Papers

Droplets in complex environments often encounter compositional gradients that drive their propulsion. For example, surfactant gradients induce surface-tension-driven propulsion via the Marangoni effect. Here, we show that such propulsion emerges generically, even in the absence of surfactants. Employing a thin-interface approximation, we derive a compact expression for the droplet velocity in terms of droplet size, viscosity, the sensitivity of surface tension to a regulating component, and the chemical potential gradient of that component. Our theory reveals that droplets move toward regions of lower stability, as encoded in the morphology of the phase diagram, particularly near critical points. Numerical simulations confirm these results, which establish a general route to predicting and designing droplet motility from the phase behavior of complex fluids.

Tracking neurite morphology over time helps characterize structural changes during neuronal development and deterioration, but long-term time-lapse imaging is resource-intensive and difficult to scale. Forecasting future morphology could reduce this burden. Existing neurite digital-twin models such as gated spatiotemporal attention (gSTA) produce a single deterministic forecast without representing variability among plausible futures. We introduce Morphology-Gated Residual Diffusion (MGRD), a compact stochastic surrogate that jointly forecasts twenty future neurite-morphology frames from ten observed frames while conditioning on morphology features derived from the latest observation. On controlled phase-field trajectories, MGRD reduces trajectory-wise mean MAE by 9.7% relative to a matched control while updating 4.46 times fewer parameters. On human iPSC-derived neuron microscopy, MGRD improves all four reported metrics over gSTA, including a 39.6% reduction in trajectory-wise mean MAE and a 45.3% increase in skeleton F1. Without mouse-domain retraining or fine-tuning, MGRD also improves MAE and skeleton F1 on mouse cortical-neurosphere microscopy across 10-40-min sampling intervals and forecast horizons beyond 13 hours. Repeated sampling provides a case-level variance score for ranking forecast difficulty. Retaining approximately 60% of the lowest-variance cases reduces mean MAE by 17.6% on iPSC microscopy and 16.8% on simulation data. MGRD uses 1.01% of gSTA's parameters, requires less than one tenth of its training-update time, and generates a 50-step DDIM trajectory 7.9% faster when morphology features are cached. These results establish MGRD as a compact stochastic surrogate for neurite-morphology forecasting and case prioritization across simulation and microscopy datasets.

Many models of collective behavior write headings, beliefs, and meanings in one experimenter-defined frame. Organisms do not live there: each represents the world in a private space, and comparison requires translation. Consensus becomes an existence problem before it becomes a dynamical one. Reciprocal pairwise translations need not compose consistently around a loop. This return transformation (the holonomy) can expose a mismatch no isolated reciprocal pair can carry. We develop a gauge-covariant theory in which physical predictions are invariant under private relabeling. For reciprocal unitary translations, the kernel of the connection Laplacian is isomorphic to the joint fixed space of loop holonomies: a collective can hold in common exactly what all its loops leave unchanged. A blind-subgroup criterion identifies invisible defects. Common-frame comparison, such as in traditional models of collective behaviour, occupies the flat sector. For independent uniform translations from a finite group $G$, a connected graph with $E$ relations among $N$ individuals is flat with probability $|G|^{-(E-N+1)}$. Exact cycle spectra determine persistence under linear relaxation. The consequence is operational as well as structural. For unrecorded routes under a specified model with isotropic Gaussian source and readout noise, we derive the smallest mean-squared error achievable by any decoder. At fixed signal-to-noise ratio, the jointly preserved feature fraction fixes its long-route limit. Networks with identical loop angles can differ in recoverable content when their preserved axes differ. The relational geometry of a collective sets both the states it can share and the content it can recover.

Quantitative characterization of the mechanical properties of cells and tissues is essential for understanding disease progression and tissue regeneration. Optical tweezers (OT) enable the direct application of biologically relevant forces; however, OT has been limited to single axial indentations of cells, thereby restricting throughput. Furthermore, the use of quadrant photodiodes is insufficient for assessing the large displacements required for biomechanical characterization of tissues. We present light-sheet optical tweezers as a force transducer (LOFT), an approach that improves the throughput by at least 3x through simultaneous multiparticle trapping and parallelized characterization under sub-nN forces. LOFT is achieved by uniquely integrating light-sheet illumination for extended trapping, femtosecond-pulsed lasers to augment the optical gradient force, and videography-based particle tracking for observation of force transduction. The platform is validated through single-cell indentation experiments. We then apply LOFT to myocardial tissue, revealing significant biomechanical differences between healthy and infarcted regions; the interpretation of which is further supported by quantitative multiphoton imaging using the same optical source and platform. This work represents the first demonstration of OT for the mechanical testing of intact soft tissues, and establishes LOFT as a versatile, multifunctional platform for high-throughput, minimally invasive, mechanical characterization of complex biological systems in situ.

How a growing tissue organizes its own homeostatic state is a central question in the physics of living matter. We show that when a growing epithelial sheet counteracts increasing cell density by mechanically squeezing cells out of its plane, a homeostatic in-plane pressure emerges as a generalization of a yield stress. We find that in the quasistatic growth limit the homeostatic state is marginally stable, with a pseudogap in the distribution of local distances to the extrusion threshold pressure. Because such mechanically induced extrusions arise from an instability of individual cells, the pseudogap is imprinted in the distribution of cell areas. This provides an image-based way to test for presence of mechanically induced extrusions and we identify this signature in the developing wing epithelium of D.~melanogaster. We expect the same principles to apply to confined three-dimensional tissues.

Dendritic silhouettes are cheap. Pond ice neurons, diffusion-limited aggregates, wiring-minimizing arbors, and biological neurons can share a branching statistic because they share a growth instability, not because they are functionally similar. We take that observation as a modeling constraint. The ice neuron only structurally resembles a biological neuron. A biological neuron carries an internal state and a field that it helps generate, letting geometry, dynamics, and field co-sculpt one another. In our construction, the ice neuron is the zero-gain limit of an interfacial system in which a FitzHugh–Nagumo state lives on the moving front and writes back into the field that drives it, with dimensionless gain $\gamma$. At $\gamma=0$, morphology and internal dynamics decouple into a Mullins–Sekerka growth band and a damped oscillator. Finite $\gamma$ deforms the spectrum, shifts the selected instability, and opens an oscillatory region below the isolated Hopf threshold. On a dendrite grown at $\gamma=0$ and then frozen, field closure increases distal persistence without changing the geometry; its first-order effect remains positive across repeated realizations of the same growth rule and localizes to a small set of non-cable field shortcuts. Nonlinear dynamics remain finite beyond the linear instability: below threshold, closure is almost the transmission; at spike amplitude, it is a correction to a regenerative cable event. A dendritic tree therefore is not intrinsically a structural spandrel. Shape alone is morphology without an internal state or a source term. That is the dendritic silhouette of the ice neuron. Excitability adds an active cable. Field closure is the biophysical mélange in which the neuron helps write the field that acts back on it, sculpting its dynamics and, during growth, its structure. That is a biological neuron.

A general framework for inferring the computational role of spike-timing-dependent plasticity (STDP) does not currently exist. Here, we develop a game-theoretic description for a canonical, convergent neural circuit with general STDP and postsynaptic-potential (PSP) kernels. Parity-matched STDP-PSP interactions induce a potential game among presynaptic neurons, whereas parity-mismatched interactions induce a zero-sum game. These components, respectively, implement contrastive PCA and flow selection; their weighted interplay determines learning dynamics and computation for arbitrary STDP rules.

From interstitial space to luminal cavities, fluid pressure and flow can remodel, reshape and even redefine a biological tissue. Fluids can either govern or react to mechanical interactions between cells. However, measuring flows at cellular scales is difficult, which makes it challenging to understand tissue hydraulics. Here, we develop a theoretical approach that captures cellular mechanics and fluid flow in one framework. We find that hydraulics can drastically influence tissue behavior. Hydraulic coupling between cell shape and size governs a tissue's response to osmotic shock, while tuning a tissue's permeabilities can channel fluid either between or across cell membranes. In active tissues, hydraulics can suppress cell mobility to the point of fracture, where we discover a hydraulic ratchet that drives fluid out of cells to generate small luminal spaces. We find experimental evidence that hydraulics can suppress cell motion in early stage zebrafish embryos injected with a thickening agent, which indicates that hydraulics may generally govern the behaviors of many multicellular systems.

We introduce a coarse-grained interacting-spin model for two-dimensional cell motility, in which the cell perimeter is discretized into stochastic binary spins that switch between active and inactive states. Each perimeter spin represents a "motile-unit" that is a source of protrusive force and retrograde flow when active. Long-range interactions between the motile-units arise through a polarity cue advected by the collective actin retrograde flow, providing a minimal realization of spontaneous symmetry breaking and self-propulsion. The model exhibits three dynamical phases, a random walk phase, persistent random walk phase, and an intermittent bistable phase characterized by run-and-tumble migration. Additional nearest-neighbor interactions modulate speed and persistence without altering the overall phase structure. Owing to its simplicity, the framework naturally incorporates external cues, reproducing chemotactic migration, steering by localized optogenetic activation, and directional decision-making (symmetry breaking) under competing stimuli. The model introduces a new class of active-particle model in which both speed and polarity emerge from internal stochastic spin dynamics, rather than being imposed as particle-level variables, offering a framework for the study of cell migration and extends the scope of active-matter physics.

We investigate energy fluctuations of solvated DNA in three conformations: G-quadruplex, Hairpin, and Duplex. Our comprehensive molecular dynamics (MD) simulations demonstrate that the time-series of interaction energies for DNA self, DNA-water and DNA-ion show 1/f noise with a universal decay exponent $\beta \simeq 0.90$. We show that DNA topology and structural rigidity modulate its dynamic coupling with the surrounding hydration shell and mobile counter-ions. This coupling critically shapes the 1/f noise profile: DNA self energies in flexible structures (G-quadruplex, Hairpin) display pronounced low-frequency modes absent in the rigid Duplex. These findings reveal how the interplay between DNA topology and environmental coupling governs different stochastic behavior in biologically relevant forms of DNA.

Active matter systems can generate mechanical stresses that deform their surroundings, providing a route to transport and shape dynamics far from equilibrium. Deformable vesicles containing active particles offer a minimal setting in which such active stresses are directly coupled to boundary mechanics. Here, we use numerical simulations to investigate a two-dimensional, fixed-area vesicle filled with chiral active particles interacting through excluded volume and polar alignment. We find that the coupling between particle chirality and vesicle deformation produces distinct modes of collective motion, including run-and-tumble-like migration, rotor-like dynamics, and persistent spinning. Most notably, we show that vesicle rotation is non-monotonic in chirality: at fixed activity, an optimal chirality maximizes the rotational velocity. We develop an analytical theory that relates the vesicle rotation to the effective torque generated by the chiral active particles. The theory identifies the competition underlying the optimal chirality and predicts a scale-invariant dependence of the rotational velocity on activity and chirality. This scaling collapses simulation results obtained over different activity strengths onto a universal curve. Our results establish a general mechanism by which chirality and collective alignment regulate the transmission of active stresses to deformable boundaries, providing a framework for understanding transport and rotational dynamics in confined active systems.

Organisms' foraging strategies are shaped by a trade-off between search area and local capture efficiency. This trade-off leads individuals to adapt their foraging area to an optimal value, impacting population dynamics. Here we study the effect of multiple foraging areas in a predator-prey model composed of three trophic levels. The interactions between predators and prey occur only within a limited neighborhood of the predators, where adaptation can occur over generations. We assume a trade-off where local predation efficiency is inversely proportional to the foraging area. These dynamics were implemented computationally via cellular automata and analytically via Master Equations with mean-field and pair approximations. Unlike the mean-field approximation, the pair approximation reproduced the dependence of population density on foraging area observed in the simulations. However, the simulations showed that the optimal foraging area does not maximize population density. Moreover, we found that a polymorphic population emerged, where not a single optimal strategy but a range of optimal strategies can coexist. Using the framework of Adaptive Dynamics, we confirm that the range of optimal areas is not the one that maximizes population size, but the Evolutionary Stable Strategy that can invade a population and not be invaded.

Endovascular implants prevent intracranial aneurysm rupture by altering the mechanical and hemodynamic environment at the aneurysm neck. Yet many in silico workflows prescribe or reconstruct the post-deployment geometry before computing flow, leaving unresolved the mechanics that create the clinically relevant interface. Here we review braided intraluminal flow diverters, intrasaccular devices, and emerging flow-disruption concepts across deployment mechanics, inter-wire and wire-wall contact, superelasticity, wall apposition, pore geometry, computational fluid dynamics, and fluid-structure interaction. We connect these modeling choices to neck coverage, malapposition, migration, deformation, and durability, and distinguish established evidence from mechanistic inference and prospective hypotheses. We argue that model fidelity should match the clinical question: prescribed or fast placement may support screening, whereas questions of coverage, apposition, compaction, and migration benefit from mechanically plausible deployment states. An interface-resolved mechanics-to-flow framework, supported by measurable validation targets and standardized reporting, could improve device design and enable more reliable patient-specific treatment planning.

Wide-field mid-infrared photothermal (MIP) imaging enables high-speed, chemically specific imaging at sub-micrometer spatial resolution through several possible contrast mechanisms, including scattering change, fluorescence modulation, and phase change. Each mechanism offers distinct advantages, yet existing wide-field MIP instruments have typically been limited to a single contrast mechanism so far, requiring a dedicated instrument for each. Here, we introduce a switchable multi-contrast wide-field MIP microscope that allows the photothermal readout mechanism (based on scattering-, fluorescence-, or quantitative phase imaging (QPI)) to be matched to the sample and imaging conditions. We characterize the spectral fidelity and signal-to-noise (SNR) ratio of each mechanism using 5 \mu m polystyrene (PS) beads, and the effective spatial resolution using 300 nm PS beads. Scattering- and fluorescence-based detection achieved a sub-500 nm measured point spread function full width at half maximum, while QPI-based detection reached approximately 900 nm but provided up to 26-fold higher SNR than scattering. We further demonstrate imaging across a range of samples, including A549 cells in buffer, mouse lung tissue section, bacteria, and SU8 polymer at 1.4 and 5 \mu m thickness, with a field of view exceeding 200 \mu m. Comparison across these samples shows that each contrast mechanism offers distinct trade-offs in resolution, sensitivity, and applicability, guiding readout-strategy selection by sample type. These results establish a flexible, switchable multi-contrast platform for wide-field MIP imaging, with broad applicability across polymer and biological samples.

Posture control in slender bodies such as snakes and eels arises from the interplay between passive deformation, active internal actuation, and task-level constraints. We formulate a general framework for the selection of stable postures in active elastic filaments subject to distributed forcing from gravity and fluid drag, by combining the constraints of mechanical equilibrium with optimal control theory. Our theory leads to a minimal description in terms of parameters governing the competition between hydrodynamic and gravitational loading, elasticity, and activity. We show that posture selection reflects a trade-off between control cost, function and dynamical stability, leading to the coexistence of distinct solution branches and abrupt transitions between them. Applying the theory to sessile eels in flow, we recover the experimentally observed transition from upright to reclining postures and predict scaling laws for body shape and exposed length. More generally, our results provide a unified perspective on how active filaments can regulate geometry to maintain function in external fields, with implications for biological and artificial systems.

Many proteins function through transitions between conformational states, yet rare states are rarely sampled by diffusion models trained on an equilibrium ensemble, demanding better sampling methods. We introduce METALICA, which implements Metadynamics on a pretrained diffusion model via Replica Exchange. It accumulates a bias potential along a Collective Variable, repels new samples from previous ones through biased sampling, and reweights samples onto the unbiased distribution. METALICA holds one replica per diffusion level, forming a Markov Chain that evolves through inter-replica communication and is refined in place as the bias grows. METALICA is the dual of sequential control, in which Sequential Monte Carlo parallelizes the sampler over a batch of particles. Parallelism over the levels of the diffusion-time schedule instead allows METALICA to generate samples from long chains, essential for the discovery of rare events, with accuracy set by run length rather than by the memory available. We validate on a bimodal target with known free energies, then apply METALICA to the unfolding of a protein. At a budget for which sequential control yields no unfolded structure, METALICA populates the basin and resolves a second free energy minimum.

Inferring directed effective interactions from neuronal spike trains is a central inverse problem in statistical physics and computational neuroscience. Kinetic Ising models provide a tractable framework for this task, but their application to neural data typically requires binning spike trains into binary activity variables, discarding within-bin timing and conflating collective network dynamics with single-neuron history effects. We introduce SpiKIsing, a latent-variable model that separates these two levels of description. A discrete-time asymmetric kinetic Ising model describes collective network activity, while continuous-time, history-dependent point processes generate the observed spikes conditional on the latent states, accounting explicitly for refractoriness and post-spike recovery. We derive a variational mean-field expectation-maximization scheme in which the point-process likelihood enters as an effective observation field, enabling joint inference of latent activity, network couplings, and emission parameters. The framework extends naturally to maximum-a-posteriori inference with structured priors, including sparsity and a hierarchical extension favouring Dale-consistent outgoing interactions. We validate parameter recovery on matched synthetic data and test the method on spike trains generated by a recurrent conductance-based leaky integrate-and-fire network. In this setting, SpiKIsing recovers sparse connection structure and correctly classifies all excitatory and inhibitory neurons despite the substantial mismatch between the data-generating dynamics and the SpiKIsing model.

Even exact knowledge of the Markov generator at one environmental condition does not determine how that generator changes with the environment unless additional reaction-structure information is supplied. We establish this non-identifiability for mass-action reaction networks driven by a chemostatted species. Distinct chemical embeddings can share the same generator and path law at a reference concentration u0 while differing in how the chemostat enters individual reaction channels. Changing integer chemostat reactant molecularities and rescaling the corresponding kinetic constants preserves all propensities at u0 . This ambiguity already occurs for low-molecularity elementary reactions: a one-species birth–death example has identical path measures at the reference condition but dimensionless stationary sensitivities one and zero. Single-condition data can therefore determine the observed Markov dynamics at u0 without determining their parametric response. As an illustration of the complementary role of prior chemical structure, we also show that a known stoichiometric integral coordinate imposes a conditional zero-frequency identity within the linear-noise approximation.

The pace of evolution depends on how rapidly new phenotypes arise. We show that neutral Wright-Fisher evolution exhibits anomalous first passage despite diffusive mutations. The mean time for the first individual to reach a prescribed phenotypic distance scales approximately as $(\sigma^2)^{-3/2}$ with mutation variance $\sigma^2$. Two crossovers bound this regime, with inverse-variance scaling on either side. Combining coalescent theory with Kardar-Parisi-Zhang (KPZ) fluctuations at the dilute population edge, we develop an edge-KPZ theory of all three regimes. The anomaly persists under weak selection.

Upstream swimming drives bacterial spreading and surface colonization. Many pathogens encounter fluid flows as they infect the intestines, lungs, and urinary tract, so how bacteria use their flagella to counter these flows matters for disease and treatment. Yet how morphology and flagellar arrangement govern motility against flow remains unknown. Here, we investigate the biophysical determinants of rheotaxis by combining microfluidics, directed evolution, genetics, holography, and hydrodynamics simulations. Using upstream swimming competitions, we find that peritrichous E. coli and S. enterica rapidly outcompete monotrichous P. aeruginosa and V. cholerae, accumulating upstream at densities up to five orders of magnitude higher, even though Vibrio swims three times as fast. Motility selection experiments show that rheotaxis increases with flagellar number and length, confirmed by overexpressing the master regulator flhD/C. Three-dimensional holography and single-cell tracking reveal that multiflagellarity stabilizes surface residence and promotes the weathervane effect that reorients cells upstream, a mechanism further supported by simulations that fully resolve flagellar arrangement and fluid-structure interactions. These results establish multiflagellarity as a key facilitator of upstream navigation, governed by near-wall residence and shear-driven reorientation rather than by swimming speed.

The last decade has seen the development of powerful methods for learning complex structure from high-dimensional data. These advances have brought to the foreground fundamental connections between subdisciplines of physics, applied mathematics, and machine learning. In this review, we bring together some of these ideas, often expressed in different languages, to highlight a conceptual thread that links five distinct fields: control theory, optimal transport, probabilistic inference, non-equilibrium thermodynamics, and machine learning. A common theme is the optimization of free-energy-like functionals under dynamical or statistical constraints. We offer a guided tour through this thread and present selected applications in reinforcement learning, variational inference, and generative modeling. The review does not assume prior familiarity with these topics, and begins with principles originating from physics.

We investigate the structural information retained in the distribution of explosion ion trajectories from proteins subjected to strong ionization. Using molecular-dynamics simulations and machine-learning analysis benchmarked against an analytical approach, we show that low-resolution structural information can be retrieved from the explosion distributions alone. An ensemble of convolutional neural networks trained on simulated spherical ion maps recovers the radius of gyration and the three semi-axes of an ellipsoidal molecular envelope with prediction errors of 1.2 Å and 1.5 Å, respectively, while an analytical ellipsoid charge model returns similar estimates and performs best for globular structures. We further investigate how higher-level structural information and symmetries can be extrapolated from ion measurements. This study supports the viability for structural determination of single proteins without large-scale X-ray facilities.

Cells in connective tissues reside within the extracellular matrix (ECM), which consists of a fibrous mesh that exhibits non-linear strain-stiffening behavior, driven by a transition from bending-to-stretching-dominated deformation. While bulk rheology captures macroscopic mechanical properties, cells actively sense and respond to local microscale heterogeneities and stiffness anisotropy in their environment. Characterizing ECM micromechanics is therefore essential for understanding the mechanical cues experienced by cells. This study quantifies local stiffness anisotropy in stretched fibrous gels by combining experimental and numerical approaches. Experimentally, we utilized optical tweezers microrheology to measure local stiffness in fibrin gels subjected to uniaxial stretch. The gels demonstrated gradual local stiffening along both the tensile and perpendicular axes, with a more profound increase along the tensile axis, resulting in local anisotropy. To investigate the physical parameters driving this phenomenon, we developed a 3D finite element model of a discrete random fiber network, successfully replicating the experimental local stiffening and anisotropy. Numerical analysis further revealed that within the sub-isostatic region, both fiber thickness and network connectivity strongly influence local anisotropy: slender fibers and higher connectivity amplify the anisotropy by up to an order of magnitude. This contributes to the formation of a highly anisotropic local environment, thereby playing a significant role in directing mechanically driven biological processes, such as cell migration and durotaxis. Our simulations also indicate that local micromechanical responses may differ from the material's global stiffening behaviors, highlighting the need for characterization at the microscopic scale.

Slender elastic objects constrained to curved surfaces are ubiquitous in soft systems, with examples ranging from DNA wrapping around histones to actin filaments forming contractile rings on the cell membrane during cytokinesis. In the continuum limit, the conformation of these effectively one-dimensional (1D) objects is governed by both the geometry and mechanics of the embedding surface, and the elasticity of the object. Existing phenomenological typically describe such behavior through elastic energy minimization that incorporates bending and twisting, but neglect stretching that may be important for filaments with finite cross-section or are highly incompatible with the underlying surface. Here we present a coarse-grained geometric theory of 1D elastic curves constrained on rigid surfaces, derived from the first principles. For an isotropic material, our model emerges naturally in terms of the Young's modulus, Poisson's ratio, and area moments of inertia. The resulting effective energy functional explicitly includes stretching in addition to bending and twisting. We minimize it to determine the equilibrium curve conformations on different zero, positive, or negative Gaussian rigid surfaces. Our theory provides a general framework for analyzing the equilibrium configurations of surface-bound elastic curves in biologically and physically relevant settings.

Across biological scales, from cytoskeletal networks to whole tissues, orientational order and topological defects arise within complex three-dimensional geometries. However, quantifying nematic order orientational order with head-to-tail symmetry remains challenging: 2D projections introduce geometric distortions, while current 3D methods often struggle to resolve distinct nematic fields within curved or multilayer structures. Here, we introduce NEMO, a modular Python framework for the depth-resolved quantification of tangential nematic order and surface morphology. By reconstructing biological surfaces as triangulated meshes, NEMO projects curved intensity layers, extracts local nematic directors, and computes locally averaged nematic tensors within the tangent plane. The pipeline identifies topological defects and computes their topological charge by accounting for the Gaussian curvature of the underlying surface. Furthermore, NEMO quantifies tissue morphology through inter-surface distance and surface-fitted estimates of Gaussian and mean curvatures. We show the capacities of this framework using a synthetic nematic film on a vesicle and experimental actin organisation in Hydra. By combining customisable projections with surface-constrained analysis, NEMO provides a unified framework for quantifying the interplay between orientational order and geometry across scales.

Chirality, a systematic rotational bias in the motion of a particle, arises in a wide range of physical and biological systems, from charged colloids in magnetic fields to swimming bacteria near surfaces. While its effects in homogeneous environments are well understood, the interplay between chirality and structural disorder has remained largely unexplored. Here we investigate the chiral random walk on two-dimensional percolation clusters above the percolation threshold, combining numerical simulations with an analytically tractable annealed-disorder approximation. We find that the long-time diffusion coefficient depends non-monotonically on both the chirality parameter and the obstacle density: for every obstacle density above the percolation threshold, there exists an optimal chirality that enhances diffusion relative to the achiral walk. We show that the optimal chirality is set by an edge-adhering mechanism: maximum diffusion is achieved when the persistence length of the wall-adhering motion matches half the typical obstacle cluster perimeter. This yields a closed-form prediction for the optimal chirality in terms of geometric properties of the medium alone, which we verify across the full range of obstacle densities studied. The enhancement extends to first-passage statistics, where chirality shortens typical search times at strong disorder while lengthening them at weak disorder, with direct implications for biological navigation in disordered environments.

A single-molecule experiment on a driven enzyme or motor resolves only a few of the transitions the machine makes, yet one would like to know how much free energy it dissipates in total, including on the steps that stay hidden. The mean and the fluctuations of the currents on the watched transitions are shown to certify this hidden dissipation, with no knowledge of the transition rates and no access to the hidden transitions: when the watched transitions span the cycles of the network, the observed-current covariance recovers the full density-contracted quadratic current geometry, including the contribution of transitions that are never seen. The mechanism is that fluctuations are set by the dynamical activity, or traffic, the symmetric partner of the current. Contracting the large-deviation cost of empirical currents over density fluctuations identifies the observed-current covariance with a traffic-weighted metric, and turns partial observation into a minimum-energy completion problem over the unseen cycles, whose solution is the certified hidden cost. Existing current-fluctuation uncertainty relations bound dissipation from chosen currents but do not say when partial observation fixes the hidden contribution; the cycle-observability condition derived here does. The statements concern long-time means and fluctuations; finite-time estimates require separate error control.

DNA nanostructures are emerging as programmable components for engineering synthetic cell membranes, yet how their collective packing and deformability regulate molecular dynamics at membrane interfaces remains poorly understood. Here, we investigate the packing and mobility of DNA nanostars with tunable stiffness on lipid-coated droplets. The negatively charged nanostars spontaneously adsorb onto cationic membranes, and their interfacial packing is changed by the bulk DNA concentration and droplet size, which together determine the number of encapsulated nanostars. Combining fluorescence recovery after photobleaching experiments with coarse-grained simulations, we reveal distinct packing-dynamics relationships for rigid and soft nanostars. For rigid nanostars, diffusion first decreases gradually and then drops sharply with increasing interfacial packing, approaching a dynamically arrested state consistent with jamming-like behavior. In contrast, at equivalent experimental conditions, soft nanostars systematically reach lower interfacial packing fractions and show a weaker decrease in apparent mobility. This behavior is consistent with their weaker membrane affinity, which facilitates adsorption-desorption with the bulk. When this exchange is suppressed in simulations, crowding reduces the lateral diffusion of both nanostar types, but produces distinct dense configurations: soft nanostars become strongly deformed, whereas rigid nanostars largely retain their shape and form interlocked, gear-like arrangements. Nanostar adsorption also impedes lipid diffusion, while differences in membrane affinity result in distinct lipid mobile fractions. These findings reveal how the interplay between nanostar packing and deformability regulates molecular transport at membrane interfaces, providing a physical design principle for tuning lateral fluidity and crowding in artificial cells.

We present Tomography-NMR, an open-source Python package that reconstructs quantum density matrices from spectroscopic measurement data. The package implements a complete analysis pipeline for two-qubit quantum state tomography based on the product operator formalism: raw time-domain signals are Fourier-transformed into frequency-domain spectra, spectral peak intensities are mapped to expansion coefficients of the density matrix, and the full quantum state is reconstructed. Three integration methods are provided for different use cases: direct peak height measurement and fixed-parameter numerical integration require no theoretical reference and are suited to unknown states, achieving fidelities of approximately 98% on a benchmark set of known states, while a systematic parameter optimization against a known target state achieves reconstruction fidelities exceeding 99% for the same benchmark states. While the detailed theoretical framework for quantum state tomography is well established, the practical procedures for extracting density matrices from experimental spectra are often inadequately documented in the literature and obscured within proprietary software. This package addresses that gap by providing a fully transparent, reproducible implementation of every analysis step, from spectral preprocessing to density matrix visualization. The software has been validated on experimentally prepared two-qubit states measured via nuclear magnetic resonance (NMR) spectroscopy of coupled $^{31}$P nuclei. Average reconstruction fidelities range from 0.975 to 0.995 across a benchmark set of 20 two-qubit states, including the computational basis states, Bell states, and the outputs of three fundamental quantum gates (CNOT, H, and T). Although developed for NMR, the modular architecture facilitates adaptation to other spectroscopic platforms and alternative measurement protocols.

Modelling retinal haemodynamics is crucial for understanding retinal microcirculation but is computationally demanding because it involves coupling between the vasculature and surrounding tissue across multiple scales. This computational burden has been substantially alleviated by a recent analytic solution on the planar disc that enables lumping the capillary bed and surrounding tissue into an effective resistor. However, that formulation treats the retina as a flat surface, whereas the retina is a curved surface with a finite anterior aperture. In this work, we develop a nontrivial and physiologically necessary extension to spherical-cap tissue domains with varying apertures, where surface curvature and finite-aperture boundaries complicate solving coupled Darcy equations on a curved manifold. Using a stereographic projection and a decoupling transformation, we derive an analytic solution for the capillary-tissue system on the spherical cap that represents flow in both the capillary bed and interstitial tissue more realistically while retaining the efficient resistor formulation, a key advantage of the planar-disc formulation. This solution is coupled to one-dimensional (1D) arteriolar and venular flows to obtain a multiscale description of retinal haemodynamics. Using a vasculature model designed to capture retinal vascular features, we show that the multiscale model's predictions are consistent with experimental data. We further explore aperture effects using both a fixed hemispherical vasculature and aperture-dependent vasculature. The aperture affects retinal haemodynamics mainly through changes in the constructed vasculature itself, whereas the surface-averaged pressures and relative terminal flow distributions remain nearly unchanged. This framework provides a foundation for studying retinal pathophysiology on more anatomically realistic domains.