Neural general circulation models for weather and climate.

General circulation models (GCMs) are the foundation of weather and climate prediction1,2. GCMs are physics-based simulators that combine a numerical solver for large-scale dynamics with tuned representations for small-scale processes such as cloud formation. Recently, machine-learning models trained on reanalysis data have achieved comparable or better skill than GCMs for deterministic weather forecasting3,4. However, these models have not demonstrated improved ensemble forecasts, or shown sufficient stability for long-term weather and climate simulations. Here we present a GCM that combines a differentiable solver for atmospheric dynamics with machine-learning components and show that it can generate forecasts of deterministic weather, ensemble weather and climate on par with the best machine-learning and physics-based methods. NeuralGCM is competitive with machine-learning models for one- to ten-day forecasts, and with the European Centre for Medium-Range Weather Forecasts ensemble prediction for one- to fifteen-day forecasts. With prescribed sea surface temperature, NeuralGCM can accurately track climate metrics for multiple decades, and climate forecasts with 140-kilometre resolution show emergent phenomena such as realistic frequency and trajectories of tropical cyclones. For both weather and climate, our approach offers orders of magnitude computational savings over conventional GCMs, although our model does not extrapolate to substantially different future climates. Our results show that end-to-end deep learning is compatible with tasks performed by conventional GCMs and can enhance the large-scale physical simulations that are essential for understanding and predicting the Earth system.

Programming patchy particles for materials assembly design.

Direct design of complex functional materials would revolutionize technologies ranging from printable organs to novel clean energy devices. However, even incremental steps toward designing functional materials have proven challenging. If the material is constructed from highly complex components, the design space of materials properties rapidly becomes too computationally expensive to search. On the other hand, very simple components such as uniform spherical particles are not powerful enough to capture rich functional behavior. Here, we introduce a differentiable materials design model with components that are simple enough to design yet powerful enough to capture complex materials properties: rigid bodies composed of spherical particles with directional interactions (patchy particles). We showcase the method with self-assembly designs ranging from open lattices to self-limiting clusters, all of which are notoriously challenging design goals to achieve using purely isotropic particles. By directly optimizing over the location and interaction of the patches on patchy particles using gradient descent, we dramatically reduce the computation time for finding the optimal building blocks.

Recurrent flow patterns as a basis for two-dimensional turbulence: Predicting statistics from structures.

A dynamical systems approach to turbulence envisions the flow as a trajectory through a high-dimensional state space [Hopf, Commun. Appl. Maths 1, 303 (1948)]. The chaotic dynamics are shaped by the unstable simple invariant solutions populating the inertial manifold. The hope has been to turn this picture into a predictive framework where the statistics of the flow follow from a weighted sum of the statistics of each simple invariant solution. Two outstanding obstacles have prevented this goal from being achieved: 1) paucity of known solutions and 2) the lack of a rational theory for predicting the required weights. Here, we describe a method to substantially solve these problems, and thereby provide compelling evidence that the probability density functions (PDFs) of a fully developed turbulent flow can be reconstructed with a set of unstable periodic orbits. Our method for finding solutions uses automatic differentiation, with high-quality guesses constructed by minimizing a trajectory-dependent loss function. We use this approach to find hundreds of solutions in turbulent, two-dimensional Kolmogorov flow. Robust statistical predictions are then computed by learning weights after converting a turbulent trajectory into a Markov chain for which the states are individual solutions, and the nearest solution to a given snapshot is determined using a deep convolutional autoencoder. In this study, the PDFs of a spatiotemporally chaotic system have been successfully reproduced with a set of simple invariant states, and we provide a fascinating connection between self-sustaining dynamical processes and the more well-known statistical properties of turbulence.

Braiding, twisting, and weaving microscale fibers with capillary forces.

Soft materials made from braided or woven microscale fibers can display unique properties that can be exploited in electromagnetic, mechanical, and biomedical applications. These properties depend on the topology of the braids or weaves-that is, the order in which fibers cross one another. Current industrial braiding and weaving machines cannot easily braid or weave micrometer-scale fibers into controllable topologies; they typically apply forces that are large enough to break the fibers, and each machine can typically make only one topology. Here we use a 3D-printed device called a "capillary machine" to manipulate micrometer-scale fibers without breaking them. The operating principle is the physics of capillary forces: as the machines move vertically, they exert lateral capillary forces on floating objects, which in turn move small fibers connected to them. We present a new type of capillary machine that is based on principles of braid theory. It implements all the possible fiber-swapping operations for a set of four fibers and can therefore make any four-strand topology, including braids, twists, hierarchical twists, and weaves. We make these different topologies by changing the pattern of vertical motion of the machine. This approach is a mechanically simple, yet versatile way to make micro- and nano-textiles. We describe the prospects and limitations of this new type of machine for applications.

A computational toolbox for the assembly yield of complex and heterogeneous structures.

The self-assembly of complex structures from a set of non-identical building blocks is a hallmark of soft matter and biological systems, including protein complexes, colloidal clusters, and DNA-based assemblies. Predicting the dependence of the equilibrium assembly yield on the concentrations and interaction energies of building blocks is highly challenging, owing to the difficulty of computing the entropic contributions to the free energy of the many structures that compete with the ground state configuration. While these calculations yield well known results for spherically symmetric building blocks, they do not hold when the building blocks have internal rotational degrees of freedom. Here we present an approach for solving this problem that works with arbitrary building blocks, including proteins with known structure and complex colloidal building blocks. Our algorithm combines classical statistical mechanics with recently developed computational tools for automatic differentiation. Automatic differentiation allows efficient evaluation of equilibrium averages over configurations that would otherwise be intractable. We demonstrate the validity of our framework by comparison to molecular dynamics simulations of simple examples, and apply it to calculate the yield curves for known protein complexes and for the assembly of colloidal shells.

Nonequilibrium sensing of volatile compounds using active and passive analyte delivery.

Although sensor technologies have allowed us to outperform the human senses of sight, hearing, and touch, the development of artificial noses is significantly behind their biological counterparts. This largely stems from the sophistication of natural olfaction, which relies on both fluid dynamics within the nasal anatomy and the response patterns of hundreds to thousands of unique molecular-scale receptors. We designed a sensing approach to identify volatiles inspired by the fluid dynamics of the nose, allowing us to extract information from a single sensor (here, the reflectance spectra from a mesoporous one-dimensional photonic crystal) rather than relying on a large sensor array. By accentuating differences in the nonequilibrium mass-transport dynamics of vapors and training a machine learning algorithm on the sensor output, we clearly identified polar and nonpolar volatile compounds, determined the mixing ratios of binary mixtures, and accurately predicted the boiling point, flash point, vapor pressure, and viscosity of a number of volatile liquids, including several that had not been used for training the model. We further implemented a bioinspired active sniffing approach, in which the analyte delivery was performed in well-controlled 'inhale-exhale' sequences, enabling an additional modality of differentiation and reducing the duration of data collection and analysis to seconds. Our results outline a strategy to build accurate and rapid artificial noses for volatile compounds that can provide useful information such as the composition and physical properties of chemicals, and can be applied in a variety of fields, including disease diagnosis, hazardous waste management, and healthy building monitoring.

Measuring intramolecular connectivity in long RNA molecules using two-dimensional DNA patch-probe arrays.

We describe a simple method to infer intramolecular connections in a population of long RNA molecules in vitro. First we add DNA oligonucleotide "patches" that perturb the RNA connections, then we use a microarray containing a complete set of DNA oligonucleotide "probes" to record where perturbations occur. The pattern of perturbations reveals couplings between different regions of the RNA sequence, from which we infer connections as well as their prevalences in the population. We validate this patch-probe method using the 1,058-nucleotide RNA genome of satellite tobacco mosaic virus (STMV), which has previously been shown to have multiple long-range connections. Our results not only indicate long duplexes that agree with previous structures but also reveal the prevalence of competing connections. Together, these results suggest that globally-folded and locally-folded structures coexist in solution. We show that the prevalence of connections changes when pseudouridine, an important component of natural and synthetic RNA molecules, is substituted for uridine in STMV RNA.

Nucleic Acid Structure Prediction Including Pseudoknots Through Direct Enumeration of States: A User's Guide to the LandscapeFold Algorithm.

Here we detail the LandscapeFold secondary structure prediction algorithm and how it is used. The algorithm was previously described and tested in (Kimchi O et al., Biophys J 117(3):520-532, 2019), though it was not named there. The algorithm directly enumerates all possible secondary structures into which up to two RNA or single-stranded DNA sequences can fold. It uses a polymer physics model to estimate the configurational entropy of structures including complex pseudoknots. We detail each of these steps and ways in which the user can adjust the algorithm as desired. The code is available on the GitHub repository https://github.com/ofer-kimchi/LandscapeFold .

Uncovering the mechanism for aggregation in repeat expanded RNA reveals a reentrant transition.

RNA molecules aggregate under certain conditions. The resulting condensates are implicated in human neurological disorders, and can potentially be designed towards specified bulk properties in vitro. However, the mechanism for aggregation-including how aggregation properties change with sequence and environmental conditions-remains poorly understood. To address this challenge, we introduce an analytical framework based on multimer enumeration. Our approach reveals the driving force for aggregation to be the increased configurational entropy associated with the multiplicity of ways to form bonds in the aggregate. Our model uncovers rich phase behavior, including a sequence-dependent reentrant phase transition, and repeat parity-dependent aggregation. We validate our results by comparison to a complete computational enumeration of the landscape, and to previously published molecular dynamics simulations. Our work unifies and extends published results, both explaining the behavior of CAG-repeat RNA aggregates implicated in Huntington's disease, and enabling the rational design of programmable RNA condensates.

Beyond quality and quantity: Spatial distribution of contact encodes frictional strength.

Classically, the quantity of contact area A_{R} between two bodies is considered a proxy for the force of friction. However, bond density across the interface-quality of contact-is also relevant, and contemporary debate often centers around the relative importance of these two factors. In this work, we demonstrate that a third factor, often overlooked, plays a significant role in static frictional strength: The spatial distribution of contact. We perform static friction measurements, µ, on three pairs of solid blocks while imaging the contact plane. By using linear regression on hundreds of image-µ pairs, we are able to predict future friction measurements with three to seven times better accuracy than existing benchmarks, including total quantity of contact area. Our model has no access to quality of contact, and we therefore conclude that a large portion of the interfacial state is encoded in the spatial distribution of contact, rather than its quality or quantity.

3D-printed machines that manipulate microscopic objects using capillary forces.

Objects that deform a liquid interface are subject to capillary forces, which can be harnessed to assemble the objects1-4. Once assembled, such structures are generally static. Here we dynamically modulate these forces to move objects in programmable two-dimensional patterns. We 3D-print devices containing channels that trap floating objects using repulsive capillary forces5,6, then move these devices vertically in a water bath. Because the channel cross-sections vary with height, the trapped objects can be steered in two dimensions. The device and interface therefore constitute a simple machine that converts vertical to lateral motion. We design machines that translate, rotate and separate multiple floating objects and that do work on submerged objects through cyclic vertical motion. We combine these elementary machines to make centimetre-scale compound machines that braid micrometre-scale filaments into prescribed topologies, including non-repeating braids. Capillary machines are distinct from mechanical, optical or fluidic micromanipulators in that a meniscus links the object to the machine. Therefore, the channel shapes need only be controlled on the scale of the capillary length (a few millimetres), even when the objects are microscopic. Consequently, such machines can be built quickly and inexpensively. This approach could be used to manipulate micrometre-scale particles or to braid microwires for high-frequency electronics.

Programming interactions in magnetic handshake materials.

The ability to rapidly manufacture building blocks with specific binding interactions is a key aspect of programmable assembly. Recent developments in DNA nanotechnology and colloidal particle synthesis have significantly advanced our ability to create particle sets with programmable interactions, based on DNA or shape complementarity. The increasing miniaturization underlying magnetic storage offers a new path for engineering programmable components for self assembly, by printing magnetic dipole patterns on substrates using nanotechnology. How to efficiently design dipole patterns for programmable assembly remains an open question as the design space is combinatorially large. Here, we present design rules for programming these magnetic interactions. By optimizing the structure of the dipole pattern, we demonstrate that the number of independent building blocks scales super linearly with the number of printed domains. We test these design rules using computational simulations of self assembled blocks, and experimental realizations of the blocks at the mm scale, demonstrating that the designed blocks give high yield assembly. In addition, our design rules indicate that with current printing technology, micron sized magnetic panels could easily achieve hundreds of different building blocks.

Correlation Tracking: Using simulations to interpolate highly correlated particle tracks.

Despite significant advances in particle imaging technologies over the past two decades, few advances have been made in particle tracking, i.e., linking individual particle positions across time series data. The state-of-the-art tracking algorithm is highly effective for systems in which the particles behave mostly independently. However, these algorithms become inaccurate when particle motion is highly correlated, such as in dense or strongly interacting systems. Accurate particle tracking is essential in the study of the physics of dense colloids, such as the study of dislocation formation, nucleation, and shear transformations. Here, we present a method for particle tracking that incorporates information about the correlated motion of the particles. We demonstrate significant improvement over the state-of-the-art tracking algorithm in simulated data on highly correlated systems.

COVID-19 Open-Data a global-scale spatially granular meta-dataset for coronavirus disease.

This paper introduces the COVID-19 Open Dataset (COD), available at goo.gle/covid-19-open-data . A static copy is of the dataset is also available at https://doi.org/10.6084/m9.figshare.c.5399355 . This is a very large "meta-dataset" of COVID-related data, containing epidemiological information, from 22,579 unique locations within 232 different countries and independent territories. For 62 of these countries we have state-level data, and for 23 of these countries we have county-level data. For 15 countries, COD includes cases and deaths stratified by age or sex. COD also contains information on hospitalizations, vaccinations, and other relevant factors such as mobility, non-pharmaceutical interventions and static demographic attributes. Each location is tagged with a unique identifier so that these different types of information can be easily combined. The data is automatically extracted from 121 different authoritative sources, using scalable open source software. This paper describes the format and construction of the dataset, and includes a preliminary statistical analysis of its content, revealing some interesting patterns.

A machine-learning based objective measure for ALS disease severity.

Amyotrophic Lateral Sclerosis (ALS) disease severity is usually measured using the subjective, questionnaire-based revised ALS Functional Rating Scale (ALSFRS-R). Objective measures of disease severity would be powerful tools for evaluating real-world drug effectiveness, efficacy in clinical trials, and for identifying participants for cohort studies. We developed a machine learning (ML) based objective measure for ALS disease severity based on voice samples and accelerometer measurements from a four-year longitudinal dataset. 584 people living with ALS consented and carried out prescribed speaking and limb-based tasks. 542 participants contributed 5814 voice recordings, and 350 contributed 13,009 accelerometer samples, while simultaneously measuring ALSFRS-R scores. Using these data, we trained ML models to predict bulbar-related and limb-related ALSFRS-R scores. On the test set (n = 109 participants) the voice models achieved a multiclass AUC of 0.86 (95% CI, 0.85-0.88) on speech ALSFRS-R prediction, whereas the accelerometer models achieved a median multiclass AUC of 0.73 on 6 limb-related functions. The correlations across functions observed in self-reported ALSFRS-R scores were preserved in ML-derived scores. We used these models and self-reported ALSFRS-R scores to evaluate the real-world effects of edaravone, a drug approved for use in ALS. In the cohort of 54 test participants who received edaravone as part of their usual care, the ML-derived scores were consistent with the self-reported ALSFRS-R scores. At the individual level, the continuous ML-derived score can capture gradual changes that are absent in the integer ALSFRS-R scores. This demonstrates the value of these tools for assessing disease severity and, potentially, drug effects.

Identifying Cell Type-Specific Chemokine Correlates with Hierarchical Signal Extraction from Single-Cell Transcriptomes.

Biological data is inherently heterogeneous and high-dimensional. Single-cell sequencing of transcripts in a tissue sample generates data for thousands of cells, each of which is characterized by upwards of tens of thousands of genes. How to identify the subsets of cells and genes that are associated with a label of interest remains an open question. In this paper, we integrate a signal-extractive neural network architecture with axiomatic feature attribution to classify tissue samples based on single-cell gene expression profiles. This approach is not only interpretable but also robust to noise, requiring just 5% of genes and 23% of cells in an in silico tissue sample to encode signal in order to distinguish signal from noise with greater than 70% accuracy. We demonstrate its applicability in two real-world settings for discovering cell type-specific chemokine correlates: predicting response to immune checkpoint inhibitors in multiple tissue types and classifying DNA mismatch repair status in colorectal cancer. Our approach not only significantly outperforms traditional machine learning classifiers but also presents actionable biological hypotheses of chemokinemediated tumor immunogenicity.

Programming cell growth into different cluster shapes using diffusible signals.

Advances in genetic engineering technologies have allowed the construction of artificial genetic circuits, which have been used to generate spatial patterns of differential gene expression. However, the question of how cells can be programmed, and how complex the rules need to be, to achieve a desired tissue morphology has received less attention. Here, we address these questions by developing a mathematical model to study how cells can collectively grow into clusters with different structural morphologies by secreting diffusible signals that can influence cellular growth rates. We formulate how growth regulators can be used to control the formation of cellular protrusions and how the range of achievable structures scales with the number of distinct signals. We show that a single growth inhibitor is insufficient for the formation of multiple protrusions but may be achieved with multiple growth inhibitors, and that other types of signals can regulate the shape of protrusion tips. These examples illustrate how our approach could potentially be used to guide the design of regulatory circuits for achieving a desired target structure.

Phase separation in fluids with many interacting components.

Fluids in natural systems, like the cytoplasm of a cell, often contain thousands of molecular species that are organized into multiple coexisting phases that enable diverse and specific functions. How interactions between numerous molecular species encode for various emergent phases is not well understood. Here, we leverage approaches from random-matrix theory and statistical physics to describe the emergent phase behavior of fluid mixtures with many species whose interactions are drawn randomly from an underlying distribution. Through numerical simulation and stability analyses, we show that these mixtures exhibit staged phase-separation kinetics and are characterized by multiple coexisting phases at steady state with distinct compositions. Random-matrix theory predicts the number of coexisting phases, validated by simulations with diverse component numbers and interaction parameters. Surprisingly, this model predicts an upper bound on the number of phases, derived from dynamical considerations, that is much lower than the limit from the Gibbs phase rule, which is obtained from equilibrium thermodynamic constraints. We design ensembles that encode either linear or nonmonotonic scaling relationships between the number of components and coexisting phases, which we validate through simulation and theory. Finally, inspired by parallels in biological systems, we show that including nonequilibrium turnover of components through chemical reactions can tunably modulate the number of coexisting phases at steady state without changing overall fluid composition. Together, our study provides a model framework that describes the emergent dynamical and steady-state phase behavior of liquid-like mixtures with many interacting constituents.

Microscopic origins of the crystallographically preferred growth in evaporation-induced colloidal crystals.

Unlike crystalline atomic and ionic solids, texture development due to crystallographically preferred growth in colloidal crystals is less studied. Here we investigate the underlying mechanisms of the texture evolution in an evaporation-induced colloidal assembly process through experiments, modeling, and theoretical analysis. In this widely used approach to obtain large-area colloidal crystals, the colloidal particles are driven to the meniscus via the evaporation of a solvent or matrix precursor solution where they close-pack to form a face-centered cubic colloidal assembly. Via two-dimensional large-area crystallographic mapping, we show that the initial crystal orientation is dominated by the interaction of particles with the meniscus, resulting in the expected coalignment of the close-packed direction with the local meniscus geometry. By combining with crystal structure analysis at a single-particle level, we further reveal that, at the later stage of self-assembly, however, the colloidal crystal undergoes a gradual rotation facilitated by geometrically necessary dislocations (GNDs) and achieves a large-area uniform crystallographic orientation with the close-packed direction perpendicular to the meniscus and parallel to the growth direction. Classical slip analysis, finite element-based mechanical simulation, computational colloidal assembly modeling, and continuum theory unequivocally show that these GNDs result from the tensile stress field along the meniscus direction due to the constrained shrinkage of the colloidal crystal during drying. The generation of GNDs with specific slip systems within individual grains leads to crystallographic rotation to accommodate the mechanical stress. The mechanistic understanding reported here can be utilized to control crystallographic features of colloidal assemblies, and may provide further insights into crystallographically preferred growth in synthetic, biological, and geological crystals.

A holistic approach for suppression of COVID-19 spread in workplaces and universities.

As society has moved past the initial phase of the COVID-19 crisis that relied on broad-spectrum shutdowns as a stopgap method, industries and institutions have faced the daunting question of how to return to a stabilized state of activities and more fully reopen the economy. A core problem is how to return people to their workplaces and educational institutions in a manner that is safe, ethical, grounded in science, and takes into account the unique factors and needs of each organization and community. In this paper, we introduce an epidemiological model (the "Community-Workplace" model) that accounts for SARS-CoV-2 transmission within the workplace, within the surrounding community, and between them. We use this multi-group deterministic compartmental model to consider various testing strategies that, together with symptom screening, exposure tracking, and nonpharmaceutical interventions (NPI) such as mask wearing and physical distancing, aim to reduce disease spread in the workplace. Our framework is designed to be adaptable to a variety of specific workplace environments to support planning efforts as reopenings continue. Using this model, we consider a number of case studies, including an office workplace, a factory floor, and a university campus. Analysis of these cases illustrates that continuous testing can help a workplace avoid an outbreak by reducing undetected infectiousness even in high-contact environments. We find that a university setting, where individuals spend more time on campus and have a higher contact load, requires more testing to remain safe, compared to a factory or office setting. Under the modeling assumptions, we find that maintaining a prevalence below 3% can be achieved in an office setting by testing its workforce every two weeks, whereas achieving this same goal for a university could require as much as fourfold more testing (i.e., testing the entire campus population twice a week). Our model also simulates the dynamics of reduced spread that result from the introduction of mitigation measures when test results reveal the early stages of a workplace outbreak. We use this to show that a vigilant university that has the ability to quickly react to outbreaks can be justified in implementing testing at the same rate as a lower-risk office workplace. Finally, we quantify the devastating impact that an outbreak in a small-town college could have on the surrounding community, which supports the notion that communities can be better protected by supporting their local places of business in preventing onsite spread of disease.