Drive-specific selection in multistable mechanical networks.

Systems with many stable configurations abound in nature, both in living and inanimate matter, encoding a rich variety of behaviors. In equilibrium, a multistable system is more likely to be found in configurations with lower energy, but the presence of an external drive can alter the relative stability of different configurations in unexpected ways. Living systems are examples par excellence of metastable nonequilibrium attractors whose structure and stability are highly dependent on the specific form and pattern of the energy flow sustaining them. Taking this distinctively lifelike behavior as inspiration, we sought to investigate the more general physical phenomenon of drive-specific selection in nonequilibrium dynamics. To do so, we numerically studied driven disordered mechanical networks of bistable springs possessing a vast number of stable configurations arising from the two stable rest lengths of each spring, thereby capturing the essential physical properties of a broad class of multistable systems. We found that there exists a range of forcing amplitudes for which the attractor states of driven disordered multistable mechanical networks are fine-tuned with respect to the pattern of external forcing to have low energy absorption from it. Additionally, we found that these drive-specific attractor states are further stabilized by precise matching between the multidimensional shape of their orbit and that of the potential energy well they inhabit. Lastly, we showed evidence of drive-specific selection in an experimental system and proposed a general method to estimate the range of drive amplitudes for drive-specific selection.

Self-organized computation in the far-from-equilibrium cell.

Recent progress in our understanding of the physics of self-organization in active matter has pointed to the possibility of spontaneous collective behaviors that effectively compute things about the patterns in the surrounding patterned environment. Here, we describe this progress and speculate about its implications for our understanding of the internal organization of the living cell.

Machine learning outperforms thermodynamics in measuring how well a many-body system learns a drive.

Diverse many-body systems, from soap bubbles to suspensions to polymers, learn and remember patterns in the drives that push them far from equilibrium. This learning may be leveraged for computation, memory, and engineering. Until now, many-body learning has been detected with thermodynamic properties, such as work absorption and strain. We progress beyond these macroscopic properties first defined for equilibrium contexts: We quantify statistical mechanical learning using representation learning, a machine-learning model in which information squeezes through a bottleneck. By calculating properties of the bottleneck, we measure four facets of many-body systems' learning: classification ability, memory capacity, discrimination ability, and novelty detection. Numerical simulations of a classical spin glass illustrate our technique. This toolkit exposes self-organization that eludes detection by thermodynamic measures: Our toolkit more reliably and more precisely detects and quantifies learning by matter while providing a unifying framework for many-body learning.

Low rattling: A predictive principle for self-organization in active collectives.

Self-organization is frequently observed in active collectives as varied as ant rafts and molecular motor assemblies. General principles describing self-organization away from equilibrium have been challenging to identify. We offer a unifying framework that models the behavior of complex systems as largely random while capturing their configuration-dependent response to external forcing. This allows derivation of a Boltzmann-like principle for understanding and manipulating driven self-organization. We validate our predictions experimentally, with the use of shape-changing robotic active matter, and outline a methodology for controlling collective behavior. Our findings highlight how emergent order depends sensitively on the matching between external patterns of forcing and internal dynamical response properties, pointing toward future approaches for the design and control of active particle mixtures and metamaterials.

Design of conditions for self-replication.

A "self-replicator" is usually understood to be an object of definite form that promotes the conversion of materials in its environment into a nearly identical copy of itself. The challenge of engineering novel, micro- or nanoscale self-replicators has attracted keen interest in recent years, both because exponential amplification is an attractive method for generating high yields of specific products and, also, because self-reproducing entities have the potential to be optimized or adapted through rounds of iterative selection. Substantial steps forward have been achieved both in the engineering of particular self-replicating molecules and in the characterization of the physical basis for possible mechanisms of self-replication. At present, however, there is a need for a theoretical treatment of what physical conditions are most conducive to the emergence of novel self-replicating structures from a reservoir of building blocks on a desired time scale. Here we report progress in addressing this need. By analyzing the kinetics of a toy chemical model, we demonstrate that the emergence of self-replication can be controlled by coarse, tunable features of the chemical system, such as the fraction of fast reactions and the width of the rate constant distribution. We also find that the typical mechanism is dominated by the cooperation of multiple interconnected reaction cycles as opposed to a single isolated cycle. The quantitative treatment presented here may prove useful for designing novel self-replicating chemical systems.

Nonequilibrium associative retrieval of multiple stored self-assembly targets.

Many biological systems rely on the ability to self-assemble different target structures using the same set of components. Equilibrium self-assembly suffers from a limited capacity in such cases, due to an increasing number of decoy states that grows rapidly with the number of targets encoded. Moreover, improving the kinetic stability of a target at equilibrium carries the price of introducing kinetic traps, leading to slower assembly. Using a toy physical model of interacting particles, we demonstrate that local driving can improve both the assembly time and kinetic stability of multitarget self-assembly, as well as reduce fluctuations around the target configuration. We further show that the local drive can result in a steady-state probability distribution over target structures that deviates from the Boltzmann distribution in a way that depends on the types of interactions that stabilize the targets. Our results illustrate the role that nonequilibrium driving plays in overcoming tradeoffs that are inherent to equilibrium assemblies.

Active regeneration unites high- and low-temperature features in cooperative self-assembly.

Cytoskeletal filaments are capable of self-assembly in the absence of externally supplied chemical energy, but the rapid turnover rates essential for their biological function require a constant flux of adenosine triphosphate (ATP) or guanosine triphosphate (GTP) hydrolysis. The same is true for two-dimensional protein assemblies employed in the formation of vesicles from cellular membranes, which rely on ATP-hydrolyzing enzymes to rapidly disassemble upon completion of the process. Recent observations suggest that the nucleolus, p granules, and other three-dimensional membraneless organelles may also demand dissipation of chemical energy to maintain their fluidity. Cooperative binding plays a crucial role in the dynamics of these higher-dimensional structures, but is absent from classic models of one-dimensional cytoskeletal assembly. In this paper, we present a thermodynamically consistent model of active regeneration with cooperative assembly, and compute the maximum turnover rate and minimum disassembly time as a function of the chemical driving force and the binding energy. We find that these driven structures resemble different equilibrium states above and below the nucleation barrier. In particular, we show that the maximal acceleration under large binding energies unites infinite-temperature local fluctuations with low-temperature nucleation kinetics.

Self-Organized Resonance during Search of a Diverse Chemical Space.

Recent studies of active matter have stimulated interest in the driven self-assembly of complex structures. Phenomenological modeling of particular examples has yielded insight, but general thermodynamic principles unifying the rich diversity of behaviors observed have been elusive. Here, we study the stochastic search of a toy chemical space by a collection of reacting Brownian particles subject to periodic forcing. We observe the emergence of an adaptive resonance in the system matched to the drive frequency, and show that the increased work absorption by these resonant structures is key to their stabilization. Our findings are consistent with a recently proposed thermodynamic mechanism for far-from-equilibrium self-organization.

Spontaneous fine-tuning to environment in many-species chemical reaction networks.

A chemical mixture that continually absorbs work from its environment may exhibit steady-state chemical concentrations that deviate from their equilibrium values. Such behavior is particularly interesting in a scenario where the environmental work sources are relatively difficult to access, so that only the proper orchestration of many distinct catalytic actors can power the dissipative flux required to maintain a stable, far-from-equilibrium steady state. In this article, we study the dynamics of an in silico chemical network with random connectivity in an environment that makes strong thermodynamic forcing available only to rare combinations of chemical concentrations. We find that the long-time dynamics of such systems are biased toward states that exhibit a fine-tuned extremization of environmental forcing.

Minimum energetic cost to maintain a target nonequilibrium state.

In the absence of external driving, a system exposed to thermal fluctuations will relax to equilibrium. However, the constant input of work makes it possible to counteract this relaxation and maintain the system in a nonequilibrium steady state. In this article, we use the stochastic thermodynamics of Markov jump processes to compute the minimum rate at which energy must be supplied and dissipated to maintain an arbitrary nonequilibrium distribution in a given energy landscape. This lower bound depends on two factors: the undriven probability current in the equilibrium state and the distance from thermal equilibrium of the target distribution. By showing the consequences of this result in a few simple examples, we suggest general implications for the required energetic costs of macromolecular repair and cytosolic protein localization.

Measurement of Rapid Protein Diffusion in the Cytoplasm by Photo-Converted Intensity Profile Expansion.

The fluorescence microscopy methods presently used to characterize protein motion in cells infer protein motion from indirect observables, rather than measuring protein motion directly. Operationalizing these methods requires expertise that can constitute a barrier to their broad utilization. Here, we have developed PIPE (photo-converted intensity profile expansion) to directly measure the motion of tagged proteins and quantify it using an effective diffusion coefficient. PIPE works by pulsing photo-convertible fluorescent proteins, generating a peaked fluorescence signal at the pulsed region, and analyzing the spatial expansion of the signal. We demonstrate PIPE's success in measuring accurate diffusion coefficients in silico and in vitro and compare effective diffusion coefficients of native cellular proteins and free fluorophores in vivo. We apply PIPE to measure diffusion anomality in the cell and use it to distinguish free fluorophores from native cellular proteins. PIPE's direct measurement and ease of use make it appealing for cell biologists.

Dissipation Bounds All Steady-State Current Fluctuations.

Near equilibrium, small current fluctuations are described by a Gaussian distribution with a linear-response variance regulated by the dissipation. Here, we demonstrate that dissipation still plays a dominant role in structuring large fluctuations arbitrarily far from equilibrium. In particular, we prove a linear-response-like bound on the large deviation function for currents in Markov jump processes. We find that nonequilibrium current fluctuations are always more likely than what is expected from a linear-response analysis. As a small-fluctuations corollary, we derive a recently conjectured uncertainty bound on the variance of current fluctuations.

Dissipative adaptation in driven self-assembly.

In a collection of assembling particles that is allowed to reach thermal equilibrium, the energy of a given microscopic arrangement and the probability of observing the system in that arrangement obey a simple exponential relationship known as the Boltzmann distribution. Once the same thermally fluctuating particles are driven away from equilibrium by forces that do work on the system over time, however, it becomes significantly more challenging to relate the likelihood of a given outcome to familiar thermodynamic quantities. Nonetheless, it has long been appreciated that developing a sound and general understanding of the thermodynamics of such non-equilibrium scenarios could ultimately enable us to control and imitate the marvellous successes that living things achieve in driven self-assembly. Here, I suggest that such a theoretical understanding may at last be emerging, and trace its development from historic first steps to more recent discoveries. Focusing on these newer results, I propose that they imply a general thermodynamic mechanism for self-organization via dissipation of absorbed work that may be applicable in a broad class of driven many-body systems.

Structural Basis for Modulation of Quality Control Fate in a Marginally Stable Protein.

The human von Hippel-Lindau (VHL) tumor suppressor is a marginally stable protein previously used as a model substrate of eukaryotic refolding and degradation pathways. When expressed in the absence of its cofactors, VHL cannot fold and is quickly degraded by the quality control machinery of the cell. We combined computational methods with in vivo experiments to examine the basis of the misfolding propensity of VHL. By expressing a set of randomly mutated VHL sequences in yeast, we discovered a more stable mutant form. Subsequent modeling suggested the mutation had caused a conformational change affecting cofactor and chaperone interaction, and this hypothesis was then confirmed by additional knockout and overexpression experiments targeting a yeast cofactor homolog. These findings offer a detailed structural basis for the modulation of quality control fate in a model misfolded protein and highlight burial mode modeling as a rapid means to detect functionally important conformational changes in marginally stable globular domains.

Quantitative theory of hydrophobic effect as a driving force of protein structure.

Various studies suggest that the hydrophobic effect plays a major role in driving the folding of proteins. In the past, however, it has been challenging to translate this understanding into a predictive, quantitative theory of how the full pattern of sequence hydrophobicity in a protein shapes functionally important features of its tertiary structure. Here, we extend and apply such a phenomenological theory of the sequence-structure relationship in globular protein domains, which had previously been applied to the study of allosteric motion. In an effort to optimize parameters for the model, we first analyze the patterns of backbone burial found in single-domain crystal structures, and discover that classic hydrophobicity scales derived from bulk physicochemical properties of amino acids are already nearly optimal for prediction of burial using the model. Subsequently, we apply the model to studying structural fluctuations in proteins and establish a means of identifying ligand-binding and protein-protein interaction sites using this approach.

Statistical physics of self-replication.

Self-replication is a capacity common to every species of living thing, and simple physical intuition dictates that such a process must invariably be fueled by the production of entropy. Here, we undertake to make this intuition rigorous and quantitative by deriving a lower bound for the amount of heat that is produced during a process of self-replication in a system coupled to a thermal bath. We find that the minimum value for the physically allowed rate of heat production is determined by the growth rate, internal entropy, and durability of the replicator, and we discuss the implications of this finding for bacterial cell division, as well as for the pre-biotic emergence of self-replicating nucleic acids.

Confinement to organelle-associated inclusion structures mediates asymmetric inheritance of aggregated protein in budding yeast.

The division of the S. cerevisiae budding yeast, which produces one mother cell and one daughter cell, is asymmetric with respect to aging. Remarkably, the asymmetry of yeast aging coincides with asymmetric inheritance of damaged and aggregated proteins by the mother cell. Here, we show that misfolded proteins are retained in the mother cell by being sequestered in juxtanuclear quality control compartment (JUNQ) and insoluble protein deposit (IPOD) inclusions, which are attached to organelles. Upon exposure to stress, misfolded proteins accumulate in stress foci that must be disaggregated by Hsp104 in order to be degraded or processed to JUNQ and IPOD. Cells that fail to deliver aggregates to an inclusion pass on aggregates to subsequent generations.

Allostery in protein domains reflects a balance of steric and hydrophobic effects.

Allosteric conformational change underlies biological function in many proteins. Allostery refers to a conformational event in which one region of a protein undergoes structural rearrangement in response to a stimulus applied to a different region of the same protein. Here, I show for a variety of proteins that a simple, phenomenological model of the dependence of protein conformation on hydrophobic burial energy allows one to compute low-energy conformational fluctuations for a given sequence by using linear programming to find optimized combinations of sequence-specific hydrophobic burial modes that satisfy steric constraints. From these fluctuations one may calculate allosteric couplings between different sites in a protein domain. Although the physical basis of protein structure is complex and multifactorial, a simplified description of conformational energy in terms of the hydrophobic effect alone is sufficient to give a mechanistic explanation for many biologically important allosteric events.

Role of solvation effects in protein denaturation: from thermodynamics to single molecules and back.

Protein stability often is studied in vitro through the use of urea and guanidinium chloride, chemical cosolvents that disrupt protein native structure. Much controversy still surrounds the underlying mechanism by which these molecules denature proteins. Here we review current thinking on various aspects of chemical denaturation. We begin by discussing classic models of protein folding and how the effects of denaturants may fit into this picture through their modulation of the collapse, or coil-globule transition, which typically precedes folding. Subsequently, we examine recent molecular dynamics simulations that have shed new light on the possible microscopic origins of the solvation effects brought on by denaturants. It seems likely that both denaturants operate by facilitating solvation of hydrophobic regions of proteins. Finally, we present recent single-molecule fluorescence studies of denatured proteins, the analysis of which corroborates the role of denaturants in shifting the equilibrium of the coil-globule transition.

Polyglutamine shows a urea-like affinity for unfolded cytosolic protein.

Noting that the glutamine (Q) amino acid side-chain bears a striking resemblance to urea, the chemical denaturant, we argue on biophysical grounds that polyQ chains should possess a potent denaturant activity. Using live-cell confocal microscopy, we demonstrate that the surface of a polyQ inclusion denatures cytosolic proteins by binding and trapping them in an immobilized ring. We also show the reverse effect: that elevated local concentrations of unfolded protein in the cytosol can drive the co-localization and accumulation of short polyQ tracts that normally do not aggregate. Such a urea-like mechanism explains many past observations about polyQ-driven disruption of proteostasis and neurodegeneration.