Physical Review Research

The relationship between genotypic and phenotypic variation is determined by the complex interaction of genetic and environmental factors. While statistical methods capable of detecting such interactions exist, an axiomatic mathematical framework that seamlessly describes the combined effects of genetic modifications and environmental exposures on a common scale is lacking. In this report, buffering concepts are used to construct a measurement system that enables the geometric representation of both gene-by-gene and gene-by-environment interactions on the extended complex plane (i.e., as projections on the Riemann sphere). In this manner, any such interaction, or combination thereof, can be precisely defined and quantified as the deviation from the neutral value calculated through the applicable complex transformation. When thus conceptualized, the framework's parameterization defines the "state space" of a given measurable phenotype along both the real and imaginary dimensions, thus establishing an unambiguous and broadly applicable method for determining the phenotypic value expected upon combinatorial changes in genetic and/or environmental variables. Remarkably, by applying these methods, it is possible to quantify the effects of any gene-by-environment interaction using the equation, AGxE=Im([z]obs*zexp)/2, where zobs and zexp are complex numbers representing the observed and expected phenotypes of a given genotype expressed in terms of the buffering parameters, and b.

Diffuse gliomas are deadly because the individual tumor cells invade - they travel far from the imageable mass, so it is impossible to remove the tumor completely. On the cellular level, glioma cells seem to be in either a "go" state (in which they do not divide) or a "grow" state (in which they do not migrate). We investigate what this tiny choice has to say about the large-scale speed of the invasion front and whether the implication is sufficiently strong to rule out the classical description of the Fisher-Kolmogorov-Petrovsky-Piskunov (Fisher-KPP) type, in which a single phenotype migrates and proliferates. We derive a two-phenotype reaction-diffusion model with density-dependent switching, and we prove the cooperative (quasi-monotone) structure and the associated comparison principle and study travelling-wave solutions of the model. A leading-edge linearization gives minimal front speed as minimizer of an explicit dispersion relation, and direct simulation verifies the predicted speed. In the experimentally relevant fast switching limit, we find a closed-form expression for the speed, that is, we obtain an effective Fisher-KPP equation with rescaled diffusivity and growth rate, with the fractions of the phenotypes. The "go-or-grow" (GoG) front can move at a maximum speed of half the Fisher speed for the same single-cell motility $D$ and proliferation rate $r$, which occurs only when the cells divide their time equally between the two phenotypes. This bound is directly testable: measurement of the front speed, plus independent determination of $D$ and $r$, discriminates the two hypotheses, and in the GoG case, yields recovery of the phenotype balance. We then extend the result to anisotropic (DTI-informed) invasion along white-matter tracts and discuss implications for understanding clinical measurements of growth rate.

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.

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.

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.

Cetaceans reduce the net cost of sustained swimming through intermittent locomotion, alternating active fluking with unpowered gliding. The energy balance of this strategy is central to understanding survival rates, population sustainability, and the effects of anthropogenic and environmental pressures. While active-phase energetics have been characterized extensively, the glide phase remains largely unexplored. Here we derive the optimal glide duration (Topt) and the maximum glide duration beyond which energy savings vanish (Tzero) for three odontocetes spanning a 20-fold range in body mass, using high-fidelity CAD models and wall-modeled large eddy simulations. We show analytically that speed retention at Topt and mass-specific peak energy savings are both fully determined by the active-to-passive drag ratio, propulsive efficiency, and swimming speed, independently of body morphometry and drag coefficient, and are therefore invariant across species at any given speed. These passive-phase optima extend the known size-independent active-phase invariants to the glide phase, towards a scale-independent energetic framework for burst-and-glide locomotion in small cetaceans.

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.

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.

Phages must locate and bind to bacterial surface receptors to initiate infection. Their tail fiber configuration critically influences this process. We develop a stochastic model describing surface search as a renewal process, incorporating attachment, detachment, and target-finding steps. Using both numerical simulations and analytical calculations, we quantify how tail fiber number, attachment-detachment rates, and geometric constraints impact the mean and the distribution of time to successful adsorption. Notably, the search efficiency shows a nonmonotonic dependence on tail fibers number, governed by a trade-off between binding stability and diffusion-mediated mobility. This optimum shifts depending on the effective bacterial density, target radius, and fiber reach. Short fiber reach imposes severe geometric constraints, reducing mobility at high tail fiber counts and leading to performance degradation. Our findings suggest that phage adsorption strategies are shaped by a balance between anchoring and exploration, with evolutionary implications for tail fiber design and infection efficiency.

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.

What drove nucleic acids (NA) to associate with proteins (PR) at the Origins of Life? We reason from polymer physics and the Central Dogma (CD) that the fitness value of cooperating through a division of labor - NA for replication fidelity and PR for functional fitness - is much higher than for either polymer alone. Our model shows a Pareto Front, where NA and PR can bootstrap each other to achieve autocatalytic cooperativity towards biology.

Despite extensive study of cellular mechanisms underlying long-term potentiation, no single specific protein or gene has been identified which encodes an individual unit of information, or memory bit. Indeed, the brain engram remains a knowledge gap. The theory of exclusion led us to cancel one-by-one several unrealistic biological options, suggesting that the explanation resides somewhere else. Superposition of up to concentric 300 myelin layers, spiraled, and highly compacted wrapping a single axon and each wrap could host hundreds to thousands of niches, as memory cells, collectively consisting of a massive array of cells. The disjointed 3D spatial superposition allows storage of charges, nodes not facing from a layer to next. The thickness of a single myelin layer ranges from 7.0 to 20 nm. The dimension scale is approximately the exact dimensions of the charge trap, the tunnel and dielectric also equipping current AI microchips. Stored charges are positive ions, with similar effect whether charges are negative or positive charges creating an electromagnetic field. To write data, following an action potential, this voltage applies to the control gates of the myelin layers producing an ionic charge injection. This causes charges to gain energy and tunnel through the myelin layer across Ranvier nodes, via quantum tunneling, and deep into the concentric myelin multilayers. This is creating an insulated trapping of K+ ions isolated from the system. In a long white matter tract bundle, the near-perfect isolation of millions of axons within compressed myelin wrap-ion channel K+/Na+ systems provides quantum coherence and precision of asynchronous firing property. The injected ionic charges (K+) become physically stuck in traps within the myelin layers. The K+ ions may not move freely, completely trapped after AP ceases. Mirroring a single-bit, single-level-cell, a trapped ionic charge (ions K+) may represent a 1, while an empty cell (absence of K+) represents a 0. The trial-and-error process, with a Bayesian inference which may have also been the core evolution of the learning human brain. Based on selected mathematical equations, we analyzed the general scheme on how deep learning may be embedded in the brain

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.

Rotating helices have been utilized for many purposes, including the transport of solid material and fluids within man-made machines, for a little over two millennia. Here, we show that the rotation of a biological helical molecule--a DNA duplex--can move water and ions through a nanoscale pore. While the rotation-induced flow of water is generated by the steric shape of the DNA molecule, an even faster transport of cations is caused by electrostatic interactions. The rotation-induced ion flux is found to depend on the cation type, offering potential utility for ion separation. Finally, we show that the torque-driven duplex can move ions against a concentration gradient, realizing the Archimedes screw principle at the nanoscale.

Animals navigating complex vertical environments must secure stable footholds, a challenge for species without feet. While arboreal climbing has evolved repeatedly in snakes, the physical mechanisms they use to scale broad, nearly flat surfaces remain poorly understood. By measuring three-dimensional body kinematics and per-contact forces on a smooth vertical wall with protruding posts, we show that cornsnakes climb by dynamically balancing forces across a highly redundant network of 5 to 16 simultaneous contacts--far exceeding the three contacts minimally required for physical stability. Using a computational model and a robotic climber, we demonstrate that while simple body undulations and passive friction are mechanically sufficient to climb this terrain, snakes systematically deviate from this passive baseline. While downward climbing relies primarily on friction, ascending snakes actively generate positive mechanical work at their contacts to propel themselves. Furthermore, we found that whenever a snake engages a new contact, it triggers a stereotyped, system-wide redistribution of force that seamlessly integrates the new foothold without disrupting whole-body balance. These results reveal how a continuous, flexible body can transform sparse environmental features into a robust, fault-tolerant network. This mechanism provides a biomechanical framework for understanding the repeated evolution of limbless climbing and offers physical principles for designing agile robots for unstructured terrain.

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.

AO_SCPLOWBSTRACTC_SCPLOWEarly tumor detection is critical for improving patient survival and recovery. Clinically, tissue palpation is routinely used to identify regions of abnormal stiffness, a hallmark of many pathological conditions. However, palpation is restricted to anatomically accessible sites and remains highly operator dependent. Here, we introduce a method for real-time quantitative stiffness mapping using an unmodified commercial endoscope, with the goal of enhancing diagnostic capabilities and restoring mechanical feedback during endoscopic procedures. Our approach combines shear wave elastography with speckle imaging and an innovative synchronization strategy that enables the measurement of shear wave propagation using an unmodified commercial endoscope. The resulting wave fields are analyzed with the noise-correlation-inspired (NCI) method[1], providing pixel-wise estimates of shear wave velocity and, consequently, quantitative maps of local tissue stiffness. The method demonstrated robust performance in both benchtop and endoscopic configurations. Validation was achieved on polymer phantoms as well as on ex vivo and in vivo biological tissues, highlighting its potential for minimally invasive biomechanical imaging and real-time tissue characterization.

Protein-RNA binding and biomolecular condensation are two key processes underlying the assembly and function of ribonucleoprotein (RNP) condensates. However, the understanding of the physical consequences of their interplay is still incomplete. To investigate this coupling, here we develop a minimal coarse-grained molecular model that combines specific, saturable protein-RNA binding with multivalent protein-protein interactions. Our results show that RNA acts as a molecular scaffold whose ability to promote condensation depends on the distribution of bound proteins across RNA molecules. This provides a simple microscopic explanation for both RNA-length-dependent condensation and re-entrant phase behavior, showing that condensate dissolution at high RNA concentration can emerge from entropic effects without requiring explicit electrostatic interactions. Conversely, condensate assembly markedly enhances effective protein-RNA binding, demonstrating that substantial changes in binding behavior can emerge without changes in intrinsic affinity. This provides a general physical mechanism through which condensates can reshape molecular competition between RNA-binding proteins. Together, these findings establish a framework linking RNA binding and biomolecular condensation, illustrating how their interplay governs condensate assembly.

Auxetic metamaterials exhibit negative Poisson's ratio behaviors due to their architecture of periodically arranged unit cells. Although mechanical metamaterials are well established at the macroscale, programmable auxetic units remain scarce at the nanoscale. DNA origami offers a promising platform to bridge this gap, but design principles for dynamically deformable 3D auxetic nanostructures remain largely unexplored. Here, we develop design strategies for such 3D auxetic metastructures built from wireframe DNA origami. As a model system, we use a 3D re-entrant triangular unit composed of double-stranded DNA (dsDNA) bundle edges connected by single-stranded DNA (ssDNA) joints. Using coarse-grained molecular dynamics (MD) and umbrella-sampling free-energy simulations, we examine how edge design and joint-connection scheme govern auxetic responses and the energetics of the structural transformation. Our results show that auxetic performance and deformation energetics emerge from the coupled effects of DNA bundle rigidity and connector mechanics at the joints. This study provides mechanistic insights and design guidelines for programmable auxetic motion and energetics in 3D DNA origami metamaterials, advancing the development of stimuli-responsive nanomechanical devices.

Directed migration along chemical gradients controls immune surveillance, development, and cancer invasion. However, the same chemical cue can produce different responses depending on its concentration and whether cells move alone or in groups. For example, in steep gradients, isolated malignant lymphocyte cells migrate away from the chemoattractant source, whereas clusters of the same cells continue to migrate toward it. Here, combining computational modeling and experimental observations, we show that this reversal is governed by coupled mechanisms acting across molecular, cellular, and collective scales. At the single-cell level, our model predicts that receptor endocytosis generates a feedback that produces a nonmonotonic surface receptor density with increasing chemoattractant concentration. Above a critical concentration that depends on the cell's volume-to-sensing-area ratio, receptor depletion reverses cell polarity and drives chemorepulsion. However, in clusters, cell-cell contacts reduce the membrane area exposed to ligand, increasing the volume-to-sensing-area ratio, thus increasing the critical concentration and preserving chemotaxis. An agent-based model incorporating these mechanisms quantitatively reproduces the sign reversal of the migration index across gradient steepness and cluster size. We show that collective rearrangements further stabilize chemoattraction with exchanges between the cluster rim and core helping remove chemorepulsive cells from the leading edge, keeping their fraction below the threshold required to reverse cluster migration. The model further predicts, and experiments confirm, that increasing ambient ligand concentration while keeping the gradient fixed reduces cluster chemoattraction. Our results identify receptor trafficking, cell geometry, and cluster fluidity as physical determinants of collective directional decision-making, with implications for immune cell homing, tissue morphogenesis, and cancer dissemination.