Physical Review Letters

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.

Protein folding is the process by which a polypeptide chain organizes into its three-dimensional structure through a balance of stabilizing and destabilizing interactions encoded by the sequence. A central question in protein biophysics is how thermodynamic factors guide a polypeptide toward its native folded state despite the rugged energy landscape and the competing influence of nonnative interactions. In many biomolecular processes, cooperativity provides a mechanism by which multiple weak interactions act collectively to generate a robust response. In the context of protein folding, such cooperative effects may arise when the formation of one native contact enhances the stability or likelihood of nearby native contacts, thereby promoting collective organization toward the folded state. At the same time, folding is opposed by the much larger number of non-native interactions, whose heterogeneity can introduce frustration and destabilize folding even when the average native bias favors the folded phase. The interplay of these competing effects in determining foldability remains unclear in statistical-mechanical models. Here, we address this problem using a one-dimensional spin-glass model of protein folding with explicit shared-residue cooperative interactions encoded through wedge-based motifs. We show that modest cooperative bias can stabilize folding even where the noncooperative system remains unfolded, whereas non-native energetic fluctuation suppresses folding and shifts the transition to higher cooperative strengths. We further find that partial cooperative coverage is sufficient to lower the folding threshold. Therefore, the model provides a mean-field framework for incorporating cooperative interaction strength into the native one-dimensional model of protein folding and for describing how local cooperativity reshapes the folding transition.

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.

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.

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.

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.

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.

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.

The chirality of proteins originates at the C stereocentre of each L-amino acid, and is expressed in secondary structure as the consistent twist of -helices and {beta}-sheets. How far does this handedness propagate as secondary-structure elements pack into a tertiary fold? This question is central to the development of neural networks for the design of heterochiral and mixed-chirality proteins containing mirror-image D-amino acids. Such networks are most effectively trained on the far more abundant structural data available for natural all-L proteins, yet in practice they must generate and evaluate the reflected, D-configured counterparts, which are not explicitly represented in the training set. Here, I develop a spatial tessellation-based parity-odd descriptor, the signed volume of Delaunay tetrahedra (VD), to measure how chirality is distributed in protein structure. Reflecting a structure only flips the sign of any parity-odd descriptor, so the asymmetry of the VD distribution quantifies the chirality of a given sequence-local or tertiary structural element. I find that the signed Delaunay volume distribution within individual secondary-structure elements is strongly asymmetric, but this handedness largely cancels once elements pack against one another. The resulting tertiary distribution is nearly symmetric across a broad range of structures, from monomers to protein-protein and protein-ligand complexes. Individual folds can nonetheless be strongly handed at the tertiary scale, solenoid and repeat proteins most of all, yet across a broad sample of the fold universe this handedness cancels, leaving the ensemble near-achiral. Tertiary packing is therefore only weakly chiral, with the small residual handedness greatest at binding interfaces and near-zero in the buried core. How much chirality a model perceives in a D-protein is thus largely a choice of representation, a trade-off between reflection symmetry and the richness of structural information the representation retains. Because VDreduces the parity-odd content of each structural element to a single scalar while capturing tertiary protein packing, it offers a natural representation for the design of heterochiral complexes and mixed-chirality proteins. Significance StatementThe macromolecules of life are handed, and this mirror-asymmetry is built into every protein at the scale of its amino-acid monomers. Local segments of proteins are also strongly handed. Alpha helices and beta sheets are consistently right-handed. Does this handedness build up through the layers of a proteins structure, as in some synthetic polymers, or cancel? Using a geometric test across thousands of structures, we find that it largely cancels: the 3D-packing of a folded protein, when described as a tetrahedral tessellation, is almost symmetric under reflection, though its building blocks are not. This means that the design of mirror-image D-protein binders, which are attractive as protease-resistant, low-immunogenicity drug candidates, could rely on AI models trained only on natural L-proteins, using representations developed here.

Cells communicate with their environment by integrating signals, often chemical in nature, triggered by specific molecules bind to specific membrane-bound receptors, resulting in a downstream signaling cascade. Arguably, G-protein-coupled receptors (GPCRs) constitute the most pharmacologically important family of such receptors, binding small molecules, peptides, lipids, and hormones with high specificity. However, despite a highly conserved fold and sequence similarity, GPCRs are still mostly studied on a case-by-case basis. Here, we infer a general, evolutionarily conserved mechanism of class A GPCR activation. By leveraging coevolution and machine learning methods applied to all class A GPCRs structures, we derive a mathematical description (a so-called collective variable - CV) of the receptor's activation state which is independent of its sequence. Then, we bias molecular dynamics simulations along this CV to obtain transitions between activation states of a diverse set of class A GPCR family members. To demonstrate that our model generalizes beyond GPCRs in our training set, we obtain conformational transitions of an orphan receptor, GPR183. Finally, we show that we can model ligand effect on the receptors by converging Free Energy Surfaces of activation of the {beta}2-adrenergic receptor within this common mechanism framework. These results, to our knowledge, prove for the first time the existence of a mechanism uniting all class A GPCRs. Our approach thus facilitates direct comparisons between receptors and opens up the possibility of structural and dynamical studies of many orphan and understudied GPCRs. It also serves as a blueprint for inferring family-wide protein mechanisms.

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.

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 perform a large-scale computational characterization of the map of protein primary to secondary structure using an AVR3a class protein effector domain from the plant pathogen P. palmivora as a case study. We formulate a modified site-scanning approach for exploring the neutral component of secondary structure phenotypes based on predictions from the machine-learning algorithm Porter 5 and apply it to the AVR3a phenotype. We predict a set of sensitive sites within the effector domain that are generally located at or near the boundaries of structured regions, with restrictions on the possible amino acid residues at these sites dictated by the secondary structure type that they participate in within the WT. We characterize a set of mutated phenotypes derived through the exploration of the neutral component of the WT effector domain, selecting them so that they span a range including both very rarely and very commonly seen secondary structures, and that they include both secondary structures nearly identical to the WT and ones far removed from it. We find that all these diverse phenotypes have an estimated robustness of the same order as that of the WT, and that the robustness scales logarithmically phenotype frequency, as seen in other genotype-to-phenotype maps. Furthermore, we observe that the dependence of the estimated phenotype frequency on the Kolmogorov complexity indicates simplicity bias in the protein secondary structure map.

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.

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.

Protein structure predictors achieve high single-state accuracy, but it remains unclear whether they can recover functionally relevant conformational ensembles or account for the presence of ligands and/or binding partners. Here, we benchmark AlphaFold3, Boltz-2, Chai-1, and BioEmu on four canonical multi-state proteins (Pf-MATE, LAO, SecA, and {beta}2AR), quantifying state bias and sampling breadth against experimental reference structures. Models frequently default to a dominant state represented in the PDB; small-molecule ligands have weak or inconsistent effects, while large protein partners drive clear conformational switching between states. Multiple sequence alignment (MSA)-based approaches (AF-Cluster and random subsampling) recapitulate similar biases, indicating that this behavior is not unique to newer architectures. These results underscore current limitations for multi-state protein structure prediction and structure-guided ligand discovery. TOC Graphic O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=111 SRC="FIGDIR/small/737860v1_ufig1.gif" ALT="Figure 1"> View larger version (12K): org.highwire.dtl.DTLVardef@3bf389org.highwire.dtl.DTLVardef@1f1c436org.highwire.dtl.DTLVardef@188ea8aorg.highwire.dtl.DTLVardef@1de236e_HPS_FORMAT_FIGEXP M_FIG C_FIG

Chromatin is an actively remodeled polymeric system whose organization emerges from the interplay of equilibrium interactions and ATP-dependent processes. Recent in vitro experiments show that nucleosome spacing and ATP-dependent remodeler activity significantly influence chromatin condensate properties. Here, guided by these observations, we develop a hierarchy of coarse-grained models that systematically dissect the roles of nucleosome spacing, remodeler-mediated binding-unbinding kinetics, and active force generation in governing condensate dynamics. We demonstrate that nucleosome spacing heterogeneity is a key determinant of condensate material properties. Condensates formed from regularly spaced fibers exhibit enhanced internal mixing, whereas those assembled from disordered spacing develop pronounced structural correlations, increased entanglement, and suppressed internal dynamics. Incorporating remodeler-like binding-unbinding nonequilibrium kinetics drives local structural reorganization, leading to condensate swelling and a substantial acceleration of internal relaxation. In condensates of heterogeneous fibers, contrasts in spacing and activity robustly drive spatial segregation, giving rise to stable core-shell architectures. Strikingly, when dipolar forces are coupled to hydrodynamic interactions, serving as a minimal representation of active nucleosome translocation, condensates exhibit enhanced center-of-mass motion. Together, our results establish a predictive coarse-grained framework that quantitatively links structural heterogeneity and active processes to emergent chromatin-like condensate organization, mechanics, and transport.

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.

Conventional LD measures such as r2 perform poorly in the rare common regime, particularly in asymmetric configurations such as nested haplotype structure. Because r2 is symmetric and quadratic, it removes directional structure in two ways: squaring discards the sign, or phase, retained by the signed LD coefficient D, while symmetric normalization hides the asymmetry between the conditional probabilities P(A|B) and P(B|A). Although D recovers the phase, it is locus symmetric and unnormalized; its magnitude is hard to compare across frequency regimes and it does not by itself express which way the asymmetry runs. We therefore analyze the conditional-probability asymmetry {Delta} = P(A|B) - P(B|A), together with r2 and D, as distinct scalar functions on the haplotype simplex under the Fisher information metric. The conditional probabilities P(A|B) and P(B|A) are bounded in [0, 1], directly express carrier-set inclusion, and are more readily visualized than D. Moreover, their difference admits the exact decomposition {Delta} = M + C into a marginal frequency term M and an LD-coupled term C. Prior work has characterized either the mathematical behavior of LD normalizations across allele-frequency space or the Fisher geometry of the haplotype simplex, but not their connection. We bridge this gap by showing that the geometric structure of the simplex explains why LD measures disagree in the rare common regime and why symmetric normalizations such as r2 lose directional information. We show that the fixed-frequency leaf is intrinsically anisotropic, positively curved, and frequency-dependent under the Fisher metric. These geometric predictions are tested empirically , in phased 1000 Genomes data1 and a two locus Wright Fisher model, in a companion paper (Ichikawa, preprint); the present note develops the geometry itself. Keywords: linkage disequilibrium; Fisher information metric; haplotype simplex; rare variant; conditional-probability asymmetry; nested haplotype structure