Papers

Time-resolved infrared spectroscopy probes protein dynamics over timescales spanning more than ten orders of magnitude, yet the molecular motions underlying the observed kinetic signatures have remained elusive. Here we combine transient infrared spectroscopy with nonequilibrium molecular dynamics simulations to establish a direct connection between experimental relaxation times and local structural motions. Studying single-domain allosteric proteins, we find that inter-residue contact distances provide the structural representation that most faithfully reproduces the experimental dynamics. Correlation analysis identifies localized networks of coordinated contacts that mediate communication between secondary-structure elements. The characteristic timescales of these contact networks quantitatively match the experimentally observed relaxation processes, enabling each kinetic step to be assigned to a specific molecular motion. Applied to allosteric signal propagation in PDZ3 and photoinduced ligand unbinding in PDZ2, this framework provides an atomistic picture of hierarchical protein relaxation and establishes a general framework for connecting transient infrared spectroscopy with the molecular mechanisms of protein dynamics.

We introduce a bioinspired microactuator fabricated via a one-step meniscus guided 3D nanoprinting technique. This technique directly produces a freestanding three dimensional composite architecture by integrating a rigid nanoparticle framework with a hygroscopic polymer matrix in a single, assembly free process. Inspired by the functional integration of rigid and compliant components in insect exoskeletal joint, our design synergistically combines load-bearing strength and humidity-driven swelling in a single microscale pillar. Comprehensive experiments, including comparative control structures and microscopic analysis, elucidated the actuation mechanism: the nanoparticle scaffold provides mechanical support while the polymeric phase provides volumetric expansion, yielding large reversible elongation under humidity with preserved structural integrity. The resulting AuNP PVP microactuator shows humidity responsive actuation at the microscale, with representative demonstrations of repeated humidity cycling and load lifting up to approximately 800 times its estimated own weight under the tested conditions. Variant geometries such as hinged pillars demonstrate how axial swelling can be converted into bending motion, and an optical configuration shows how actuation can modulate reflected light signals. This nanoprinting approach provides a simple strategy for constructing bioinspired soft microactuators with humidity-responsive deformation and potential applicability in microscale sensing, optical modulation, and adaptive microdevices.

Microbial populations generally evolve in fluctuating environments under time-varying conditions. These are often described by binary switching models, sometimes seen as coarse-grained feast-famine cycles, in which resource availability switches abruptly between abundant and scarce conditions. However, experimental studies suggest that feast-famine environments actually exhibit more complex temporal dynamics. Here, we study how two strains, one growing slightly slower than the other, compete for the same resources in fluctuating environments comprising a finite number of intermediate states, each having its own carrying capacity. Environmental switching between these states and their carrying capacities represents gradual changes in nutrient availability. This class of multi-state stochastic switching models can be interpreted as a coarse-grained description of feast–famine cycles and allows us to investigate strain competition under the gradual recovery and depletion of resources. By computational and analytical means, we characterise the population dynamics in these multi-state fluctuating environments. In particular, we study how the switching rates and distribution of carrying capacities affect the population-size statistics, fixation probability, and mean fixation time. By comparing these results with their counterparts in binary environments, we clarify how the frequency and amplitude of environmental fluctuations influence population dynamics in coarse-grained feast-famine cycles.

We establish a self-consistent 2D hydrothermodynamic analytical model for high-intensity focused ultrasound tumor ablation. Expanding compressible Navier-Stokes equations to second order demonstrates that a stationary cellular matrix suppresses acoustic streaming ($\mathbf{v}_2 = 0$). This constraint forces the absorbed wave momentum flux to convert entirely into localized, time-averaged static pressure gradients ($\nabla \langle p_2 \rangle = \mathbf{F}_2$), bridging non-linear hydrodynamics with thermodynamic dissipation. Solving the non-diffusive Pennes bioheat equation under a $1.0\,\text{s}$ top-hat pulse reveals that a spherically focusing geometry ($\propto 1/r^2$) overrides exponential damping past a critical geometric threshold ($r_{\text{crit}} = 2x_0$), preventing upstream skin overheating. We derive an optimization criterion where the absorption coefficient matches half the inverse target depth ($\alpha = 1/2x_0$). Solving the non-isothermal Arrhenius integral yields a sharp lesion boundary radius at $r_b = 0.75\,w_0$, where the volume average reaches $72.1^\circ\text{C}$ while the core peaks at $90.0^\circ\text{C}$. Post-pulse 2D free-space Green's function convolution confirms immediate monotonic thermal decay ($\partial \theta/\partial t' < 0$) outside this boundary. This closed-form framework provides explicit scaling laws for non-invasive wave-matter thermal confinement, bypassing computationally heavy numerical simulations.

Scaling relations linking species size, abundance, and resource availability are among the most robust empirical regularities in ecology. However, a mechanistic explanation for how these community-level laws emerge from ecological processes remains elusive. Here, we address this gap by developing a minimal spatially explicit dynamical framework for forest communities that incorporates seed dispersal, growth limited by local light availability, local competition, and global resource constraints grounded in metabolic scaling principles. By deriving an analytical solution for the tree-size distribution, we show that its stationary state exhibits two distinct power-law regimes whose exponents are controlled by the relative strength of resource and spatial competition. The crossover between these regimes is set by the interplay between seed injection and local resource availability, establishing an explicit link between the scaling exponent of the size distribution and forest condition. Finally, we show that boundary disturbances can break the ecological balance between competing species and induce effects that propagate deeply into the forest bulk, far beyond the single-plant dispersal range. Together, these results provide a unifying dynamical perspective on forest scaling laws with potential applications to a broad range of biological communities.

The mean first-passage time (MFPT) provides a universal temporal measure of transport, reaction, search, and switching processes in physical, chemical, and biological systems. Understanding how MFPTs respond to perturbations is therefore crucial for prediction and control, yet a systematic theory has been lacking. We establish a compact theoretical framework for linear and nonlinear MFPT response in continuous-time Markov processes. The key tool is an exact correspondence that maps the intrinsically transient response of MFPTs onto the steady-state response of an auxiliary system. This correspondence yields exact and universal response relations for MFPTs between arbitrary state pairs, expressed entirely in terms of unperturbed MFPTs and steady-state probabilities. We then obtain a factorized physical decomposition of the MFPT response into linear upstream, linear downstream, and nonlinear contributions. Further corollaries include response-curve inference rules, fundamental bounds on MFPT responses, analytical expressions for higher-order responses of MFPTs and steady-state probabilities, and multi-rate response formulas. Additionally, our result offers computational advantages in calculating both MFPTs and steady-state distributions. Finally, a biologically motivated folding network is analyzed, and a recently reported paradox on MFPT is clarified.

There is a growing demand for minimally invasive methods to analyze intracellular processes and signaling activities in individual living cells, including the identification of tumorigenic cell subpopulations. However, most conventional analytical methods require cell lysis, precluding repeated measurements in the same cell over time, or rely on exogenous labels and reporters that may perturb cellular function. Various applications based on vertical nanotubes have been developed that enable live cell monitoring and analysis by electroporation with low voltages. However, the extent and duration of membrane permeability and kinetics of membrane repair remain elusive. Here, we built a plasmonic platform with the capacity of surface enhanced Raman spectroscopy (SERS) to monitor the electroporation-induced membrane permeability dynamics in individual live cells attached onto 100-nm diameter nanotubes of 2 um height. Fibronectin was employed as extracellular matrix (ECM)-coating to facilitate cell attachment onto nanotubes. Using fluorescent-dye delivery as an independent validation method, we show that the fabricated nanostructures induce localized electrical permeabilization of the plasma membrane and enable monitoring of its subsequent recovery. We further use SERS to track molecular changes at the membrane during permeabilization and resealing. The SERS spectra provide molecular-level insight into changes in membrane-associated components and the ECM during electroporation and subsequent membrane recovery. Real time monitoring of pulse induced molecular changes holds great promise for characterizing intracellular signaling, cellular states, and cellular heterogeneity at the single cell level, including the identification of tumorigenic subpopulations. This capacity could facilitate the development of novel biosensing assay.

Collective motion in self-propelled particle systems has been widely studied using the Vicsek model, which relies on pairwise alignment interactions. We introduce a generalized Vicsek model that incorporates higher-order (triadic) alignment interactions. Using agent-based simulations and mean-field theory, we demonstrate that pure triadic alignment induces a discontinuous phase transition, evidenced by hysteresis, a double-well free-energy landscape, and a Binder cumulant minimum that deepens with system size, whereas the standard pairwise model exhibits a continuous transition at the same system sizes. We further show that higher-order interactions require higher particle densities to sustain collective order and produce sharper fluctuation peaks near the transition with lower critical noise. These results establish that the microscopic structure of the alignment interaction, whether pairwise or many-body, is an independent control parameter for the order of the phase transition in active matter, with implications for understanding collective behavior in biological and synthetic systems.

Finite-memory optical tracers encode upstream transport histories rather than instantaneous local flow velocities. We introduce optical-memory transport (OMT) imaging, a framework in which finite memory couples internal-state relaxation to transport through memory kernels. Under structured illumination, these histories are converted into measurable complex spatial-frequency response, whose local transfer-function limit yields constant-velocity inversion. Fisher-information analysis establishes kernel-dependent information limits and design principles for finite-memory transport imaging.

How many distinguishable labels can a biological oscillator carry? Proposals invoking collective vibrational modes, endogenous electromagnetic fields, microtubule excitations and oscillatory phase codes are each debated on grounds particular to themselves, with no shared standard for comparison. We show that spectral distinguishability alone bounds the number of labels by the quality factor, M <= Q = 2 pi nu tau. This follows from the relation between linewidth and coherence time, so it is independent of substrate, of mechanism, and of any position on quantum effects in biology, and it can be evaluated from two published quantities. Applied to a recently proposed 30 GHz intracolumnar microwave field in cortex, it gives Q = 0.19: the linewidth exceeds the carrier five-fold. The obvious rescue, that a driven emitter can be spectrally narrower than its gain medium, requires a resonant cavity, and the model's own geometry forbids one. An independent bound on metabolic power is exceeded by five to nine orders of magnitude. Six further criteria follow from the same standpoint, including a two-sided persistence window requiring a label to be both readable and rewritable. Screening eleven carriers, only the low-frequency neural rhythms pass. High-frequency molecular carriers are eliminated by brevity, not by the fragility the debate has assumed.

Computational head models are typically applied to isolated impacts, leaving repeated head loading largely unexplored. An Ogden-Roxburgh Mullins damage formulation was implemented in a high-fidelity finite element head model to represent loading-history-dependent softening during cyclic brain-tissue deformation. Repeated-loading histories derived from mixed martial arts head-impact data were applied and compared with damage-free hyperelastic (HE) and linear visco-hyperelastic (LVHE) model variants. Under five identical single-axis cycles, Mullins-type softening progressively increased strain and strain rate metrics relative to the HE model. Mullins-based injury probabilities progressively exceeded strain-based HE predictions and diverged from unchanged kinematics-based predictions, indicating that neglecting prior softening may underestimate injury risk. In a randomized twenty-cycle multiaxial sequence, cycles of similar kinematic intensity produced different deformation and injury-risk estimates depending on prior softening. HE and LVHE models predicted higher injury probabilities initially, whereas the Mullins-based model produced the largest later-cycle estimates and highest probability of at least one injury over the sequence. Regional amplification depended on loading direction and prior softening, with no direction-independent trend among brain substructures. Gyral elements exhibited higher cumulative maximum principal strain than sulcal elements, which showed greater amplification relative to initial responses. These findings demonstrate that short-term damage-mediated softening can substantially amplify tissue deformation and injury-risk estimates beyond damage-free head models under the same loading histories. Further experimental characterization of cyclic brain-tissue softening is needed to improve models of repeated head loading and traumatic brain injury.

Cells often estimate chemical concentrations from only a few diffusing molecules, whose stochastic motion limits sensing precision. We consider a perfect monitoring instrument that records the instantaneous molecular density throughout a finite region without perturbing the concentration field or distinguishing molecular identities. The standard Berg-Purcell estimator weights all positions uniformly. Here we derive the optimal spatial weighting within a large class of unbiased estimators for both concentration and gradient sensing. Variance minimization maps to an electrostatic problem. Surprisingly, although the instrument monitors the entire volume, the optimal estimator assigns all weight to its boundary, reducing the uncertainty in both concentration and gradient sensing. We extend the results to arbitrary geometries and spatial dimensions.

We present an asymptotic analysis of two diffusive capture problems in general smooth closed three-dimensional geometries with multiple small reactive boundary patches of arbitrary shapes. (i) The narrow escape problem seeks to determine the escape rate of Brownian particles from an enclosed region through small boundary windows. (ii) The related Berg-Purcell (or narrow entrance) problem seeks to resolve the capture rate for signaling molecules diffusing outside the cell and entering through localized reactions at membrane-bound receptors. We obtain matched asymptotic solutions of these two problems and thus address the long-standing challenge of describing the role that curvature and local reactivities play in modulating diffusive capture rates. Our explicit expansions quantify local effects on diffusive capture through the sizes, shapes, and reactivities of the patches together with the principal curvatures of the manifold at each patch. In turn, we examine global effects on diffusive capture such as the spatial configuration of patches on the manifold, as encloded by the associated surface Neumann Green's function and its regular part. The accuracy of our asymptotic formulas is validated against a full numerical solution for an ellipsoidal domain. Overall, our results yield new insights on how geometry and stochasticity combine to shape the dynamics of various biological processes.

Biological recognition rarely rests on one strong bond. It works by forming many weak ones at once, between crowded, deformable surfaces in water. This review develops that process as a problem in statistical mechanics. Counting the ways two multivalent objects can bind proves to be the classical monomer-dimer problem on a graph, with a rigorous consequence: the apparent switching of multivalent binding is always a smooth crossover, never a phase transition. Three constraints follow. A repulsive surface layer is obligatory rather than a design choice; bonds do not act independently; and since free energies enter rates exponentially, small changes in receptor number shift binding lifetimes by orders of magnitude. One set of equations then covers antibodies, lipoproteins, and T cell recognition. In each, what decides the outcome is not the strength of any single bond but how a fixed total is spread over many: affinity is a property of a molecule, selectivity a property of an assembly.

The remarkable sensitivity, compressive nonlinearity, and frequency selectivity of the mammalian cochlea arise from an active process that amplifies the passive mechanical response of the basilar membrane. Outer hair cells are widely regarded as the primary effectors of this active process in the basal regions of the cochlea. This active contribution progressively decreases with increasing stimulus level. Motivated by these observations, a minimal cochlear model is investigated in which each location is represented by a forced damped oscillator with an exponential displacement-dependent active feedback. The oscillators are coupled through the cochlear fluid and also by elastic and dissipative longitudinal interactions to form a one-dimensional distributed model. The model reproduces key features of cochlear mechanics, including level-dependent amplification, compressive nonlinearity, frequency selectivity, traveling-wave propagation, and phase accumulation. Comparison with a simplified cubic nonlinear model has been carried out. Even though the cubic nonlinearity describes the response for weak stimuli, at higher stimulus levels it deviates from the exponential model and fails to reproduce the gradual transition towards predominantly passive behavior. Longitudinal coupling broadens the frequency response, modifies the traveling wave profile, and increases phase accumulation. The proposed model provides a simple physical framework for understanding how local active processes and longitudinal mechanical interactions together shape the nonlinear response of the cochlea.

Boolean networks are widely used to model gene regulatory Attractors of Boolean networks model stable gene-expression patterns, yet deriving their properties from network structure remains an open problem. We solve this problem for critical $K=1$ networks by showing that their feedback loops induce a permutation whose order bounds the average attractor length both above and below by universal constant factors. This correspondence allows classical results from combinatorics and number theory to be applied directly to Boolean network dynamics. We find three distinct asymptotic scales for both average and maximum attractor lengths: typical networks scale as $\exp[(1/8+o(1))(\ln N)^2]$, the ensemble means grow as $\exp[N^{1/3+o(1)}]$, and extremal networks attain $\exp[(1+o(1))\sqrt{N\ln N}]$. Thus, ensemble averages are governed by rare network realizations and are unrepresentative of typical dynamics.

Cell unjamming in dense tissues is a complex but essential process in embryogenesis and cancer metastasis. Increasing evidence suggests that nuclear mechanics and density effects play a vital role in collective cell unjamming. However, state-of-the-art cell-shape-based theories fail to include nuclear and density effects, while computer models featuring rigid nuclei disagree with experimental observations of elongated nuclei promoting unjamming. Here, we introduce a computational model of confluent cells with explicitly deformable nuclei to study the dynamics of cell unjamming. Our simulations show an unjamming transition controlled by nuclear size and shape, reconciling conflicting theories of density-driven versus shape-driven mechanisms. We predict general relations connecting cellular and nuclear shape to collective cell motion, verified experimentally in distinct monolayers of MCF-10A and MDA-MB-436 breast cells, with striking accuracy. Our work establishes a rational connection between nuclear mechanics and tissue-scale rigidity transitions, highlighting the nucleus's key role in collective cell unjamming.

In cell biology, computational models of biological systems range from minimal representations with a handful of parameters to whole-cell simulations tracking thousands of molecular species across a complete cell cycle. While these models span a continuum of detail, increasing complexity changes what they capture and are able to explain, what they can predict, and how they can fall short. A model contributes to understanding only when it makes novel predictions, reveals an unexpected coupling between processes, or fails in a way that identifies missing parameters. We contend that what is important for understanding is not the number of components or spatial dimensions a model contains, but the ratio of free parameters to the experimental constraints available to pin them down, and whether we can see why it produces the behaviors it does. Large-scale agent-based models of cytoskeletal dynamics or tissue mechanics that are built on a small number of physically grounded rules can reveal rich self-organization behavior precisely because their parameter spaces are small enough to explore systematically. By contrast, when free parameters grow faster than the data available to constrain them, models become progressively harder to interpret – and even disprove –regardless of their biological scope. We argue that the field needs to reconsider the goal of complex models. We should move away from trying to include as many parameters as possible and instead aim for systematic comparisons with simpler representations, dynamical analysis, and explicit model hierarchies that trace how cellular behavior emerges from its parts.

The first-passage time is the natural observable of reaction completion, yet how its mean responds to a rate change has lacked a general constraint. We show that the logarithmic sensitivity of the mean first-passage time of any finite Markov chain to any rate is bounded by one in magnitude, and that these sensitivities sum to -1. Together the two laws form a conserved control budget: speeding completion through some transitions must be paid for by others, and a coordinated change shifts the completion time only as far as the budget allows. Raising an activation barrier or shifting the depth of a well moves many rates at once, yet neither can shift the completion time further than a single rate could. The budget caps kinetic-proofreading discrimination at the checkpoint count, and prices it in sensitivity to substrate concentration.

Spatial confinement profoundly impacts the transport and self-organization of active matter across diverse biological systems. While the collective orders in confined active matter have been extensively characterized, how geometric constraints reshape near-field flows and the resulting inter-particle correlations remains largely unexplored. In this study, we combine experiments and hydrodynamic simulations to investigate inter-particle correlations within quasi-two-dimensional Chlamydomonas reinhardtii suspensions. We reveal two disentangled modes characterizing cell pairs: a dipolar mode and an entrainment mode, which exhibit a density- and distance-dependent competition. Combining single-cell flow field analysis, hydrodynamic simulations, and active-passive mixtures, we link these two modes to singular hydrodynamics and lubrication-induced entrainment. Our results demonstrate that spatiotemporal correlations in confined active matter are fundamentally rooted in the interplay of these two hydrodynamic mechanisms.

Proteins occupy heterogeneous free-energy landscapes in which high-entropy ensembles converge toward compact, low-energy basins with multiple sub-states. Molecular dynamics can access these landscapes at atomic resolution, but exhaustive sampling remains computationally demanding. Meanwhile, most quantum approaches target only single optimal structures, leaving full ensemble energetic heterogeneity unexplored. We introduce a residue-level, gate-based quantum circuit framework for coarse-graining protein thermodynamics. Each amino acid is represented as a two-state qubit (stabilised vs. excited solvation state) based on residue solvation energetics. A structure-informed entanglement block then encodes covalent and non-covalent contacts using parameterised controlled gates, embedding correlations across the residue-interaction network. Sampling the circuit ($\sim 10^6$ measurements) yields binary thermodynamic microstates used to compute protein energy distributions, residue-level statistical couplings, energetic sensitivities, and information gains relative to total free energy. We showcase the framework on the benchmark Trp-cage miniprotein 1L2Y (TC5b) and 9GDL, a disulfide-stabilised Trp-cage-fortified exenatide chimera. For 1L2Y, the circuit reproduces a structured, folding-funnel-like energy distribution. Comparative analysis with 9GDL reveals shifts in global energy distributions and residue-level stability profiles. Coupling and information-theoretic analyses localise residues associated with ensemble reorganisation, while multi-body couplings show the circuit resolves both direct and indirect statistical correlations. This framework expands quantum protein modelling beyond single-structure optimisation toward ensemble-level characterisation, capturing key features of rugged energy landscapes to guide protein design, mutation mapping, and allosteric pathway identification.

Excitable and oscillatory responses are widespread in cell signaling, but how these arise in the same system is unclear. We propose a minimal model of a saddle node bifurcation on an invariant circle, where slow fluctuations modulate transitions between excitable and oscillatory states, and noise drives excitability. Fitting the model to cell signaling data from embryonic stem cells reveals that these cells operate close to the bifurcation. Proximity to the bifurcation allows the cell to tune different dynamic states, suggesting a general principle for versatile cell signaling.

Insomnia disorder is defined at the syndrome level, yet similar complaints can arise from different abnormalities in sleep regulation, state transition, state stabilization, spatial recruitment, architectural sequencing, and state perception. We propose a multiaxial dynamical framework whose principal contribution is organizational: a candidate profile is specified by the dynamical operation that fails, the sleep stage or boundary at which it fails, and its causal status. Objective sleep duration, age, circadian phase, comorbidity, medication exposure, and night-to-night variability are modifier/covariate dimensions rather than additional mechanistic classes. A local Landau-Ginzburg formalism, adopted from prior cortical and sleep-dynamics work, supplies a phenomenological language for nested hypotheses. Its relaxational form applies only to boundary-local dynamics under an approximate gradient description; non-gradient escape requires an action or quasipotential treatment, and whole-night REM-NREM sequencing requires reactive or oscillatory dynamics. Routine polysomnography usually identifies effective combinations rather than curvature, escape action, bias, noise, and relaxation separately. The strongest boundary-level evidence concerns sleep onset, where published results are consistent with bifurcation-like or bistable dynamics but do not yet exclude a driven smooth transition produced by the homeostatic-circadian ramp. The remaining operation classes are hypothesis-generating extensions. The taxonomy is judged by pragmatic utility, including improved communication, stratification, and prediction; the scalar-field implementation and specific dynamical profiles are separately falsifiable. The framework is a phenomenological organizing model rather than a new diagnosis, validated biomarker, or treatment-selection system.

Bistability, the existence of two alternative stable states with distinct basins of attraction, is common across ecology and many other biological, chemical, and physical systems. In spatially extended systems, the invasion of one state by the other proceeds through nucleation, the fluctuation-driven growth of a droplet beyond a critical size. Classical Nucleation Theory (CNT) quantifies this process using the energy landscape, but this description relies on detailed balance, the condition of microscopic reversibility that holds at equilibrium. Ecological dynamics generally violate detailed balance and are described not by a single scalar field but by several coupled, non-conserved abundances–a vector order parameter–for which no general nucleation theory exists. Here we derive such a theory for reaction-diffusion systems with a non-conserved vector order parameter, valid both close to the binodal, where invasion proceeds through propagating fronts, and close to the spinodal, where the metastable state loses stability. Extensive numerical computations of the quasipotential confirm the theory in both regimes. We show that the mathematical structure of CNT survives out of equilibrium, once energetic quantities are replaced by dynamical properties of fronts: the front speed plays the role of the bulk free-energy difference between phases, and the diffusivity that of the surface tension. Applied to the two-species Lotka-Volterra model, an archetypal system of bistable ecological antagonism, our theory shows that strong interspecific competition generates a pronounced depletion region within fronts, where the total abundance falls well below carrying capacity. This vectorial structure, invisible to a scalar description based on species frequency alone, makes invasion exponentially harder as competition strengthens at fixed competitive advantage–a prediction testable in microbial systems.

In recent years, non-reciprocity has been explored as a ubiquitous manifestation of non-equilibrium activity at the microscopic scales for various active matter systems, from mixtures of chemically active enzymes, colloids, and droplets, to engineered light-controlled active colloids and robotic meta-materials. A commonly used minimal model to describe the dynamics of a binary mixture of conserved species with non-reciprocal interactions is the non-reciprocal Cahn-Hilliard (NRCH) model. The model is characterized by a temperature-like tuning parameter, which can trigger phase separation, and a non-reciprocal coupling, which can lead to the formation of spatio-temporal patterns, as it represents an intrinsic source of non-equilibrium activity and breaks parity and time-reversal symmetries. Here, we study the scaling behavior of the NRCH model near the critical point using perturbative dynamical renormalization group techniques. We find that structural and dynamical correlations are controlled by different correlation lengths, both of which diverge at the critical point, but governed by different scaling laws. In particular, while the structural correlations are always controlled by temperature and the classical Wilson-Fisher critical exponent, the dynamical correlation length exhibits multiple scaling regimes in which either temperature or non-reciprocal coupling can dominate as the key tuning parameter, with a new critical exponent characterizing the divergence. The critical point corresponds to a conserved equilibrium-like dynamics with odd mobility, which we denote as the odd Cahn-Hilliard (OCH) model. Our findings may have important implications on how living systems can control phase separation and spatio-temporal pattern formation using the rates of catalytic reactions, and in general metabolism, as control parameters.

We present a statistical-mechanics framework for computing equilibrium binding constants $K$ in the dilute limit. From first principles, we derive a general expression relating $K$ to the relative populations of the bound and unbound states. Its transparency has twofold advantage: it makes the origin of the unbound-state volumetric term explicit, and it allows one to track exactly how an imposed volume restraint propagates through the expression. This makes $K$ directly computable, as restrained simulations can account for the volumetric contribution exactly, under the physically mild assumption of a homogeneous unbound state. The resulting estimators are computable from histograms of any suitably defined reaction coordinate, and determine unambiguously how the boundaries of the thermodynamic states of interest must be defined. We apply our framework to the cucurbit[7]uril/1-adamantanol host–guest complex and the galactonate–DgoT ligand–protein complex. Our results show that commonly used single-bin estimators depart from the theoretically correct one by $\approx 1$~kcal/mol in both systems. This shift originates in the definition of the bound state: by anchoring that definition to what state-of-the-art experiments resolve, the theory turns it from a hidden assumption into a controlled input, and provides a principled route to absolute binding affinities from molecular simulations.

Local detailed balance restricts transport by self-propulsion in static activity landscapes. We show that a delayed speed adaptation (“delayed motility/kinesis”) generically breaks this symme try, inducing directed transport in asymmetric periodic motility profiles and enhancing diffusion in symmetric ones. Both effects occur for run-and-tumble, active Brownian, and inertial active particles, without requiring potential interactions, walls, imposed gradients, higher dimensions, or translational diffusion. Their magnitudes, and even current reversals, are conveniently tuned via the delay time, which establishes delayed motility as a versatile generic and experimentally accessible mechanism for autonomous self-steering and transport control in motile-active-matter circuity.

Sleep staging provides a reproducible clinical description, but it does not by itself explain why some boundaries are abrupt while others are graded, or why transition windows contain instability, synchrony, and apparent state coexistence. We develop a local Landau-Ginzburg phenomenology in which each boundary is represented by motion in an effective potential of a spatially extended, noisy, dissipative neural field. A latent cortical-ordering coordinate phi is inferred from prespecified EEG/PSG observables through a measurement model designed to avoid circularity. The canonical boundaries are treated separately. Existing data support a fold-like loss of wake stability at sleep onset; whether that fold lies on a globally bistable cusp with hysteresis remains open. N1-to-N2 and N2-to-N3 are posed as continuous-like ordering crossovers, NREM-to-REM as a candidate first-order-like desynchronizing switch, and a possible within-N3 mixed or tricritical-like regime as a speculative hypothesis. The Ginzburg term adds spatial predictions - growth of correlation length and local-to-global recruitment - that are absent from scalar sleep-onset models. We specify the evidence needed to distinguish bifurcation, coexistence, noise-driven escape, smooth crossover, and scoring-induced discontinuity. Illustrative time-dependent Ginzburg-Landau simulations reproduce the proposed signature classes. A synthetic classification experiment partially distinguished six archetypes (cross-validated accuracy 0.49 +/- 0.005; balanced baseline 0.17), with little change under a noise-regime shift. These analyses establish the internal consistency and testability of the framework, not the proposed taxonomy in human sleep. Transition-centered EEG validation is required before clinical or neuromodulation applications are pursued.

Morphogenesis involves the coordination of multiple cellular processes that occur simultaneously within developing tissues. During early Drosophila embryogenesis, neuroblast (NB) ingression occurs concurrently with germ band extension (GBE), yet whether these processes interact mechanistically remains unclear. Here, we combine mathematical modelling with quantitative live imaging to investigate whether tissue-level mechanics during GBE influence NB ingression dynamics. Mathematical modelling predicted that reducing tissue fluidity through impaired cellular rearrangements should slow NB ingression by increasing mechanical resistance. Experimental analysis of mutants in which cell intercalation and GBE are disrupted revealed a dramatic reduction in tissue fluidity. However, NB ingression rates remained largely unaffected when tissue fluidity decreased. Incorporating cell-intrinsic myosin anisotropy and endocytosis-contractility coupling into our mathematical model rescued the rate of neuroblast ingression in solid-like tissues. Thus, our findings suggest that cell-intrinsic mechanisms, rather than tissue-level fluidity, maintain ingression kinetics. More broadly, these results illustrate how developmental systems can achieve robustness by insulating critical cellular events from tissue-level mechanical variability.