arXiv subjects

Matthew P. Leighton

Publications and source records attributed to Matthew P. Leighton.

18 recordsLinked to original sources

arXiv2026

A behavior-environment information loop drives sensory navigation

As organisms navigate the environment to locate critical resources, their behavioral actions must be tightly coupled to their sensory inputs. Here, we introduce an information-theoretic framework that quantifies this coupling using transfer entropy, which measures information flow between sensory inputs and behavioral outputs. Information flow from sensory inputs to behavior defines a "reactive" component of a navigational strategy, whereas information flow from behavior to sensory inputs defines an "active" component, whereby actions shape subsequent sensory experiences. Analyzing these bidirectional information flows enables us to both predict navigational performance and dissect navigation strategies from trajectories. Using a minimal model that captures the active and reactive components, we connect macroscopic performance to microscopic information flows. We then apply the framework to experimentally measured trajectories of bacteria, worms, and flies, as well as to machine learning agents navigating sensory landscapes. Across systems, bidirectional information flow reliably predicts navigation efficiency, revealing a common behavioral-environment feedback loop. Decomposing active and reactive information flows further exposes distinct strategies underlying bacterial chemotaxis, the spatial dependency of the navigation strategy in fly olfactory navigation, and the learned policies of a reinforcement-trained agent. Together, these results establish bidirectional information flow as a unifying principle for understanding navigation in biological and artificial systems.

physics.bio-ph↗

arXiv2026

On the Information Required for Feedback Control

Biological systems across scales, along with many engineering problems, must control noisy systems with limited information. Here we study information-limited feedback control of stochastic systems to achieve target steady states, and derive a lower bound on the information rate from controlled system to controller. This framework allows us to obtain performance-information Pareto frontiers for wide-ranging control problems with limited information. For systems with state-independent passive dynamics, the bound is saturated by an explicit optimal control protocol which probabilistically time-reverses the passive dynamics. We showcase these results through applications to nonlinear particle localization, microbial navigation, and experimentally realized information engines.

cond-mat.stat-mech↗

arXiv2026

Discrete turn strategies emerge in information-limited navigation

Navigation up a smooth sensory gradient is one of the simplest behavioural tasks, and some organisms solve it by making continuous adjustments to their course. Bacteria instead employ a variety of discrete strategies, including run and tumble motion, direction reversals, and turns by specific angles. Here we ask what drives the choice of these strategies, framing the problem as maximising up-gradient speed with a given amount of sensory information per unit time. We find that, without directional information on which way to turn, behavioural strategies that take discrete actions perform better than gradual steering. As the amount of information is increased, we see a series of transitions between optimal strategies, including a shift from direction reversals to fully re-orienting tumbles. Among more complex re-orientation strategies, we show that discrete turn angles are best, and observe transitions in the number of angles employed by the optimal strategy. More broadly, such emergent simplicity in behaviour is a tractable example of a widespread phenomenon in which biology chooses a discrete solution, despite the underlying physics being continuous.

physics.bio-ph↗

arXiv2026

Hunting for Maxwell's Demon in the Wild

The paradox of Maxwell's demon motivated the development of information thermodynamics and the creation of nanoscale information engines. We now understand that machines such as the molecular motors within cells can in principle harvest fluctuations and thereby operate as a Maxwell demon -- but do they? Answering this question would seemingly require simultaneous measurement of all system degrees of freedom, which is generally intractable in single-molecule experiments. Here, we derive a simple statistical estimator to infer both the direction and magnitude of subsystem heat flows, and thus determine whether -- and how strongly -- a motor operates as a Maxwell demon. The estimator uses only trajectory measurements for a single degree of freedom. Simulating both colloidal information engines and kinesin molecular motors, we show that our estimator can precisely and accurately detect Maxwell-demon behavior with experimentally accessible resolution and quantities of data. Moreover, we find that kinesin transitions to a Maxwell-demon mechanism in the presence of nonequilibrium noise, with a corresponding increase in velocity consistent with experiments. These findings suggest that molecular motors may have evolved to leverage active fluctuations within cells.

cond-mat.stat-mech↗

arXiv2026

Information thermodynamics of cellular ion pumps

The framework of bipartite stochastic thermodynamics is a powerful tool to analyze a composite system's internal thermodynamics. It has been used to study the components of different molecular machines such as ATP synthase. However, this approach has not yet been used to describe ion-transporting proteins despite their high-level functional similarity. Here we study the bipartite thermodynamics of the sodium-potassium pump in the nonequilibrium steady state. Using a physically intuitive partition between the ATP-consuming subsystem and the ion-transporting subsystem, we find considerable information flow comparable to other molecular machines, and Maxwell-demon behavior in the ATP-consuming subsystem. We vary ion concentrations and transmembrane voltage in a range including the neuronal action potential, and find that the information flow inverts during depolarization.

cond-mat.stat-mech↗

arXiv2025

Decomposing Non-Markovian History Dependence

Non-Markovian stochastic processes are ubiquitous in biology. Nevertheless, we lack a general framework for quantifying historical dependencies. In this Letter, we propose an information-theoretic approach to decompose history dependence in systems with non-Markovian dynamics, quantifying the information encoded in dependencies of each order. In minimal models of non-Markovian dynamics, we show that this framework correctly captures the underlying historical dependencies, even when autocorrelations do not. In prolonged recordings of fly behavior, we find that the scaling of non-Markovian dependencies is invariant across timescales from fractions of a second to minutes. Despite this invariance, the overall amount of non-Markovian information is non-monotonic, suggesting a unique timescale on which historical dependencies are strongest.

cond-mat.stat-mech↗

arXiv2025

Tractable Model for Tunable Non-Markovian Dynamics

Non-Markovian dynamics are ubiquitous across physics, biology, and engineering. Yet our understanding of non-Markovian processes significantly lags that of simpler Markovian processes, due largely to a lack of tractable models. In this article, we present a minimal model of non-Markovian dynamics in which the current state copies past states with arbitrary history dependence. We show that many properties of this process can be studied analytically, providing insight into the relationships between history dependence, autocorrelations, and information-theoretic metrics like entropy and dynamical information. Strikingly, we find that autocorrelations can fail, even qualitatively, to capture the underlying dependencies. Ultimately, this model serves as a tractable sandbox for exploring non-Markovian dynamics.

cond-mat.stat-mech↗

arXiv2025

Coarse-graining dynamics to maximize irreversibility

In many far-from-equilibrium biological systems, energy injected by irreversible processes at microscopic scales propagates to larger scales to fulfill important biological functions. But given dissipative dynamics at the microscale, how much irreversibility can persist at the macroscale? Here, we propose a model-free coarse-graining procedure that merges microscopic states to minimize the amount of lost irreversibility. Beginning with dynamical measurements, this procedure produces coarse-grained dynamics that retain as much information as possible about the underlying irreversibility. In synthetic and experimental data spanning molecular motors, biochemical oscillators, and recordings of neural activity, we derive simplified descriptions that capture the essential nonequilibrium processes. These results provide the tools to study the fundamental limits on the emergence of macroscopic irreversibility.

cond-mat.stat-mech↗

arXiv2024

Flow of Energy and Information in Molecular Machines

Molecular machines transduce free energy between different forms throughout all living organisms. While truly machines in their own right, unlike their macroscopic counterparts molecular machines are characterized by stochastic fluctuations, overdamped dynamics, and soft components, and operate far from thermodynamic equilibrium. In addition, information is a relevant free-energy resource for molecular machines, leading to new modes of operation for nanoscale engines. Towards the objective of engineering synthetic nanomachines, an important goal is to understand how molecular machines transduce free energy to perform their functions in biological systems. In this review we discuss the nonequilibrium thermodynamics of free-energy transduction within molecular machines, with a focus on quantifying energy and information flows between their components. We review results from theory, modeling, and inference from experiments that shed light on the internal thermodynamics of molecular machines, and ultimately explore what we can learn from considering these interactions.

cond-mat.stat-mech↗

arXiv2024

Information Arbitrage in Bipartite Heat Engines

Heat engines and information engines have each historically served as motivating examples for the development of thermodynamics. While these two types of systems are typically thought of as two separate kinds of machines, recent empirical studies of specific systems have hinted at possible connections between the two. Inspired by molecular machines in the cellular environment, which in many cases have separate components in contact with distinct sources of fluctuations, we study bipartite heat engines. We show that a bipartite heat engine can only produce net output work by acting as an information engine. Conversely, information engines can only extract more work than the work consumed to power them if they have access to different sources of fluctuations, i.e., act as heat engines. We illustrate these findings first through an analogy to economics and a cyclically controlled 2D ideal gas. We then explore two analytically tractable model systems in more detail: a Brownian-gyrator heat engine which we show can be reinterpreted as a feedback-cooling information engine, and a quantum-dot information engine which can be reinterpreted as a thermoelectric heat engine. Our results suggest design principles for both heat engines and information engines at the nanoscale, and ultimately imply constraints on how free-energy transduction is carried out in biological molecular machines.

cond-mat.stat-mech↗

arXiv2023

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.

cond-mat.stat-mech↗

arXiv2023

Torsion and Bistability of Double-Twist Elastomers

We investigate the elastic properties of anisotropic elastomers with a double-twist director field, which is a model for collagen fibrils or blue phases. We observe a significant Poynting-like effect, coupling torsion (fibril twist) and extension. For freely-rotating boundary conditions, we identify a structural bistability at very small extensional strains which undergoes a saddle-node bifurcation at a critical strain -- at approximately 1% strain for a parameterization appropriate for collagen fibrils. With clamped boundary conditions appropriate for many experimental setups, the bifurcation is not present. We expect significant helical shape effects when fixed torsion does not equal the equilibrium torsion of freely-rotating boundary conditions, due to residual torques.

cond-mat.soft↗

arXiv2023

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 $\mathrm{F}_\mathrm{o}$ and $\mathrm{F}_1$ subunits of ATP synthase and that of kinesin pulling a diffusive cargo.

cond-mat.stat-mech↗

arXiv2022

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.

cond-mat.stat-mech↗

arXiv2022

Performance scaling and trade-offs for collective motor-driven transport

Motor-driven intracellular transport of organelles, vesicles, and other molecular cargo is a highly collective process. An individual cargo is often pulled by a team of transport motors, with numbers ranging from only a few to several hundred. We explore the behavior of these systems using a stochastic model for transport of molecular cargo by an arbitrary number N of motors obeying linear Langevin dynamics, finding analytic solutions for the N-dependence of the velocity, precision of forward progress, energy flows between different system components, and efficiency. In two opposing regimes, we show that these properties obey simple scaling laws with N. Finally, we explore trade-offs between performance metrics as N is varied, providing insight into how different numbers of motors might be well-matched to distinct contexts where different performance metrics are prioritized.

cond-mat.stat-mech↗

arXiv2021

D-band strain underestimates fibril strain for twisted collagen fibrils at low strains

Collagen fibrils are the main structural component of load-bearing tissues such as tendons, ligaments, skin, the cornea of the eye, and the heart. The D-band of collagen fibrils is an axial periodic density modulation that can be easily characterized by tissue-level X-ray scattering. During mechanical testing, D-band strain is often used as a proxy for fibril strain. However, this approach ignores the coupling between strain and molecular tilt. We examine the validity of this approximation using an elastomeric collagen fibril model that includes both the D-band and a molecular tilt field. In the low strain regime, we show that the D-band strain substantially underestimates fibril strain for strongly twisted collagen fibrils -- such as fibrils from skin or corneal tissue.

physics.bio-ph↗

arXiv2021

Chiral phase-coexistence in compressed double-twist elastomers

We adapt the theory of anisotropic rubber elasticity to model cross-linked double-twist liquid crystal cylinders such as exhibited in biological systems. In mechanical extension we recover strain-straightening, but with an exact expression in the small twist-angle limit. In compression, we observe coexistence between high and low twist phases. Coexistence begins at small compressive strains and is robustly observed for any anisotropic cross-links and for general double-twist functions -- but disappears at large twist angles. Within the coexistence region, significant compression of double-twist cylinders is allowed at constant stress. Our results are qualitatively consistent with previous observations of swollen or compressed collagen fibrils, indicating that this phenomenon may be readily accessible experimentally.

physics.bio-ph↗

arXiv2020

Non-equilibrium Growth and Twist of Cross-Linked Collagen Fibrils

The lysyl oxidase (LOX) enzyme that catalyses cross-link formation during the assembly of collagen fibrils in vivo is too large to diffuse within assembled fibrils, and so is incompatible with a fully equilibrium mechanism for fibril formation. We propose that enzymatic cross-links are formed at the fibril surface during the growth of collagen fibrils; as a consequence no significant reorientation of previously cross-linked collagen molecules occurs inside collagen fibrils during fibril growth in vivo. By imposing local equilibrium only at the fibril surface, we develop a coarse-grained quantitative model of in vivo fibril structure that incorporates a double-twist orientation of collagen molecules and a periodic D-band density modulation along the fibril axis. Radial growth is controlled by the density of available collagen molecules around the fibril. In contrast with earlier equilibrium models of fibril structure, we find that all fibrils can exhibit a core-shell structure that is controlled only by the fibril radius. At small radii a core is developed with a linear double-twist structure as a function of radius. Within the core the double-twist structure is largely independent of the D-band. Within the shell at larger radii, the structure approaches a constant twist configuration that is strongly coupled with the D-band. We suggest a stable radius control mechanism that corneal fibrils can exploit near the edge of the linear core regime; while larger tendon fibrils can use a cruder version of growth control that does not select a preferred radius.

physics.bio-ph↗