Probing the chemical 'reactome' with high-throughput experimentation data

High-throughput experimentation (HTE) has the potential to improve our understanding of organic chemistry by systematically interrogating reactivity across diverse chemical spaces. Notable bottlenecks include few publicly available large-scale datasets and the need for facile interpretation of these data's hidden chemical insights. Here we report the development of a high-throughput experimentation analyser, a robust and statistically rigorous framework, which is applicable to any HTE dataset regardless of size, scope or target reaction outcome, which yields interpretable correlations between starting material(s), reagents and outcomes. We improve the HTE data landscape with the disclosure of 39,000+ previously proprietary HTE reactions that cover a breadth of chemistry, including cross-coupling reactions and chiral salt resolutions. The high-throughput experimentation analyser was validated on cross-coupling and hydrogenation datasets, showcasing the elucidation of statistically significant hidden relationships between reaction components and outcomes, as well as highlighting areas of dataset bias and the specific reaction spaces that necessitate further investigation.

Deconvoluting low yield from weak potency in direct-to-biology workflows with machine learning

High throughput and rapid biological evaluation of small molecules is an essential factor in drug discovery and development. Direct-to-biology (D2B), whereby compound purification is foregone, has emerged as a viable technique in time efficient screening, specifically for PROTAC design and biological evaluation. However, one notable limitation is the prerequisite of high yielding reactions to ensure the desired compound is indeed the compound responsible for biological activity. Herein, we report a machine learning based yield-assay deconfounder capable of deconvoluting low yield from low potency to identify false negatives. We validated this approach by identifying promising SARS-CoV-2 main protease inhibitors with nanomolar activity that rivaled potency observed from the standard D2B workflow. Furthermore, we show how our framework can be utilized in a broad, in silico screen to produce compounds of similar potency as a D2B assay.

Predictive Minisci late stage functionalization with transfer learning

Structural diversification of lead molecules is a key component of drug discovery to explore chemical space. Late-stage functionalizations (LSFs) are versatile methodologies capable of installing functional handles on richly decorated intermediates to deliver numerous diverse products in a single reaction. Predicting the regioselectivity of LSF is still an open challenge in the field. Numerous efforts from chemoinformatics and machine learning (ML) groups have made strides in this area. However, it is arduous to isolate and characterize the multitude of LSF products generated, limiting available data and hindering pure ML approaches. We report the development of an approach that combines a message passing neural network and 13C NMR-based transfer learning to predict the atom-wise probabilities of functionalization for Minisci and P450-based functionalizations. We validated our model both retrospectively and with a series of prospective experiments, showing that it accurately predicts the outcomes of Minisci-type and P450 transformations and outperforms the well-established Fukui-based reactivity indices and other machine learning reactivity-based algorithms.

Open science discovery of potent noncovalent SARS-CoV-2 main protease inhibitors

We report the results of the COVID Moonshot, a fully open-science, crowdsourced, and structure-enabled drug discovery campaign targeting the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) main protease. We discovered a noncovalent, nonpeptidic inhibitor scaffold with lead-like properties that is differentiated from current main protease inhibitors. Our approach leveraged crowdsourcing, machine learning, exascale molecular simulations, and high-throughput structural biology and chemistry. We generated a detailed map of the structural plasticity of the SARS-CoV-2 main protease, extensive structure-activity relationships for multiple chemotypes, and a wealth of biochemical activity data. All compound designs (>18,000 designs), crystallographic data (>490 ligand-bound x-ray structures), assay data (>10,000 measurements), and synthesized molecules (>2400 compounds) for this campaign were shared rapidly and openly, creating a rich, open, and intellectual property-free knowledge base for future anticoronavirus drug discovery.

Accelerating antiviral drug discovery: lessons from COVID-19

During the coronavirus disease 2019 (COVID-19) pandemic, a wave of rapid and collaborative drug discovery efforts took place in academia and industry, culminating in several therapeutics being discovered, approved and deployed in a 2-year time frame. This article summarizes the collective experience of several pharmaceutical companies and academic collaborations that were active in severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) antiviral discovery. We outline our opinions and experiences on key stages in the small-molecule drug discovery process: target selection, medicinal chemistry, antiviral assays, animal efficacy and attempts to pre-empt resistance. We propose strategies that could accelerate future efforts and argue that a key bottleneck is the lack of quality chemical probes around understudied viral targets, which would serve as a starting point for drug discovery. Considering the small size of the viral proteome, comprehensively building an arsenal of probes for proteins in viruses of pandemic concern is a worthwhile and tractable challenge for the community.

Data-driven discovery of molecular photoswitches with multioutput Gaussian processes

Photoswitchable molecules display two or more isomeric forms that may be accessed using light. Separating the electronic absorption bands of these isomers is key to selectively addressing a specific isomer and achieving high photostationary states whilst overall red-shifting the absorption bands serves to limit material damage due to UV-exposure and increases penetration depth in photopharmacological applications. Engineering these properties into a system through synthetic design however, remains a challenge. Here, we present a data-driven discovery pipeline for molecular photoswitches underpinned by dataset curation and multitask learning with Gaussian processes. In the prediction of electronic transition wavelengths, we demonstrate that a multioutput Gaussian process (MOGP) trained using labels from four photoswitch transition wavelengths yields the strongest predictive performance relative to single-task models as well as operationally outperforming time-dependent density functional theory (TD-DFT) in terms of the wall-clock time for prediction. We validate our proposed approach experimentally by screening a library of commercially available photoswitchable molecules. Through this screen, we identified several motifs that displayed separated electronic absorption bands of their isomers, exhibited red-shifted absorptions, and are suited for information transfer and photopharmacological applications. Our curated dataset, code, as well as all models are made available at https://github.com/Ryan-Rhys/The-Photoswitch-Dataset.

Rapid discovery of stable materials by coordinate-free coarse graining

A fundamental challenge in materials science pertains to elucidating the relationship between stoichiometry, stability, structure, and property. Recent advances have shown that machine learning can be used to learn such relationships, allowing the stability and functional properties of materials to be accurately predicted. However, most of these approaches use atomic coordinates as input and are thus bottlenecked by crystal structure identification when investigating previously unidentified materials. Our approach solves this bottleneck by coarse-graining the infinite search space of atomic coordinates into a combinatorially enumerable search space. The key idea is to use Wyckoff representations, coordinate-free sets of symmetry-related positions in a crystal, as the input to a machine learning model. Our model demonstrates exceptionally high precision in finding unknown theoretically stable materials, identifying 1569 materials that lie below the known convex hull of previously calculated materials from just 5675 ab initio calculations. Our approach opens up fundamental advances in computational materials discovery.

The age-dependent association of risk factors with pancreatic cancer

BACKGROUND

Pancreatic cancer presents as advanced disease in >80% of patients; yet, appropriate ages to consider prevention and early detection strategies are poorly defined. We investigated age-specific associations and attributable risks of pancreatic cancer for established modifiable and non-modifiable risk factors.

PATIENTS AND METHODS

We included 167 483 participants from two prospective US cohort studies with 1190 incident cases of pancreatic cancer during >30 years of follow-up; 5107 pancreatic cancer cases and 8845 control participants of European ancestry from a completed multicenter genome-wide association study (GWAS); and 248 893 pancreatic cancer cases documented in the US Surveillance, Epidemiology, and End Results (SEER) Program. Across different age categories, we investigated cigarette smoking, obesity, diabetes, height, and non-O blood group in the prospective cohorts; weighted polygenic risk score of 22 previously identified single nucleotide polymorphisms in the GWAS; and male sex and black race in the SEER Program.

RESULTS

In the prospective cohorts, all five risk factors were more strongly associated with pancreatic cancer risk among younger participants, with associations attenuated among those aged >70 years. The hazard ratios comparing participants with three to five risk factors with those with no risk factors were 9.24 [95% confidence interval (CI) 4.11-20.77] among those aged ≤60 years, 3.00 (95% CI 1.85-4.86) among those aged 61-70 years, and 1.46 (95% CI 1.10-1.94) among those aged >70 years (Pheterogeneity = 3×10-5). These factors together were related to 65.6%, 49.7%, and 17.2% of incident pancreatic cancers in these age groups, respectively. In the GWAS and the SEER Program, the associations with the polygenic risk score, male sex, and black race were all stronger among younger individuals (Pheterogeneity ≤0.01).

CONCLUSIONS

Established risk factors are more strongly associated with earlier-onset pancreatic cancer, emphasizing the importance of age at initiation for cancer prevention and control programs targeting this highly lethal malignancy.

Achieving robustness to aleatoric uncertainty with heteroscedastic Bayesian optimisation

Bayesian optimisation is a sample-efficient search methodology that holds great promise for accelerating drug and materials discovery programs. A frequently-overlooked modelling consideration in Bayesian optimisation strategies however, is the representation of heteroscedastic aleatoric uncertainty. In many practical applications it is desirable to identify inputs with low aleatoric noise, an example of which might be a material composition which displays robust properties in response to a noisy fabrication process. In this paper, we propose a heteroscedastic Bayesian optimisation scheme capable of representing and minimising aleatoric noise across the input space. Our scheme employs a heteroscedastic Gaussian process surrogate model in conjunction with two straightforward adaptations of existing acquisition functions. First, we extend the augmented expected improvement heuristic to the heteroscedastic setting and second, we introduce the aleatoric noise-penalised expected improvement (ANPEI) heuristic. Both methodologies are capable of penalising aleatoric noise in the suggestions. In particular, the ANPEI acquisition yields improved performance relative to homoscedastic Bayesian optimisation and random sampling on toy problems as well as on two real-world scientific datasets. Code is available at: https://github.com/Ryan-Rhys/Heteroscedastic-BO

Expanding the Repertoire of Low-Molecular-Weight Pentafluorosulfanyl-Substituted Scaffolds

The pentafluorosulfanyl (‐SF₅) functional group is of increasing interest as a bioisostere in medicinal chemistry. A library of SF₅‐containing compounds, including amide, isoxazole, and oxindole derivatives, was synthesised using a range of solution‐based and solventless methods, including microwave and ball‐mill techniques. The library was tested against targets including human dihydroorotate dehydrogenase (HDHODH). A subsequent focused approach led to synthesis of analogues of the clinically used disease modifying anti‐rheumatic drugs (DMARDs), Teriflunomide and Leflunomide, considered for potential COVID‐19 use, where SF₅ bioisostere deployment led to improved inhibition of HDHODH compared with the parent drugs. The results demonstrate the utility of the SF₅ group in medicinal chemistry.

SARS-CoV-2 infects the human kidney and drives fibrosis in kidney organoids

Kidney failure is frequently observed during and after COVID-19, but it remains elusive whether this is a direct effect of the virus. Here, we report that SARS-CoV-2 directly infects kidney cells and is associated with increased tubule-interstitial kidney fibrosis in patient autopsy samples. To study direct effects of the virus on the kidney independent of systemic effects of COVID-19, we infected human-induced pluripotent stem-cell-derived kidney organoids with SARS-CoV-2. Single-cell RNA sequencing indicated injury and dedifferentiation of infected cells with activation of profibrotic signaling pathways. Importantly, SARS-CoV-2 infection also led to increased collagen 1 protein expression in organoids. A SARS-CoV-2 protease inhibitor was able to ameliorate the infection of kidney cells by SARS-CoV-2. Our results suggest that SARS-CoV-2 can directly infect kidney cells and induce cell injury with subsequent fibrosis. These data could explain both acute kidney injury in COVID-19 patients and the development of chronic kidney disease in long COVID.

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COVID-19 patients present tubulo-interstitial kidney fibrosis compared with controls

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SARS-CoV-2 infection stimulates profibrotic signaling in human kidney organoids

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SARS-CoV-2 infection can be inhibited by a protease blocker in human kidney organoids

Discovery of SARS-CoV-2 main protease inhibitors using a synthesis-directed de novo design model

The SARS-CoV-2 main viral protease (M^pro) is an attractive target for antivirals given its distinctiveness from host proteases, essentiality in the viral life cycle and conservation across coronaviridae. We launched the COVID Moonshot initiative to rapidly develop patent-free antivirals with open science and open data. Here we report the use of machine learning for de novo design, coupled with synthesis route prediction, in our campaign. We discover novel chemical scaffolds active in biochemical and live virus assays, synthesized with model generated routes.

We discovered potent SARS-CoV-2 main protease inhibitors using synthesis-directed molecular design.

Data-driven approximations to the bridge function yield improved closures for the Ornstein-Zernike equation

A key challenge for soft materials design and coarse-graining simulations is determining interaction potentials between components that give rise to desired condensed-phase structures. In theory, the Ornstein-Zernike equation provides an elegant framework for solving this inverse problem. Pioneering work in liquid state theory derived analytical closures for the framework. However, these analytical closures are approximations, valid only for specific classes of interaction potentials. In this work, we combine the physics of liquid state theory with machine learning to infer a closure directly from simulation data. The resulting closure is more accurate than commonly used closures across a broad range of interaction potentials.

Bayesian unsupervised learning reveals hidden structure in concentrated electrolytes

Electrolytes play an important role in a plethora of applications ranging from energy storage to biomaterials. Notwithstanding this, the structure of concentrated electrolytes remains enigmatic. Many theoretical approaches attempt to model the concentrated electrolyte by introducing the idea of ion pairs, with ions either being tightly "paired" with a counter-ion or "free" to screen charge. In this study, we reframe the problem into the language of computational statistics and test the null hypothesis that all ions share the same local environment. Applying the framework to molecular dynamics simulations, we find that this null hypothesis is not supported by data. Our statistical technique suggests the presence of two distinct local ionic environments at intermediate concentrations, whose differences surprisingly originate in like charge correlations rather than unlike charge attraction. Through considering the effect of these "aggregated" and "non-aggregated" states on bulk properties including effective ion concentration and dielectric constant, we identify a scaling relation between the effective screening length and theoretical Debye length, which applies across different dielectric constants and ion concentrations.

Quantitative interpretation explains machine learning models for chemical reaction prediction and uncovers bias

Organic synthesis remains a major challenge in drug discovery. Although a plethora of machine learning models have been proposed as solutions in the literature, they suffer from being opaque black-boxes. It is neither clear if the models are making correct predictions because they inferred the salient chemistry, nor is it clear which training data they are relying on to reach a prediction. This opaqueness hinders both model developers and users. In this paper, we quantitatively interpret the Molecular Transformer, the state-of-the-art model for reaction prediction. We develop a framework to attribute predicted reaction outcomes both to specific parts of reactants, and to reactions in the training set. Furthermore, we demonstrate how to retrieve evidence for predicted reaction outcomes, and understand counterintuitive predictions by scrutinising the data. Additionally, we identify Clever Hans predictions where the correct prediction is reached for the wrong reason due to dataset bias. We present a new debiased dataset that provides a more realistic assessment of model performance, which we propose as the new standard benchmark for comparing reaction prediction models.

Archetypal landscapes for deep neural networks

The predictive capabilities of deep neural networks (DNNs) continue to evolve to increasingly impressive levels. However, it is still unclear how training procedures for DNNs succeed in finding parameters that produce good results for such high-dimensional and nonconvex loss functions. In particular, we wish to understand why simple optimization schemes, such as stochastic gradient descent, do not end up trapped in local minima with high loss values that would not yield useful predictions. We explain the optimizability of DNNs by characterizing the local minima and transition states of the loss-function landscape (LFL) along with their connectivity. We show that the LFL of a DNN in the shallow network or data-abundant limit is funneled, and thus easy to optimize. Crucially, in the opposite low-data/deep limit, although the number of minima increases, the landscape is characterized by many minima with similar loss values separated by low barriers. This organization is different from the hierarchical landscapes of structural glass formers and explains why minimization procedures commonly employed by the machine-learning community can navigate the LFL successfully and reach low-lying solutions.

Perspective: new insights from loss function landscapes of neural networks

We investigate the structure of the loss function landscape for neural networks subject to dataset mislabelling, increased training set diversity, and reduced node connectivity, using various techniques developed for energy landscape exploration. The benchmarking models are classification problems for atomic geometry optimisation and hand-written digit prediction. We consider the effect of varying the size of the atomic configuration space used to generate initial geometries and find that the number of stationary points increases rapidly with the size of the training configuration space. We introduce a measure of node locality to limit network connectivity and perturb permutational weight symmetry, and examine how this parameter affects the resulting landscapes. We find that highly-reduced systems have low capacity and exhibit landscapes with very few minima. On the other hand, small amounts of reduced connectivity can enhance network expressibility and can yield more complex landscapes. Investigating the effect of deliberate classification errors in the training data, we find that the variance in testing AUC, computed over a sample of minima, grows significantly with the training error, providing new insight into the role of the variance-bias trade-off when training under noise. Finally, we illustrate how the number of local minima for networks with two and three hidden layers, but a comparable number of variable edge weights, increases significantly with the number of layers, and as the number of training data decreases. This work helps shed further light on neural network loss landscapes and provides guidance for future work on neural network training and optimisation.

Identifying degradation patterns of lithium ion batteries from impedance spectroscopy using machine learning

Forecasting the state of health and remaining useful life of Li-ion batteries is an unsolved challenge that limits technologies such as consumer electronics and electric vehicles. Here, we build an accurate battery forecasting system by combining electrochemical impedance spectroscopy (EIS)—a real-time, non-invasive and information-rich measurement that is hitherto underused in battery diagnosis—with Gaussian process machine learning. Over 20,000 EIS spectra of commercial Li-ion batteries are collected at different states of health, states of charge and temperatures—the largest dataset to our knowledge of its kind. Our Gaussian process model takes the entire spectrum as input, without further feature engineering, and automatically determines which spectral features predict degradation. Our model accurately predicts the remaining useful life, even without complete knowledge of past operating conditions of the battery. Our results demonstrate the value of EIS signals in battery management systems.

Forecasting the state of health and remaining useful life of batteries is a challenge that limits technologies such as electric vehicles. Here, the authors build an accurate battery performance forecasting system using machine learning.

Fluctuation-induced force in homogeneous isotropic turbulence

Understanding force generation in nonequilibrium systems is a notable challenge in statistical physics. We uncover a fluctuation-induced force between two plates immersed in homogeneous isotropic turbulence using direct numerical simulations. The force is a nonmonotonic function of plate separation. The mechanism of force generation reveals an intriguing analogy with fluctuation-induced forces: In a fluid, energy and vorticity are localized in regions of defined length scales. When varying the distance between the plates, we exclude energy structures modifying the overall pressure on the plates. At intermediate plate distances, the intense vorticity structures (worms) are forced to interact in close vicinity between the plates. This interaction affects the pressure in the slit and the force between the plates. The combination of these two effects causes a nonmonotonic attractive force with a complex Reynolds number dependence. Our study sheds light on how length scale-dependent distributions of energy and high-intensity vortex structures determine Casimir forces.

Geometry of Energy Landscapes and the Optimizability of Deep Neural Networks

Deep neural networks are workhorse models in machine learning with multiple layers of nonlinear functions composed in series. Their loss function is highly nonconvex, yet empirically even gradient descent minimization is sufficient to arrive at accurate and predictive models. It is hitherto unknown why deep neural networks are easily optimizable. We analyze the energy landscape of a spin glass model of deep neural networks using random matrix theory and algebraic geometry. We analytically show that the multilayered structure holds the key to optimizability: Fixing the number of parameters and increasing network depth, the number of stationary points in the loss function decreases, minima become more clustered in parameter space, and the trade-off between the depth and width of minima becomes less severe. Our analytical results are numerically verified through comparison with neural networks trained on a set of classical benchmark datasets. Our model uncovers generic design principles of machine learning models.

Validating the validation: reanalyzing a large-scale comparison of deep learning and machine learning models for bioactivity prediction

Machine learning methods may have the potential to significantly accelerate drug discovery. However, the increasing rate of new methodological approaches being published in the literature raises the fundamental question of how models should be benchmarked and validated. We reanalyze the data generated by a recently published large-scale comparison of machine learning models for bioactivity prediction and arrive at a somewhat different conclusion. We show that the performance of support vector machines is competitive with that of deep learning methods. Additionally, using a series of numerical experiments, we question the relevance of area under the receiver operating characteristic curve as a metric in virtual screening. We further suggest that area under the precision–recall curve should be used in conjunction with the receiver operating characteristic curve. Our numerical experiments also highlight challenges in estimating the uncertainty in model performance via scaffold-split nested cross validation.

Molecular Transformer unifies reaction prediction and retrosynthesis across pharma chemical space

Predicting how a complex molecule reacts with different reagents, and how to synthesise complex molecules from simpler starting materials, are fundamental to organic chemistry. We show that an attention-based machine translation model - Molecular Transformer - tackles both reaction prediction and retrosynthesis by learning from the same dataset. Reagents, reactants and products are represented as SMILES text strings. For reaction prediction, the model "translates" the SMILES of reactants and reagents to product SMILES, and the converse for retrosynthesis. Moreover, a model trained on publicly available data is able to make accurate predictions on proprietary molecules extracted from pharma electronic lab notebooks, demonstrating generalisability across chemical space. We expect our versatile framework to be broadly applicable to problems such as reaction condition prediction, reagent prediction and yield prediction.

Molecular Transformer: A Model for Uncertainty-Calibrated Chemical Reaction Prediction

Organic synthesis is one of the key stumbling blocks in medicinal chemistry. A necessary yet unsolved step in planning synthesis is solving the forward problem: Given reactants and reagents, predict the products. Similar to other work, we treat reaction prediction as a machine translation problem between simplified molecular-input line-entry system (SMILES) strings (a text-based representation) of reactants, reagents, and the products. We show that a multihead attention Molecular Transformer model outperforms all algorithms in the literature, achieving a top-1 accuracy above 90% on a common benchmark data set. Molecular Transformer makes predictions by inferring the correlations between the presence and absence of chemical motifs in the reactant, reagent, and product present in the data set. Our model requires no handcrafted rules and accurately predicts subtle chemical transformations. Crucially, our model can accurately estimate its own uncertainty, with an uncertainty score that is 89% accurate in terms of classifying whether a prediction is correct. Furthermore, we show that the model is able to handle inputs without a reactant-reagent split and including stereochemistry, which makes our method universally applicable.

Bayesian semi-supervised learning for uncertainty-calibrated prediction of molecular properties and active learning

We report a statistically principled method to quantify the uncertainty of machine learning models for molecular properties prediction. We show that this uncertainty estimate can be used to judiciously design experiments.

Predicting bioactivity and physical properties of small molecules is a central challenge in drug discovery. Deep learning is becoming the method of choice but studies to date focus on mean accuracy as the main metric. However, to replace costly and mission-critical experiments by models, a high mean accuracy is not enough: outliers can derail a discovery campaign, thus models need to reliably predict when it will fail, even when the training data is biased; experiments are expensive, thus models need to be data-efficient and suggest informative training sets using active learning. We show that uncertainty quantification and active learning can be achieved by Bayesian semi-supervised graph convolutional neural networks. The Bayesian approach estimates uncertainty in a statistically principled way through sampling from the posterior distribution. Semi-supervised learning disentangles representation learning and regression, keeping uncertainty estimates accurate in the low data limit and allowing the model to start active learning from a small initial pool of training data. Our study highlights the promise of Bayesian deep learning for chemistry.

Screening Lengths in Ionic Fluids

The decay of correlations in ionic fluids is a classical problem in soft matter physics that underpins applications ranging from controlling colloidal self-assembly to batteries and supercapacitors. The conventional wisdom, based on analyzing a solvent-free electrolyte model, suggests that all correlation functions between species decay with a common decay length in the asymptotic far field limit. Nonetheless, a solvent is present in many electrolyte systems. We show using an analytical theory and molecular dynamics simulations that multiple decay lengths can coexist in the asymptotic limit as well as at intermediate distances once a hard sphere solvent is considered. Our analysis provides an explanation for the recently observed discontinuous change in the structural force across a thin film of ionic liquid-solvent mixtures as the composition is varied, as well as reframes recent debates in the literature about the screening length in concentrated electrolytes.

Controlling Polyelectrolyte Adsorption onto Carbon Nanotubes by Tuning Ion-Image Interactions

Understanding and controlling polyelectrolyte adsorption onto carbon nanotubes is a fundamental challenge in nanotechnology. Polyelectrolytes have been shown to stabilize nanotube suspensions through adsorbing onto the nanotube surface, and polyelectrolyte-coated nanotubes are emerging as building blocks for complex and addressable self-assembly. Conventional wisdom suggests that polyelectrolyte adsorption onto nanotubes is driven by specific chemical or van der Waals interactions. We develop a simple mean-field model and show that ion-image attraction significantly effects adsorption onto conducting nanotubes at low salt concentrations. Our theory suggests a simple strategy to selectively and reversibly functionalize carbon nanotubes on the basis of their electronic structures, which in turn modify the ion-image attraction.

Optimal Design of Experiments by Combining Coarse and Fine Measurements

In many contexts, it is extremely costly to perform enough high-quality experimental measurements to accurately parametrize a predictive quantitative model. However, it is often much easier to carry out large numbers of experiments that indicate whether each sample is above or below a given threshold. Can many such categorical or "coarse" measurements be combined with a much smaller number of high-resolution or "fine" measurements to yield accurate models? Here, we demonstrate an intuitive strategy, inspired by statistical physics, wherein the coarse measurements are used to identify the salient features of the data, while the fine measurements determine the relative importance of these features. A linear model is inferred from the fine measurements, augmented by a quadratic term that captures the correlation structure of the coarse data. We illustrate our strategy by considering the problems of predicting the antimalarial potency and aqueous solubility of small organic molecules from their 2D molecular structure.

Scaling Analysis of the Screening Length in Concentrated Electrolytes

The interaction between charged objects in an electrolyte solution is a fundamental question in soft matter physics. It is well known that the electrostatic contribution to the interaction energy decays exponentially with object separation. Recent measurements reveal that, contrary to the conventional wisdom given by the classic Poisson-Boltzmann theory, the decay length increases with the ion concentration for concentrated electrolytes and can be an order of magnitude larger than the ion diameter in ionic liquids. We derive a simple scaling theory that explains this anomalous dependence of the decay length on the ion concentration. Our theory successfully collapses the decay lengths of a wide class of salts onto a single curve. A novel prediction of our theory is that the decay length increases linearly with the Bjerrum length, which we experimentally verify by surface force measurements. Moreover, we quantitatively relate the measured decay length to classic measurements of the activity coefficient in concentrated electrolytes, thus showing that the measured decay length is indeed a bulk property of the concentrated electrolyte as well as contributing a mechanistic insight into empirical activity coefficients.

Controlling turbulent drag across electrolytes using electric fields

Reversible in operando control of friction is an unsolved challenge that is crucial to industrial tribology. Recent studies show that at low sliding velocities, this control can be achieved by applying an electric field across electrolyte lubricants. However, the phenomenology at high sliding velocities is yet unknown. In this paper, we investigate the hydrodynamic friction across electrolytes under shear beyond the transition to turbulence. We develop a novel, highly parallelised numerical method for solving the coupled Navier-Stokes Poisson-Nernst-Planck equation. Our results show that turbulent drag cannot be controlled across dilute electrolytes using static electric fields alone. The limitations of the Poisson-Nernst-Planck formalism hint at ways in which turbulent drag could be controlled using electric fields.

Switching the Structural Force in Ionic Liquid-Solvent Mixtures by Varying Composition

The structure and interactions in electrolytes at high concentration have implications from energy storage to biomolecular interactions. However, many experimental observations are yet to be explained in these mixtures, which are far beyond the regime of validity of mean-field models. Here, we study the structural forces in a mixture of ionic liquid and solvent that is miscible in all proportions at room temperature. Using the surface force balance to measure the force between macroscopic smooth surfaces across the liquid mixtures, we uncover an abrupt increase in the wavelength above a threshold ion concentration. Below the threshold concentration, the wavelength is determined by the size of the solvent molecule, whereas above the threshold, it is the diameter of a cation-anion pair that determines the wavelength.

Underscreening in concentrated electrolytes

Screening of a surface charge by an electrolyte and the resulting interaction energy between charged objects is of fundamental importance in scenarios from bio-molecular interactions to energy storage. The conventional wisdom is that the interaction energy decays exponentially with object separation and the decay length is a decreasing function of ion concentration; the interaction is thus negligible in a concentrated electrolyte. Contrary to this conventional wisdom, we have shown by surface force measurements that the decay length is an increasing function of ion concentration and Bjerrum length for concentrated electrolytes. In this paper we report surface force measurements to test directly the scaling of the screening length with Bjerrum length. Furthermore, we identify a relationship between the concentration dependence of this screening length and empirical measurements of activity coefficient and differential capacitance. The dependence of the screening length on the ion concentration and the Bjerrum length can be explained by a simple scaling conjecture based on the physical intuition that solvent molecules, rather than ions, are charge carriers in a concentrated electrolyte.

Long range electrostatic forces in ionic liquids

Experimental evidence for long range surface forces in ionic liquids is collated and examined, key outstanding questions are identified, and possible mechanisms underpinning these long range forces are explored.

Microscopic mechanism of thermomolecular orientation and polarization

Recent molecular dynamics simulations show that thermal gradients can induce electric fields in water that are comparable in magnitude to electric fields seen in ionic thin films and biomembranes. This surprising non-equilibrium phenomenon of thermomolecular orientation is also observed more generally in simulations of polar and non-polar size-asymmetric dumbbell fluids. However, a microscopic theory linking thermomolecular orientation and polarization to molecular properties is yet unknown. Here, we formulate an analytically solvable microscopic model of size-asymmetric dumbbell molecules in a temperature gradient using a mean-field, local equilibrium approach. Our theory reveals the relationship between the extent of thermomolecular orientation and polarization, and molecular volume, size anisotropy and dipole moment. Predictions of the theory agree quantitatively with molecular dynamics simulations. Crucially, our framework shows how thermomolecular orientation can be controlled and maximized by tuning microscopic molecular properties.

Dissecting the self-assembly kinetics of multimeric pore-forming toxins

Pore-forming toxins are ubiquitous cytotoxins that are exploited by both bacteria and the immune response of eukaryotes. These toxins kill cells by assembling large multimeric pores on the cell membrane. However, a quantitative understanding of the mechanism and kinetics of this self-assembly process is lacking. We propose an analytically solvable kinetic model for stepwise, reversible oligomerization. In biologically relevant limits, we obtain simple algebraic expressions for the rate of pore formation, as well as for the concentration of pores as a function of time. Quantitative agreement is obtained between our model and time-resolved kinetic experiments of Bacillus thuringiensis Cry1Ac (tetrameric pore), aerolysin, Staphylococcus aureus α-haemolysin (heptameric pores) and Escherichia coli cytolysin A (dodecameric pore). Furthermore, our model explains how rapid self-assembly can take place with low concentrations of oligomeric intermediates, as observed in recent single-molecule fluorescence experiments of α-haemolysin self-assembly. We propose that suppressing the concentration of oligomeric intermediates may be the key to reliable, error-free, self-assembly of pores.

Ion-Image Interactions and Phase Transition at Electrolyte-Metal Interfaces

The arrangement of ions near a metallic electrode is crucial to energy storage in electrical double-layer capacitors. Classic Poisson-Boltzmann theory predicts that the charge stored in the double layer is a continuous function of applied voltage. However, recent experiments and simulations strongly suggest the presence of a voltage-induced first-order phase transition in the electrical double layer, leading to a hysteretic response: the capacitance-voltage relation is dependent on whether the voltage is increasing or decreasing. By developing a simple analytical model, we show that ion-image interaction could explain this phase transition. Moreover, our model shows that the presence of phase transition depends on the bulk energy of the ionic liquid. Our results justify mixing ionic liquids with solvents as a way to achieve large capacitance and avoid hysteresis.

The Electrostatic Screening Length in Concentrated Electrolytes Increases with Concentration

According to classical electrolyte theories interactions in dilute (low ion density) electrolytes decay exponentially with distance, with the Debye screening length the characteristic length scale. This decay length decreases monotonically with increasing ion concentration due to effective screening of charges over short distances. Thus, within the Debye model no long-range forces are expected in concentrated electrolytes. Here we reveal, using experimental detection of the interaction between two planar charged surfaces across a wide range of electrolytes, that beyond the dilute (Debye-Hückel) regime the screening length increases with increasing concentration. The screening lengths for all electrolytes studied-including aqueous NaCl solutions, ionic liquids diluted with propylene carbonate, and pure ionic liquids-collapse onto a single curve when scaled by the dielectric constant. This nonmonotonic variation of the screening length with concentration, and its generality across ionic liquids and aqueous salt solutions, demonstrates an important characteristic of concentrated electrolytes of substantial relevance from biology to energy storage.

Dynamics of Ion Transport in Ionic Liquids

A gap in understanding the link between continuum theories of ion transport in ionic liquids and the underlying microscopic dynamics has hindered the development of frameworks for transport phenomena in these concentrated electrolytes. Here, we construct a continuum theory for ion transport in ionic liquids by coarse graining a simple exclusion process of interacting particles on a lattice. The resulting dynamical equations can be written as a gradient flow with a mobility matrix that vanishes at high densities. This form of the mobility matrix gives rise to a charging behavior that is different to the one known for electrolytic solutions, but which agrees qualitatively with the phenomenology observed in experiments and simulations.

Are Room-Temperature Ionic Liquids Dilute Electrolytes?

An important question in understanding the structure of ionic liquids is whether ions are truly "free" and mobile, which would correspond to a concentrated ionic melt, or are rather "bound" in ion pairs, that is, a liquid of ion pairs with a small concentration of free ions. Recent surface force balance experiments from different groups have given conflicting answers to this question. We propose a simple model for the thermodynamics and kinetics of ion pairing in ionic liquids. Our model takes into account screened ion-ion, dipole-dipole, and dipole-ion interactions in the mean-field limit. The results of this model suggest that almost two-thirds of the ions are free at any instant, and ion pairs have a short lifetime comparable to the characteristic time scale for diffusion. These results suggest that there is no particular thermodynamic or kinetic preference for ions to reside in pairs. We therefore conclude that ionic liquids are concentrated, rather than dilute, electrolytes.

Charging dynamics of supercapacitors with narrow cylindrical nanopores

We present a coarse-grained, continuum kinetic theory for charging supercapacitors with narrow cylindrical nanopores. The theory reveals that the occupancy of a nonpolarized pore and the energy barrier for ion-ion interdiffusion are the key issues controlling the different regimes of dynamic response. For 'ionophobic' pores, where the pore is empty at no applied voltage, charge density advances into the pore via diffusion-like dynamics. The mechanism of charging an 'ionophilic' pore is starkly different: for moderate ionophilicities, co-ions are expelled from the pore in a front-like manner, with significant 'congestion' at the pore entrance predicted for strong ionophilicity. We thus show that pore ionophilicity is detrimental to the speed of charging/discharging cycles, whereas making pores more ionophobic can substantially accelerate charging and cyclic recharging.

Single-file charge storage in conducting nanopores

Charging of a conducting tubular nanopore in a nanostructured electrode is treated using an exactly solvable 1D lattice model, including ion correlations screened by ion-image interactions. Analytical expressions are obtained for the accumulated charge and capacitance as a function of voltage. They show that the mechanism of charge storage, and the qualitative form of the capacitance-voltage curve, are sensitive to how favorable it is for ions to occupy the unpolarized pore, and the pore radius. Qualitative predictions of the theory are corroborated by Monte Carlo simulations. These results highlight the effect of ion affinity to unpolarized pores on the charge and energy storage in supercapacitors. Furthermore, they suggest that the question of the occupancy of unpolarized pores could be answered by measuring the capacitance-voltage dependence.

Alternative radical pairs for cryptochrome-based magnetoreception

There is growing evidence that the remarkable ability of animals, in particular birds, to sense the direction of the Earth's magnetic field relies on magnetically sensitive photochemical reactions of the protein cryptochrome. It is generally assumed that the magnetic field acts on the radical pair [FAD•- TrpH•+] formed by the transfer of an electron from a group of three tryptophan residues to the photo-excited flavin adenine dinucleotide cofactor within the protein. Here, we examine the suitability of an [FAD•- Z•] radical pair as a compass magnetoreceptor, where Z• is a radical in which the electron spin has no hyperfine interactions with magnetic nuclei, such as hydrogen and nitrogen. Quantum spin dynamics simulations of the reactivity of [FAD•- Z•] show that it is two orders of magnitude more sensitive to the direction of the geomagnetic field than is [FAD•- TrpH•+] under the same conditions (50 µT magnetic field, 1 µs radical lifetime). The favourable magnetic properties of [FAD•- Z•] arise from the asymmetric distribution of hyperfine interactions among the two radicals and the near-optimal magnetic properties of the flavin radical. We close by discussing the identity of Z• and possible routes for its formation as part of a spin-correlated radical pair with an FAD radical in cryptochrome.

Interionic interactions in conducting nanoconfinement

Interionic interactions in conducting nanopores determine how counterions may be packed in the pores subject to the applied voltage. In ideal metals, interactions are exponentially screened by metallic electrons. However, modern nanoporous electrodes are predominantly made of carbon materials. To what extent is this screening affected by a different mode of dielectric response in such materials? To answer this question we study Coulomb interaction of charges in cylindrical and slit pores that allow finite electric field penetration into the pore walls, as well as the Coulomb interaction in a nanogap between two thin walls of graphene modeled by a non-local dielectric function. In all cases studied the screening was found to be subtly different than in metallic nanopores, but still strong enough to support realization of the so called superionic state in such pores.

Statics and dynamics of electroactuation with single-charge-carrier ionomers

A simple theory of electromechanical transduction for single-charge-carrier double-layer electroactuators is developed, in which the ion distribution and curvature are mutually coupled. The obtained expressions for the dependence of the curvature and charge accumulation on the applied voltage, as well as the electroactuation dynamics, are compared with literature data. The mechanical or sensor performance of such electroactuators appears to be determined by just three cumulative parameters, with all of their constituents measurable, permitting a scaling approach to their design.

The effect of brimonidine tartrate on retinal blood flow in patients with ocular hypertension

PURPOSE

To study the effects of topical brimonidine tartrate 0.2%, an alpha(2)-agonist ocular hypotensive drug, on retinal capillary blood flow in patients with ocular hypertension.

METHODS

The study was a double-masked, randomized, placebo-controlled trial set in a tertiary eye center. Ocular hypertensive patients with repeatable intraocular pressures greater than 21 mm Hg and normal visual fields and optic disks were consecutively recruited. After an eye examination, baseline retinal blood flow measurements were made with confocal scanning laser Doppler flowmetry in one study eye. Patients were then randomly assigned to receive either brimonidine or placebo (saline) twice daily for 8 weeks. Blood flow and intraocular pressure measurements were then repeated after 4 and 8 weeks.

RESULTS

Seventeen patients were randomly assigned to receive brimonidine, and 14 received placebo. One patient in each group failed to complete the study. The mean group differences in baseline age and intraocular pressure were not statistically significant (59. 23 [+/-10.24] and 52.23 [+/-16.46] years, respectively, and 24.84 [+/-2.08] and 24.56 [+/-2.85] mm Hg, respectively). Brimonidine reduced intraocular pressure by 17.90% and 16.17% at 4 and 8 weeks, respectively, with a significant difference in treatment effect compared with the placebo group (P <.007). The group difference in treatment effect in any of the three hemodynamic parameters velocity, volume, and flow was within 8% and not significantly different at 4 or 8 weeks (P.360). Based on a type I error of 0.05, our study had a power greater than or equal to 75% to detect group differences in treatment effect of greater than or equal to 15% to 20%.

CONCLUSIONS

Brimonidine reduces intraocular pressure without altering retinal capillary blood flow in patients with ocular hypertension.

The effect of brimonidine tartrate on retinal blood flow in patients with ocular hypertension [corrected]

PURPOSE

To study the effects of topical brimonidine tartrate 0.2%, an alpha2-agonist ocular hypotensive drug, on retinal capillary blood flow in patients with ocular hypertension.

METHODS

The study was a double-masked, randomized, placebo-controlled trial set in a tertiary eye center. Ocular hypertensive patients with repeatable intraocular pressures greater than 21 mm Hg and normal visual fields and optic disks were consecutively recruited. After an eye examination, baseline retinal blood flow measurements were made with confocal scanning laser Doppler flowmetry in one study eye. Patients were then randomly assigned to receive either brimonidine or placebo (saline) twice daily for 8 weeks. Blood flow and intraocular pressure measurements were then repeated after 4 and 8 weeks.

RESULTS

Seventeen patients were randomly assigned to receive brimonidine, and 14 received placebo. One patient in each group failed to complete the study. The mean group differences in baseline age and intraocular pressure were not statistically significant (59.23 [+/-10.24] and 52.23 [+/-16.46] years, respectively, and 24.84 [+/-2.08] and 24.56 [+/-2.85] mm Hg, respectively). Brimonidine reduced intraocular pressure by 17.90% and 16.17% at 4 and 8 weeks, respectively, with a significant difference in treatment effect compared with the placebo group (P < .007). The group difference in treatment effect in any of the three hemodynamic parameters velocity, volume, and flow was within 8% and not significantly different at 4 or 8 weeks (P > .360). Based on a type I error of 0.05, our study had a power greater than or equal to 75% to detect group differences in treatment effect of greater than or equal to 15% to 20%.

CONCLUSIONS

Brimonidine reduces intraocular pressure without altering retinal capillary blood flow in patients with ocular hypertension.