Physical Review Letters

Two-dimensional accounts of consciousness that distinguish global integration from functional diversity are empirically supported [1,2] but lack a formal phase-structure: they do not specify the nature of the transition between the two regimes, the order parameter that governs it, or the quantitative predictions that follow. We provide this structure. We propose that the dimensionality of the neural correlation structure, operationalised as the Participation Ratio of the covariance eigenspectrum, constitutes a second, independent order parameter D that governs a phase transition distinct from global integration {Phi}. Formalised through a Landau-Ginzburg free energy functional F[{Phi}, D], this transition defines a Redundant Integrated State {Delta} (high {Phi}, low D) in which globally integrated mental function is present but phenomenal experience is absent, a thermodynamic phase, not a point on a continuum. The framework generates three falsifiable predictions absent from prior work: (i) a power-law scaling D* [~] |{Phi} - {Phi}_c|^{nu} with measurable critical exponent{nu} ; (ii) a diverging susceptibility {chi}_D = {partial}D/{partial}{Phi} at the consciousness threshold, quantifiable from perturbational EEG; (iii) an explicit dissociation between MCS and VS patients in the ({Phi}, D) space, with MCS predicted to occupy state {Delta}. These predictions are directly testable with existing methodology and are not generated by any current theory of consciousness.

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.

The emergence of amino acids (AAs) and nucleobases (NBs) across meteorites, interstellar ices, and laboratory shock experiments presents a paradox: why do these specific molecular motifs--a minuscule subset of organic chemistrys combinatorial space--appear repeatedly across diverse environments, in the absence of biological selection? We identify a physical mechanism, prebiotic selection, which biases driven chemical systems toward configurations with high stationary probability p*(x) under sustained entropy flux. The bias is quantified by an information quasi-potential {Phi}I (x) = - ln p*(x), entering the overdamped Langevin dynamics O_FD O_INLINEFIG[Formula 1]C_INLINEFIGM_FD(1)C_FD where {Sigma} is the local entropy production rate (Schnakenberg 1976). {Phi}I is defined self-consistently via the full non-equilibrium stationary density, avoiding the circularity of identifying it with a scalar potential. Two central theorems underlie the framework. Theorem 1 establishes that {nabla}{Sigma} and {nabla}{Phi}I are generically linearly independent off equilibrium, so the dynamics is genuinely two-field. Theorem 2 (structural constraints on single-field gradient dynamics) shows that single-field models on compact manifolds (i) produce yield curves that are at most unimodal under linear driving, and (ii) combine disjoint perturbations additively, giving superlinearity factor S = 1 + O(||{delta} V ||2). The observed superlinear synergy of Ferris et al. (1996) lies far outside this perturbative bound and therefore requires the two-field structure of EOM-IFF; the non-monotonic peak of Blank et al. (2001) is consistent with two-field dynamics and also with single-field dynamics in the unimodal-with-peak case of Theorem 2 part 1, so it does not by itself discriminate. From these results, we: (i) define a formal substrate-minimal criterion for prebiotic selection; (ii) show consistency with the non-monotonic shock-synthesis yield of Blank et al. (2001) (R2 = 0.885, peak at P* = 28.4 {+/-} 1.4 GPa); (iii) show consistency with the superlinear clay-catalysed RNA polymerisation of Ferris et al. (1996) (synergy factor S {approx} 5.75, robust under {+/-}1-nucleotide measurement uncertainty); and (iv) state two further falsifiable predictions awaiting dedicated experimental tests. Every lemma and theorem is accompanied by explicit assumptions, regime of validity, and regime of failure; the frameworks scope is what it claims, not more. Prebiotic selection is identified as a physical process distinct from and prior to biological selection, offering a unified account of chemical convergence in carbon-nitrogen chemistry under sustained entropy flux.

Brain dynamics can be described in three different convenient mathematical languages, namely connectome harmonics, turbulence and complex harmonics (CHARM). Here we demonstrate that these theoretical frameworks can be rigorously unified, under the functional calculus, as one self-adjoint operator and its single spectral measure. The connectome Laplacian carries that measure; the harmonics are its spectral projections, the turbulence smoothing kernel is its resolvent, and the CHARM form is its unitary propagator. The bridge that makes this exact is a textbook fact: The exponential distance rule, which is the empirical kernel of the turbulence model, is the Greens function of a screened Laplacian, so the local order parameter is the phase field passed through the resolvent of the same operator whose eigenfunctions are the harmonics. A single shared control parameter, the spectral gap, simultaneously yields the cortical hierarchy, the turbulent information cascade and the structured interference the CHARM form measures. This unification makes a strong predictive claim. If the harmonic projections, the turbulence resolvent and the CHARM propagator really are three functions of one operator, then any structural perturbation that re-tunes the operator must move all three signatures in unison and must do so with a single coupling. We test this prediction with a pharmacological perturbation by lysergic acid diethylamide (LSD), which is known to change the emotional state, by empirically perturbing the operator with a 5-HT2A receptor density map and asking whether one scalar coupling can simultaneously predict the multi-scale turbulence shift observed, through the resolvent, and the macroscale harmonic energy redistribution, through first-order Rayleigh-Schrodinger perturbation theory. We found that the two independent functional domains respond in unison to one structural perturbation of one operator. The identity is exact as operator calculus and its purchase on the brain depends on a single load-bearing seam, the degree heterogeneity of the connectome, which we make explicit. We propose that this single-operator structure is the necessary mathematical scaffolding of our Entangled Loop theory.

Reentrant phase transitions, in which multicomponent systems phase separate at intermediate concentrations but dissolve at experimentally accessible higher concentrations, are ubiquitous in mixtures such as biomolecular condensates. We show that introducing reversible dimerization into a multicomponent Flory-Huggins model and integrating out the dimer state generate an effective three-body repulsion that reshapes phase diagram geometry. This emergent higher-order interaction arises naturally from an interaction competition and mass-action equilibrium, providing a microscopic explanation to the previously phenomenological three-body interaction. We derive a closed-form phase boundary equation capturing phase separation and reentrant dissolution in this minimal model, and predict explicit interdependence between competition strength, emergent many-body interactions, and dissociation constants. We recover and extend the reentrant phase boundary scaling relations through interaction renormalization, with regime of validity. We apply our model to G3BP1-RNA-suramin and explain the underlying mechanisms from the physical parameters inferred from reentrant phase boundaries.

Transcription factors organize into liquid-like condensates to facilitate gene expression, yet the physical mechanisms governing their formation and properties remain poorly understood. We study the size statistics of transcriptional condensates in human HAP1 cells using widefield and super-resolution microscopy tagging the epigenetic reader BRD4. We find that hubs that appear monolithic in widefield resolve into clusters of smaller droplets that resist coarsening. We link this size control to Active Model B+, a non-equilibrium field theory that captures a regime of reverse Ostwald ripening out of thermal equilibrium. In this regime, chemically driven currents cause larger droplets to transfer mass back to smaller ones, stabilizing a state of microphase segregation. The observed exponential size distribution of BRD4 foci quantitatively matches our numerical simulations, suggesting a universal physical picture for the non-equilibrium self-limitation of cellular condensates.

Arterial thrombosis is initiated when mechanical forces in flowing blood exceed the activation thresholds of platelets and von Willebrand factor (vWF). Despite extensive experimental characterization of shear-induced platelet aggregation, a unified theoretical framework that maps hemodynamic forcing onto clot nucleation is lacking. Here we present Force-Gated Thrombosis (FGT), a non-equilibrium mechanical theory that treats thrombus formation as a continuous phase transition driven by an effective mechanical forcing {Sigma} ={sigma} + |{nabla}{sigma}| + {beta}{varepsilon}, which combines local wall shear stress{sigma} , shear gradient |{nabla}{sigma}|, and extensional strain rate{varepsilon} . We introduce a dimensionless Thrombosis Number {Theta} = ({Sigma}/{Sigma}c)(P/P0)m(C/C0)n, which incorporates platelet concentration P and coagulation factor concentration C, and governs the transition between stable flow ({Theta} < 1) and active clot growth ({Theta} > 1). The thrombus density is represented by a scalar order parameter{varphi} whose dynamics follow a Ginzburg- Landau free energy functional. For a simplified stenosed artery we derive an analytic closed-form thrombosis onset criterion and a critical flow rate [Formula], where{delta} is stenosis severity. Linear stability analysis shows that perturbations grow at rate{omega} (k) = {Lambda}({Theta}) - D{varphi}k2, becoming unstable when {Theta} > 1. Near threshold the clot volume fraction scales as{varphi} [~] ({Theta} - 1)1/2, a mean-field critical exponent consistent with Ginzburg- Landau theory. Systematic comparison with fifteen published experimental and computational datasets spanning shear rates from 100 to 15,000 s-1 confirms that FGT correctly predicts the existence, location, and approximate severity of pathological thrombus formation across diverse vascular geometries. The theory provides a quantitative bridge between single-molecule mechanobiology and macroscale clinical thrombosis, and yields experimentally testable predictions distinguishing FGT from purely biochemical models.

The hierarchical organization of multiphase biomolecular condensates into core-shell architectures is a fundamental problem in soft matter and biophysics. While classical explanations rely on hierarchies of interfacial tension ({gamma}) between coexisting liquids, the ultralow tensions of condensates (0.1-1 {micro}N/m) render such hierarchies potentially fragile. We introduce a robust assembly principle based on Polymer-Assisted Condensation (PAC), in which a single polymer species dictates the entire structure. The polymer nucleates a dense core by recruiting a condensation-incompetent protein (P1). A second incompetent protein (P2), which is repelled or otherwise thermodynamically disfavored from entering the polymer-rich core, is nonetheless recruited to the interface by weak attraction to P1, forming a stable shell. This effective repulsion-driven layering operates across a wide parameter space without requiring{gamma} asymmetries and yields a robust structure that is impervious to concentration fluctuations and environmental perturbations. Phase-field modeling and molecular simulations establish this mechanism and capture key features of nucleolar organization. Our work reveals a general physical pathway for encoding spatial order in soft, multicomponent fluids.

Bacterial propulsion is powered by torque generated by the flagellar motor and transmitted to the flagellum through the hook, a short deformable structure acting as a flexible joint. Despite the hook being essential for propulsion, the physical mechanism governing torque transmission remains poorly characterized. Here, we show that the torque consists of two components: one parallel to the flagellum, responsible for rapid spin, and another along the motor axis, which induces precession of the former component. Evidence of such a two-component torque also emerge in bead assay experiments, where the attached bead can exhibit complex trajectories rather than simple circular motion. We introduce a minimal mechanical model that captures both the spin/precession dynamics and the commonly observed circular orbits.

How is it possible to double the lifespan of an organism already close to death? Many biological theories of aging fail to explain this phenomenon. At the Physics of Aging workshop, we presented and discussed late-life lifespan extension in Caenorhabditis elegans to illustrate how a simple stochastic dynamical systems model can account for dramatic geriatric interventions. We build on a Langevin-type instability framework in which aging is a manifestation of dynamical instability-a scenario where stochastic fluctuations amplify over time, driving the system toward a failure thresh-old at which death occurs as a first-passage event. The instability rate (equivalently, the inverse of the mortality-rate doubling time) quantifies the speed of this divergence: a larger means faster exponential growth of z, a steeper Gompertz slope, and a shorter lifespan. The failure threshold zmax{approx} /g, where g is the strength of nonlinear feedback, marks the point beyond which the system diverges irreversibly--physiologically, the saturation of metabolic and regulatory capacity. Within this dynamical-systems framework, auxin-induced degradation of the insulin/IGF-1 receptor DAF-2 in very old animals is naturally interpreted as a late shift in stability parameters that nearly doubles remaining lifespan without resetting accumulated structural damage. This interpretation reconciles the persistence of many senescent pathologies with restored proteostasis and stress resilience, and it shows that targeting the dynamical instability of the regulatory network-rather than reversing damage--can strongly reshape survival trajectories in unstable animals. More broadly, our work exemplifies how physics-inspired low-dimensional stochastic models can capture key features of aging, and we hope it will inspire more collaborations between biologists and physicists to work on late-life interventions.

Mechanical properties of epithelial tissues play essential roles in morphogenesis and physiological function. In this study, we analytically derived the in-plane bulk modulus, shear modulus, and Poissons ratio of a three-dimensional cell vertex model of epithelial monolayers. We showed that the model can robustly reproduce a near-zero in-plane Poissons ratio, a mechanical feature reported in cultured epithelial tissues. Numerical simulations further confirmed that the theoretically predicted Poissons ratio accurately describes the response of the model under finite, biologically relevant strains. In addition, the model exhibits not only morphological bistability between squamous-like and columnar-like states, but also mechanical bistability characterized by distinct elastic responses. Together, these results provide a minimal three-dimensional framework that links cell-scale mechanical interactions and epithelial morphology to tissue-scale elastic properties.

This Perspective formally proposes Particle Biology as a unifying theoretical framework to address the critical bottleneck in current life science research. Current life science research has reached a critical bottleneck. While the field has advanced to the study of 3D genomic spatial configurations and chromosomal organization, it remains largely descriptive and confined to the macromolecular level. This approach lacks a first-principles understanding of the underlying physical forces that drive biological processes. This Perspective formally proposes Particle Biology as a unifying theoretical framework. We establish an axiomatic system positing that life phenomena are fundamentally emergent spatiotemporal patterns of electromagnetic forces among atoms, electrons, and nuclei operating far from thermodynamic equilibrium. By defining biological states through the Biological Hamiltonian and mapping biochemical pathways to multidimensional Potential Energy Surfaces (PES), we bridge the gap between descriptive biology and predictive physics. We categorize core research technologies into three modalities--seeing, computing, and controlling particles--facilitated by advancements in Cryo-EM, AlphaFold 3, and Boron Neutron Capture Therapy (BNCT). Ultimately, the trajectory of molecular biology has evolved from cells to DNA and onto the 3D spatial genome, yet it cannot go deeper within current paradigms. The next logical evolution is to move beyond the macromolecular bottleneck to focus on the electromagnetic interactions between atoms and ions--the true Particle Biology level--to redefine disease and intervention.

Since the earliest microscopic observations, the geometric organisation of cells has captured biologists interest. Recent work by Gorgi et al. showed that bacterial colony organisation, including biofilms, can be explained across diverse species by radial expansion from fixed initial seeding sites and contact-inhibited growth, with little need for species-specific mechanisms. Here, we extend this geometric framework by incorporating seeding time as an additional driver of colony organisation. Using simulations and analytical models for expected colony size, we show that staggered seeding yields order of magnitude increases in the expected size of early seeded founder colonies. At realistic biofilm growth rates, a 2-day lag between founder and subsequent colony seeding produces an approximately 10-fold increase in expected founder size, while a 1-week lag produces a 25-fold increase. These findings provide a simple geometric basis for biological priority effects, illustrating temporal advantage alone can generate substantial spatial dominance, with implications for cardiovascular devices where host and bacterial cells compete in a race for the surface.

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.

The classical model of bacterial flagellar motility posits a rotary engine driven by proton motive force (pmf), with torque generated by stator-rotor interactions and transmitted through a flexible hook to a helical filament. Despite decades of acceptance, this model faces fundamental challenges in thermodynamics, structural mechanics, evolutionary parsimony, and direct observational evidence. We develop and quantitatively test the murburn model, a new paradigm for bacterial motility in which water, produced as an inevitable byproduct of metabolic redox activity, is ejected via the basal secretory module and channelled along the spiral grooves of the flagellar filament. The ejected flow creates a local shear field that induces a transverse bending wave; the precession of this wave is observed as apparent rotation and generates thrust through anisotropic viscous drag, without any rotary motor, ion gradient, or axial rotation. The principal contribution of this work is a self-contained, first-principles treatment of this mechanism: for a unipolar flagellated cell we derive the governing low-Reynolds-number elastohydrodynamic relations from slender-body theory and show that physiologically realistic rates of metabolic water production reproduce the observed swimming speeds and apparent-rotation frequencies at a small fraction of the cellular energy budget, while direct jet propulsion is quantitatively excluded. Building on this derivation, we provide a force-balance comparison of the competing propulsion mechanisms, obtain a set of falsifiable predictions that distinguish the murburn model from the rotary motor, and report a structural analysis of cryo-EM flagellar-hook architectures that reveals solvent-accessible radial canals consistent with lateral water transport. The same single principle accounts for swimming, tumbling, gliding, spirochete undulation, and archaeal motility, without requiring rotating shafts, ion-gradient coupling, or complex switching mechanisms.

Budding is a fundamental membrane-remodeling process central to many cellular functions and is exploited by numerous enveloped viruses to acquire their lipid envelopes. Despite extensive molecular characterization, the physical mechanisms that determine whether budding proceeds to completion or becomes stalled remain unclear. Here, we develop a theoretical model based on the Helfrich elastic formalism to investigate how membrane geometry and boundary conditions regulate the elastic energy of viral budding. We analyze two representative cases: budding from a flat membrane, characteristic of HIV-1 and alphaviruses, and budding from a vesicle, as observed for SARS-CoV-2 in the ER-Golgi intermediate compartment (ERGIC). Our results reveal distinct energetic pathways: vesicle-like geometries exhibit a stronger energetic bias toward closure, whereas flat membranes develop extended low-slope regions in the energy landscape that can hinder completion. Relaxing far-field boundary constraints reduces the energetic cost associated with membrane area conservation and renders the flat-membrane case energetically comparable to the vesicle case, providing a physical explanation for why viruses frequently bud adjacent to one another or within pre-curved membrane regions. Comparison with thin-section TEM images of alphavirus budding shows results consistent with the theoretical membrane profiles. Together, these findings establish how curvature coupling, boundary flexibility, and local membrane geometry cooperate to control the efficiency and completion of membrane budding.

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 thought to play a pivotal role in cellular organization by regulating biochemical reactants in space and time. Sustained molecular fluxes across condensate boundaries, together with the participation of phase-separating molecules in active chemical reactions such as ATP hydrolysis, call for a nonequilibrium description. Here, we propose a self-consistent framework in which diffusion-drift dynamics and chemical reactions are coupled through a conditional free energy, defined as the excess contribution to the chemical potential. Self-consistency is achieved by deriving this quantity from the same free-energy functional that governs molecular interactions and phase separation. We apply the framework to a minimal client-scaffold system and investigate how active chemical processes and phase separation interact at steady state. In doing so, our approach recovers the fundamental rules previously identified for the emergence of nonequilibrium steady-state fluxes. The model shows that active reactions involving the scaffold molecules can regulate the phase behavior of the condensate. Moreover, nonequilibrium steady-state fluxes are maximal near the boundary between the phase-separated and homogeneous regimes, suggesting that condensates sustaining molecular transport may operate close to their stability threshold. In the same region, client fluxes are also enhanced, revealing an indirect coupling between scaffold activity and client transport. These results provide a baseline for developing more detailed theories of chemically active condensates.

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 Poisson-Nernst-Planck (PNP) system is an accurate model of electrodiffusion of ionic species. It is commonly used in situations where nanoscale resolution is required, for instance close to ion channels in the membranes of biological cells. The inherent stiffness of the equations has made them challenging to solve and has limited the applicability of the system. In particular, the time step required for stable solutions has typically needed to be very short (nanoseconds), which makes simulations on the time scale of an action potential (milliseconds) difficult. Recently, it has been observed that avoiding operator splitting and instead solving the concentration equations and the electrostatic equation in a coupled manner relaxes the time-step limitation considerably. However, no theoretical explanation of this observation has been provided. Here, we aim to explain why the coupled scheme allows much larger time steps. We illustrate the mechanism by considering special cases that define necessary, but not sufficient, conditions for stability. We also show that these conditions remain relevant for the fully coupled PNP model in 3D.