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Cooking is a tangible, familiar, and delicious tool for teaching physics, which is easy to implement in a university setting. Through our courses at Harvard and UCLA, each year we are engaging hundreds of undergraduate students, primarily non-science majors, in science concepts and the scientific research process. We find that weekly lectures by chefs and professors, paired with edible lab experiments, generate enthusiasm and provide strong motivation for students to learn physics. By the end of the course, students are able to conduct independent scientific research and present their results in a final science fair. Given the considerable broad appeal of food and cooking, the topic could be adapted to other post-secondary as well as secondary-level courses.

The precise control of complex reactions is critical for biological processes, yet our inability to design for specific outcomes limits the development of synthetic analogs. Here, we leverage differentiable simulators to design nontrivial reaction pathways in colloidal assemblies. By optimizing over external structures, we achieve controlled disassembly and particle release from colloidal shells. Lastly, we characterize the role of configurational entropy in the structure via both forward calculations and optimization, inspiring new parameterizations of designed colloidal reactions.

The ionosphere is a layer of weakly ionized plasma bathed in Earth's geomagnetic field extending about 50-1,500 kilometres above Earth 1 . The ionospheric total electron content varies in response to Earth's space environment, interfering with Global Satellite Navigation System (GNSS) signals, resulting in one of the largest sources of error for position, navigation and timing services 2 . Networks of high-quality ground-based GNSS stations provide maps of ionospheric total electron content to correct these errors, but large spatiotemporal gaps in data from these stations mean that these maps may contain errors 3 . Here we demonstrate that a distributed network of noisy sensors-in the form of millions of Android phones-can fill in many of these gaps and double the measurement coverage, providing an accurate picture of the ionosphere in areas of the world underserved by conventional infrastructure. Using smartphone measurements, we resolve features such as plasma bubbles over India and South America, solar-storm-enhanced density over North America and a mid-latitude ionospheric trough over Europe. We also show that the resulting ionosphere maps can improve location accuracy, which is our primary aim. This work demonstrates the potential of using a large distributed network of smartphones as a powerful scientific instrument for monitoring Earth., Competing Interests: Competing interests The authors are employees of Google and own shares in the company., (© 2024. The Author(s).)

Accelerating text input in augmentative and alternative communication (AAC) is a long-standing area of research with bearings on the quality of life in individuals with profound motor impairments. Recent advances in large language models (LLMs) pose opportunities for re-thinking strategies for enhanced text entry in AAC. In this paper, we present SpeakFaster, consisting of an LLM-powered user interface for text entry in a highly-abbreviated form, saving 57% more motor actions than traditional predictive keyboards in offline simulation. A pilot study on a mobile device with 19 non-AAC participants demonstrated motor savings in line with simulation and relatively small changes in typing speed. Lab and field testing on two eye-gaze AAC users with amyotrophic lateral sclerosis demonstrated text-entry rates 29-60% above baselines, due to significant saving of expensive keystrokes based on LLM predictions. These findings form a foundation for further exploration of LLM-assisted text entry in AAC and other user interfaces., (© 2024. The Author(s).)

General circulation models (GCMs) are the foundation of weather and climate prediction 1,2 . 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 forecasting 3,4 . 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., (© 2024. The Author(s).)

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., Competing Interests: Competing interests statement:M.P.B. is an employee Google Research and S.S.S. an employee of OpenAI.

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., Competing Interests: Competing interests statement:P.N. and M.P.B. are employees and hold stock ownership in Google, a company that makes machine learning technology.

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.

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., (© 2023. The Author(s).)

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.

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., (© 2023. The Author(s).)

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 ., (© 2023. Springer Science+Business Media, LLC, part of Springer Nature.)

Objects that deform a liquid interface are subject to capillary forces, which can be harnessed to assemble the objects 1-4 . 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 forces 5,6 , 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., (© 2022. The Author(s), under exclusive licence to Springer Nature Limited.)

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.

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.

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., (© 2022. The Author(s).)

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., (© 2022. The Author(s).)

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.

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.

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., Competing Interests: The authors declare no competing interest.

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., Competing Interests: The authors have declared that no competing interests exist.

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., Competing Interests: At the time of work, SFP, JG, DW, SN, RL, BF, MB, SS, MDE, MKB, VK, ARM, SS, MP, NS, LJM, PV, RMC, VM, VSL, and MF were employees of and owned equity in Verily Life Sciences. While this manuscript does not explicitly mention Verily’s Healthy At Work program, the models presented herein are used in that program.

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., Competing Interests: The authors declare no competing interest., (Copyright © 2021 the Author(s). Published by PNAS.)

Numerical simulation of fluids plays an essential role in modeling many physical phenomena, such as weather, climate, aerodynamics, and plasma physics. Fluids are well described by the Navier-Stokes equations, but solving these equations at scale remains daunting, limited by the computational cost of resolving the smallest spatiotemporal features. This leads to unfavorable trade-offs between accuracy and tractability. Here we use end-to-end deep learning to improve approximations inside computational fluid dynamics for modeling two-dimensional turbulent flows. For both direct numerical simulation of turbulence and large-eddy simulation, our results are as accurate as baseline solvers with 8 to 10× finer resolution in each spatial dimension, resulting in 40- to 80-fold computational speedups. Our method remains stable during long simulations and generalizes to forcing functions and Reynolds numbers outside of the flows where it is trained, in contrast to black-box machine-learning approaches. Our approach exemplifies how scientific computing can leverage machine learning and hardware accelerators to improve simulations without sacrificing accuracy or generalization., Competing Interests: Competing interest statement: The authors are employees of Google, which sells hardware and software for machine learning. A patent filing has been submitted based on this work., (Copyright © 2021 the Author(s). Published by PNAS.)

Most velocimetry approaches for fluid flows measure linear components of the velocity vector; yet, the angular velocity components, particularly at small scales in turbulent flows, also need to be resolved to study energy transfer and other important flow characteristics. Here, we detail an optical sensor approach to determine a component of the angular velocity vector. This approach uses beams of structured light and a machine learning-based analysis. We discuss the methodology to train the machine learning model and test it in experimentally validated simulations. This approach represents an interesting new direction for fluid flow velocimetry which may be extended to sense other flow parameters by selecting different light structures.

Gene expression profiles of a cellular population, generated by single-cell RNA sequencing, contains rich information about biological state, including cell type, cell cycle phase, gene regulatory patterns, and location within the tissue of origin. A major challenge is to disentangle information about these different biological states from each other, including distinguishing from cell lineage, since the correlation of cellular expression patterns is necessarily contaminated by ancestry. Here, we use a recent advance in random matrix theory, discovered in the context of protein phylogeny, to identify differentiation or ancestry-related processes in single-cell data. Qin and Colwell [C. Qin, L. J. Colwell, Proc. Natl. Acad. Sci. U.S.A. 115, 690-695 (2018)] showed that ancestral relationships in protein sequences create a power-law signature in the covariance eigenvalue distribution. We demonstrate the existence of such signatures in scRNA-seq data and that the genes driving them are indeed related to differentiation and developmental pathways. We predict the existence of similar power-law signatures for cells along linear trajectories and demonstrate this for linearly differentiating systems. Furthermore, we generalize to show that the same signatures can arise for cells along tissue-specific spatial trajectories. We illustrate these principles in diverse tissues and organisms, including the mammalian epidermis and lung, Drosophila whole-embryo, adult Hydra , dendritic cells, the intestinal epithelium, and cells undergoing induced pluripotent stem cells (iPSC) reprogramming. We show how these results can be used to interpret the gradual dynamics of lineage structure along iPSC reprogramming. Together, we provide a framework that can be used to identify signatures of specific biological processes in single-cell data without prior knowledge and identify candidate genes associated with these processes., Competing Interests: The authors declare no competing interest., (Copyright © 2021 the Author(s). Published by PNAS.)

The inverse problem of designing component interactions to target emergent structure is fundamental to numerous applications in biotechnology, materials science, and statistical physics. Equally important is the inverse problem of designing emergent kinetics, but this has received considerably less attention. Using recent advances in automatic differentiation, we show how kinetic pathways can be precisely designed by directly differentiating through statistical physics models, namely free energy calculations and molecular dynamics simulations. We consider two systems that are crucial to our understanding of structural self-assembly: bulk crystallization and small nanoclusters. In each case, we are able to assemble precise dynamical features. Using gradient information, we manipulate interactions among constituent particles to tune the rate at which these systems yield specific structures of interest. Moreover, we use this approach to learn nontrivial features about the high-dimensional design space, allowing us to accurately predict when multiple kinetic features can be simultaneously and independently controlled. These results provide a concrete and generalizable foundation for studying nonstructural self-assembly, including kinetic properties as well as other complex emergent properties, in a vast array of systems., Competing Interests: The authors declare no competing interest., (Copyright © 2021 the Author(s). Published by PNAS.)

Recent advances in synthetic posttranslational protein circuits are substantially impacting the landscape of cellular engineering and offer several advantages compared to traditional gene circuits. However, engineering dynamic phenomena such as oscillations in protein-level circuits remains an outstanding challenge. Few examples of biological posttranslational oscillators are known, necessitating theoretical progress to determine realizable oscillators. We construct mathematical models for two posttranslational oscillators, using few components that interact only through reversible binding and phosphorylation/dephosphorylation reactions. Our designed oscillators rely on the self-assembly of two protein species into multimeric functional enzymes that respectively inhibit and enhance this self-assembly. We limit our analysis to within experimental constraints, finding (i) significant portions of the restricted parameter space yielding oscillations and (ii) that oscillation periods can be tuned by several orders of magnitude using recent advances in computational protein design. Our work paves the way for the rational design and realization of protein-based dynamic systems., (Copyright © 2020 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution License 4.0 (CC BY).)

The essence of turbulent flow is the conveyance of energy through the formation, interaction, and destruction of eddies over a wide range of spatial scales-from the largest scales where energy is injected down to the smallest scales where it is dissipated through viscosity. Currently, there is no mechanistic framework that captures how the interactions of vortices drive this cascade. We show that iterations of the elliptical instability, arising from the interactions between counter-rotating vortices, lead to the emergence of turbulence. We demonstrate how the nonlinear development of the elliptical instability generates an ordered array of antiparallel secondary filaments. The secondary filaments mutually interact, leading to the formation of even smaller tertiary filaments. In experiments and simulations, we observe two and three iterations of this cascade, respectively. Our observations indicate that the elliptical instability could be one of the fundamental mechanisms by which the turbulent cascade develops., (Copyright © 2020 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC).)

Collagen consists of three peptides twisted together through a periodic array of hydrogen bonds. Here we use this as inspiration to find design rules for programmed specific interactions for self-assembling synthetic collagenlike triple helices, starting from disordered configurations. The assembly generically nucleates defects in the triple helix, the characteristics of which can be manipulated by spatially varying the enthalpy of helix formation. Defect formation slows assembly, evoking kinetic pathologies that have been observed to mutations in the primary collagen amino acid sequence. The controlled formation and interaction between defects gives a route for hierarchical self-assembly of bundles of twisted filaments.

Programmable self-assembly of smart, digital, and structurally complex materials from simple components at size scales from the macro to the nano remains a long-standing goal of material science. Here, we introduce a platform based on magnetic encoding of information to drive programmable self-assembly that works across length scales. Our building blocks consist of panels with different patterns of magnetic dipoles that are capable of specific binding. Because the ratios of the different panel-binding energies are scale-invariant, this approach can, in principle, be applied down to the nanometer scale. Using a centimeter-sized version of these panels, we demonstrate 3 canonical hallmarks of assembly: controlled polymerization of individual building blocks; assembly of 1-dimensional strands made of panels connected by elastic backbones into secondary structures; and hierarchical assembly of 2-dimensional nets into 3-dimensional objects. We envision that magnetic encoding of assembly instructions into primary structures of panels, strands, and nets will lead to the formation of secondary and even tertiary structures that transmit information, act as mechanical elements, or function as machines on scales ranging from the nano to the macro., Competing Interests: The authors declare no competing interest., (Copyright © 2019 the Author(s). Published by PNAS.)

Neuronal activity induces changes in blood flow by locally dilating vessels in the brain microvasculature. How can the local dilation of a single vessel increase flow-based metabolite supply, given that flows are globally coupled within microvasculature? Solving the supply dynamics for rat brain microvasculature, we find one parameter regime to dominate physiologically. This regime allows for robust increase in supply independent of the position in the network, which we explain analytically. We show that local coupling of vessels promotes spatially correlated increased supply by dilation.

The accurate prediction of RNA secondary structure from primary sequence has had enormous impact on research from the past 40 years. Although many algorithms are available to make these predictions, the inclusion of non-nested loops, termed pseudoknots, still poses challenges arising from two main factors: 1) no physical model exists to estimate the loop entropies of complex intramolecular pseudoknots, and 2) their NP-complete enumeration has impeded their study. Here, we address both challenges. First, we develop a polymer physics model that can address arbitrarily complex pseudoknots using only two parameters corresponding to concrete physical quantities-over an order of magnitude fewer than the sparsest state-of-the-art phenomenological methods. Second, by coupling this model to exhaustive enumeration of the set of possible structures, we compute the entire free energy landscape of secondary structures resulting from a primary RNA sequence. We demonstrate that for RNA structures of ∼80 nucleotides, with minimal heuristics, the complete enumeration of possible secondary structures can be accomplished quickly despite the NP-complete nature of the problem. We further show that despite our loop entropy model's parametric sparsity, it performs better than or on par with previously published methods in predicting both pseudoknotted and non-pseudoknotted structures on a benchmark data set of RNA structures of ≤80 nucleotides. We suggest ways in which the accuracy of the model can be further improved., (Copyright © 2019 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

The numerical solution of partial differential equations (PDEs) is challenging because of the need to resolve spatiotemporal features over wide length- and timescales. Often, it is computationally intractable to resolve the finest features in the solution. The only recourse is to use approximate coarse-grained representations, which aim to accurately represent long-wavelength dynamics while properly accounting for unresolved small-scale physics. Deriving such coarse-grained equations is notoriously difficult and often ad hoc. Here we introduce data-driven discretization, a method for learning optimized approximations to PDEs based on actual solutions to the known underlying equations. Our approach uses neural networks to estimate spatial derivatives, which are optimized end to end to best satisfy the equations on a low-resolution grid. The resulting numerical methods are remarkably accurate, allowing us to integrate in time a collection of nonlinear equations in 1 spatial dimension at resolutions 4× to 8× coarser than is possible with standard finite-difference methods., Competing Interests: The authors declare no conflict of interest., (Copyright © 2019 the Author(s). Published by PNAS.)

Deep neural networks have achieved state-of-the-art accuracy at classifying molecules with respect to whether they bind to specific protein targets. A key breakthrough would occur if these models could reveal the fragment pharmacophores that are causally involved in binding. Extracting chemical details of binding from the networks could enable scientific discoveries about the mechanisms of drug actions. However, doing so requires shining light into the black box that is the trained neural network model, a task that has proved difficult across many domains. Here we show how the binding mechanism learned by deep neural network models can be interrogated, using a recently described attribution method. We first work with carefully constructed synthetic datasets, in which the molecular features responsible for "binding" are fully known. We find that networks that achieve perfect accuracy on held-out test datasets still learn spurious correlations, and we are able to exploit this nonrobustness to construct adversarial examples that fool the model. This makes these models unreliable for accurately revealing information about the mechanisms of protein-ligand binding. In light of our findings, we prescribe a test that checks whether a hypothesized mechanism can be learned. If the test fails, it indicates that the model must be simplified or regularized and/or that the training dataset requires augmentation., Competing Interests: The authors declare no conflict of interest.

Creating a selective gel that filters particles based on their interactions is a major goal of nanotechnology, with far-reaching implications from drug delivery to controlling assembly pathways. However, this is particularly difficult when the particles are larger than the gel's characteristic mesh size because such particles cannot passively pass through the gel. Thus, filtering requires the interacting particles to transiently reorganize the gel's internal structure. While significant advances, e.g., in DNA engineering, have enabled the design of nano-materials with programmable interactions, it is not clear what physical principles such a designer gel could exploit to achieve selective permeability. We present an equilibrium mechanism where crosslink binding dynamics are affected by interacting particles such that particle diffusion is enhanced. In addition to revealing specific design rules for manufacturing selective gels, our results have the potential to explain the origin of selective permeability in certain biological materials, including the nuclear pore complex.

Lichens fix carbon dioxide from the air to build biomass. Crustose and foliose lichens grow as nearly flat, circular disks. Smaller individuals grow slowly, but with small, steady increases in radial growth rate over time. Larger individuals grow more quickly and with a roughly constant radial velocity maintained over the lifetime of the lichen. We translate the coffee drop effect to model lichen growth and demonstrate that growth patterns follow directly from the diffusion of carbon dioxide in the air around a lichen. When a lichen is small, carbon dioxide is fixed across its surface, and the entire thallus contributes to radial growth, but when a lichen is larger carbon dioxide is disproportionately fixed at the edges of an individual, which are the primary drivers of growth. Tests of the model against data suggest it provides an accurate, robust, and universal framework for understanding the growth dynamics of both large and small lichens in nature., (© 2018 The Authors.)

A ubiquitous feature of bacterial communities is the existence of spatial structures. These are often coupled to metabolism, whereby the spatial organization can improve chemical reaction efficiency. However, it is not clear whether or how a desired colony configuration, for example, one that optimizes some overall global objective, could be achieved by individual cells that do not have knowledge of their positions or of the states of all other cells. By using a model which consists of cells producing enzymes that catalyze coupled metabolic reactions, we show that simple, local rules can be sufficient for achieving a global, community-level goal. In particular, even though the optimal configuration varies with colony size, we demonstrate that cells regulating their relative enzyme levels based solely on local metabolite concentrations can maintain the desired overall spatial structure during colony growth. We also show that these rules can be very simple and hence easily implemented by cells. Our framework also predicts scenarios where additional signaling mechanisms may be required., Competing Interests: The authors declare no conflict of interest.

The nasal cavity is a vital component of the respiratory system that heats and humidifies inhaled air in all vertebrates. Despite this common function, the shapes of nasal cavities vary widely across animals. To understand this variability, we here connect nasal geometry to its function by theoretically studying the airflow and the associated scalar exchange that describes heating and humidification. We find that optimal geometries, which have minimal resistance for a given exchange efficiency, have a constant gap width between their side walls, while their overall shape can adhere to the geometric constraints imposed by the head. Our theory explains the geometric variations of natural nasal cavities quantitatively, and we hypothesize that the trade-off between high exchange efficiency and low resistance to airflow is the main driving force shaping the nasal cavity. Our model further explains why humans, whose nasal cavities evolved to be smaller than expected for their size, become obligate oral breathers in aerobically challenging situations., Competing Interests: The authors declare no conflict of interest.

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.

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.

The relationship between the microstructure of a porous medium and the observed flow distribution is still a puzzle. We resolve it with an analytical model, where the local correlations between adjacent pores, which determine the distribution of flows propagated from one pore downstream, predict the flow distribution. Numerical simulations of a two-dimensional porous medium verify the model and clearly show the transition of flow distributions from δ-function-like via Gaussians to exponential with increasing disorder. Comparison to experimental data further verifies our numerical approach.

Complex behaviors are typically associated with animals, but the capacity to integrate information and function as a coordinated individual is also a ubiquitous but poorly understood feature of organisms such as slime molds and fungi. Plasmodial slime molds grow as networks and use flexible, undifferentiated body plans to forage for food. How an individual communicates across its network remains a puzzle, but Physarum polycephalum has emerged as a novel model used to explore emergent dynamics. Within P. polycephalum , cytoplasm is shuttled in a peristaltic wave driven by cross-sectional contractions of tubes. We first track P. polycephalum 's response to a localized nutrient stimulus and observe a front of increased contraction. The front propagates with a velocity comparable to the flow-driven dispersion of particles. We build a mathematical model based on these data and in the aggregate experiments and model identify the mechanism of signal propagation across a body: The nutrient stimulus triggers the release of a signaling molecule. The molecule is advected by fluid flows but simultaneously hijacks flow generation by causing local increases in contraction amplitude as it travels. The molecule is initiating a feedback loop to enable its own movement. This mechanism explains previously puzzling phenomena, including the adaptation of the peristaltic wave to organism size and P. polycephalum 's ability to find the shortest route between food sources. A simple feedback seems to give rise to P. polycephalum 's complex behaviors, and the same mechanism is likely to function in the thousands of additional species with similar behaviors., Competing Interests: The authors declare no conflict of interest.

Colloidal particles endowed with specific time-dependent interactions are a promising route for realizing artificial materials that have the properties of living ones. Previous work has demonstrated how this system can give rise to self-replication. Here, we introduce the process of colloidal catalysis, in which clusters of particles catalyze the creation of other clusters through templating reactions. Surprisingly, we find that simple templating rules generically lead to the production of huge numbers of clusters. The templating reactions among this sea of clusters give rise to an exponentially growing catalytic cycle, a specific realization of Dyson's notion of an exponentially growing metabolism. We demonstrate this behavior with a fixed set of interactions between particles chosen to allow a catalysis of a specific six-particle cluster from a specific seven-particle cluster, yet giving rise to the catalytic production of a sea of clusters of sizes between 2 and 11 particles. The fact that an exponentially growing cycle emerges naturally from such a simple scheme demonstrates that the emergence of exponentially growing metabolisms could be simpler than previously imagined., Competing Interests: The authors declare no conflict of interest.

Many powders employed in the food and pharmaceutical industries are produced through spray drying because it is a cost efficient process that offers control over the particle size. However, most commercially available spray-driers cannot produce drops with diameters below 1 μm, limiting the size of spray-dried particles to values above 300 nm. We recently developed a microfluidic spray-drier that can form much smaller drops than commercially available spray-driers. This is achieved through a two-step process: first, the microfluidic spray-drier operates in the dripping regime to form 100 μm diameter primary drops in air and, second, subjects them to high shear stresses due to supersonic flow of air to break them into many much smaller secondary drops. In this paper, we describe the two essential steps required to form sub-μm diameter airborne drops inside microfluidic channels. We investigate the influence of the device geometry on the ability to operate the microfluidic spray-drier in the dripping regime. Moreover, we describe how these primary drops are nebulized into many secondary drops that are much smaller than the smallest dimension of the spray-drier channels.