Physical Review E

1Although resources are typically distributed continuously in space, species distributions often organize into discrete clusters. In his seminal paper [36], Turing demonstrated that such clusters can spontaneously arise in population densities, even when populations evolve in environments with continuously varying conditions. This phenomenon is known as Turing instability. In this work, we focus on two models grounded in population dynamics: a one-dimensional model based on the nonlocal Fisher-KPP equation, and a two-dimensional model involving an environmental gradient. We show that phenotypic clusters (sometimes referred to as "species") emerge in these models. We prove that they do not emerge because of Turing instability, but because of stochasticity, and that they disappear when stochasticity is reduced. First, for both models, we start our simulations with initial populations uniformly distributed in the state space. We show that phenotypic clusters quickly emerge and that the distances between them depend on the population size, that is, on the degree of stochasticity. Next, we start from already clearly defined phenotypic clusters. We identify three regimes in the connection between population size, the initial distances between clusters, and the distances between clusters at equilibrium. Last, on the two-dimensional model, we relax the hypothesis of complete clonality by varying the effective recombination rate, explore its effect on phenotypic clustering, and show that phenotypic clustering decays drastically with slight recombination.

The Poisson-Nernst-Planck (PNP) system is an accurate model of electrodiffusion of ionic species. It is commonly used in situations where nanoscale resolution is required, for instance close to ion channels in the membranes of biological cells. The inherent stiffness of the equations has made them challenging to solve and has limited the applicability of the system. In particular, the time step required for stable solutions has typically needed to be very short (nanoseconds), which makes simulations on the time scale of an action potential (milliseconds) difficult. Recently, it has been observed that avoiding operator splitting and instead solving the concentration equations and the electrostatic equation in a coupled manner relaxes the time-step limitation considerably. However, no theoretical explanation of this observation has been provided. Here, we aim to explain why the coupled scheme allows much larger time steps. We illustrate the mechanism by considering special cases that define necessary, but not sufficient, conditions for stability. We also show that these conditions remain relevant for the fully coupled PNP model in 3D.

A major challenge in neuroscience is to predict how currents in nanodomains affect voltage and ionic concentrations. Cable and Rall theory provide analytic current-voltage relations by neglecting concentration gradients, and the impact of concentration gradients is usually studied numerically with the Poisson-Nernst-Planck (PNP) model. A precise quantitative understanding of the combined dynamics remains limited because analytic current-voltage-concentration relations are missing. In this work we derive such relations using a novel approach based on cross-diffusion equations. For narrow cylindrical domains, we derive time-dependent and steady-state expressions that explicitly show how currents affect voltage and ionic concentrations. We find that the influx of only one ion can significantly change the concentrations of all the other ions even if no channels for these ions are present. After a current injection we compute a biphasic voltage transient where the small-time asymptotic corresponds to the steady-state solution of the cable equation. We show that the accuracy of cable theory prediction for the voltage depends on how the current is distributed among the various ions. Finally, we develop an iterative method to accurately compute steady-state profiles for voltage and concentrations using first-order results by subdividing a cylinder into small segments.

Take-off is a fast and energy-efficient strategy for bipedal animals, such as birds, to achieve rapid movement; however, how muscle physiology scales to govern this universal behavior remains unresolved. Research in other species physiologies is not readily applicable. As a result, important questions, whether theropod dinosaurs such as Tyrannosaurus rex were capable of jumping, remain unanswered. In this article, we coupled Lagrangian dynamics with Hills muscle equations and developed new experimental methods to quantify joint rotational stiffness and damping, thereby enabling a systematic description of lower-limb mechanics. The approach establishes a novel kinetic framework that links muscle contractile properties to lower-limb performance without invoking control optimization. Animal observations and tabletop mechanisms validate the framework. The mechanics model reveals that the take-off time of about 0.1 s across body masses of 0.003 to 90 kg is achievable, as heavier birds generate proportionally higher reaction forces. Additionally, Tyrannosaurus rex should be capable of jumping, based on the available physiology data. Beyond evolutionary insights, our framework provides a new methodology for analyzing the mechanical properties of biological joints and informing the design of scalable bio-inspired robots.

Rhythm is a key building block of human music, speech and numerous other human activities. Understanding the computational substrates of rhythm perception requires models that bridge algorithmic function with biological implementation. We propose a physiologically grounded spiking neural network (SNN) framework to investigate the emergent representation and interpretation of auditory rhythms. Utilizing a recurrent SNN architecture trained on an auditory entrainment task, we characterize the networks latent dynamics through the analysis of firing rates and membrane potential fluctuations. Our results demonstrate that simulated neural populations exhibit phase-locking to the stimulus beat, with endogenous oscillations driven by rhythmic input. We further show that anticipatory dynamics--characterized by pre-stimulus depolarization--emerge naturally from the networks synaptic plasticity and temporal integration properties, rather than from explicitly defined oscillators. By treating network layers as functional analogs of cortical populations, this framework allows for the application of spectral and information-theoretic analyses typical of empirical electrophysiology. More in general, this approach establishes SNNs as robust exploratory tools for uncovering how predictive coding and rhythmic entrainment arise from the inherent constraints of biological neural computation.

The awake brain is known to display asynchronous (AS) states during periods of attention and arousal, but the responsiveness properties of such states remain unclear. Here, we investigate this question using computational models of spiking networks of excitatory and inhibitory neurons, mimicking recurrently-connected networks in layer 2/3 of the cerebral cortex. The networks can generate a continuum of AS states, but with different responsiveness characteristics. By using a mean-field model to infer the dynamic properties of the system, we find that there are two families of AS states, which we call "underdamped" (UD) and "overdamped" (OD). Responsiveness is maximised at the transition between OD and UD states, which identifies a "working point" that may present advantageous computational properties.

Mechanical properties of epithelial tissues play essential roles in morphogenesis and physiological function. In this study, we analytically derived the in-plane bulk modulus, shear modulus, and Poissons ratio of a three-dimensional cell vertex model of epithelial monolayers. We showed that the model can robustly reproduce a near-zero in-plane Poissons ratio, a mechanical feature reported in cultured epithelial tissues. Numerical simulations further confirmed that the theoretically predicted Poissons ratio accurately describes the response of the model under finite, biologically relevant strains. In addition, the model exhibits not only morphological bistability between squamous-like and columnar-like states, but also mechanical bistability characterized by distinct elastic responses. Together, these results provide a minimal three-dimensional framework that links cell-scale mechanical interactions and epithelial morphology to tissue-scale elastic properties.

Parameter estimation in nonlinear biological dynamical systems is a difficult inverse problem because the governing equations are often stiff or oscillatory, the data are sparse and noisy, and the objective landscape is non-convex. Physics-informed neural networks (PINNs) offer an alternative to purely simulation-based calibration by representing state trajectories with neural networks while penalizing violations of the governing equations. This paper studies the empirical reliability of PINNs for recovering the parameters of the repressilator, a synthetic genetic oscillator formed by three cyclically repressive genes. We use synthetic time-series generated from the standard ordinary differential equation model and train inverse PINNs to estimate the production parameter {beta} and the Hill coefficient n. The study varies observation noise, partial observation of repressors, sampling density, sensitivity to initial parameter guesses, and the difference between stable and oscillatory regimes. The results show that PINNs can reconstruct trajectories accurately when the model structure is correct and the three repressors are observed, but parameter recovery is more fragile than trajectory fitting. Noise, sparse sampling, unobserved variables, and unfavorable initial guesses increase the risk of biased estimates. The stable regime is easier to reconstruct, whereas the oscillatory regime provides richer information but also exposes optimization sensitivity. These findings support PINNs as a useful reverse-engineering tool for small gene-regulatory ODE models, while highlighting the need for repeated runs, uncertainty reporting, and experimental designs that improve identifiability.

Understanding how biological shape and movement interact with surrounding fluids represents a fundamental challenge at the intersection of biology, physics, and engineering. Fish locomotion exemplifies this challenge: body morphology and swimming kinematics together determine the hydrodynamic forces and flow structures that enable efficient propulsion and maneuverability. Whereas biologists have long sought to connect morphological variation to swimming performance, traditional morphometric approaches provide limited insight into the fluid mechanical consequences of shape differences. Similarly, although computational fluid dynamics can reveal detailed flow physics, simulating hydrodynamics across diverse and dynamic morphologies remains prohibitively expensive for systematic investigation. To bridge this gap, we introduce a data-driven framework that connects fish body shape dynamics to hydro-dynamic performance through compact morphospace parameterization and reduced-order modeling. Using CFD simulations of 15 fish species from the Digital Life Project database (www.digitallife3d.org/3d-model), we generate hydrodynamic datasets capturing the shape-flow relationship. Principal Component Analysis (PCA) extracts four dominant shape parameters from dorsal body profiles, which are then integrated into an Inverse-Design with Dynamic Mode Decomposition (ID-DMD) framework to model the resulting fluid dynamics. The resulting modal analysis suggests that locomotion strategies emerge from specific shape-flow interactions. We further demonstrate the frameworks utility through single- and multi-objective shape optimization, showing how it enables efficient exploration of the morphology-hydrodynamics relationship. This approach offers a novel analysis and design tool for understanding how biological form and motion interact with fluid mechanics, with applications ranging from bio-inspired vehicle development to evolutionary biomechanics.

In previous studies by the author on binocular vision with the asymmetric eye (AE), which models a healthy human eye with misaligned optical components, the results were primarily presented in the Rodrigues vector (RV) framework and supported by simulations and 3D visualizations in GeoGebras dynamic geometry environment. In this paper, the novel geometric kinematics of the human eye, that is, the eye with misaligned optics, and simplified assumptions about the eye rotations (the eyes translational movements are disregarded), are developed within the framework of rigid-body rotations. The originality of the analysis lies in a precise geometric decomposition of a full rotation of the eyes posture into a torsion-free rotation (the geodesic part) and a torsional rotation (the non-geodesic extension of the geodesic part). This decomposition is extended to the corresponding decomposition of the angular velocity. A novel derivation of the eyes angular velocity from the RV formulation of the eye kinematics is proposed.

1Correlations between cellular variables, such as gene-expression levels, provide insights into regulatory mechanisms. We focus here on correlations between mRNA and protein levels and re-examine previously derived analytical predictions. We test this prediction on single-cell E. coli data and see substantial disagreement. We hypothesize that this discrepancy arises from the assumption of constant cell volume and develop a theoretical framework for mRNA-protein correlations in growing and dividing cells. Within this framework, we derive an analytical expression for mRNA- protein correlations and show that explicit incorporation of growth and division substantially alters these correlations. The resulting relation is invariant to upstream transcriptional dynamics, and we validate it using stochastic simulations across multiple gene-regulatory architectures. Finally, we show that the derived predictions are consistent with the E. coli data.

Bacterial communities grow as dynamic populations that respond to their environments. A clinically relevant example is the inactivation of beta-lactam antibiotics by intracellular beta-lactamase in E. faecalis resistant strains. In these populations, resistant bacteria act as antibiotic sinks, detoxifying the environment and allowing sensitive bacteria to survive treatment through a cooperative interaction. In this work, we study strongly coupled planktonic and biofilm populations of mixed sensitive-resistant E. faecalis bacteria under antibiotic stress using fluorescent microscopy. The presence of resistant bacteria in the system benefits both resistant and sensitive cells, leading to mixed planktonic and biofilm populations at super-inhibitory drug concentrations. We show that a beta-lactam antibiotic with or without the addition of a beta-lactam inhibitor can lead to a population inversion effect, characterized by a non-monotonic relation between initial and final fractions of resistant bacteria. The effect is observed in both the planktonic and biofilm populations and is modulated by the total initial cell density. A well-mixed model with competition mediated by resource sharing and cooperation from global degradation of toxins predicts the experimentally observed behavior. These observations suggest underlying population-level mechanisms that are largely independent of biofilm spatial structure.

With the development of microfluidics, it has now become possible to assess the susceptibility of bacteria to antibiotics at the single-cell level instead of relying on population measurements. Such studies are particularly relevant when the growth of bacterial population in the presence of antibiotics is heterogeneous. Here, we build a model to describe such a case, and apply it to experimental measurements on a small population of E. Coli exposed to ciprofloxacin, a drug which is well known for triggering a bistable response.

Darwinian fitness is equated here with invasion fitness and defined as the quantity determining the fate--certain extinction or possible spread--of a single mutant type. We derive it, together with its phenotypic derivative, for evolution in group-structured populations under limited genetic mixing, where the demography of the focal species and its environment is modeled as a discrete-time stochastic process. Reproduction, physiological development, dispersal, and survival are influenced by interactions within and between groups and by environmental fluctuations within and across generations. Using multitype branching processes in random environments, we show that invasion fitness is predicted by a stochastic growth rate that can be represented biologically in two meaningful genealogical ways. First, as the long-term geometric mean of the expected per-capita number of mutant copies produced per time step by a representative member of the mutant lineage. Second, as the the long-term geometric mean of the expected reproductive-value-weighted per-capita number of mutant copies produced by such an individual. This latter representation is useful for computing the phenotypic directional derivative of invasion fitness. Moreover, this derivative can be written as an actor-centered inclusive-fitness effect derived from properties of the resident population process. This effect depends on class-specific fitness differentials, relatedness, reproductive values, and class frequencies. However, unless generation- and class-specific fitness defines a stochastic matrix, the derivative does not separate stochastic reproductive values from relatedness and class frequencies, and must be evaluated by simulations. In summary, we formalize invasion fitness biologically quite generally and show how Hamiltons marginal rule is deduced from it.

The phenomenon of splitting was originally observed in hamsters which, after prolonged exposure to constant light, exhibit two rest/wake cycles within a subjective day. Splitting is a consequence of the left and right suprachiasmatic nuclei (SCN) falling out of synchrony. While it is known that split activity is characterized by an antiphase relationship between the left and right SCN and between the core and shell within each hemisphere, the role of the commissural projections that connect the right and left SCN is not known. In the present study, we investigate the impact of the inter-hemispheric connections on the split and unsplit dynamics of a computational model of the bilateral SCN. Our model has 4 nodes corresponding to each right and left core and shell. We simulated our bilateral model under different lighting conditions and measured its period and the phase relationships among the 4 nodes. To further characterize the dynamics of the system, we performed a bifurcation analysis. We found that the bilateral model automatically splits unless entrained by bright light/dark cycles, or unless it has excitatory inter-hemispheric connections. This suggests that excitatory cross-connections may be important for freerunning behavior. We found that constant light of varying intensities transitions the model between split and unsplit activity only in very limited conditions, but the strength and polarity of the contralateral connections play a much greater role in this dynamical transition. These findings suggest that splitting may involve plasticity of the inter-hemispheric connections of the SCN.

Cooperative and competitive interactions among individuals harvesting resources can shape environmental states, such as prey abundance. In turn, environmental conditions feed back to influence strategic interactions. Eco-evolutionary game theory studies how these feedbacks shape the co-evolution of behavior and environment. Existing models typically assume deterministic, noise-free environmental dynamics. However, real environments are inherently stochastic, for example due to finite resources, and noise can qualitatively alter social outcomes. Here, we incorporate stochastic environmental dynamics into eco-evolutionary game theory. When environmental change is slow relative to strategy updates, we show that behavior reflects a mixture of the games associated with low and high environmental states, often yielding outcomes qualitatively distinct from deterministic predictions. In particular, environmental stochasticity can eliminate bistability and enforce dominance of a single behavior. When environmental dynamics are faster, populations have less opportunity to track fluctuations, and behavior converges toward strategies that are optimal on average. Stochasticity can even causes persistent oscillations in the tragedy of commons, in regimes where classical models predict stability. Our framework provides a tractable approach for analyzing social behavior linked to environmental dynamics how noise shapes long-term eco-evolutionary outcomes.

This work focuses on the global and partial identification problem for fractional differential equations. We provide a general numerical procedure based on global and local optimization algorithms with two refinements for biological systems that ensure solution positivity and homogeneous parameter units. The method is applied to a new fractional model of Dengue outbreak called the Fractional Homogeneous Nishiura (FHN) model, calibrated using data of newly infected people in Cape Verde. We show that our identification method yields a better fit between data and model solutions than previous approaches and that our FHN model captures the dynamics of Dengue more closely than existing systems.

Time-resolved measurements are central to calibrating mechanistic dynamical models, but current inference frameworks typically assume that reported measurement times are exact. In practice, actual sampling times may deviate from reported times because of sample-handling delays, imper-fect synchronization, or reporting errors. Here, we present a Bayesian framework for parameter inference in ordinary differential equation models that explicitly accounts for uncertainty in measurement times. We formulate latent measurement times as random variables and derive a joint and marginalized posterior. To compute the marginal likelihood efficiently, we augment the original dynamical system with additional state variables that evaluate the required integrals during numerical simulation. This reduces the dimensionality of the estimation problems and allows for efficient and reliable Markov chain Monte Carlo sampling. Across synthetic examples and a published model of carotenoid cleavage in Arabidopsis thaliana, neglecting time uncertainty led to biased estimates and overconfident uncertainty quantification, whereas the proposed marginalized formulation recovered reliable parameter estimates while substantially improving sampling efficiency and scalability. These results identify measurement time uncertainty as an important source of variability in dynamic modeling and establish posterior marginalization as a practical strategy for robust mechanistic inference.

Neuronal computation depends on the balance between excitation and inhibition, yet how this balance is implemented across the dendritic tree remains unclear. Classical views predict that inhibition should be most effective near the soma or along the path from excitation to output, but many interneuron subtypes preferentially target remote dendritic compartments. This apparent paradox is sharpened by active dendrites, where local NMDA spikes, calcium plateaus and backpropagating action potentials can make distal branches powerful contributors to somatic firing. Here we develop an analytical framework that extracts general principles of inhibition from biophysically detailed multi-compartment simulations. By reformulating the implicit voltage update of detailed neuron models as a matrix recursion, we derive exact voltage sensitivities to inhibitory synaptic perturbations. This leads to a unified {Phi}-a law: the somatic impact of inhibition factorizes into a global dendritic susceptibility term and a local synaptic perturbation term. Using this law to map inhibitory leverage and identify optimal inhibitory interventions, we show that active dendritic excitation can shift inhibitory hot zones from perisomatic regions toward distal or intermediate compartments. Across neocortical, hippocampal and striatal neuron models, the same response law explains convergent inhibitory strategies despite distinct cellular mechanisms. Our framework turns detailed numerical simulation into analytical theory, providing a general principle for how diverse dendritic inhibition controls active neurons.

As the duration of space flights increases, so does the need to optimize off-planet microbial growth. Microbes can both be unintentionally brought into space and cause human disease or be intentionally harnessed for on-site bioengineering functions. However, optimizing microbial growth is challenging due to an insufficient understanding of how microbial communities are affected by the extraterrestrial environment. To address this gap, we have modified a previously developed model for cell growth in microgravity. By improving the functional form used for cell growth as well as the code usability, we enable further research into how microbial communities are influenced by gravity. Applying this model to isolate individual effects of gravity on cell growth indicates that a lack of gravity-driven flow decreases cell growth in microgravity, while the absence of sedimentation increases cell growth in microgravity. These opposite effects likely contribute to the system-dependent effects of microgravity observed experimentally.