Papers

Information sharing, threat perception, and collective evasion highlight the advantages of swarm intelligence. Here, we study the behavior of flocks of cognitive agents, based on numerical simulations of the augmented inertial spin model, with an explicit predator. Each agent on the predator-facing side of the flock perceives the threat, triggering collective turns through local interactions. We show that the augmented inertial spin model sustains nearly linear information propagation in the under-damped regime, even with realistic flocking interactions such as local collision avoidance and swarm cohesion in addition to alignment. The turning distance of the flock to a stationary predator scales with the ratio $\Delta_p/(v_0\sqrt{\eta})$, identifying an optimal balance between response strength $\Delta_p$, flock speed $v_0$, and damping $\eta$ of information propagation. Fragmentation arises when different parts of the flock turn in different directions, however, fast information propagation can synchronize these responses and maintain flock cohesion while under pursuit. For two predators, a combination of stability analysis and simulations reveals a stark contrast between flock and single-particle reactions, with scattering angle shaped by flock geometry, predator position, and the heterogeneous responses of the detecting front. Together, these results show how information propagation, flock geometry, and dynamics together shapes collective escape, providing general principles relevant to both biological flocks and robotic swarms.

Topological entanglements are central to understanding and predicting the properties of polymer melts. Yet, they make equilibrium sampling computationally challenging, as decorrelation times grow rapidly with chain length. Here, we introduce a Monte Carlo scheme that bypasses typical computational bottlenecks by working in a self-assembly ensemble rather than at fixed composition. Strictly local moves efficiently propagate backbone reconnections across scales while conserving the number of linear chains, achieving near-linear scaling of decorrelation time with system size, $\tau_{\rm eq}\sim V^{1.0}$. With this method, formulated for a fully-packed lattice, we equilibrate periodic systems totalling up to $\simeq 1.1\times 10^9$ monomers, accessing a universal melt regime insensitive to lattice details. We analyze intra- and inter-chain entanglements for chains of up to $N\simeq 5 \times 10^5$ monomers, revealing that they manifest as localized knots and links rather than as global tangles. Finally, we show that the magnitude of the Gauss linking integral between neighbouring chains grows only as $N^{1/4}$.

How do neural representations of neighbors become collective material behavior? Harmonic Theory (HT) reduces bearing representations to signed perceptual channels traceable to sensory acuity, decision dynamics, and interaction distance. Here we derive a nonlocal kinetic and hydrodynamic theory from the HT particle law without introducing heading alignment. The resulting fields retain HT's order-resolved perceptual spectrum and keep the neural and sensory origin of each coefficient visible. The theory predicts a torque-driven density instability: HT's direct-approach channel turns agents toward density excesses, while self-propulsion carries them inward. For isotropic spatial interactions and positive rotational diffusion, perceptual channel $n$ generically first affects conserved density at spatial order $k^{2n}$, and the full radial transforms select finite pattern wavelengths. Two populations can share the same long-wave instability threshold yet select different initial pattern spacings because their higher perceptual channels differ. Beyond onset, the one-particle continuum sustains a bidirectional nematic column; a prescribed, symmetry-allowed two-stream response amplifies a directional imbalance into sustained polar flow. In a distinct pure-repulsion regime, one-particle calculations show polar transport and translating transverse bands, with late pattern selection sensitive to numerical transport. The framework connects neural and sensory mechanisms to continuum coefficients, instabilities, and alignment-free collective motion.

Behavioral variability reflects differences in internal and external parameters and provides a substrate for natural selection. However, uncovering its structure is challenging because behavior evolves nonlinearly across multiple timescales. Our goal is to reconstruct phenotypic variation from finite behavioral observations without prescribing the scales at which individuals should be compared. To achieve this, we introduce a multiscale dissimilarity that compares dynamics across all statistically resolvable resolutions by constructing reduced transfer operators at progressively finer scales and weighting their differences by finite-sampling uncertainty. This dissimilarity defines a geometry of dynamical phenotypes, which we reconstruct using diffusion maps. We show that the resulting phenotypic coordinates locally follow the parameter directions to which dynamics are most sensitive. We validate our approach in a stochastic model and apply it to bacterial and larval zebrafish behavior. In bacteria, we identify run speed as a major component of inter-individual variability, associated with the chemotaxis protein CheB. In zebrafish, we find that prior prey experience reshapes behavioral dynamics and phenotypic variability, with paramecia experience concentrating fish in a prey-capture-associated region of phenotypic space. Together, these results provide a framework for identifying internal and environmental variables that structure dynamical phenotypes across scales.

We generalize the Furusawa–Kaneko model, a simple model of intracellular catalytic reaction networks, to multicatalyst reactions and analyze the generalized model using dynamical mean-field theory. In the thermodynamic and dense-network limit, we derive exact effective equations and analyze their fixed points for arbitrary degree distributions. Under nutrient-poor conditions, network heterogeneity suppresses the metabolic–starvation transition irrespective of the number of catalysts per reaction. In contrast, under nutrient-rich conditions, the bifurcation structure changes with the number of catalysts. With one catalyst per reaction, only continuous transitions occur, whereas two or more catalysts give rise to bistable phases and discontinuous transitions. The bifurcation structure also differs between two and three catalysts per reaction, with three catalysts allowing bistability between metabolic states with different cell growth rates. Our results provide a possible mechanism for bistability and abrupt switching in metabolic dynamics.

Life support equipment coupled to the human lungs forms a complex, nonlinear dynamic system. Current respiratory mask test standards rely on sinusoidal breathing machines and surrogate trachea geometries that substantially reduce physiologically relevant airway inertance. This paper shows that the ISO 16900-5 trachea does not generate physiologically meaningful exhalation momentum, limiting the ability of standard test configurations to reveal valve dynamics relevant to human use. A physiologically motivated “lip-nozzle” surrogate is introduced as a diagnostic tool to restore realistic momentum transfer, enabling observation of exhalation behavior that is not observable under existing test conditions. Nonlinear dynamic simulations incorporating this surrogate reveal a force-balanced operating regime in which exhalation-jet momentum can offset flow-induced valve resistance, in one representative case reversing exhalation mean effective pressure from resistive to assistive. This effect depends on the relationship between the valve's restoring force and lift, representing a design consideration relevant to future valve development. Implications for mask design, valve placement, and future test methods are discussed. This work does not propose new performance limits or acceptance criteria; rather, it demonstrates how current test fixtures suppress inertance- and momentum-driven effects that can materially influence exhalation valve dynamics.

Calcium homeostasis is maintained by an endocrine network comprising parathyroid hormone (PTH), calcitriol and calcitonin, which defends serum calcium at the expense of skeletal reserves. Serum calcium is therefore an unreliable indicator of nutritional calcium status, and empirical supplementation remains common. This narrative review proposes a clinical–metabolic approach to estimating individual calcium requirements that integrates bone mineral density (BMD), vitamin D status and the compensatory PTH response. We make three contributions. First, we present a sigmoidal phosphate–PTH model in which a glucose-dependent gain term ($\Delta k_{\mathrm{gluc}}$) captures the heightened parathyroid sensitivity associated with dysglycaemia, and we illustrate it with simulated values for healthy adults, women and individuals with gluco-osteoporosis. Second, we translate the model into a four-step decision algorithm that frames the intake gap as a net balance of intestinal absorption, renal excretion and bone turnover. Third, we incorporate the osteocyte–osteoblast bioenergetic axis (sclerostin/Wnt signalling, GLUT1-mediated glucose uptake, aerobic glycolysis and osteocalcin–insulin crosstalk) to explain why calcium supplementation may be ineffective when cellular energy supply or insulin sensitivity is impaired. The framework aims to prevent secondary hyperparathyroidism, avoid over supplementation and preserve skeletal integrity. The model values are simulated and require prospective clinical validation.

Microvesicles (MVs), a type of cell-secreted extracellular vesicle (EV), are essential for various biological processes such as local and long-distance intercellular communication and the disposal of unwanted materials. Recent evidence suggests that overexpression of MUC1 glycoproteins facilitates MV formation on the cell membrane, but the mechanism underlying this nonequilibrium process remains unknown. Here, the kinetics of glycocalyx-driven MV formation is studied in the framework of Onsager's variational principle. Using this deterministic theory, we first show that the process of MV formation is accelerated for the denser and thicker glycocalyx-grafted cell membrane and can be improved by reducing the ionic strength or enhancing the degree of glycocalyx ionization. Intriguingly, we further discover that there exists an optimal glycocalyx coverage for the fastest formation of MVs. We then investigated the process of MV formation using a stochastic approach. Our results suggest that the transition rate is not constant, leading to the prediction of a shorter formation time compared to the deterministic approach. These findings provide valuable insights into the regulation of membrane morphology and MV secretion by the glycocalyx, with implications for both understanding and modulating these processes.

Ribonucleic acid (RNA) functions through conformational changes that are not fully captured by static structures. However, large-scale standardized RNA dynamics data remain limited, and existing approaches typically treat trajectory generation and dynamics understanding as separate objectives. Here, we introduce RNADynBench, a standardized RNA molecular dynamics (MD) benchmark with 2585 quality-controlled 100-ns all-atom trajectories and leakage-controlled splits. Building on RNADynBench, we develop RNADynNet, a unified model for RNA dynamics learning that uses a shared backbone for both trajectory generation and dynamics fingerprint extraction from a single conformer. It combines coordinate denoising, single-frame-to-trajectory alignment, and physical grounding to connect all-atom trajectory generation with dynamics representation learning. Physical grounding improves both generated dynamics and the physical information recoverable from these fingerprints. Across both test sets, including the high-flexibility challenge set, the generated trajectories achieve RMSF correlations of 0.875 and 0.766, while single-conformer predictions show comparable agreement with MD-derived dynamics. RNADynBench and RNADynNet together establish a benchmark and unified modeling framework for generating and understanding RNA dynamics.

A conducting network improves access to its interior only by spending material, so architectures compare only at equal budget. We redistribute conductance under a power-law resource law $\C_{\alpha}=\sum_e a_e w_e^{\alpha}$ and measure access by the reciprocal of the mean pairwise effective resistance. When the cost is strictly convex the allocation is unique and every admissible edge keeps positive conductance; at $\alpha=1$ uniqueness survives but an edge can be priced out. The marginal worth of an edge is then its squared biharmonic distance, a Murray-type balance whose balanced quantity is global rather than junction-local. The same optimum scores any weighted network at its own budget, separating an allocation factor from a topological one. Under concave cost the marginal price of an incipient channel diverges, the feasible set is nonconvex, and conductance condenses onto sparse backbones. The uniform star and the uniform complete graph cross at $\alpha_c(n)=\log(n/2)/\log(n-1)$, near which intermediate states beat both. Up to $n=64$ the best states found grow approximately linearly in $n$, so channels per node change much less than the active fraction does. Loops are governed instead by a collapse exponent $\alpha^{*}(n)$, resolved to $0.005$ at every size: it rises from $0.555$ at $n=8$ to $0.675$ at $n=64$, and the collapse across it is abrupt, the support at $n=64$ falling from $133$ active edges to the $63$ of a spanning tree. A fixed exponent therefore changes character with size by crossing this boundary. One prescribed source and sink instead gives a loopless optimum.

During embryonic development and cancer progression, clusters of cells migrate collectively following external cues. Such migrating cell clusters have been modeled as active droplets wetting a substrate. So far, this active wetting model assumed the cluster to take the symmetric shape of a spherical cap. Here, in contrast, we experimentally show that migrating clusters of frog neural crest cells have asymmetric height profiles, with a lower contact angle at the front than at the rear. We then extend the active wetting model by deriving an equation for the cluster shape, which becomes part of the solution rather than an assumption. Our model shows that shape asymmetry can arise from the asymmetric tractions that drive cluster migration: They generate a pressure gradient across the tissue which, via the Young-Laplace equation, leads to a curvature gradient on the cluster's upper surface. Finally, by fitting the theoretical predictions to the measured height profile, we estimate the tissue viscosity. Overall, our results provide a general mechanism for the emergence of asymmetric shapes in migrating cell clusters, understood as active droplets on a wettability gradient.

The cell cortex and cell adhesion contribute to the mechanics of epithelial cells and hence tissues. Vertex models of epithelia represent the cell cortex and cell adhesion, but these models mostly ignore the other subcellular structures that compose the cytoplasm surrounded by the cortex. Here, we reveal the mechanical consequences of these structures in a minimal vertex model of an epithelial monolayer, in which the single-cell energy includes a cytoplasmic contribution that represents, e.g., the cost of confinement of cytosolic polymers. Strikingly, our simulations show that the buckling transition of the monolayer under compression becomes discontinuous in an intermediate range of values of the associated cytoplasmic modulus. By asymptotic solution of this buckling problem in the continuum limit of the model, we explain this reentrant behaviour in terms of the tricritical points of a sixth-order Landau theory. Our results thus underline how cell-scale mechanics beyond the cortex and cell adhesion can change emergent, tissue-scale behaviour even qualitatively.

We study an equilibrium system, where linear molecules with a rigid charge distribution interact via the mean-field generated by the Coulomb coupling. We focus on the nonlinear regime, which is valid close to external charges immersed in the system. The finite molecular size in this regime leads to a nonlocal response at short distances. First, we show that the mean-field potential is non-monotonic, i.e., like charges can attract each other. Second, we show that the polarization induced by an external charge (and hence its solvation structure) depends on the sign of this charge, violating the effective C-symmetry of the macroscopic electrodynamics. We identify several scenarios of this effect, characterize it with the free energy and entropy differences, and compare it with analogous effects in asymmetric electrolytes described by nonlinear Poisson-Boltzmann equations.

Many physical and biological systems -foams, membranes, elastic shells, or tissue sheets- can be mathematically described as 2D surfaces. These surfaces can host complex dynamics, like reaction-diffusion systems, and undergo drastic deformations. Here, we present triangulax, an open-source Python library for simulations and geometry processing that discretizes surfaces using triangular meshes available at https://github.com/nikolas-claussen/triangulax. It combines two features. First, discrete differential geometry provides coordinate-free discretization, which allows simulating strongly deforming surfaces. Second, the library is built on the machine-learning framework JAX, so mesh-based energies and entire simulations can be differentiated automatically (including simulations with stochastic forces or topological modifications). This simplifies multi-physics simulations by computing forces automatically and allows fitting model parameters to experimental data or design objectives. We implement an algorithm to preserve mesh quality in strongly deforming surfaces and apply it to a model of membrane mechanics coupled to an on-membrane concentration field. We validate our approach against exact solutions and existing software, and demonstrate triangulax across a range of problems, including membrane mechanics, vertex models, and inverse design of a shape-morphing elastomer sheet.

Peptide sequence governs both the structures formed through supramolecular assembly and the dynamics by which they emerge, but predicting either requires resolving slow collective processes among many interacting molecules. Molecular dynamics (MD) provides microscopic insight into these processes, yet the long timescales of assembly and the vast peptide sequence space make systematic exploration computationally demanding. We introduce SupraTITO, a transferable generative molecular dynamics (GenMD) framework for supramolecular systems, demonstrated through peptide self-assembly. SupraTITO learns transferable implicit transfer operators (TITO) conditioned on peptide sequence, molecular topology, and periodic geometry, allowing configurations to be propagated over physical intervals much longer than an MD integration step. On a comprehensive dipeptide benchmark, SupraTITO generalizes to held-out sequences and reproduces sequence-dependent structures and dynamics while maintaining molecular integrity over long rollouts. Compared with direct ensemble prediction trained on the same trajectory data, SupraTITO more accurately reproduces assembly structures while also resolving their temporal evolution. The learned dynamics generalize across peptide concentrations, including dilute conditions not represented during training. These results extend transferable GenMD to collective dynamics in periodic supramolecular systems and provide a foundation for modeling related processes beyond peptide assembly.

Bacterial swarming is the collective expansion of dense populations of motile cells across hydrated soft surfaces, yet gravity is usually treated as a fixed background condition in standard horizontal assays. We used surface inclination to examine how agar-surface orientation relative to gravity affects the expansion of Enterobacter sp. SM3 swarms. Colony expansion depended non-monotonically on inclination, with the strongest spreading at intermediate inclinations and weaker expansion under shallow or near-inverted conditions. Paired up-facing acute and down-facing obtuse configurations with the same tilt magnitude showed different expansion responses, suggesting that swarm expansion depended on both tilt magnitude and which side of the agar surface faced upward relative to gravity. Inclination also produced downhill-biased colony morphologies. PIV analysis showed generally lower mean activity under inclination than in the flat references, with a non-monotonic angular response and inward increases in speed and spatial velocity-correlation length. The downhill tip showed slower motion, shorter spatial correlations and smaller vortex cores than the upper region. To interpret the macroscopic trends, we extended a two-phase thin-film model by introducing an effective gravity coupling projected normal and tangential to the agar surface. Simulations suggest that the surface-tangential component mainly drives lateral redistribution, whereas the surface-normal component modifies film pressure and thereby pressure-dependent water replenishment, helping distinguish up-facing from down-facing configurations.

Spectroscopy reads structure by sending a structured probe into a system and measuring what comes back. Here we apply this principle to animal decision-making. Harmonic Theory casts choice as motion on an angular landscape over heading, whose Fourier components form an animal's decision spectrum. We show that the arrangement of cues enters that landscape as a structure factor, so it factors like a diffraction amplitude, and symmetry imposes selection rules: a p-fold cue array annihilates every harmonic that is not a multiple of p, and sweeping two cues apart draws a notch through each harmonic. Cue geometry becomes a tunable probe: the experimenter sets which harmonics an experiment can see. We read these spectra from public recordings of flies, schooling fish, larval zebrafish, mice and a swimming alga, and from the fly's neural compass, where symmetric scenes suppress the forbidden harmonics and breaking that symmetry restores them. Measuring the compass form factor favours the theory's smooth bump over its square one, and raising cue contrast narrows that bump in every fly. A width fitted to one harmonic then predicts the next. Cue geometry is a spectrometer for decisions, and symmetry sets what it can see.

Harnessing active matter to power functional devices has attracted growing interest. We propose a minimal battery model for storing energy extracted from active matter and derive its charging and discharging characteristics analytically. When the energetic cost of sustaining activity is included, the charging power-efficiency trade-off becomes loop-like and the efficiency attains a finite-time maximum, in sharp contrast to passive energy devices.

Dengue virus (DENV) is an enveloped flavivirus of major public health importance. Its envelope (E) protein mediates viral entry through homodimer dissociation and subsequent membrane fusion, making it one of the principal targets for antiviral strategies. To investigate the molecular determinants of this process, we performed steered molecular dynamics (SMD) simulations of the E protein ectodomain (ecE) dimer from DENV-2 and DENV-3 under variable pH and temperature conditions. Force-extension analyses revealed a highly stable interface for both serotypes, with rupture forces exceeding 1000 pN. pH and temperature had modest effects on overall mechanical resistance. However, DENV-3 displayed a distinct sensitivity to thermal stress compared to DENV-2. We identified a robust, asymmetric dissociation pathway across all conditions, characterized by a metastable intermediate state involving partial dimer opening and exposure of the fusion loop (FL). This intermediate exposes an immunodominant epitope and persists under physiological conditions, suggesting it as a viable target for therapeutic intervention. The primary contributions to the interfacial interaction network were found to arise from van der Waals interactions, followed by hydrogen bonds, salt bridges, and pi-cation interactions. DENV-3 exhibited a slightly greater contribution from polar interactions involving domains EDI, EDII, and EDIII. Furthermore, pairwise occupancy analysis identified pH-sensitive contacts that are disrupted under acidic conditions, particularly in DENV-3, providing mechanistic insight into the early stages of ecE dissociation. Together, these findings provide structural insights into the dissociation mechanism, identifying key metastable states and pH-sensitive interactions that could be exploited to develop antivirals that stabilize the dimer and prevent viral fusion.

Beyond a critical Toner–Tu drive, bacterial turbulence exhibits universal statistics, including a parameter-independent energy spectrum $E(k)\sim k^{-3/2}$. We show that the same universal state can be reached not only by increasing activity, but also by strengthening nonlinear advection, weakening nonlinear saturation, or tuning the Swift–Hohenberg instability. Motivated by the competition between these processes, we identify the independent dimensionless groups governing the dynamics and construct a Reynolds-like control parameter from them. A single critical value, calibrated from the known activity-controlled transition, predicts the onset of universality along the other parameter routes and collapses them onto a common threshold. These results identify a dynamical organizing parameter for the onset of universal active turbulence and provide a Reynolds-like measure for the Toner–Tu–Swift–Hohenberg universality class.

Membrane curvature has been shown to bias the location of lipid or protein domains, but the roles of bending rigidity, spontaneous curvature, Gaussian bending modulus, and line tension are difficult to separate in general. We develop a small-domain description for a membrane whose shape is held fixed, e.g. by strong adhesion to a curved substrate. Combining a local Helfrich energy with the small-area isoperimetric expansion gives a position-dependent energy determined by the local mean and Gaussian curvatures. We identify four generic regimes of curvature preference whose boundaries depend on only two dimensionless parameters. On specific membrane shapes with complex curvature, we show that this curvature preference determines the energy landscapes experienced by small domains, which are strongly dependent on the size of the domain through the line tension contribution. For example, on an oblate-shaped membrane, very small domains tend to localize at the poles, whereas larger domains prefer to localize at the equator. Whether this transition is continuous or discontinuous is found to strongly depend on the spontaneous curvature of the domain. This ordering suggests a mechanism by which small domains can collect and coalesce at one location before relocating as they grow.

The regular bending waves of cilia and flagella provide an iconic model system for the collective dynamics of molecular motors. The known regular arrangement of dynein motors in a cilium's axoneme allows us to connect mesoscopic cilia properties, such as axonemal bending stiffness, to microscopic motor properties, such as the force exerted by an individual motor. We estimate the active force generated by the collection of dynein molecular motors in $\mathit{Chlamydomonas}$ axonemes using previous estimates of its bending stiffness. Divided by the maximal possible number of active motor heads, this provides a lower bound of ${>}10\,\mathrm{pN}$ for the peak force generated by a motor head, which exceeds typical stall forces ${<}5\,\mathrm{pN}$ of molecular motors. This discrepancy suggests that either the bending stiffness of microtubules and axonemes was previously overestimated, or that collective force generation in dense motor arrays can surpass the sum of expected contributions of individual motors.

Non-equilibrium systems challenge the standard definitions of phases and phase transitions from equilibrium statistical physics. For example, in active fluids continuous energy injection at the microscale drives the system intrinsically out of equilibrium. This process gives rise to collective turbulent-like flows whose onset remains poorly defined. Here we show that the onset corresponds to an activity-driven phase transition, marked by the emergence of a system-spanning critical backbone of vorticity nodal lines. Combining two independent experiments, microtubule kinesin active nematics and dense suspensions of swimming bacteria, with large-scale simulations of active nematics and fluctuating nematohydrodynamics, we show that this transition occurs at a critical activity threshold. Below this threshold, vorticity structures are fragmented and vortex centres form only finite, mechanically floppy networks. Above this threshold, the nodal lines of the vorticity field percolate and the vortex centres form a rigid, system-spanning cluster. The geometric transition is characterised by the emergence of critical percolation statistics for the vorticity nodal lines, while the mechanical transition reflects the emergence of a vortex configuration that shows rigidity percolation statistics for vortex centres. We show that both transitions are absent in equilibrium systems that obey detailed balance, demonstrating that the transition is intrinsically non-equilibrium. These results establish an experimentally accessible definition of fully developed active turbulence, linking microscopic activity to macroscopic geometry, and mechanics of living systems.

Tetrahymena calcium-binding protein (Tcb2) forms Ca$^{2+}$-responsive networks that exhibit contractile behavior, yet how Ca$^{2+}$ concentration controls their local mechanical response remains poorly understood. Here, we use optical tweezers to perform active microrheology on reconstituted Tcb2 networks inside a microfluidic device that enables precise control of Ca$^{2+}$ concentration, allowing systematic tuning of network structure and mechanics. We find that increasing Ca$^{2+}$ from 1 to 100~mM enhances the effective stiffness by nearly two orders of magnitude, from $\sim$1$\times$10$^{-3}$ to $\sim$7$\times$10$^{-2}$~pN/nm, corresponding to a transition from a viscosity-dominated to a more elastic and mechanically robust network. Recoil assays further reveal rapid release of stored elastic energy following deformation. After two orthogonal pulls, the bead recoils along the diagonal rather than retracing the loading path, indicating that stresses from different directions combine to produce a resultant restoring response. These results establish Tcb2 networks as a minimal, tunable system for probing chemomechanical coupling and viscoelasticity in Ca$^{2+}$-regulated protein networks.

We investigate the dynamics of spherical lipid vesicles subjected to an osmotic shock using continuum simulations of a permeable, area-incompressible fluid membrane with bending elasticity and surface viscosity. The dynamics are governed by a single dimensionless parameter $\varGamma$, which measures the relative strength of osmotic pressure and bending forces. Osmotic forcing drives a three-stage evolution comprising rapid buckling and collapse, smoothing of the resulting wrinkles and ridges, and slow folding into an invaginated morphology resembling the precursor to experimentally observed vesicle-in-vesicle structures. Linear stability analysis predicts the wavelength and growth rate of the initial buckling instability and shows that the dimensionless buckling time scales as $\varGamma^{-2}$, in quantitative agreement with simulations. At longer times, the energy budget reveals a reversal in elastic energy transfer: bending energy accumulated during buckling is released during relaxation and dissipated by membrane viscosity. A scaling analysis of the folding dynamics predicts that the dimensionless folding time scales as $\varGamma^{-2/3}$, again in excellent agreement with simulations. These results provide a continuum description of the mechanisms and widely separated timescales governing osmotically driven membrane collapse and invagination.

Viruses are among the most highly charged objects in biology, and electrostatic interactions permeate nearly every stage of their life cycle. At the same time, an empty icosahedral capsid is almost isotropic as far as the surrounding electrolyte is concerned—its charge distribution is anisotropic only at high multipole order, and electrostatic screening removes such anisotropy long before it can be probed at a distance. Here, we show that the packaged genome of a filled virus imparts a long-range electrostatic anisotropy that extends throughout the surrounding medium, which is not present for empty capsids. We support these findings with a novel Poisson–Boltzmann continuum theory where the orientational order of dsDNA enters through an anisotropic dielectric tensor and an inhomogeneous volume-charge distribution, which is coupled to a charge-regulating shell containing ionizable amino acid residues of the capsid proteins. The resulting electrostatic potential profiles show that DNA packed in an inverse-spool geometry imprints a highly inhomogeneous potential distribution on the outer capsid surface, whose angular structure is a direct result of the DNA-free axial void. At high salinity, the multipole spectrum of this distribution persists at large distances, whereas at low salt concentration, higher-order multipoles decay more rapidly away from the surface. The surviving quadrupole renders virus–wall and virus–virus interactions orientation dependent at the $k_\mathrm{B}T$ level, with a preferred orientation controlled by the sign of the external charge and the pH. Using phage $\lambda$ as a model system and checking robustness of our results on two other phages, we find the same behavior across a range of pH and ionic strengths. This identifies the packaged genome, rather than the symmetry of the capsid, as the origin of the long-range electrostatic anisotropy of a filled virus.

We study transient solute dispersion in pressure-driven micropolar flow through a concentric annulus representing a catheterized artery. The catheter is impermeable to solute, whereas the arterial wall combines irreversible removal with reversible surface retention. The exact steady micropolar velocity field is coupled to the Gill-Sankarasubramanian generalized-dispersion framework; the resulting bulk-surface hierarchy is advanced with Rannacher-damped Crank-Nicolson time stepping to determine $K_0(t)$, $K_1(t)$ and $K_2(t)$. The exchange coefficient is independent of the micropolar parameters and satisfies $-K_0(0^+)=2(\beta+\theta Da)/(1-\lambda^2)$, whereas $K_2-Pe^{-2}\sim\sigma_v^2t$ initially, so the leading short-time dispersion is hydrodynamic and independent of wall kinetics. In the weak-reaction regime, micropolarity modifies convection approximately linearly and shear dispersion quadratically through the velocity-amplitude factor. A narrow-gap analysis with $\varepsilon=1-\lambda$ gives $\bar v\sim(2-N_c)\varepsilon^2/6$ and $K_2-Pe^{-2}\sim(2-N_c)^2\varepsilon^6/7560$ for a fixed pressure gradient, revealing a sixth-power suppression of shear dispersion as the catheter approaches the arterial wall. Increasing $\lambda$ from $0.01$ to $0.30$ reduces effective convection by about a factor of $2.45$, while chemically passive shear-induced dispersion falls by a factor of $24$. The coupled formulation also yields the exact partition $\Phi_m+\Phi_s+\Phi_a=1$, separating mobile, reversibly retained and irreversibly absorbed solute. The reconstructed field quantifies reaction-modulated transverse non-uniformity, while the results distinguish hydrodynamic effects of confinement and microrotation from kinetic wall effects.

Biological processes, from molecules diffusing to their regulatory destinations to whales pursuing food or mates, are widely exploratory. Such behaviors are effective when some verifiable functional state or outcome can be reached regardless of initial conditions. In these cases, systems repeatedly undergo distinct and abortive trajectories; the process only ends when the system finds “right” outcomes. This dominance of the terminal condition (and indifference to the initial state) provokes a very different perspective than the conventional “dynamical systems” framework that has been a centerpiece of the quantitative sciences for centuries. We hypothesize that many of these problems defy the initial-condition driven or gradients on landscapes so useful in problems ranging from mechanics to electrodynamics to chemical kinetics to mass and heat transport. We examine several mathematical frameworks that capture and unify key aspects of exploratory dynamics. One powerful way of thinking of such processes is the geometric distribution, where repeated failures are punctuated by a successful trajectory. We develop intuitions for how random walks with resets accelerate search processes. We highlight fresh and surprising behaviors of search under drift, cues, and checkpoints. Last, appreciating the probability of trajectories conditioned on satisfying macroscopic final outcomes reveals a language for the potency of variation sculpted by selection in their broadest forms. This can give the fictitious appearance of the future making itself known in the present, but we view this as conceptually similar to the way “fictitious forces” arise in non-inertial reference frames. These approaches stress unity, open questions, and applications across a range of biological phenomena.

Phenotypic plasticity, the ability of cells to switch between states, is central to development, differentiation, and therapy resistance. Although it is modeled at several scales, from compartmental ODEs to phenotype-structured PDEs and single-cell stochastic equations, a framework connecting these descriptions is missing. We present such a framework. Starting from a general $n$-compartment ODE model encompassing nonlinear growth and linear transitions between phenotypes, we show, with a new, elementary and generalizable proof of a recent theorem, that under uniform competition, the long-term population distribution is solely governed by transition rates. All phenotypes become selectively neutral at saturation, and the imprint of fitness differences during growth fades at an explicit rate. Restricting transitions to neighboring states transforms the model into a discretization of a phenotype-structured reaction-diffusion-advection PDE. In this continuum model, diffusion and advection are identified from switching rates, and fitness remains asymptotically irrelevant. Interpreting the advection velocity as the negative gradient of an effective epigenetic potential transforms the PDE into a Fokker–Planck equation and converts single-cell trajectories into stochastic gradient descent (SGD) in the Langevin sense on the phenotypic landscape. Non-local transitions, such as mutations, are incorporated via an integro-differential term, yielding a unified model with reaction, gradient flow, diffusion, and jumps. State-dependent noise reshapes the effective landscape without altering the underlying potential. This gives cancer a route to elevated plasticity that static, single-cell snapshots cannot distinguish from a changed landscape. This framework provides a physical interpretation of Waddington's landscape, where cells perform SGD, and cancer corresponds to a corrupted landscape.

Curvature and topology jointly organize defects in two-dimensional crystals, but their combined role remains unresolved when competing lattice symmetries coexist with spatially varying curvature. We use simulated-annealing Langevin dynamics to study Hertzian particles forming coexisting hexagonal (Hex) and square (Sq) lattices on prolate and oblate ellipsoids. Mapping reduced density and aspect ratio reveals a broad sequence of scar and domain-based morphologies in both Hex-dominant and Sq-dominant backgrounds. Latitude-resolved comparisons show that Gaussian curvature biases defects toward its maxima under weak deformation. Strong prolateness, however, confines high curvature to small polar caps that cannot independently accommodate all defect motifs. Defects then spread toward lower-curvature latitudes to relieve defect crowding and elastic repulsion. In the Hex-dominant regime, this competition drives vertex-contacted domains with neutralized corner contacts, and compensating positive defects locate away from the poles. The Sq-dominant regime features Hex-rich triangular domains, bridged states, and linear or open scars similarly reorganized by curvature anisotropy. On oblate ellipsoids, the extended equatorial high-curvature belt allows defects to separate azimuthally while remaining curvature-localized. This work elucidates that nonuniform curvature can engineer rich defect patterns by selecting the spatial distribution of topological charge and the connectivity of finite defect motifs.