Journal of The Royal Society Interface

Patient-derived tumour spheroids are increasingly used as engineered three-dimensional tissue models for studying tumour growth, nutrient limitation, and therapeutic response. However, extracting quantitative, mechanistically interpretable information from longitudinal imaging data remains challenging. Here, we present a three-dimensional phase-field framework for modelling patient-derived tumour spheroids as continuum, self-organising tissues. The model captures the coupled evolution of viable and necrotic cell fractions through nutrient-limited growth, death, and mechanically and thermodynamically mediated motion, using seven biologically interpretable effective parameters. Key experimental observables emerge naturally from nutrient-growth coupling, without imposing explicit species interfaces or quiescent layers. The framework was quantitatively calibrated against longitudinal imaging data from melanoma spheroids across two cell lines and three initial seeding densities. Across all conditions, simulations reproduced the temporal evolution of all measured observables with low relative error ({approx} 3{sigma} of experimental data), and direct comparison with an established Greenspan-type ODE model demonstrated comparable or improved predictive accuracy. Parameter identifiability analysis revealed weak individual parameter constraints, yet model predictions remained robust, a profile consistent with biological models. We demonstrate that a general PDE-based growth framework can match or outperform a dedicated spheroid model while remaining fully biologically interpretable. Beyond predictive accuracy, the phase-field formulation naturally resolves internal mechanical structure, providing access to quantities that are not directly experimentally observable. These results establish that mechanistically grounded continuum models can be quantitatively calibrated to routine spheroid imaging data, offering a foundation for integrating spatial and mechanical information into the interpretation of organoid-based assays. Graphical Abstract O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=77 SRC="FIGDIR/small/717345v1_ufig1.gif" ALT="Figure 1"> View larger version (21K): org.highwire.dtl.DTLVardef@1cb3b45org.highwire.dtl.DTLVardef@1a053d5org.highwire.dtl.DTLVardef@dffe34org.highwire.dtl.DTLVardef@1aa0b72_HPS_FORMAT_FIGEXP M_FIG C_FIG

Large commercial and military aircraft can operate in a wide range of turbulent conditions, except during extreme weather events such as cyclones. Smaller man-made vehicles, such as micro aerial vehicles (MAVs) and nano aerial vehicles (NAVs), are significantly more sensitive to routine environmental wind fluctuations, making them difficult to control. In contrast, insects exhibit remarkable stability in naturally gusty conditions. Despite this, few studies have systematically investigated the impact of gusts and turbulence on insect flight performance. To address this gap and to gain fundamental insights into insect flight stability under gusty conditions, we examined the flight of freely flying black soldier flies subjected to a discrete head-on aerodynamic gust in a controlled laboratory environment. Flight motions were recorded using two high-speed cameras, and body and wing kinematics were analyzed across 14 distinct cases. In response to the gust, we observed consistent features across the cases: (1) asymmetry in wing stroke amplitude, (2) large changes in body roll angle--up to 160{degrees}--occurring over approximately two wing beats ([~]20 ms) with recovery over [~]9 wing beats, (3) transient pitch-down attitude, and (4) deceleration in the flight direction. These rapid responses, combining passive and active control mechanisms, provide insight into the flight control strategies employed by insects. The findings offer valuable guidance for the design of MAVs and NAVs capable of robustly responding to gusts and unsteady airflow in natural environments.

Network-based epidemic models have been instrumental in understanding how contact structure shapes infectious disease dynamics, yet widely used frameworks such as Erd[o]s-Renyi, configuration-model, and stochastic block networks do not explicitly capture the combination of fully accessible (saturated) within-group interactions and constrained between-group connectivity characteristic of many real-world settings. Here, we introduce the Multi-Clique (MC) network model, a generative framework in which individuals are organised into fully connected cliques representing stable contact groups (e.g., households, classrooms, or workplaces), with a limited number of external connections governing inter-group transmission. Using stochastic susceptible-infectious-recovered (SIR) simulations on degree-matched networks, we compare epidemic dynamics on MC networks with those on classical random graph models. Despite having an identical mean degree, MC networks exhibit systematically distinct behaviour, including slower epidemic growth, reduced peak prevalence, increased fade-out probability, and delayed time to peak. These effects arise from rapid within but constrained between clique transmission, creating structural bottlenecks that standard models do not capture. The MC framework provides an interpretable, data-driven representation of recurrent contact structure, with parameters that map directly to observable quantities such as household and classroom sizes. By isolating the role of intergroup connectivity, the model offers a basis for evaluating targeted intervention strategies that reduce between-group mixing while preserving within-group interactions. Our results highlight the importance of explicitly representing the real-life clique-based network structure in epidemic models and suggest that classical degree-matched networks may systematically overestimate epidemic speed and intensity in structured populations.

Movement is costly, and animals are under strong selective pressure to move efficiently, yet, in patchy, dynamic landscapes, decision-making is inherently uncertain. We quantify the energetic savings achieved by using up-to-date information presented within social cues for reducing movement costs. We use an agent-based model, founded on realistic aeronautical rules and parametrised on the Andean condor (Vultur gryphus), to study movement in patchy landscapes. By explicitly considering altitude, flight results in a sequence of soaring and gliding in the 3D space. We investigate how the cost of movement to an overall goal varies when birds use social information from others that are either fixed in space or moving collectively to the common goal, and under different risk-taking speed strategies, from slow and cautious to fast and risky. The value of social information is operationalised as energetic savings in units of basal metabolic rate. Under low predictability, agents with intermediate risk and high social-information use exhibit lowest movement costs, with up to 41% energy savings over asocial movement. By extending classical aeronautical theory to social and variable environments we demonstrate the adaptive value of social information for efficient movement in patchy, unpredictable landscapes.

PurposeColonic motility disorders, including diarrhea-predominant irritable bowel syndrome and slow-transit constipation, impose a major clinical burden. Although high-resolution colonic manometry reveals characteristic spatiotemporal motor patterns, such as high-amplitude propagating contractions and cyclic motor pattern in healthy individuals, these patterns are often altered or absent in disease. Understanding how these patterns arise from underlying pacemaker, neural, and mechanical mechanisms is essential for improving treatment strategies. MethodsWe developed a biophysical whole-colon model that integrates an Interstitial Cells of Cajal-inspired oscillator network, enteric nervous system reflexes, a pressure-gated modulation element motivated by rectosigmoid brake behavior, and a nonlinear tube law describing colon wall mechanics. The model simulates spatiotemporal pressure patterns along the colon and allows systematic variation of physiological parameters associated with pacemaker activity, neural reflex control, and distal gating. ResultsA small set of parameters reproduces three illustrative motility patterns corresponding to healthy motility, diarrhea-predominant irritable bowel syndrome, and slow-transit constipation. The simulated pressure maps recapitulate key features observed in high-resolution manometry, including propagation direction, regional patterning of contractions, and case-specific changes in amplitude and coordination. Sensitivity analysis suggests that proximal excitation strength and waveform morphology strongly influence global motility metrics. ConclusionOur study presents a simple, biophysical framework for reproducing clinically observed colonic motor patterns and exploring their disruption in disease. More broadly, the model may help interpret clinical manometry in mechanistic terms and support hypothesis-driven in silico studies of colonic motility disorders.

Despite its ubiquity in natural flows, the effects of turbulence on fish locomotion and behavior remain poorly understood. The prevailing hypothesis is that these effects depend on the spatial and temporal scales of the turbulence relative to the fishs size and swimming speed. But in conventional facilities, turbulence usually increases with mean flow, which forces higher swimming speeds and can leave these relative scales unchanged. We therefore present a novel experimental facility that leverages a jet array to decouple the turbulence from the mean flow and systematically control its scales. This approach allows the ratio of turbulent to fish inertial scales to be varied over an order of magnitude, providing a controlled framework for quantifying fish-turbulence interactions. The facility also supports experiments probing strategies fish may use to cope with turbulence, including collective behaviors. Insights from this work have broader implications for ecological studies and engineering applications, including the design of effective fishways and bio-inspired underwater vehicles.

Mitochondria often form branching membrane networks distributed throughout the cell interior. In many, though not all, cell types, these networks are observed to consist of one large connected component together with many smaller fragments. Why does this pattern arise? Does it reflect a specific biological function, an external biophysical constraint, or something simpler? Using results from extremal graph theory, we prove a new theorem which suggests that, under a sufficiently broad sampling of the space of mitochondria-like graphs, the predominance of three-way junctions makes the appearance of a large component likely. This suggests that, in some settings, a large component may serve as a useful null model for mitochondrial network structure rather than requiring a dedicated explanation. More broadly, our result points towards testable predictions, since systematic deviations from this baseline may help reveal additional constraints or mechanisms shaping mitochondrial morphology.

Muscle mass significantly influences skeletal muscle behaviour, potentially explaining why traditional massless Hill-type models struggle to predict the forces generated by larger muscles during dynamic, submaximal contractions. However, the applicability of mass-enhanced Hill-type models in human locomotion remains unexplored. Here, we compared the predicted force from a 1D mass-enhanced Hill-type muscle model with a traditional 1D massless Hill-type muscle model across a range of experimentally measured human movements. Kinematic and electromyographic data were collected from twenty participants performing locomotor tasks and supplemented with existing cycling data. Muscle size was geometrically scaled by factors from 0.1 to 10, which causes lengths to be scaled proportionally, cross-sectional area and peak isometric force F0 with the square, and mass with the cube of the factor. Muscle tissue mass (inertia) and cadence increased the differences between mass-enhanced and massless predictions of force and power. At high cadence and the largest scale, the normalized root mean square difference between force traces reached 7% of F0, (averaged across muscles). However, differences between models were minimal (<1%) at human-sized scale 1. Real muscle additionally deforms in 3D, we still do not know the extent to which this extra dimensionality affects muscle forces for these human movements.

Humans control movement through motor primitives that generate discrete and rhythmic actions. We investigated whether and how speed may drive a transition between discrete and rhythmic organization in walking, and whether muscle synergy changes are associated with kinematic shifts. Eighteen healthy adults walked on a treadmill during incremental and decremental trials (0.5-5 km/h in 0.5 km/h steps). Kinematics and bilateral lower-limb EMG were recorded. Smoothness was quantified using log dimensionless jerk (LDJ) and spectral arc length (SPARC). Both metrics indicated lower smoothness at low speeds and progressively stabilized as speed increased, with a transition region around 3-3.5 km/h showing inter-individual variability. In parallel, EMG synergies showed speed-dependent increases in dimensionality (2[-&gt;]3[-&gt;]4), consistent with module merging at slower speeds. Overall, these findings reveal coordinated kinematic and neuromuscular shifts with speed, indicating a transition from a discrete-dominated regime at low speeds toward a more stable rhythmic pattern at higher speeds.

Infectious disease dynamics are strongly shaped by human mobility, social structure, and heterogeneous contact patterns, yet many epidemic models do not jointly capture these features. This study develops a spatial metapopulation epidemic model incorporating recurrent group-switch interactions to represent real-world transmission processes. Building on the Movement-Interaction-Return framework, the model integrates household structure, age-stratified contacts, and mobility between locations within a single SEIR framework. Using UK demographic, mobility, and social contact data, the model quantifies how within- and between-group interactions, mobility rates, and location connectivity influence epidemic spread. Both deterministic and stochastic simulations are implemented to analyse outbreak dynamics, variability, and fade-out probabilities for COVID-19-like and Ebola-like infections. Results shows that highly connected locations drive faster transmission, earlier epidemic peaks, and greater difficulty in containment, whereas larger but less connected locations tend to produce slower, more localised outbreaks despite their population size. Comparative analysis reveals that COVID-19-like infections spread rapidly and remain difficult to control even under interventions, while Ebola-like infections exhibit slower dynamics and are more effectively contained, particularly under targeted measures. Non-pharmaceutical interventions, particularly widespread closures, substantially reduce infections, hospitalisations, and deaths, although effectiveness depends on timing and pathogen characteristics. These findings highlight the importance of integrating mobility, clustering, and demographic heterogeneity to inform targeted and effective epidemic control strategies.

Genetic surveillance is increasingly used to track malaria transmission, yet genomic metrics can respond nonlinearly to changes in transmission intensity and depend on the diversity already present in the parasite population. Here, we present a stochastic agent-based model of hu-man-mosquito transmission that integrates SEIS-like epidemiological dynamics with within-host Plasmodium falciparum haplotype dynamics. By varying the maximum mosquito biting rate and the initial parasite diversity, we examine how transmission intensity and standing diversity jointly shape mixed infections, recombination, and long-term population structure across a continuous transmission gradient. Our study revealed a sequential pattern in which increasing biting intensity first increases infection prevalence and multiplicity of infection, then expands opportunities for outcrossing, and only thereafter increases effective recombination and recombinant haplotype generation. These responses are strongest in low- to intermediate transmission and tend to plateau at higher transmission levels. Initial population diversity constrains the amount of diversity that can be maintained and the magnitude of recombination output, while temporal trajectories show that haplotype evenness can pass through transient non-equilibrium phases before stabilizing. Together, these results show that the structure of the parasite population is shaped not by trans-mission intensity alone but by its interaction with standing genetic diversity. Furthermore, this study works to clarify when and how genomic metrics reliably reflect transmission conditions across heterogeneous malaria settings.

Cytokine-mediated communication is a central mechanism by which immune cells coordinate activation, differentiation and proliferation. While mechanistic reaction-diffusion models provide detailed descriptions of cytokine secretion and uptake at the cellular scale, their computational cost limits their applicability to large and densely packed cell populations. Previously employed approximations of cytokine diffusion fields rely on assumptions that neglect the influence of cellular geometry and volume exclusion. In this work, we study a macroscopic description of cytokine diffusion and reaction dynamics based on homogenization techniques, rigorously linking microscopic reaction-diffusion formulations to effective continuum models. The resulting homogenized equations replace discrete responder cells with a continuous density, while retaining essential features of cellular uptake and excluded-volume effects. Further, we show that in regimes with approximate radial symmetry, classical Yukawa-type solutions emerge as limiting cases of the homogenized model, provided appropriate correction factors are included. Overall, our approach allows efficient multiscale modeling of cytokine signaling in complex immune-cell environments.

Cancer therapeutics are increasingly incorporating engineered receptors due to their ability to detect extracellular ligands and initiate intracellular responses that regulate gene expression. By redesigning these natural signaling systems, synthetic receptors hold great potential for use in novel cell-based therapies. One particularly promising direction is modifying the Notch receptor, a transmembrane protein that naturally mediates ligand-dependent signaling at the cell surface to regulate cell proliferation and differentiation in neurogenesis. Both the intracellular and extracellular domains of Notch can be replaced with alternative domains, creating the family of modified Notch receptors known as synthetic Notch (synNotch). In existing synNotch-activated chimeric antigen receptor (CAR) T-cells, the extracellular domain can be engineered to adjust binding affinity for a specific cancer antigen, enabling precise tuning of therapeutic activity while minimizing off-target effects. To quantify and inform such tuning, we develop differential equations models of synNotch receptor signaling and subsequent gene expression. The mathematical models couple activation dynamics on fast timescales (characteristic of receptor-ligand interactions) and on slow timescales (characteristic of downstream gene expression dynamics). Global Sobol sensitivity analysis of the proposed models highlights parameters that yield the greatest variability in synNotch signal transduction and gene expression, indicating their potential to be engineered for different functions in future cancer therapeutics. For the receptor-ligand interactions in the synNotch model, we find that ligand association and ligand-independent activation are the most sensitive parameters. In the downstream gene expression model, promoter strength and degradation rates of mRNA and gene product are found to be most amenable to engineering.

Clonal hematopoiesis of indeterminate potential (CHIP) is an age-associated condition linked to chronic inflammation and an increased risk of cardiovascular diseases and hematological malignancies. People with HIV (PWH) exhibit a higher prevalence of CHIP than the general population, but the mechanisms underlying this association remain unclear. In particular, it is unknown whether the excess burden of CHIP reflects earlier emergence of mutant clones, altered clonal expansion dynamics, or differences in selective pressures acting on hematopoietic stem cells. We reconstructed longitudinal trajectories of CHIP variant allele frequency (VAF) in 52 PWH using serial peripheral blood samples spanning up to 25 years from the Swiss HIV Cohort Study. We used spline-based modelling to estimate clone size and growth dynamics, and dynamic time warping to identify common trajectory patterns. Associations between clonal dynamics and longitudinal immune parameters were assessed using linear mixed-effects models. Trajectories in PWH were compared with publicly available longitudinal CHIP data from the SardiNIA population cohort. We identified heterogeneous clonal dynamics consistent with known gene-specific fitness patterns. Larger clone size was associated with lower CD4 T-cell count and lower CD4/CD8 ratio. Compared with the general population cohort, PWH showed higher VAF across the observed age range and steeper early trajectory increases, while long-term expansion rates were broadly similar. Greater variability in clonal dynamics among PWH suggests a stronger contribution of host environmental factors to clonal fitness. These findings support a model in which HIV-associated immune dysregulation alters the hematopoietic fitness landscape, contributing to earlier detectable clonal expansion and increased burden of CHIP in PWH.

Clavicle fractures often exhibit markedly different clinical outcomes: some patients recover acceptable function despite shortening or displacement, whereas others with apparently similar deformity develop persistent pain, functional loss, or poor healing. To explain this distinction, we propose a minimal nonlinear mechanical model for prognostic analysis of clavicle fractures. The model describes the interaction between fracture-related shortening and compensatory shoulder-girdle posture through a reduced equilibrium equation incorporating stiffness, geometric nonlinearity, and shortening-posture coupling. Within this framework, we analyze equilibrium branches, local stability, and the emergence of critical thresholds. We show that post-fracture destabilization can be interpreted as a fold bifurcation, while more complex parameter dependence gives rise to cusp-type structures and multistability. These bifurcation mechanisms provide a mathematical explanation for sudden deterioration after injury or treatment, as well as for strong inter-individual variability. We further introduce an optimization principle based on a utility functional to guide treatment planning. The analysis predicts that the optimal safe correction should lie strictly below the bifurcation threshold, thereby generating a natural safety margin. Although the model is simplified and has not yet been calibrated against patient data, it nevertheless provides a theoretical framework for understanding why fracture prognosis may deteriorate abruptly near critical mechanical conditions and offers a dynamical-systems interpretation of empirical treatment thresholds used in clinical practice.

Drumming--rhythmic, percussive sound production using body parts or external objects--is rare among non-human animals, with confirmed tool-assisted cases previously limited to primates and Palm Cockatoos. Here, we report the first documented instance of spontaneous, tool-assisted drumming in a Galah (Eolophus roseicapilla). A captive, male Galah produced rhythmic tapping by striking a coconut shell against a metal bowl. Across 14 recorded sessions, the bird displayed consistent temporal structure characterised by two stable tapping rates (approximately 0.8 s and 0.2 s inter-onset intervals) arranged into recurring phrases. This pattern indicates a simple hierarchical rhythmic organisation with a 4:1 ratio between metrical levels. The birds behaviour emerged without training, apparent reinforcement, or known exposure to conspecific or human drumming models, suggesting an intrinsic capacity for rhythmic tool use. Although the function of the behaviour remains unclear--play, nutrient extraction, or communicative signalling--these observations extend known rhythmic and tool-using abilities within cockatoos and raise new evolutionary questions. Our findings highlight the potential for rhythmically structured, instrumental behaviour to arise in a broader range of avian taxa than previously recognised, motivating further comparative and experimental work on the cognitive and biomechanical foundations of drumming in parrots.

Spectral similarity is often judged with a single metric such as RMSE, yet this can be misleading: physically different errors can produce similar scores. This is a critical limitation for computational biomechanics, where spectral agreement underpins both model validation and machine-learning loss design. Here, we develop a multi-metric framework for objective spectral biofidelity and test whether it better captures meaningful disagreement across complex frequency-domain responses. We evaluated 12 complementary similarity metrics, including CORA and ISO/TS 18571, using controlled spectral perturbations that mimic common real-world deviations such as resonance shifts, localized spikes, and broadband tilts. We then applied the framework to an SBI-tuned finite-element middle-ear model to assess convergence with training dataset size and robustness to measurement noise across repeated stochastic runs. No single metric performed reliably across all distortion types. Shape-based metrics tracked resonance morphology but could miss vertical scaling, whereas MaxError remained important for narrowband anomalies that smoother metrics underweighted. CORA and ISO 18571 did not consistently outperform simpler metrics. Rank aggregation using Borda count provided a robust consensus across metrics, enabling objective identification of training-data saturation and noise thresholds beyond which similarity rankings became unstable. These results show that spectral biofidelity cannot be reduced to a single norm. A multi-metric consensus provides a clearer and more physically meaningful basis for comparing experimental and simulated spectra, and offers a more defensible foundation for data-fidelity terms in physics-informed and simulation-based machine learning.

Understanding how fish navigate complex natural environments requires bridging fine-scale biomechanics with ecological behavior. We investigated the volitional movement and energetics of wild red drum (Sciaenops ocellatus) across laboratory, mesocosm, and field settings. Using flow-respirometry, we quantified metabolic costs and swimming kinematics under ecologically relevant flow conditions shaped by bluff bodies mimicking mangrove roots and oyster mounds. Fish swimming in turbulent wakes exhibited reduced oxygen consumption and altered tailbeat dynamics, especially at high flow speeds. In a large outdoor mesocosm, dual accelerometers revealed a rich behavioral repertoire, including maneuvering and rest, which is not easily observable in confined lab settings. Spectral analysis and clustering identified eight distinct locomotory states, highlighting the limitations of summed acceleration metrics. Field telemetry tracked wild red drum across a 54 km estuarine corridor for a three-year period through an array of 36 acoustic receivers, revealing movement patterns shaped by tidal flow and physical habitats. Hydrodynamic modeling revealed that while laboratory trials demonstrated substantial energetic savings at high flows (approaching 100 cm/s), wild fish were detected predominantly in low-velocity microhabitats (<30 cm/s) near structurally complex features. This mismatch suggests that habitat selection is an adaptive strategy driven by ecological factors such as foraging opportunities, predation refuge, and site fidelity, rather than hydrodynamic efficiency alone. Our multi-scalar approach demonstrates that while flow-structure interactions can reduce locomotor costs for fish, habitat use in the wild reflects broader ecological constraints, offering a framework for integrating biomechanics, physiology, and ecology in conservation-relevant contexts.

The basic reproduction number of an infectious disease is known to depend on the structure of contacts between individuals in a population. This relationship has been explored mathematically through two well-known models: one which depends on a matrix of contact rates between different demographic groups, and another which depends on the variability of contact rates over the population. Here we introduce a model that combines and generalises these two approaches. We derive a formula for the basic reproduction number and validate it through comparisons to simulated outbreaks. Applying this method to contact survey data collected in Belgium between 2020 and 2022, we find that our model produces higher estimates of the basic reproduction number and larger relative changes over periods when social contact behaviour was changing during the COVID-19 pandemic. Our analysis suggests some practical considerations when using contact data in models of infectious disease transmission.

Oscillatory behaviour is important in multiple biological contexts. However, the inherent nonlinearity and high dimensionality of mathematical models in biology makes proving the existence and the localization of limit cycle oscillations challenging. Here, we provided an elementary proof for the existence and a method for rigorously localizing the oscillatory solutions in a class of benchmark biomolecular oscillators. To construct the proof, we used a geometric approach based on Brouwers Fixed Point theorem. We constructed a toroidal-like manifold within a positively invariant set by removing the hypervolume containing the fixed point and the trajectories converging to it along its stable manifold. We showed that the vector field describing the system dynamics maps a cross section of the toroidal-like manifold onto itself. The existence of a limit cycle solution in this manifold was guaranteed by Brouwers Fixed Point theorem. For different sets of initial conditions in these cross-sections, we used an interval-based Reachability Analysis to localize the oscillatory behaviour that complements the Brouwers Fixed Point theorem approach. These results add a simple and elegant approach to demonstrating the existence of limit cycles in biomolecular systems as well as a method for rigorous localization of the region of existence.