Dissection and integration of bursty transcriptional dynamics for complex systems.

RNA velocity estimation is a potentially powerful tool to reveal the directionality of transcriptional changes in single-cell RNA-sequencing data, but it lacks accuracy, absent advanced metabolic labeling techniques. We developed an approach, TopicVelo, that disentangles simultaneous, yet distinct, dynamics by using a probabilistic topic model, a highly interpretable form of latent space factorization, to infer cells and genes associated with individual processes, thereby capturing cellular pluripotency or multifaceted functionality. Focusing on process-associated cells and genes enables accurate estimation of process-specific velocities via a master equation for a transcriptional burst model accounting for intrinsic stochasticity. The method obtains a global transition matrix by leveraging cell topic weights to integrate process-specific signals. In challenging systems, this method accurately recovers complex transitions and terminal states, while our use of first-passage time analysis provides insights into transient transitions. These results expand the limits of RNA velocity, empowering future studies of cell fate and functional responses.

Active oscillatory associative memory.

Traditionally, physical models of associative memory assume conditions of equilibrium. Here, we consider a prototypical oscillator model of associative memory and study how active noise sources that drive the system out of equilibrium, as well as nonlinearities in the interactions between the oscillators, affect the associative memory properties of the system. Our simulations show that pattern retrieval under active noise is more robust to the number of learned patterns and noise intensity than under passive noise. To understand this phenomenon, we analytically derive an effective energy correction due to the temporal correlations of active noise in the limit of short correlation decay time. We find that active noise deepens the energy wells corresponding to the patterns by strengthening the oscillator couplings, where the more nonlinear interactions are preferentially enhanced. Using replica theory, we demonstrate qualitative agreement between this effective picture and the retrieval simulations. Our work suggests that the nonlinearity in the oscillator couplings can improve memory under nonequilibrium conditions.

Cluster-Spin-Glass Magnetic Behavior and Morphology in the Coordination Polymer Alloys FeyCo1-yBTT.

We report the synthesis of a series of pseudo-1D coordination polymer (CP) materials with the formula FeyCo1-yBTT (BTT = 1,3,5-benzenetrithiolate). These materials were structurally characterized by PXRD Rietveld, EXAFS, and PDF analyses, revealing that the CP superstructure enables a continuous and isomorphous alloy between the two homometallic compounds. Lower Fe loadings exhibit emergent spin glass magnetic behavior, such as memory effects and composition-dependent spin glass response time constants ranging from 6.9 × 10-9 s to 1.8 × 10-6 s. These data are consistent with the formation of spin clusters within the lattice. The magnetic behavior in these materials was modeled via replica exchange Monte Carlo simulation, which provides a good match for the experimentally measured spin glassing and magnetic phase transitions. These findings underscore how the rigid superstructure of CP and MOF scaffolds can enable the systematic tuning of physical properties, such as the spin glass behavior described here.

Dissection and Integration of Bursty Transcriptional Dynamics for Complex Systems.

RNA velocity estimation is a potentially powerful tool to reveal the directionality of transcriptional changes in single-cell RNA-seq data, but it lacks accuracy, absent advanced metabolic labeling techniques. We developed a novel approach, TopicVelo, that disentangles simultaneous, yet distinct, dynamics by using a probabilistic topic model, a highly interpretable form of latent space factorization, to infer cells and genes associated with individual processes, thereby capturing cellular pluripotency or multifaceted functionality. Focusing on process-associated cells and genes enables accurate estimation of process-specific velocities via a master equation for a transcriptional burst model accounting for intrinsic stochasticity. The method obtains a global transition matrix by leveraging cell topic weights to integrate process-specific signals. In challenging systems, this method accurately recovers complex transitions and terminal states, while our novel use of first-passage time analysis provides insights into transient transitions. These results expand the limits of RNA velocity, empowering future studies of cell fate and functional responses.

A unified model for the dynamics of ATP-independent ultrafast contraction.

In nature, several ciliated protists possess the remarkable ability to execute ultrafast motions using protein assemblies called myonemes, which contract in response to Ca2+ ions. Existing theories, such as actomyosin contractility and macroscopic biomechanical latches, do not adequately describe these systems, necessitating development of models to understand their mechanisms. In this study, we image and quantitatively analyze the contractile kinematics observed in two ciliated protists (Vorticella sp. and Spirostomum sp.), and, based on the mechanochemistry of these organisms, we propose a minimal mathematical model that reproduces our observations as well as those published previously. Analyzing the model reveals three distinct dynamic regimes, differentiated by the rate of chemical driving and the importance of inertia. We characterize their unique scaling behaviors and kinematic signatures. Besides providing insights into Ca2+-powered myoneme contraction in protists, our work may also inform the rational design of ultrafast bioengineered systems such as active synthetic cells.

Direct synthesis and chemical vapor deposition of 2D carbide and nitride MXenes.

Two-dimensional transition-metal carbides and nitrides (MXenes) are a large family of materials actively studied for various applications, especially in the field of energy storage. MXenes are commonly synthesized by etching the layered ternary compounds, called MAX phases. We demonstrate a direct synthetic route for scalable and atom-economic synthesis of MXenes, including compounds that have not been synthesized from MAX phases, by the reactions of metals and metal halides with graphite, methane, or nitrogen. The direct synthesis enables chemical vapor deposition growth of MXene carpets and complex spherulite-like morphologies that form through buckling and release of MXene carpet to expose fresh surface for further reaction. The directly synthesized MXenes showed excellent energy storage capacity for lithium-ion intercalation.

Giant Gateable Osmotic Power Generation from a Goldilocks Two-Dimensional Polymer.

Generating electricity from a salinity gradient, known as osmotic power, provides a sustainable energy source, but it requires precise nanoscale control of membranes for maximum performance. Here, we report an ultrathin membrane, where molecule-specific short-range interactions enable giant gateable osmotic power with a record high power density (2 kW/m2 for 1 M∥1 mM KCl). Our membranes are charge-neutral two-dimensional polymers synthesized from molecular building blocks and operate in a Goldilocks regime that simultaneously maintains high ionic conductivity and permselectivity. Molecular dynamics simulations quantitatively confirm that the functionalized nanopores are small enough for high selectivity through short-range ion-membrane interactions and large enough for fast cross-membrane transport. The short-range mechanism further enables reversible gateable operation, as demonstrated by polarity switching of osmotic power with additional gating ions.

Simulating structured fluids with tensorial viscoelasticity.

We consider an immersed elastic body that is actively driven through a structured fluid by a motor or an external force. The behavior of such a system generally cannot be solved analytically, necessitating the use of numerical methods. However, current numerical methods omit important details of the microscopic structure and dynamics of the fluid, which can modulate the magnitudes and directions of viscoelastic restoring forces. To address this issue, we develop a simulation platform for modeling viscoelastic media with tensorial elasticity. We build on the lattice Boltzmann algorithm and incorporate viscoelastic forces, elastic immersed objects, a microscopic orientation field, and coupling between viscoelasticity and the orientation field. We demonstrate our method by characterizing how the viscoelastic restoring force on a driven immersed object depends on various key parameters as well as the tensorial character of the elastic response. We find that the restoring force depends non-monotonically on the rate of diffusion of the stress and the size of the object. We further show how the restoring force depends on the relative orientation of the microscopic structure and the pulling direction. These results imply that accounting for previously neglected physical features, such as stress diffusion and the microscopic orientation field, can improve the realism of viscoelastic simulations. We discuss possible applications and extensions to the method.

Remembering the Work of Phillip L. Geissler: A Coda to His Scientific Trajectory.

Phillip L. Geissler made important contributions to the statistical mechanics of biological polymers, heterogeneous materials, and chemical dynamics in aqueous environments. He devised analytical and computational methods that revealed the underlying organization of complex systems at the frontiers of biology, chemistry, and materials science. In this retrospective we celebrate his work at these frontiers.

Thermodynamic Control of Activity Patterns in Cytoskeletal Networks.

Biological materials, such as the actin cytoskeleton, exhibit remarkable structural adaptability to various external stimuli by consuming different amounts of energy. In this Letter, we use methods from large deviation theory to identify a thermodynamic control principle for structural transitions in a model cytoskeletal network. Specifically, we demonstrate that biasing the dynamics with respect to the work done by nonequilibrium components effectively renormalizes the interaction strength between such components, which can eventually result in a morphological transition. Our work demonstrates how a thermodynamic quantity can be used to renormalize effective interactions, which in turn can tune structure in a predictable manner, suggesting a thermodynamic principle for the control of cytoskeletal structure and dynamics.

From predicting to learning dissipation from pair correlations of active liquids.

Active systems, which are driven out of equilibrium by local non-conservative forces, can adopt unique behaviors and configurations. An important challenge in the design of novel materials, which utilize such properties, is to precisely connect the static structure of active systems to the dissipation of energy induced by the local driving. Here, we use tools from liquid-state theories and machine learning to take on this challenge. We first analytically demonstrate for an isotropic active matter system that dissipation and pair correlations are closely related when driving forces behave like an active temperature. We then extend a nonequilibrium mean-field framework for predicting these pair correlations, which unlike most existing approaches is applicable even for strongly interacting particles and far from equilibrium, to predicting dissipation in these systems. Based on this theory, we reveal a robust analytic relation between dissipation and structure, which holds even as the system approaches a nonequilibrium phase transition. Finally, we construct a neural network that maps static configurations of particles to their dissipation rate without any prior knowledge of the underlying dynamics. Our results open novel perspectives on the interplay between dissipation and organization out of equilibrium.

Mean-field theory for the structure of strongly interacting active liquids.

Active systems, which are driven out of equilibrium by local non-conservative forces, exhibit unique behaviors and structures with potential utility for the design of novel materials. An important and difficult challenge along the path toward this goal is to precisely predict how the structure of active systems is modified as their driving forces push them out of equilibrium. Here, we use tools from liquid-state theories to approach this challenge for a classic minimal active matter model. First, we construct a nonequilibrium mean-field framework that can predict the structure of systems of weakly interacting particles. Second, motivated by equilibrium solvation theories, we modify this theory to extend it with surprisingly high accuracy to systems of strongly interacting particles, distinguishing it from most existing similarly tractable approaches. Our results provide insight into spatial organization in strongly interacting out-of-equilibrium systems.

Mechanism for the Generation of Robust Circadian Oscillations through Ultransensitivity and Differential Binding Affinity.

Biochemical circadian rhythm oscillations play an important role in many signaling mechanisms. In this work, we explore some of the biophysical mechanisms responsible for sustaining robust oscillations by constructing a minimal but analytically tractable model of the circadian oscillations in the KaiABC protein system found in the cyanobacteria S. elongatus. In particular, our minimal model explicitly accounts for two experimentally characterized biophysical features of the KaiABC protein system, namely, a differential binding affinity and an ultrasensitive response. Our analytical work shows how these mechanisms might be crucial for promoting robust oscillations even in suboptimal nutrient conditions. Our analytical and numerical work also identifies mechanisms by which biological clocks can stably maintain a constant time period under a variety of nutrient conditions. Finally, our work also explores the thermodynamic costs associated with the generation of robust sustained oscillations and shows that the net rate of entropy production alone might not be a good figure of merit to asses the quality of oscillations.

A strong nonequilibrium bound for sorting of cross-linkers on growing biopolymers.

Understanding the role of nonequilibrium driving in self-organization is crucial for developing a predictive description of biological systems, yet it is impeded by their complexity. The actin cytoskeleton serves as a paradigm for how equilibrium and nonequilibrium forces combine to give rise to self-organization. Motivated by recent experiments that show that actin filament growth rates can tune the morphology of a growing actin bundle cross-linked by two competing types of actin-binding proteins [S. L. Freedman et al., Proc. Natl. Acad. Sci. U.S.A. 116, 16192-16197 (2019)], we construct a minimal model for such a system and show that the dynamics of a growing actin bundle are subject to a set of thermodynamic constraints that relate its nonequilibrium driving, morphology, and molecular fluxes. The thermodynamic constraints reveal the importance of correlations between these molecular fluxes and offer a route to estimating microscopic driving forces from microscopy experiments.

Energy rectification in active gyroscopic networks under time-periodic modulations.

Combinations of gyroscopic forces and nonequilibrium activity have been explored recently in rectifying energy in networks with complex geometries and topologies [Phys. Rev. X 10, 021036 (2020)2160-330810.1103/PhysRevX.10.021036]. Based on this previous work, here we study the effect of added time-periodic modulations. Numerical calculations show that the time-modulated network generates net energy transport between sites and the surroundings, even in the absence of any temperature gradients. Combining path integral formulation and diagrammatic expansion, we explain how such anomalous energy transport emerges, and show how the transport pattern in complex networks can be connected to relatively simple local structures.

Tuning shape and internal structure of protein droplets via biopolymer filaments.

Macromolecules can phase separate to form liquid condensates, which are emerging as critical compartments in fields as diverse as intracellular organization and soft materials design. A myriad of macromolecules, including the protein FUS, form condensates which behave as isotropic liquids. Here, we investigate the influence of filament dopants on the material properties of protein liquids. We find that the short, biopolymer filaments of actin spontaneously partition into FUS droplets to form composite liquid droplets. As the concentration of the filament dopants increases, the coalescence time decreases, indicating that the dopants control viscosity relative to surface tension. The droplet shape is tunable and ranges from spherical to tactoid as the filament length or concentration is increased. We find that the tactoids are well described by a model of a quasi bipolar liquid crystal droplet, where nematic order from the anisotropic actin filaments competes with isotropic interfacial energy from the FUS, controlling droplet shape in a size-dependent manner. Our results demonstrate a versatile approach to construct tunable, anisotropic macromolecular liquids.

Nucleation and shape dynamics of model nematic tactoids around adhesive colloids.

Recent experiments have shown how nematically ordered tactoid shaped actin droplets can be reorganized and divided by the action of myosin molecular motors. In this paper, we consider how similar morphological changes can potentially be achieved under equilibrium conditions. Using simulations, both atomistic and continuum, and a simple macroscopic model, we explore how the nucleation dynamics, shape changes, and the final steady state of a nematic tactoid droplet can be modified by interactions with model adhesive colloids that mimic a myosin motor cluster. We show how tactoid reorganization may occur in an equilibrium colloidal-nematic setting. We then suggest based on the simple macroscopic model how the simulation models may be extended to potentially stabilize divided tactoids.

High chemical affinity increases the robustness of biochemical oscillations.

Biochemical oscillations are ubiquitous in nature and allow organisms to properly time their biological functions. In this paper, we consider minimal Markov state models of nonequilibrium biochemical networks that support oscillations. We obtain analytical expressions for the coherence and period of oscillations in these networks. These quantities are expected to depend on all details of the transition rates in the Markov state model. However, our analytical calculations reveal that driving the system out of equilibrium makes many of these details-specifically, the location and arrangement of the transition rates-irrelevant to the coherence and period of oscillations. This theoretical prediction is confirmed by excellent agreement with numerical results. As a consequence, the coherence and period of oscillations can be robustly maintained in the presence of fluctuations in the irrelevant variables. While recent work has established that increasing energy consumption improves the coherence of oscillations, our findings suggest that it plays the additional role of making the coherence and the average period of oscillations robust to fluctuations in rates that can result from the noisy environment of the cell.

Robust oscillations in multi-cyclic Markov state models of biochemical clocks.

Organisms often use cyclic changes in the concentrations of chemical species to precisely time biological functions. Underlying these biochemical clocks are chemical reactions and transport processes, which are inherently stochastic. Understanding the physical basis for robust biochemical oscillations in the presence of fluctuations has thus emerged as an important problem. In a previous paper [C. del Junco and S. Vaikuntanathan, Phys. Rev. E 101, 012410 (2020)], we explored this question using the non-equilibrium statistical mechanics of single-ring Markov state models of biochemical networks that support oscillations. Our finding was that they can exploit non-equilibrium driving to robustly maintain the period and coherence of oscillations in the presence of randomness in the rates. Here, we extend our work to Markov state models consisting of a large cycle decorated with multiple small cycles. These additional cycles are intended to represent alternate pathways that the oscillator may take as it fluctuates about its average path. Combining a mapping to single-cycle networks based on first passage time distributions with our previously developed theory, we are able to make analytical predictions for the period and coherence of oscillations in these networks. One implication of our predictions is that a high energy budget can make different network topologies and arrangements of rates degenerate as far as the period and coherence of oscillations are concerned. Excellent agreement between analytical and numerical results confirms that this is the case. Our results suggest that biochemical oscillators can be more robust to fluctuations in the path of the oscillator when they have a high energy budget.

A mechanism for anomalous transport in chiral active liquids.

Chiral active fluids are known to have anomalous transport properties such as the so-called odd viscosity. In this paper, we provide a microscopic mechanism for how such anomalous transport coefficients can emerge. We construct an Irving-Kirkwood-type stress tensor for chiral liquids and express the transport coefficients in terms of orientation-averaged intermolecular forces and distortions of the pair correlation function induced by a flow field. We then show how anomalous transport properties can be expected naturally due to the presence of a transverse component in the orientation-averaged intermolecular forces and anomalous distortion modes of the pair correlation function between chiral active particles. We anticipate that our work can provide a microscopic framework to explain the transport properties of nonequilibrium chiral systems.