Physical Review Research

Fixational eye movements (FEMs) comprise the involuntary small scale eye motion conducted during fixation on a stationary stimulus. As a consequence, the visual information can be spread across multiple photoreceptors reducing the local signal-to-noise ratio. Yet, the signals transmitted by individual photoreceptors adapt to constant stimulation so that an entirely still scene would eventually fade from view. Because FEMs convert a stationary stimulus in the world to a temporally varying one on the retina, they can act to prevent this stimulus fading. Thus, FEMs can be understood as a sampling protocol than needs to be adjusted to the underlying processing circuitry. We analyse the impact of FEMs on the rate of information acquisition at the level of the retina for two common tasks of the human eye that typically go hand in hand: detection and localization. Here, we build a simple analytical model of visual perception, i.e. we subject a continuous receptor array to a stimulus moving across the retina as a consequence of FEMs with receptor excitations depending on past stimulation through a linear response function. Using Bayesian inference we quantify both the probability of detection and the accuracy of localization as a function of parameters controlling eye movements and stimulus. We find that localization of a stimulus is equivalent to the detection of the stimulus gradient. This allows us to discern optimal properties of eye movements for the respective tasks and provides a link between two typical psychophysical observables: detection thresholds and Vernier acuity. Our analysis suggests that typical human FEMs tend to facilitate localization at the expense of detection. Simply put, if you can see a stimulus you also know where it is. Finally, we propose a variety of experimental protocols to investigate the interplay between FEMs, detection, and localization with the potential of inferring intrinsic properties of an individuals visual system.

Primary sensory cortices often organize neurons with similar stimulus preference into spatially functional maps. Recent work in mouse primary visual cortex (V1) has established that neuronal tuning to the orientation of visual grating stimuli is organized into micro-clusters, where physically close neuron pairs (~ 20 {micro}m) share highly similar orientation preferences, but the organization is unstructured beyond this narrow range. This fine-scale organization is seemingly at odds with the underlying intracortical circuitry in mouse V1 whose spatial extent is an order of magnitude broader (100 ~ 200 {micro}m). In this study, we explore an activity-dependent synaptic plasticity model of spatially structured thalamo-cortical connectivity. We develop theory under asymptotic conditions specific for mouse V1, and derive concrete circuit conditions under which micro-clusters naturally develop. In particular, the recurrent interaction among V1 neurons requires an additional component over a micro-spatial scale, while the spatial profiles of balanced excitation and inhibition support an effective micro-scale interaction. Together, our results provide a developmental mechanism and analytical framework linking thalamo-cortical development, recurrent circuit structure, and the emergence of functional organization in primary visual cortex.

Bacteria assemble a precise number of flagella to navigate their environment, yet the molecular mechanisms underlying this robust counting remain poorly understood. We propose that robust flagellar number control does not require a strictly conserved transcriptional gene hierarchy, but instead emerges from a conserved network motif in which transcriptional feedback is coupled to the assembly progress of the flagellar C-ring. Specifically, upon C-ring growth, the ATPase FlhG is released from a non-inhibitory FlhG-FliM complex, dimerizes, and inactivates the master regulator FlrA, shutting down early flagellar gene expression. We analyze this assembly-coupled feedback mechanism using stochastic simulations and analytical calculations, revealing a trade-off between robustness to intrinsic fluctuations and to cell-to-cell variability in regulator abundance. Only at the crossover between fast and slow inactivation regimes can robustness to both noise sources be achieved simultaneously. These results provide quantitative, organism-independent insight into flagellar number control and connect to the broader problem of stochastic regulation of absorbing-state statistics.

Microbes exhibit complex dynamic behavior as the result of a large number of biochemical processes, spatial and temporal interactions, environmental variations, and evolutionary pressure. Although significant progress has been achieved in understanding microbial ecological dynamics, multiple open questions remain, including the microscopic mechanisms of growth and the roles of nutrients and stochasticity. In this work, we present a minimal theoretical approach to clarify the link between consumption of resources by microbes and their growth. A stochastic model that accounts for a single microbial species consuming a single type of resource while growing via cell division is studied analytically and via Monte Carlo computer simulations. We identify three distinct dynamical regimes of microbial growth determined by the relative magnitudes of resource uptake and division rates and initial conditions. We also show that stochasticity influences the dynamic behavior when the amounts of microbes or resources are low. The model recovers Monod growth kinetics and provides a mechanistic interpretation of the Monod constant and maximal growth rate. The theoretical framework presented captures a wide spectrum of dynamic behaviors in microbial systems, providing a clearer microscopic picture to explain their underlying complex mechanisms.

Efficient operation of neural networks has been linked to criticality in their underlying non-equilibrium excitation dynamics. However, obtaining experimental evidence of this conjecture remains challenging due to limited control and undersampling in biological systems. Here, we experimentally explore neural network criticality using an ultracold Rydberg gas as a highly controllable simulator. We highlight the similarity of the excitation spreading via Rydberg facilitation and the synaptic connection of spiking activity of neurons, giving rise to distinct absorbing and active phases. We systematically explore and resolve criticality criteria, including power-law scaling of excitation avalanches and the emergence of universal avalanche shape collapse. Crucially, we implement a controlled gain mechanism to compensate for atom loss, mimicking metabolic resource replenishment and stabilizing the system in a controlled non-equilibrium steady state. We find peak temporal correlations at the critical point and stochastic oscillations with dragon king avalanches in the active phase, consistent with predictions for systems orbiting criticality. Our work establishes facilitated Rydberg gases as a platform for investigating criticality, resource dynamics, and emergent oscillations in neural networks.

We develop a theoretical proposal linking vacuum stability and brain dynamics through superconductivity-inspired coherence, symmetry reduction, and the thermodynamic stabilization of low-entropy regimes. We take an unbroken SU(3) structure as a candidate stable residue of the low-temperature vacuum. At the neural level, we formulate a coarse-grained analog in which a two-fluid model with dissipative and coherence-supporting components describes brain dynamics. Specifically, the coherence-supporting component is proposed as a possible basis for the efficient binding and integration required to sustain a stable, unified conscious state. The proposal offers a common geometric language for relating physics and neuroscience with falsifiable signatures in coherence and state-dependent transitions. The main technical contribution is a computational algebraic model of conscious-state dynamics, where neural data are mapped to reconstructed state trajectories. Effective generators are inferred from those trajectories, and the two-fluid split is tested as a Cartan-root decomposition of su(3), with a rank-two commuting sector for coherence-preserving balance and six root directions for state transitions. This structure can be tested on neural data and contrasted with alternative dynamical models.

Biomolecular condensates are dynamic, membrane-free compartments that continuously exchange molecules with their surroundings. The dwell time, defined as the time a molecule remains inside a condensate between entry and exit, determines how extensively the molecule can explore the dense phase and encounter potential binding partners or reaction sites, thereby modulating condensate function. Motivated by our single-molecule measurements of RNA dwell times, we developed an analytical theory to understand dwell-time distributions in biomolecular condensates. Our theory predicts that the dwell-time distributions generally exhibit an early-time power-law regime followed by a late-time exponential tail. The form of the distribution encodes the rate-limiting mechanism of molecular escape: dense-phase diffusion-limited transport feature a -1.5 power law with an exponential tail set by a diffusion timescale, whereas interfacial barrier-crossing-limited transport feature a -0.5 power law with a decay governed by a barrier-crossing timescale. These distinct signatures provide a direct readout of the physical processes that control molecular retention in condensates, with implications for both natural and synthetic condensates.

Spatial proofreading is a mechanism that can enhance molecular discrimination by exploiting nonequilibrium diffusive transport between spatially separated source and readout regions. Here, we introduce a thermodynamically consistent reaction-diffusion model in which a gradient of active substrates is generated self-consistently by a reversible kinase-phosphatase switch coupled to nucleotide chemostats. The resulting chemical-potential gradient explicitly controls the nonequilibrium driving and allows the discrimination potential to be related to microscopic chemical rates and diffusive transport. A simple one-dimensional analysis shows that the ability of an enzyme to discriminate between wrong and right substrates is governed by a subtle balance between substrate-gradient confinement, controlled by phosphatase activity, the diffusive crossing time across the source-readout domain, and selective complex dissociation. We then extend the model to two-dimensional domains, showing that source, i.e. kinase, localization modulates spatial specificity by shaping the effective diffusive paths to the readout boundary. Finally, stochastic simulations reveal that molecular fluctuations generate intermittent wrong-readout events, which can be characterized through an event-weighted measure of specificity. Interestingly, we find that fluctuations promote frequent transitions to long-residence states in which discrimination is better than predicted by the deterministic estimate. Overall, our work highlights the importance of thermodynamically consistent descriptions of spatial proofreading and clarifies how energy input, transport, and spatial organization jointly shape biochemical discrimination.

Understanding how network connectivity shapes neural representations is central to systems neuroscience. While dimensionality reduction methods uncover low-dimensional manifold structure in population recordings, a rigorous framework connecting manifold geometry to network mechanisms and information encoding remains lacking. We develop a differential geometric approach for analyzing neural manifolds in rate-based recurrent networks receiving tuned feedforward inputs. We derive expressions for the pullback metric of neural manifolds, showing how input tuning curves, feedforward and recurrent synaptic connectivity shape manifold geometry. Critically, we establish that the Fisher information matrix at steady states also has the structure of a pullback metric, directly linking intrinsic manifold geometry to stimulus discriminability and information encoding. For noise with slow temporal correlations propagated through the network, we show that recurrent effects on information geometry cancel: Fisher information depends only on the feedforward connectivity. Thus, feedforward connectivity critically determines representational geometry. As an example, we demonstrate that the representation of space by a module of hexagonal grid cells is approximately isometric for random distribution of grid phases. Moreover, a linear feedforward transformation can map spatially random input tuning curves into a population of hexagonal grid cells, forming a toroidal manifold. Thus, feedforward connectivity alone can generate structured spatial representations without requiring carefully tuned recurrent connectivity or continuous attractor dynamics. Recurrent connectivity, however, is shown to improve stimulus encoding under fast noise, thereby implementing a selective noise reduction.

Biomolecular condensates are dynamic assemblies whose functions depend on continuous exchange of molecular components with the surrounding environment. While scaffold molecules drive phase separation and condensate architecture, many functional components are clients that are recruited through interactions with the scaffold-rich environment. Despite their prevalence, how client-scaffold interactions shape client exchange dynamics remains poorly understood. Here, we develop a reaction-diffusion model for client exchange in scaffold-driven condensates, in which clients switch between a scaffold-bound state and an unbound state. Bound clients exchange through scaffold-mediated transport, whereas unbound clients diffuse through the pore space of the condensate. Using the fluorescence recovery of fully photobleached condensates as a measure of client exchange, we compare transport through these two pathways with bound-unbound conversion and identify three limiting regimes. In the slow-conversion regime, bound and unbound clients recover through distinct scaffold- and pore-mediated pathways. In the intermediate-conversion regime, recovery of bound clients becomes limited by client unbinding. In the fast-conversion regime, local equilibrium between bound and unbound clients produces an effective single-state recovery. We further propose a unifying description that connects these regimes and quantitatively captures the apparent recovery timescales extracted from numerical simulations across condensate sizes. Our results provide a framework for interpreting component-specific exchange dynamics, and highlight client size, client-scaffold binding, and condensate porosity as key regulators of client turnover in multicomponent condensates.

Radiation-induced DNA double-strand breaks (DSBs) drive cellular mortality, mutagenesis, and severe evolutionary bottlenecks. While classical phenomenological models, such as the Linear-Quadratic (LQ) framework, reliably predict macroscopic population survival, they obscure the intrinsic single-cell stochasticity that governs critical rare events like tumor recurrence or the emergence of radioresistant persisters. To bridge this divide, we develop a mathematically exact stochastic differential equation (SDE) framework that models continuous DSB induction and repair as a Feller square-root process. By deriving exact closed-form expressions for the foci moments, we establish a highly efficient Maximum Likelihood Estimation (MLE) pipeline that circumvents computationally exhaustive Monte Carlo simulations, allowing the direct extraction of deterministic repair velocities and intrinsic molecular noise from empirical single-cell $\gamma$-H2AX data. Integrating this kinetic model with a cumulative damage hazard via the Feynman-Kac formalism, our framework seamlessly recovers the classic macroscopic LQ survival topology from microscopic first principles. Furthermore, systematic sensitivity analysis uncovers a fundamental evolutionary duality: while initial physical damage operates additively, ultimate cellular fate is driven by a nonlinear survival response governed by the trade-off between the damage hazard rate and intrinsic molecular noise strength. Crucially, we demonstrate that this molecular noise inherently enhances population survival. Governed by Jensen's inequality, stochastic variance acts as a non-genetic bet-hedging mechanism that buffers the population by favoring cells with transiently low damage loads. Ultimately, this exact stochastic framework bridges microscopic biophysics and macroscopic demographics, offering deep mechanistic insights into the evolutionary roots of radioresistance.

Developmental patterns can scale with size during growth, a phenomenon commonly attributed to morphogen scaling. Although patterning is orchestrated by gene regulatory networks (GRNs) activated by morphogens, how GRN dynamics interact with growth is not understood. We present a theoretical framework that integrates morphogen signalling, GRN dynamics, and tissue growth. We show that pattern scaling emerges from the interplay of GRN dynamics and growth, even in the absence of morphogen scaling. This relies on memory effects encoded in the GRNs, providing a cell-autonomous route to global scaling, and offering a general mechanism for size-invariant patterning beyond morphogen-based models.

Sequestration of gene products through diverse mechanisms forms a fundamental layer of regulation in intracellular biochemical processes, including post-translational modification, promiscuous binding to genomic decoy sites, and partitioning into membraneless compartments formed through phase separation. Here, we develop a unified stochastic framework to quantify how such sequestration-type processes, when coupled to noisy gene expression, modulate cell-to-cell variation in protein levels. In this model, protein molecules reversibly switch between active (free) and inactive (sequestered) states, whose switching rates are arbitrary functions of the molecular counts. Using exact analytical calculations and the linear noise approximation, we derive expressions for the Fano factor of the active-protein level and identify fluctuation attenuation regimes in terms of the logarithmic sensitivities of the switching rates to protein abundances. We show that inactive-protein-dependent switching, of which genomic decoy binding is a natural example, can preserve Poisson-level fluctuations in the active-protein level under appropriate conditions. Enzymatic inactivation, a type of post-translational modification, emerges as a special case of active-protein-dependent sequestration, where greater responsiveness of the inactivation propensity attenuates active-protein fluctuations. In both decoy binding and enzymatic inactivation, protecting the inactive protein from decay lowers active-protein fluctuations. Finally, a noise-buffering regime associated with intracellular phase separation is recovered when the inactive-to-active switching rate depends inversely on the inactive-protein level. Together, the examples of genomic decoy binding, enzymatic inactivation, and intracellular phase separation suggest that noise buffering observed across diverse intracellular processes is rooted in a broader class of reversible sequestration mechanisms that attenuate protein-level fluctuations.

Contact mediated cell-cell communication where direct physical contact between adjacent ligand cells and receptor cells trigger signal output is important during growth, development and regeneration of organisms. While the molecular machinery underlying contact mediated cell signaling is well explored, how the local spatial context of cells affect cell-cell contact mediated gene expression is not clear. Here, we present a vertex-based computational model to study spatial and temporal behavior of contact mediated signal output (which we refer to as output) in growing cell collectives. We consider cell-cell contact length dependent output synthesis and output degradation in receptor cells together with cell division to understand how dynamics at the scale of single cells lead to heterogeneous signal output. By tracking single receptor cells over time in growing cell collectives in silico, we show that cell growth and division lead to continuous and dynamic rearrangement of cell-cell contact between receptor and ligand cells which in turn affect the output levels. Our model predicts that the orientation of cell division plays a key role in the heterogeneity of signal output. We elucidate the link between cell mechanical properties that control cell shape, growth, and division, with signal output in receptor cells during contact mediated signaling processes.

Electrical signaling in biological systems is generally understood through the lens of single-channel biophysics, yet whether ensembles of ion channels can undergo cooperative opening and closing remains unclear. Here, we show that ensembles of voltage-gated ion channels can undergo bioelectrical order-disorder phase transitions driven by feedback between channel currents and local membrane voltage. When channels open, they carry ion-selective current that redistributes ions near the membrane and perturbs the transmembrane potential, thereby biasing the gating of nearby channels. This emergent nonequilibrium coupling generates a bona fide phase transition in ion channel ensembles. Finite-size analyses of the open-channel fraction, its fluctuations, and the distribution of collective channel states yield a voltage-temperature phase diagram with a first-order line separating collectively open and closed states and terminating at a critical point. The critical temperature is governed by a dimensionless conductance ratio set by ion transport, channel density, and confinement geometry. Applying this framework to measurements from the squid giant axon, the axon initial segment, and the nodes of Ranvier suggests that collective activation may be favored by high sodium-channel densities in large-diameter nerves, whereas the lower densities typical of potassium channels place them in an independent-gating regime.

The development and physiology of neurons rely on their microtubule organization, which is characterized by plus-end-out oriented microtubules in the axon and a mix of plus-end-out and plus-end-in oriented microtubules in dendrites. This orientational pattern is established early in neuronal development and is tightly linked to axon-dendrite differentiation. Even though multiple potentially relevant mechanisms have been proposed, fundamental questions remain: How does the microtubule organization in neurons emerge, and how does a neuron develop a single axon and multiple dendrites? Here, we address these questions at two distinct, complementary levels: at a higher level by proposing a conceptual framework, in which we classify mechanisms into three categories based on how they contribute to the microtubule organization: orientational bias, parallel amplification, and polarization; at a lower level we build a biophysical model that incorporates multiple mechanisms of microtubule dynamics in a neuron, from which, using analytical calculations and simulations, we derive insights into the emergence of microtubule organization in developing neurons. We show that geometrical effects alone can confer a bias in microtubule orientation. Parallel amplification then enhances the resulting polarity. Coupling multiple neurites to a common cell body that serves as a shared reservoir of resources allows for a polarization mechanism that ensures that the microtubule organization of one neurite becomes axonal while all others are dendritic. This framework unifies diverse molecular observations and yields experimentally testable predictions about microtubule self-organization in early neuronal development. Author summaryNeurons communicate through long protrusions called neurites, which are of two types: dendrites, which receive signals, and axons, which send signals. Their development relies primarily on microtubules, which are polar filaments with two distinct ends, known as the plus and minus ends. Microtubules self-organize into functional architectures that are significantly different between axons and dendrites. In axons, all microtubules point their plus end away from the cell body, whereas in dendrites, they point either towards the cell body or have mixed orientations depending on the species. This orientation guides intracellular transport by motors and is closely linked to whether a neurite develops into an axon or a dendrite. Despite decades of research identifying individual mechanisms, the bigger picture behind the emergence of microtubule orientation in neurons remains unclear. Here, we construct a conceptual framework and a biophysical model to identify the principles underlying the emergence of microtubule orientation in developing neurons. Our conceptual framework provides a high-level perspective on how individual mechanisms influence microtubule organization in neurites. In our concrete biophysical model, we study a selection of mechanisms to gain specific, quantitative insight into the organizational process. We propose a minimal model of a neuron that exhibits neuronal polarization, giving rise to a single axon-like neurite and multiple dendrite-like ones, consistent with experimental observations. This in silico neuron helps to explain how neurons break symmetry during development and provides a systematic way to generate and test new hypotheses about neuronal polarity.

Biomolecular condensates are widespread cellular self-assembled structures with essential functions. There are suggestions of condensates formed by different proteins being near criticality. However, systematic investigation of the criticality of condensates is absent, and critical exponents defining their universality class have not been found. Here, using long-time simulations, we show that condensates exhibit typical critical phenomena, including scale-free spatiotemporal correlations, critical slowing down, divergence of correlation length and dynamic scaling. From these scaling behaviors, a set of critical exponents is determined. Based on dynamic critical exponent, diverse condensates can be divided into two distinct universality classes, arising from differences in their molecular components and interaction types.

The collective spatial phenomenon of complement protein opsonization on nanoparticle surfaces is a key component of the immune response to viruses, engineered nanoparticles, and diseased cells. Recent work showed this opsonization follows a sharp, percolation-like transition versus the spacing d between surface-bound attachment sites, leaving two open questions: 1) whether the transition exhibits hallmarks of true criticality, such as diverging susceptibility, and 2) whether it can be distinguished from an alternative first-order cooperative (Hill-type) process producing an equally sharp threshold without true criticality. Here, we resolve both questions using a hierarchical statistical-mechanics treatment spanning stochastic, mean-field, and spatial reaction-diffusion models. The variance of two order parameters, peak complement activity and activation lifetime, diverges near threshold and sharpens systematically with system size, the defining signature of a critical point rather than a smooth cooperative response. Extending the analysis across site spacing and intrinsic kinetic rate constants traces a two-dimensional locus of critical points with consistent critical exponents throughout, establishing a single, robust universality class. The mean-field dynamic exponent for activation lifetime agrees quantitatively with the exact value predicted for the general epidemic process. Finally, a reaction-diffusion model of the nanoparticle surface shows the critical locus is set by a diffusion-limited length scale, establishing complement percolation as a fundamentally transport-limited surface reaction. These results place complement activation within the percolation universality class and identify the physical parameters, diffusion, catalysis, and decay, that govern its critical threshold, with direct implications for rational design of complement-evading nanomaterials, immunology, and evolutionary biology.

Classical neurogeometric models describe the primary visual cortex as a fibered structure in which retinal position and local orientation are coupled through the geometry of the roto-translation group. We extend this approach to the visuomotor cortex by modeling it as an assemblage of visual and motor cortical geometries. The model combines orientation-selective representations, analogous to those of the primary visual cortex, with movement-direction-selective representations, analogous to those of the primary motor cortex, in order to describe the mixed visual and motor selectivity observed in the visuomotor cortex. We introduce a coupled visuomotor structure in which visual orientation and motor direction coexist over a common spatial plane and interact through a relative-orientation constraint. Neural responses are modeled by orientation- and direction-dependent profile functions, and preference maps are obtained from vectorized population responses. Numerical simulations generate visual, motor, and mixed visuomotor response maps. A competition rule between visual and motor responses produces incidence ratios close to experimental observations in macaque visuomotor cortex. This framework provides a first neurogeometric approximation of visuomotor functional architecture and a mathematical setting for studying visually guided action.

A fundamental biological process of transcription occurs in the cell nucleus, which is a complex medium that also contains multiple heterogeneous structures known as biomolecular condensates. Interestingly, some of these condensates contain mRNA molecules in addition to proteins, suggesting an important cellular role in transcription that is not yet well understood. In this work, we develop a minimal theoretical framework for quantitative investigation of the role of reversible mRNA condensation in transcription. Our discrete-state stochastic approach accounts for the most relevant processes, allowing us to explicitly evaluate the properties of the system and clarify the effects of condensation. Analytical calculations supported by computer simulations suggest that reversible mRNA condensation influences the transcription processes by maintaining a constant level of free mRNA in the nucleoplasm while lowering the degree of stochastic noise and increasing the robustness against external perturbations. Physicochemical arguments are presented to explain these observations. The proposed theoretical framework elucidates important microscopic aspects of transcription, providing a convenient quantitative tool for investigating complex biological phenomena.