Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Cerebrospinal fluid (CSF) is a Newtonian fluid that bathes the brain and spinal cord and oscillates in response to the physiological periodic changes in brain volume, of which the cardiac cycle is a major driver. Understanding this motion is essential for clarifying its contribution to solute transport, waste clearance, and drug delivery. In this work, we study oscillatory and steady streaming flow in the cranial subarachnoid space using a lubrication-based theoretical framework. The model represents the cranial CSF compartment as a thin fluid layer bounded internally by the brain surface and externally by the dura, driven by time-dependent brain surface displacements. We first derive simplified governing equations for flow over an arbitrary smooth sphere-like brain surface and obtain analytical solutions for an idealised spherical geometry with uniform displacements. We then incorporate realistic displacement fields reconstructed from MRI measurements in healthy subjects and solve the reduced equations numerically. The results show that oscillatory forcing produces a steady streaming component that may enhance solute transport compared with diffusion alone. This work provides a mechanistic description of the flow generated by physiological brain motion and highlights the potential presence of steady streaming in cranial subarachnoid fluid dynamics.

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.

Foraging is a central decision-making behavior performed by all animals, essential to garnishing enough energy for an organism to survive. Similarly, mating is crucial for evolutionary continuity and offspring production. Mate choice is one of the central tenets of sexual selection, driving major evolutionary processes, and can be regarded as a decision-making process between potential mating partners. Often researchers have used coarse-grained models to describe macroscopic phenomenology pertaining to mate choice without detailed quantitative mechanisms of how animals use individual and environmental signals to guide their mating decisions. In this letter, we show that mate choice can be cast as a foraging problem, and we present an analytically tractable optimal foraging-inspired mechanistic theory of decision-making underlying mate choice. We begin from the premise that deciding upon which partner with which to mate is at its core a stochastic decision-making process. Agents adopt a variety of decision strategies, tuned by decision thresholds for leaving or committing to a mate. We find that sensitive leaving thresholds are favored independently of signal availability in the population. By contrast, optimal thresholds for committing to a mate depend upon signal availability in the population, with signal-rich populations generally favoring less eager strategies compared to signal-poor populations.

Cancer-associated fibroblasts (CAFs) are a central component of the tumor microenvironment that facilitate a supportive niche for cancer progression and metastasis. Experimental evidence suggests that CAFs can facilitate estrogen-independent tumor growth, thereby reducing the efficacy of anti-hormonal therapies. Understanding and quantifying the complex interactions between tumor cells, hormonal signalling, and the microenvironment are crucial for designing more effective and individualized treatment strategies. We propose a mathematical framework to explore the influence of CAFs on ER+ breast cancer progression and to evaluate strategies to mitigate their impact. We develop a system of nonlinear ordinary differential equations that substantiates the experimental observations by providing a mechanistic basis for the role of CAFs in regulating estrogen-independent growth dynamics. We then employ optimal control theory to evaluate distinct therapeutic approaches involving monotherapy or combinations of: (i) inhibition of tumor-to-CAF signaling, (ii) inhibition of CAF-to-tumor proliferative signaling, and (iii) endocrine therapy. Taken together, our results demonstrate that CAF-targeted strategies can enhance treatment efficacy across various estrogen dosing regimens. Our study provides new insights into the potential of CAF as a therapeutic target that could help to improve existing approaches for endocrine therapies.

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.

Understanding how cells migrate through confined environments is crucial for elucidating fundamental biological processes, including cancer invasion, immune surveillance, and tissue morphogenesis. The nucleus, as the largest and stiffest cellular organelle, often limits cellular deformability, making it a key factor in migration through narrow pores or highly constrained spaces. In this work, we introduce a geometric surface partial differential equation (GS-PDE) model in which the cell plasma membrane and nuclear envelope are described as evolving energetic closed surfaces governed by force-balance equations. We replicate the results of a biophysical experiment, where a microfluidic device is used to impose compressive stresses on cells by driving them through narrow microchannels under a controlled pressure gradient. The model is validated by reproducing cell entry into the microchannels. A parametric sensitivity analysis highlights the dominant influence of specific parameters, whose accurate estimation is essential for faithfully capturing the experimental setup. We found that surface tension and confinement geometry emerge as key determinants of translocation efficiency. Although tailored to this specific setup for validation purposes, the framework is sufficiently general to be applied to a broad range of cell mechanics scenarios, providing a robust and flexible tool for investigating the interplay between cell mechanics and confinement. It also offers a solid foundation for future extensions integrating more complex biochemical processes such as active confined migration.

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.

Evolutionary therapies regulate heterogeneous populations by altering selective pressures through treatment sequences in cancer and infections. This letter develops an invariant-set framework for treatment-induced containment based on positive triangular invariant sets. For periodically switched systems, sufficient conditions are derived for the existence of such invariant regions. Robustness with respect to mutation is established by showing that the invariant simplex persists under small perturbations of the subsystem matrices. In the two-phenotype case, the analysis yields an explicit mutation threshold that separates regimes in which therapy cycling maintains containment from regimes in which mutation can enable evolutionary escape. Simulations illustrate the geometry of the invariant sets and the role of mutation and dwell time in containment robustness.

A key component of intraneuronal communication is the modulation of postsynaptic firing frequencies by stochastic transmitter release from presynaptic neurons. The time interval between successive postsynaptic firings is called the inter-spike interval (ISI), and understanding its statistics is integral to neural information processing. We start with a model of an excitatory chemical synapse with postsynaptic neuron firing governed as per a classical integrate-and-fire model. Using a first-passage time framework, we derive exact analytical results for the ISI statistical moments, revealing parameter regimes driving precision in postsynaptic action potential timing. Next, we extended this analysis to include both an excitatory and an inhibitory presynaptic connection onto the same postsynaptic neuron. We consider both a fixed postsynaptic-firing threshold and a threshold that adapts based on the postsynaptic membrane potential history. Our analysis shows that the latter adaptive threshold can result in scenarios where increasing the inhibitory input frequency increases the postsynaptic firing frequency. Moreover, we characterize parameter regimes where ISI noise is hypo-exponential or hyperexponential based on its coefficient of variation being less than or higher than one, respectively.

We develop a self-consistent free-energy framework in which membrane shape and osmotic pressure are determined simultaneously in a finite reservoir by minimizing bending elasticity and solute entropy. Solute conservation makes osmotic pressure a thermodynamic variable rather than an externally prescribed parameter, producing a nonlinear coupling between membrane mechanics and solvent entropy. This coupling modifies the classical stability condition for spherical vesicles: instability emerges from global free-energy competition rather than the linear Helfrich stability criterion. The resulting critical pressures differ by orders of magnitude from Helfrich predictions and agree with simulations for small and large unilamellar vesicles. The framework is relevant to cellular environments involving biomolecular condensate confinement as well as synthetic vesicles and the development of osmotic-pressure-driven encapsulation platforms.

The interactions of droplets and filaments can lead to mutual deformations and complex combined behavior. Such interactions also occur within the cell, where biomolecular condensates, distinct liquid phases often composed of proteins, have been observed to structure and affect the organization of the cytoskeleton. In particular, biomolecular condensates have been shown to undergo characteristic deformations when cytoskeletal filaments are fully embedded within them. However, a full understanding of the underlying physical mechanisms is still missing. Here, we combine experiments with coarse-grained molecular dynamics simulations and analytical models to uncover the physical mechanisms that define emerging shapes of droplets containing filaments. We find that the surface tension of the liquid phase and the bending energy of the filament(s) suffice to accurately capture emerging shapes if the length of the filament is small compared to the liquid volume. As the volume fraction of filament(s) increases, wetting effects become increasingly important, setting physical constraints within which surface and bending energies compete to define the droplet shapes. We find that mutual deformations of condensate and filament extend accessible shapes beyond classical stability considerations, leading to structuring and entrapment of contained filaments. Shape deformations may further affect ripening dynamics that favor certain geometries. Our findings provide a physical framework for a better understanding of the possible roles of biomolecular condensates in cytoskeletal organization.

Assessing the risk of pesticides to birds requires models that can extrapolate laboratory data to realistic exposure scenarios. In this work, we propose a new modeling framework BIRDkiss (Bird - Impact on Reproduction via Diet, keep it simple and suitable) that accounts for both a simplified Dynamic Energy Budget (DEBkiss) of organisms and the toxicokinetic-toxicodynamic (TKTD) of chemical substances according to a trait-based approach, thereby reducing the number of parameters to identify and strengthening the statistical robustness of the critical endpoints. The BIRDkiss model describes how food intake and toxicant exposure affect growth and egg production in birds over time. The model is fully embedded within an R package, including routines for calibration, validation and prediction under single-compound scenarios performed via Bayesian inference using standard data from the OECD avian reproduction tests. The BIRDkiss model also allows the simulations of scenarios under both varying food availability and multi-compound exposures based on the two classical mixture-toxicity paradigms: Concentration Addition (CA) and Independent Action (IA). The results of calibration for single compounds show good results matching with observed weights and egg counts. From these calibrations, predictions for new exposure scenarios can be readily generated. For mixtures, the IA algorithm is simpler and does not require to scale variables as in CA. Simulations indicate that high food levels do not further increase egg production (saturation), whereas substantial food reductions markedly decrease reproduction because energy is reallocated to maintenance. Exposure to chemicals combined to low food availability amplify the decline in reproductive output. The ready-to-use mechanistic, open-source BIRDkiss tool enables predicting the impact of pesticides on avian reproduction under realistic dietary exposure profiles. The implementation of CA and IA models is a first step toward mechanistic assessment of chemical mixtures, although validation still requires empirical mixture data. The model highlights the importance of food availability and shows that chemical stress can exacerbate the negative effects of nutritional stress. Integrating such models into regulatory frameworks could improve the ecological relevance of risk assessments. O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=134 SRC="FIGDIR/small/712277v1_ufig1.gif" ALT="Figure 1"> View larger version (17K): org.highwire.dtl.DTLVardef@102246dorg.highwire.dtl.DTLVardef@1a58f65org.highwire.dtl.DTLVardef@695cd7org.highwire.dtl.DTLVardef@14e4329_HPS_FORMAT_FIGEXP M_FIG C_FIG

Mass-conserved reaction-diffusion systems are used as mathematical models for various phenomena such as cell polarity. Numerical simulations of this system present transient dynamics in which multiple stripe patterns converge to spatially monotonic patterns. Previous studies indicated that the transient dynamics are driven by a mass conservation law and by variations in the amount of substance contained in each pattern, which we refer to as "pattern flux". However, it is challenging to mathematically investigate these pattern dynamics. In this study, we introduce a reaction-diffusion compartment model to investigate the pattern dynamics in view of the conservation law and the pattern flux. This model is defined on multiple intervals (compartments), and diffusive couplings are imposed on each boundary of the compartments. Corresponding to the transient dynamics in the original system, we consider the dynamics around stripe patterns in the compartment model. We derive ordinary differential equations describing the pattern dynamics of the compartment model and analyze the existence and stability of equilibria for the reduced ODE with respect to the boundary parameters. For a specific parameter setting, we obtained results consistent with previous studies. Moreover, we present that the stripe patterns in the compartment model are potentially stabilized by changing the parameter, which is not observed in the original system. We expect that the methodology developed in this paper is extendable to various directions, such as membrane-induced pattern control.

Silver (Ag+) ions are known to be toxic to bacteria, cells, organisms and living systems; yet its impacts on the locomotion of surface-crawling organisms remain poorly quantified. Here we investigated the short-term (0-6 hours) effects of Ag+ ions on the locomotion of Drosophila melanogaster larvae on flat agarose surfaces containing Ag+ ions at different concentrations (0, 1, 10, and 100 mM). By quantifying their locomotion, we found that Drosophila larvae showed shorter accumulated distances and reduced crawling speed. Additionally, we quantified the go/stop dynamics and peristalsis of the larvae and observed that Ag+ ions disrupted the normal, rhythmic, peristaltic contraction of the larvae and "trapped" them in the stop phase. Such toxic effects were dependent on Ag+ concentration and exposure duration.

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.

Environmental stressors rarely affect just one brain circuit. Most studies assess single cognitive endpoints, obscuring whether vulnerabilities are global or circuit-selective and how effects distribute across interconnected systems. To address this, we used galactic cosmic radiation (GCR), a Mars mission-relevant stressor that disrupts the hippocampal-nucleus accumbens-prefrontal circuit. C57BL/6J mice received 33-ion GCR simulation (33-GCR, 0.75 Gy) or sham radiation with the Nrf2-activating compound CDDO-EA or vehicle, followed by multi-domain behavioral testing in both sexes. Under very high memory load, male Veh/33-GCR mice showed enhanced pattern separation compared to Veh/Sham males, an effect normalized by CDDO-EA. Female mice showed no radiation-induced changes in pattern separation but weighed 9-18% more than Veh/Sham females and had reduced locomotor activity. Reward-based learning differed by sex: males showed no changes, while female Veh/33-GCR mice displayed enhanced reward anticipation that was further increased by CDDO-EA alone, with both treatments contributing to elevated goal-tracking. For behavioral flexibility, CDDO-EA impaired reversal learning in males regardless of radiation, while 33-GCR impaired reversal learning in females regardless of CDDO-EA. Principal component analysis revealed that treatments disrupted specific circuit relationships while leaving others intact, consistent with selective rather than global cognitive effects. Fiber photometry showed enhanced dentate gyrus encoding activity in irradiated males under high memory load. Combined CDDO-EA/33-GCR selectively reduced dentate gyrus progenitors in females. Males and females showed distinct, circuit-selective vulnerability patterns, demonstrating that multi-domain, both-sex assessment is necessary to capture how stressors and interventions affect integrated brain function. CDDO-EA proved to be a double-edged sword: protecting one cognitive domain while impairing another, a trade-off invisible to single-endpoint assessment. This framework has immediate relevance for astronaut risk assessment and extends to any context where neuroprotective interventions are evaluated against environmental stressors.

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.

This study develops a methodological framework that combines conventional antimicrobial susceptibility testing with Particle Swarm Optimisation (PSO) to enhance toothpaste formulations, employing Escherichia coli isolated from the oral cavity as a model organism. We used the agar well diffusion method to see if two fluoride toothpastes (Oral B and My-my) could kill oral E. coli isolates at 6.25%, 12.5%, 25%, 50%, and 100% concentrations. A surrogate Random Forest model was created using these experimental data to link formulation parameters to antimicrobial activity. Then, PSO was used to find the best formulation traits. Multi-objective optimisation that looks at the trade-offs between antimicrobial effectiveness and cytotoxicity was shown as a conceptual framework. Both toothpastes showed antimicrobial activity that depended on the concentration, with Oral B being more effective (23.0 mm at 100% concentration) than My-my (20.0 mm). The PSO framework, utilised as a methodological illustration while explicitly recognising data constraints, determined hypothetical formulation parameters (sodium fluoride 1100 ppm, hydrated silica abrasive, 2.5% SLS) with an anticipated zone of inhibition of 26.3 mm. These predictions are mathematically optimal for a surrogate model that was trained on very little data (n=10 formulation points). They need a lot of experimental testing before any claims about the formulation can be made. This work is presented as a proof-of-concept methodological framework, not as validated formulation guidance.

As social beings, humans make decisions partly based on social interaction. Observing the behavior of others can lead to learning from and about them, potentially increasing trust and prompting trust-based behavioral changes. Observation-based decision making involves different neural structures. The orbitofrontal cortex (OFC) and lateral prefrontal cortex (LPFC) are known as neural structures mainly involved in processing emotional and cognitive decision values, respectively, while the anterior cingulate cortex (ACC) plays a pivotal role as a social hub, integrating the afferent expectancy signals from OFC and LPFC. This paper presents a neurocomputational model of the interplay between observational learning and trust, as well as their role in individual decision-making. Our model elucidates and predicts the emotional and rational behavioral changes of an individual influenced by observing the action-outcome association of an alleged expert. We have modeled the neurodynamics of three cortical structures (OFC, LPFC, and ACC) and their interactions, where the neural oscillatory properties, modeled with Dynamic Bayesian Probability, represent the observers attitude towards the expert and the decision options. As an example of an everyday behavioral situation related to climate change, we use the choice of transportation between home and work. The EEG-like simulation outputs from our model represent the presumed brain activity of an individual making such a choice, assuming the decision-maker is exposed to social information.

BackgroundActivated platelets release polyphosphate (polyP), a linear polymer of inorganic phosphate residues, from dense granules. Experiments performed under no-flow conditions show that polyP alters the kinetics of tissue factor (TF) pathway reactions, accelerating FXI activation by thrombin and FV activation by FXa and thrombin, and may impact inhibition by tissue factor pathway inhibitor (TFPI). How polyP influences this pathway in conjunction with platelet deposition under flow remains understudied. ObjectivesTo investigate how polyP-mediated acceleration of FV and FXI activation modulates thrombin generation under flow in TF-initiated coagulation. MethodsWe extended a previously validated mathematical model of platelet deposition and coagulation under flow to examine polyP-mediated effects following a small vascular injury during intravascular clotting. Simulations varied the surface density of TF exposed, wall shear rate, and plasma TFPI concentration. ResultsPolyP shifts the threshold TF density for a thrombin burst to lower TF densities. For TF densities above this threshold, polyP shortens the lag time to thrombin generation in a TF- and shear-rate-dependent manner. Although no explicit effect of polyP on TFPI function was included in the model, thrombin generation was much less sensitive to TFPI concentration with polyP, in a TF-dependent manner. Relative contributions of accelerations of FV and FXI activations depend on incompletely known enhancements by polyP. ConclusionsThe experimentally observed influence of polyP on TFPI function depends on TF density and may arise indirectly from accelerated FV and FXI activation, with the dominant effect arising through accelerated thrombin-mediated conversion of FV to FVa.