Biophysics of molecular gastronomy.

Chefs and scientists exploring biophysical processes have given rise to molecular gastronomy. In this Commentary, we describe how a scientific understanding of recipes and techniques facilitates the development of new textures and expands the flavor palette. The new dishes that result engage our senses in unexpected ways. PAPERCLIP.

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 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.

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.

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.

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.

Revealing lineage-related signals in single-cell gene expression using random matrix theory.

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.

Machine learning-accelerated computational fluid dynamics.

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.

Designing self-assembling kinetics with differentiable statistical physics models.

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.

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.

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.

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.

Using attribution to decode binding mechanism in neural network models for chemistry.

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.

Learning data-driven discretizations for partial differential equations.

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.

Magnetic handshake materials as a scale-invariant platform for programmed self-assembly.

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.

Local growth rules can maintain metabolically efficient spatial structure throughout growth.

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.

Physical and geometric constraints shape the labyrinth-like nasal cavity.

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.

Spontaneous emergence of catalytic cycles with colloidal spheres.

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.

Using active colloids as machines to weave and braid on the micrometer scale.

Controlling motion at the microscopic scale is a fundamental goal in the development of biologically inspired systems. We show that the motion of active, self-propelled colloids can be sufficiently controlled for use as a tool to assemble complex structures such as braids and weaves out of microscopic filaments. Unlike typical self-assembly paradigms, these structures are held together by geometric constraints rather than adhesive bonds. The out-of-equilibrium assembly that we propose involves precisely controlling the 2D motion of active colloids so that their path has a nontrivial topology. We demonstrate with proof-of-principle Brownian dynamics simulations that, when the colloids are attached to long semiflexible filaments, this motion causes the filaments to braid. The ability of the active particles to provide sufficient force necessary to bend the filaments into a braid depends on a number of factors, including the self-propulsion mechanism, the properties of the filament, and the maximum curvature in the braid. Our work demonstrates that nonequilibrium assembly pathways can be designed using active particles.