Unlocking the potential of information flow: Maximizing free-energy transduction in a model of an autonomous rotary molecular motor.

Molecular motors fulfill critical functions within all living beings. Understanding their underlying working principles is therefore of great interest. Here we develop a simple model inspired by the two-component biomolecular motor F_{o}-F_{1} ATP synthase. We analyze its energetics and characterize information flows between the machine's components. At maximum output power we find that information transduction plays a minor role for free-energy transduction. However, when the two components are coupled to different environments (e.g., when in contact with heat baths at different temperatures), we show that information flow becomes a resource worth exploiting to maximize free-energy transduction. Our findings suggest that real-world powerful and efficient information engines could be found in machines whose components are subjected to fluctuations of different strength, since in this situation the benefit gained from using information for work extraction can outweigh the costs of information generation.

Jensen bound for the entropy production rate in stochastic thermodynamics.

Bounding and estimating entropy production has long been an important goal of nonequilibrium thermodynamics. We recently derived a lower bound on the total and subsystem entropy production rates of continuous stochastic systems. This "Jensen bound" has led to fundamental limits on the performance of collective transport systems and permitted thermodynamic inference of free-energy transduction between components of bipartite molecular machines. Our original derivation relied on a number of assumptions, which restricted the bound's regime of applicability. Here we derive the Jensen bound far more generally for multipartite overdamped Langevin dynamics. We then consider several extensions, allowing for position-dependent diffusion coefficients, underdamped dynamics, and non-multipartite overdamped dynamics. Our results extend the Jensen bound to a far broader class of systems.

First-passage-time statistics of growing microbial populations carry an imprint of initial conditions.

In exponential population growth, variability in the timing of individual division events and environmental factors (including stochastic inoculation) compound to produce variable growth trajectories. In several stochastic models of exponential growth we show power-law relationships that relate variability in the time required to reach a threshold population size to growth rate and inoculum size. Population-growth experiments in E. coli and S. aureus with inoculum sizes ranging between 1 and 100 are consistent with these relationships. We quantify how noise accumulates over time, finding that it encodes-and can be used to deduce-information about the early growth rate of a population.

Efficient control protocols for an active Ornstein-Uhlenbeck particle.

Designing a protocol to efficiently drive a stochastic system is an active field of research. Here we extend such control theory to an active Ornstein-Uhlenbeck particle (AOUP) in a bistable potential, driven by a harmonic trap. We find that protocols designed to minimize the excess work (up to linear response) perform better than naive protocols with constant velocity for a wide range of protocol durations.

Information Engine in a Nonequilibrium Bath.

Information engines can convert thermal fluctuations of a bath at temperature T into work at rates of order k_{B}T per relaxation time of the system. We show experimentally that such engines, when in contact with a bath that is out of equilibrium, can extract much more work. We place a heavy, micron-scale bead in a harmonic potential that ratchets up to capture favorable fluctuations. Adding a fluctuating electric field increases work extraction up to ten times, limited only by the strength of the applied field. Our results connect Maxwell's demon with energy harvesting and demonstrate that information engines in nonequilibrium baths can greatly outperform conventional engines.

Inferring Subsystem Efficiencies in Bipartite Molecular Machines.

Molecular machines composed of coupled subsystems transduce free energy between different external reservoirs, in the process internally transducing energy and information. While subsystem efficiencies of these molecular machines have been measured in isolation, less is known about how they behave in their natural setting when coupled together and acting in concert. Here, we derive upper and lower bounds on the subsystem efficiencies of a bipartite molecular machine. We demonstrate their utility by estimating the efficiencies of the F_{o} and F_{1} subunits of ATP synthase and that of kinesin pulling a diffusive cargo.

D-SPIN constructs gene regulatory network models from multiplexed scRNA-seq data revealing organizing principles of cellular perturbation response.

Gene regulatory networks within cells modulate the expression of the genome in response to signals and changing environmental conditions. Reconstructions of gene regulatory networks can reveal the information processing and control principles used by cells to maintain homeostasis and execute cell-state transitions. Here, we introduce a computational framework, D-SPIN, that generates quantitative models of gene-regulatory networks from single-cell mRNA-seq data sets collected across thousands of distinct perturbation conditions. D-SPIN models the cell as a collection of interacting gene-expression programs, and constructs a probabilistic model to infer regulatory interactions between gene-expression programs and external perturbations. Using large Perturb-seq and drug-response datasets, we demonstrate that D-SPIN models reveal the organization of cellular pathways, sub-functions of macromolecular complexes, and the logic of cellular regulation of transcription, translation, metabolism, and protein degradation in response to gene knockdown perturbations. D-SPIN can also be applied to dissect drug response mechanisms in heterogeneous cell populations, elucidating how combinations of immunomodulatory drugs can induce novel cell states through additive recruitment of gene expression programs. D-SPIN provides a computational framework for constructing interpretable models of gene-regulatory networks to reveal principles of cellular information processing and physiological control.

A symbiotic physical niche in Drosophila melanogaster regulates stable association of a multi-species gut microbiota.

The gut is continuously invaded by diverse bacteria from the diet and the environment, yet microbiome composition is relatively stable over time for host species ranging from mammals to insects, suggesting host-specific factors may selectively maintain key species of bacteria. To investigate host specificity, we used gnotobiotic Drosophila, microbial pulse-chase protocols, and microscopy to investigate the stability of different strains of bacteria in the fly gut. We show that a host-constructed physical niche in the foregut selectively binds bacteria with strain-level specificity, stabilizing their colonization. Primary colonizers saturate the niche and exclude secondary colonizers of the same strain, but initial colonization by Lactobacillus species physically remodels the niche through production of a glycan-rich secretion to favor secondary colonization by unrelated commensals in the Acetobacter genus. Our results provide a mechanistic framework for understanding the establishment and stability of a multi-species intestinal microbiome.

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.

Optimal Control of the F1-ATPase Molecular Motor.

F1-ATPase is a rotary molecular motor that in vivo is subject to strong nonequilibrium driving forces. There is great interest in understanding the operational principles governing its high efficiency of free-energy transduction. Here we use a near-equilibrium framework to design a nontrivial control protocol to minimize dissipation in rotating F1 to synthesize adenosine triphosphate. We find that the designed protocol requires much less work than a naive (constant-velocity) protocol across a wide range of protocol durations. Our analysis points to a possible mechanism for energetically efficient driving of F1 in vivo and provides insight into free-energy transduction for a broader class of biomolecular and synthetic machines.

Bayesian Information Engine that Optimally Exploits Noisy Measurements.

We have experimentally realized an information engine consisting of an optically trapped, heavy bead in water. The device raises the trap center after a favorable "up" thermal fluctuation, thereby increasing the bead's average gravitational potential energy. In the presence of measurement noise, poor feedback decisions degrade its performance; below a critical signal-to-noise ratio, the engine shows a phase transition and cannot store any gravitational energy. However, using Bayesian estimates of the bead's position to make feedback decisions can extract gravitational energy at all measurement noise strengths and has maximum performance benefit at the critical signal-to-noise ratio.

Optimal control with a strong harmonic trap.

Quadratic trapping potentials are widely used to experimentally probe biopolymers and molecular machines and drive transitions in steered molecular-dynamics simulations. Approximating energy landscapes as locally quadratic, we design multidimensional trapping protocols that minimize dissipation. The designed protocols are easily solvable and applicable to a wide range of systems. The approximation does not rely on either fast or slow limits and is valid for any duration provided the trapping potential is sufficiently strong. We demonstrate the utility of the designed protocols with a simple model of a periodically driven rotary motor. Our results elucidate principles of effective single-molecule manipulation and efficient nonequilibrium free-energy estimation.

Dynamic and Thermodynamic Bounds for Collective Motor-Driven Transport.

Molecular motors work collectively to transport cargo within cells, with anywhere from one to several hundred motors towing a single cargo. For a broad class of collective-transport systems, we use tools from stochastic thermodynamics to derive a new lower bound for the entropy production rate which is tighter than the second law. This implies new bounds on the velocity, efficiency, and precision of general transport systems and a set of analytic Pareto frontiers for identical motors. In a specific model, we identify conditions for saturation of these Pareto frontiers.

Information Thermodynamics of the Transition-Path Ensemble.

The reaction coordinate describing a transition between reactant and product is a fundamental concept in the theory of chemical reactions. Within transition-path theory, a quantitative definition of the reaction coordinate is found in the committor, which is the probability that a trajectory initiated from a given microstate first reaches the product before the reactant. Here we develop an information-theoretic origin for the committor and show how selecting transition paths from a long ergodic equilibrium trajectory induces entropy production which exactly equals the information that system dynamics provide about the reactivity of trajectories. This equality of entropy production and dynamical information generation also holds at the level of arbitrary individual coordinates, providing parallel measures of the coordinate's relevance to the reaction, each of which is maximized by the committor.

Multidimensional minimum-work control of a 2D Ising model.

A system's configurational state can be manipulated using dynamic variation of control parameters, such as temperature, pressure, or magnetic field; for finite-duration driving, excess work is required above the equilibrium free-energy change. Minimum-work protocols in multidimensional control-parameter space have the potential to significantly reduce work relative to one-dimensional control. By numerically minimizing a linear-response approximation to the excess work, we design protocols in control-parameter spaces of a 2D Ising model that efficiently drive the system from the all-down to all-up configuration. We find that such designed multidimensional protocols take advantage of more flexible control to avoid control-parameter regions of high system resistance, heterogeneously input and extract work to make use of system relaxation, and flatten the energy landscape, making accessible many configurations that would otherwise have prohibitively high energy and, thus, decreasing spin correlations. Relative to one-dimensional protocols, this speeds up the rate-limiting spin-inversion reaction, thereby keeping the system significantly closer to equilibrium for a wide range of protocol durations and significantly reducing resistance and, hence, work.

Internal energy and information flows mediate input and output power in bipartite molecular machines.

Microscopic biological systems operate far from equilibrium, are subject to strong fluctuations, and are composed of many coupled components with interactions varying in nature and strength. Researchers are actively investigating the general design principles governing how biomolecular machines achieve effective free-energy transduction in light of these challenges. We use a model of two strongly coupled stochastic rotary motors to explore the effect of coupling strength between components of a molecular machine. We observe prominent thermodynamic characteristics at intermediate coupling strength, near that which maximizes output power: a maximum in power and information transduced from the upstream to the downstream system, and equal subsystem entropy production rates. These observations are unified through a bound on the machine's input and output power, which accounts for both the energy and information transduced between subsystems.

Stochastic microbiome assembly depends on context.

Observational studies reveal substantial variability in microbiome composition across individuals. Targeted studies in gnotobiotic animals underscore this variability by showing that some bacterial strains colonize deterministically, while others colonize stochastically. While some of this variability can be explained by external factors like environmental, dietary, and genetic differences between individuals, in this paper we show that for the model organism Drosophila melanogaster, interactions between bacteria can affect the microbiome assembly process, contributing to a baseline level of microbiome variability even among isogenic organisms that are identically reared, housed, and fed. In germ-free flies fed known combinations of bacterial species, we find that some species colonize more frequently than others even when fed at the same high concentration. We develop an ecological technique that infers the presence of interactions between bacterial species based on their colonization odds in different contexts, requiring only presence/absence data from two-species experiments. We use a progressive sequence of probabilistic models, in which the colonization of each bacterial species is treated as an independent stochastic process, to reproduce the empirical distributions of colonization outcomes across experiments. We find that incorporating context-dependent interactions substantially improves the performance of the models. Stochastic, context-dependent microbiome assembly underlies clinical therapies like fecal microbiota transplantation and probiotic administration and should inform the design of synthetic fecal transplants and dosing regimes.

Connections between efficient control and spontaneous transitions in an Ising model.

A system can be driven between metastable configurations by a time-dependent driving protocol, which uses external control parameters to change the potential energy of the system. Here we investigate the correspondence between driving protocols that are designed to minimize work and the spontaneous transition paths of the system in the absence of driving. We study the spin-inversion reaction in a 2D Ising model, quantifying the timing of each spin flip and heat flow to the system during both a minimum-work protocol and a spontaneous transition. The general order of spin flips during the transition mechanism is preserved between the processes, despite the coarseness of control parameters that are unable to reproduce more detailed features of the spontaneous mechanism. Additionally, external control parameters provide energy to each system component to compensate changes in internal energy, showing how control parameters are tuned during a minimum-work protocol to counteract underlying energetic features. This paper supports a correspondence between minimum-work protocols and spontaneous transition mechanisms.

Maximal fluctuation exploitation in Gaussian information engines.

Understanding the connections between information and thermodynamics has been among the most visible applications of stochastic thermodynamics. While recent theoretical advances have established that the second law of thermodynamics sets limits on information-to-energy conversion, it is currently unclear to what extent real systems can achieve the predicted theoretical limits. Using a simple model of an information engine that has recently been experimentally implemented, we explore the limits of information-to-energy conversion when an information engine's benefit is limited to output energy that can be stored. We find that restricting the engine's output in this way can limit its ability to convert information to energy. Nevertheless, a feedback control that inputs work can allow the engine to store energy at the highest achievable rate. These results sharpen our theoretical understanding of the limits of real systems that convert information to energy.

Steps minimize dissipation in rapidly driven stochastic systems.

Micro- and nanoscale systems driven by rapid changes in control parameters (control protocols) dissipate significant energy. In the fast-protocol limit, we find that protocols that minimize dissipation at fixed duration are universally given by a two-step process, jumping to and from a point that balances jump size with fast relaxation. Jump protocols could be exploited by molecular machines or thermodynamic computing to improve energetic efficiency, and implemented in nonequilibrium free-energy estimation to improve accuracy.