deterministic and probabilistic bounds for the error accrued by the naive approximation and establish a "blessing of dimensionality" result that is universal for a large class of rate matrices with random entries. Finally, we apply the first-order approximation within surrogate-trajectory Hamiltonian Monte Carlo for the analysis of the early spread of Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) across 44 geographic regions that comprise a state space of unprecedented dimensionality for unstructured (flexible) CTMC models within evolutionary biology.

RNA fold prediction by Monte Carlo in graph space and the statistical mechanics of tertiary interactions.

Using a graph representation of RNA structures, we have studied the ensembles of secondary and tertiary graphs two sets of RNA with Monte Carlo simulations. The first consisted of 91 target ribozyme and riboswitch sequences of moderate lengths (< 150 nt) having a variety of secondary, H-type pseudoknots and kissing loop interactions. The second set consisted of 71 more diverse sequences across many RNA families. Using a simple empirical energy model for tertiary interactions and only sequence information for each target as input, the simulations examined how tertiary interactions impact the statistical mechanics of the fold ensembles. The results show that the graphs proliferate enormously when tertiary interactions are possible, producing an entropic driving force for the ensemble to access folds having tertiary structures even though they are overall energetically unfavorable in the energy model. For each of the targets in the two test sets, we assessed the quality of the model and the simulations by examining how well the simulated structures were able to predict the native fold and compared the results to fold predictions from ViennaRNA. Our model generated good or excellent predictions in a large majority of the targets. Overall, this method was able to produce predictions of comparable quality to Vienna, but it outperformed Vienna for structures with H-type pseudoknots. The results suggest that while tertiary interactions are predicated on real-space contacts, their impacts on the folded structure of RNA can be captured by graph space information for sequences of moderate lengths, using a simple tertiary energy model for the loops, the base pairs and base stacks.

Integrating Reinforcement Learning and Monte Carlo Tree Search for enhanced neoantigen vaccine design.

Recent advances in cancer immunotherapy have highlighted the potential of neoantigen-based vaccines. However, the design of such vaccines is hindered by the possibility of weak binding affinity between the peptides and the patient's specific human leukocyte antigen (HLA) alleles, which may not elicit a robust adaptive immune response. Triggering cross-immunity by utilizing peptide mutations that have enhanced binding affinity to target HLA molecules, while preserving their homology with the original one, can be a promising avenue for neoantigen vaccine design. In this study, we introduced UltraMutate, a novel algorithm that combines Reinforcement Learning and Monte Carlo Tree Search, which identifies peptide mutations that not only exhibit enhanced binding affinities to target HLA molecules but also retains a high degree of homology with the original neoantigen. UltraMutate outperformed existing state-of-the-art methods in identifying affinity-enhancing mutations in an independent test set consisting of 3660 peptide-HLA pairs. UltraMutate further showed its applicability in the design of peptide vaccines for Human Papillomavirus and Human Cytomegalovirus, demonstrating its potential as a promising tool in the advancement of personalized immunotherapy.

Reducing overprediction of molecular crystal structures via threshold clustering.

Crystal structure prediction is becoming an increasingly valuable tool for assessing polymorphism of crystalline molecular compounds, yet invariably, it overpredicts the number of polymorphs. One of the causes for this overprediction is in neglecting the coalescence of potential energy minima, separated by relatively small energy barriers, into a single basin at finite temperature. Considering this, we demonstrate a method underpinned by the threshold algorithm for clustering potential energy minima into basins, thereby identifying kinetically stable polymorphs and reducing overprediction.

Widespread partisan gerrymandering mostly cancels nationally, but reduces electoral competition.

Congressional district lines in many US states are drawn by partisan actors, raising concerns about gerrymandering. To separate the partisan effects of redistricting from the effects of other factors including geography and redistricting rules, we compare possible party compositions of the US House under the enacted plan to those under a set of alternative simulated plans that serve as a nonpartisan baseline. We find that partisan gerrymandering is widespread in the 2020 redistricting cycle, but most of the electoral bias it creates cancels at the national level, giving Republicans two additional seats on average. Geography and redistricting rules separately contribute a moderate pro-Republican bias. Finally, we find that partisan gerrymandering reduces electoral competition and makes the partisan composition of the US House less responsive to shifts in the national vote.

De novo protein fold design through sequence-independent fragment assembly simulations.

De novo protein design generally consists of two steps, including structure and sequence design. Many protein design studies have focused on sequence design with scaffolds adapted from native structures in the PDB, which renders novel areas of protein structure and function space unexplored. We developed FoldDesign to create novel protein folds from specific secondary structure (SS) assignments through sequence-independent replica-exchange Monte Carlo (REMC) simulations. The method was tested on 354 non-redundant topologies, where FoldDesign consistently created stable structural folds, while recapitulating on average 87.7% of the SS elements. Meanwhile, the FoldDesign scaffolds had well-formed structures with buried residues and solvent-exposed areas closely matching their native counterparts. Despite the high fidelity to the input SS restraints and local structural characteristics of native proteins, a large portion of the designed scaffolds possessed global folds completely different from natural proteins in the PDB, highlighting the ability of FoldDesign to explore novel areas of protein fold space. Detailed data analyses revealed that the major contributions to the successful structure design lay in the optimal energy force field, which contains a balanced set of SS packing terms, and REMC simulations, which were coupled with multiple auxiliary movements to efficiently search the conformational space. Additionally, the ability to recognize and assemble uncommon super-SS geometries, rather than the unique arrangement of common SS motifs, was the key to generating novel folds. These results demonstrate a strong potential to explore both structural and functional spaces through computational design simulations that natural proteins have not reached through evolution.

Transport of synaptic vesicles is modulated by vesicular reversals and stationary cargo clusters.

Stationary clusters of vesicles are a prominent feature of axonal transport, but little is known about their physiological and functional relevance to axonal transport. Here, we investigated the role of vesicle motility characteristics in modulating the formation and lifetimes of such stationary clusters, and their effect on cargo flow. We developed a simulation model describing key features of axonal cargo transport, benchmarking the model against experiments in the posterior lateral mechanosensory neurons of Caenorhabditis elegans. Our simulations included multiple microtubule tracks and varied cargo motion states, and account for dynamic cargo-cargo interactions. Our model also incorporates static obstacles to vesicle transport in the form of microtubule ends, stalled vesicles and stationary mitochondria. We demonstrate, both in simulations and in an experimental system, that a reduction in reversal rates is associated with a higher proportion of long-lived stationary vesicle clusters and reduced net anterograde transport. Our simulations support the view that stationary clusters function as dynamic reservoirs of cargo vesicles, and reversals aid cargo in navigating obstacles and regulate cargo transport by modulating the proportion of stationary vesicle clusters along the neuronal process.

Random-Effects Substitution Models for Phylogenetics via Scalable Gradient Approximations.

Phylogenetic and discrete-trait evolutionary inference depend heavily on an appropriate characterization of the underlying character substitution process. In this paper, we present random-effects substitution models that extend common continuous-time Markov chain models into a richer class of processes capable of capturing a wider variety of substitution dynamics. As these random-effects substitution models often require many more parameters than their usual counterparts, inference can be both statistically and computationally challenging. Thus, we also propose an efficient approach to compute an approximation to the gradient of the data likelihood with respect to all unknown substitution model parameters. We demonstrate that this approximate gradient enables scaling of sampling-based inference, namely Bayesian inference via Hamiltonian Monte Carlo, under random-effects substitution models across large trees and state-spaces. Applied to a dataset of 583 SARS-CoV-2 sequences, an HKY model with random-effects shows strong signals of nonreversibility in the substitution process, and posterior predictive model checks clearly show that it is a more adequate model than a reversible model. When analyzing the pattern of phylogeographic spread of 1441 influenza A virus (H3N2) sequences between 14 regions, a random-effects phylogeographic substitution model infers that air travel volume adequately predicts almost all dispersal rates. A random-effects state-dependent substitution model reveals no evidence for an effect of arboreality on the swimming mode in the tree frog subfamily Hylinae. Simulations reveal that random-effects substitution models can accommodate both negligible and radical departures from the underlying base substitution model. We show that our gradient-based inference approach is over an order of magnitude more time efficient than conventional approaches.

Opinion dynamics in financial markets via random networks.

We investigate financial market dynamics by introducing a heterogeneous agent-based opinion formation model. In this work, we organize individuals in a financial market according to their trading strategy, namely, whether they are noise traders or fundamentalists. The opinion of a local majority compels the market exchanging behavior of noise traders, whereas the global behavior of the market influences the decisions of fundamentalist agents. We introduce a noise parameter, q, to represent the level of anxiety and perceived uncertainty regarding market behavior, enabling the possibility of adrift financial action. We place individuals as nodes in an Erdös-Rényi random graph, where the links represent their social interactions. At any given time, individuals assume one of two possible opinion states ±1 regarding buying or selling an asset. The model exhibits fundamental qualitative and quantitative real-world market features such as the distribution of logarithmic returns with fat tails, clustered volatility, and the long-term correlation of returns. We use Student's t distributions to fit the histograms of logarithmic returns, showing a gradual shift from a leptokurtic to a mesokurtic regime depending on the fraction of fundamentalist agents. Furthermore, we compare our results with those concerning the distribution of the logarithmic returns of several real-world financial indices.

Shear transformations in metallic glasses without excessive and predefinable defects.

Plastic flow in metallic glasses (MGs) is known to be mediated by shear transformations (STs), which have been hypothesized to preferentially initiate from identifiable local "defect" regions with loose atomic packing. Here we show that the above idea is incorrect, i.e., STs do not arise from signature structural defects that can be recognized a priori. This conclusion is reached via a realistic MG model obtained by combining molecular dynamics (MD) and Monte Carlo simulations, achieving liquid solidification at an effective cooling rate as slow as 500 K/s to approach that typical in experiments for producing bulk MGs. At shear stresses before global yielding, only about 2% of the total atoms participate in STs, each event involving typically ~10 atoms. These observations rectify the excessive content of "liquid-like regions" retained from unrealistically fast quench in MD-produced glass models. Our findings also shed light on the indeterministic aspect of the ST sites/zones, which emerge with varying spatial locations and distribution depending on specific mechanical loading conditions.

Adaptive Monte Carlo augmented with normalizing flows.

SignificanceMonte Carlo methods, tools for sampling data from probability distributions, are widely used in the physical sciences, applied mathematics, and Bayesian statistics. Nevertheless, there are many situations in which it is computationally prohibitive to use Monte Carlo due to slow "mixing" between modes of a distribution unless hand-tuned algorithms are used to accelerate the scheme. Machine learning techniques based on generative models offer a compelling alternative to the challenge of designing efficient schemes for a specific system. Here, we formalize Monte Carlo augmented with normalizing flows and show that, with limited prior data and a physically inspired algorithm, we can substantially accelerate sampling with generative models.

Trends in inequalities in the prevalence of dementia in the United States.

This paper presents estimates of the prevalence of dementia in the United States from 2000 to 2016 by age, sex, race and ethnicity, education, and a measure of lifetime earnings, using data on 21,442 individuals aged 65 y and older and 97,629 person-year observations from a nationally representative survey, the Health and Retirement Study (HRS). The survey includes a range of cognitive tests, and a subsample underwent clinical assessment for dementia. We developed a longitudinal, latent-variable model of cognitive status, which we estimated using the Markov Chain Monte Carlo method. This model provides more accurate estimates of dementia prevalence in population subgroups than do previously used methods on the HRS. The age-adjusted prevalence of dementia decreased from 12.2% in 2000 (95% CI, 11.7 to 12.7%) to 8.5% in 2016 (7.9 to 9.1%) in the 65+ population, a statistically significant decline of 3.7 percentage points or 30.1%. Females are more likely to live with dementia, but the sex difference has narrowed. In the male subsample, we found a reduction in inequalities across education, earnings, and racial and ethnic groups; among females, those inequalities also declined, but less strongly. We observed a substantial increase in the level of education between 2000 and 2016 in the sample. This compositional change can explain, in a statistical sense, about 40% of the reduction in dementia prevalence among men and 20% among women, whereas compositional changes in the older population by age, race and ethnicity, and cardiovascular risk factors mattered less.

Chemistry-informed molecular graph as reaction descriptor for machine-learned retrosynthesis planning.

Infusing "chemical wisdom" should improve the data-driven approaches that rely exclusively on historical synthetic data for automatic retrosynthesis planning. For this purpose, we designed a chemistry-informed molecular graph (CIMG) to describe chemical reactions. A collection of key information that is most relevant to chemical reactions is integrated in CIMG:NMR chemical shifts as vertex features, bond dissociation energies as edge features, and solvent/catalyst information as global features. For any given compound as a target, a product CIMG is generated and exploited by a graph neural network (GNN) model to choose reaction template(s) leading to this product. A reactant CIMG is then inferred and used in two GNN models to select appropriate catalyst and solvent, respectively. Finally, a fourth GNN model compares the two CIMG descriptors to check the plausibility of the proposed reaction. A reaction vector is obtained for every molecule in training these models. The chemical wisdom of reaction propensity contained in the pretrained reaction vectors is exploited to autocategorize molecules/reactions and to accelerate Monte Carlo tree search (MCTS) for multistep retrosynthesis planning. Full synthetic routes with recommended catalysts/solvents are predicted efficiently using this CIMG-based approach.

Fermionic wave functions from neural-network constrained hidden states.

We introduce a systematically improvable family of variational wave functions for the simulation of strongly correlated fermionic systems. This family consists of Slater determinants in an augmented Hilbert space involving "hidden" additional fermionic degrees of freedom. These determinants are projected onto the physical Hilbert space through a constraint that is optimized, together with the single-particle orbitals, using a neural network parameterization. This construction draws inspiration from the success of hidden-particle representations but overcomes the limitations associated with the mean-field treatment of the constraint often used in this context. Our construction provides an extremely expressive family of wave functions, which is proved to be universal. We apply this construction to the ground-state properties of the Hubbard model on the square lattice, achieving levels of accuracy that are competitive with those of state-of-the-art variational methods.

Collective interlayer pairing and pair superfluidity in vertically stacked layers of dipolar excitons.

Layered bosonic dipolar fluids have been suggested to host a condensate of interlayer molecular bound states. However, experimental observation has remained elusive. Motivated by two recent experimental works [C. Hubert et al., Phys. Rev. X9, 021026 (2019) and D. J. Choksy et al., Phys. Rev. B 103, 045126 (2021)], we theoretically study, using numerically exact quantum Monte Carlo calculations, the experimental signatures of collective interlayer pairing in vertically stacked indirect exciton (IX) layers. We find that IX energy shifts associated with each layer evolve nontrivially as a function of density imbalance following a nonmonotonic trend with a jump discontinuity at density balance, identified with the interlayer IX molecule gap. This behavior discriminates between the superfluidity of interlayer bound pairs and independent dipole condensation in distinct layers. Considering finite temperature and finite density imbalance conditions, we find a cascade of Berezinskii-Kosterlitz-Thouless (BKT) transitions, initially into a pair superfluid and only then, at lower temperatures, into complete superfluidity of both layers. Our results may provide a theoretical interpretation of existing experimental observations in GaAs double quantum well (DQW) bilayer structures. Furthermore, to optimize the visibility of pairing dynamics in future studies, we present an analysis suggesting realistic experimental settings in GaAs and transition metal dichalcogenide (TMD) bilayer DQW heterostructures where collective interlayer pairing and pair superfluidity can be clearly observed.