The European Physical Journal Plus

The study of tissue dynamics has been stimulated during the last decades thanks to the use of quantitative descriptions, with the development of several theoretical and computational frameworks, many of them revolving around the notion of reaction-diffusion systems, eventually with additional structure variables beyond time and space. The use of structure variables can accommodate phenotypic traits. In this work, we study a family of competition models, where a given population depends on a resource (e.g. oxygen) and several populations are competing for it. Our quantitative description incorporates phenotypic traits and heterogeneity at the level of cell cycle variations, which influence replication rates via oxygen consumption. This enables us to replicate the fitness of specific subpopulations to environmental conditions (e.g. oxygen shortage or external influences). Using numerical simulations, we show that such models display dynamical pattern formation in the form of coupled travelling wave profiles that expand or retreat at the same wave speed. The full theoretical analysis of such dynamics is quite involved; to circumvent this difficulty, we introduce a quasi-stationary approximation for the resource dynamics. We find that this approximation can reproduce the overall behaviour very accurately, with the additional benefit of allowing theoretical treatment of the reduced model. In this way, we provide estimates on the wave speed which are numerically shown to be robust across a wide range of macroscopic parameters of the full model. The wave speeds are thus found to depend strongly on the proliferation rate of the fittest population, resembling a winner-takes-all dynamics.

Within the studies of stochastic gene expression, apart from the variability of copy number of gene products, the problems of threshold crossing of those products are biologically important as they often lead to terminal cellular events. Here, we study the threshold crossing problem of the messenger ribonucleic acid (mRNA) and present an exact probability distribution of first passage times in Laplace space. The function furnishes moments of any order and also predicts the characteristic time of the exponential tail of the distribution, which we match against Gillespie simulations. We find that all the measures of relative fluctuations of the threshold crossing times show U-shapes within this simple model of mRNA, as was found earlier in more mathematically involved models of threshold crossing time statistics of proteins. Furthermore, we extend the exact formula to include the phenomenon of DNA duplication and the corresponding doubling of transcription rate. As expected, the distribution varies considerably depending on the onset of the duplication stage within the cell cycle.

Healing of the gastrointestinal (GI) tract following surgical interventions is governed by coupled mechanobiological processes and may lead to severe complications such as perforation or stricture formation. A first comprehensive mechanobiological modeling framework of GI healing is herein proposed. The framework addresses two clinically relevant applications of bioprinting: endoscopic treatment of GI tissue defects and bioprinting-assisted surgical anastomosis. Tissue remodeling is based upon a hyperelastic material model with fiber dispersion coupling the spatiotemporal reaction diffusion dynamics of fibroblasts and cytokines with collagen deposition, reorientation, and plastic deformation. An active stress formulation drives fibroblasts and myofibroblast contraction while a multiplicative decomposition approach is adopted for collagen remodeling as a permanent change. The governing equations are discretised in time with an implicit Euler scheme, finite element in space and solved by a staggered algorithm implemented in the open-source platform FEniCS. Numerical simulations show that the initial collagen fibers content and orientation strongly influence fibroblast infiltration and scar contracture formation. The study quantifies the advantage of having a collagen bioprinted architecture aligned with tissue fibers, to reduce structural remodeling distortion. The model also predicts a strong correlation between collagen deposition and luminal burst pressure during the recovery of mechanical integrity in GI anastomosis.

Non-exponential residence times give rise to history-dependent or memory effects in epidemic dynamics, yet their mathematical formulations remain fragmented. Here we develop a unified framework for a history-dependent SEIR model with general latent- and infectious-period distributions. We first establish the equivalence between the stage-age and renewal formulations and show that both admit a unified transition-flow representation. We then introduce the concept of a transition-flow multiplier, which provides a direct link between residence-time distributions and transition flows. When the multiplier is a weighted sum of shifted power functions, the model admits an exact representation in terms of Riemann-Liouville or tempered Riemann-Liouville fractional operators, providing a first-principles foundation for fractional epidemic models. Finally, using Euler-Lotka equations and stochastic-order arguments, we characterize how the latent- and infectious-period distributions shape epidemic growth and decay. A longer latent period slows both early growth and late decay, while, at fixed means, greater variability in the latent period accelerates early growth but slows late decay, whereas greater variability in the infectious period slows both.

A fundamental biological process of transcription occurs in the cell nucleus, which is a complex medium that also contains multiple heterogeneous structures known as biomolecular condensates. Interestingly, some of these condensates contain mRNA molecules in addition to proteins, suggesting an important cellular role in transcription that is not yet well understood. In this work, we develop a minimal theoretical framework for quantitative investigation of the role of reversible mRNA condensation in transcription. Our discrete-state stochastic approach accounts for the most relevant processes, allowing us to explicitly evaluate the properties of the system and clarify the effects of condensation. Analytical calculations supported by computer simulations suggest that reversible mRNA condensation influences the transcription processes by maintaining a constant level of free mRNA in the nucleoplasm while lowering the degree of stochastic noise and increasing the robustness against external perturbations. Physicochemical arguments are presented to explain these observations. The proposed theoretical framework elucidates important microscopic aspects of transcription, providing a convenient quantitative tool for investigating complex biological phenomena.

BackgroundPlatelet activation in flowing blood is a multiscale process in which vessel-scale hemodynamics, red blood cell (RBC) mechanics, adhesive receptor interactions, and intracellular signalling jointly determine thrombotic risk. Individual components are well studied, but a single reduced description that carries each explicitly from vessel-scale flow to mechanosensitive calcium entry, with dimensionally consistent couplings, remains uncommon. ObjectivesWe develop and analyse a reduced, six-module mechanobiological framework for platelet priming spanning the cascade from hemodynamic shear to mechanosensitive calcium entry, and we delineate which elements are supported by existing evidence and which are new, testable hypotheses. MethodsThe framework comprises six coupled modules: (I) hemodynamic forcing from the incompressible Navier-Stokes equations, with an objective principal-strain-rate measure for extensional flow; (II) RBC-mediated platelet margination and near-wall delivery, closed by a near-wall arrival flux; (III) von Willebrand factor (VWF) activation with a bounded kernel and glycoprotein Ib (GPIb) catch-slip capture, resolved through an explicit contact area and a bond-dependent mobility that progressively immobilises wall-interacting platelets; (IV) a single-load membrane-stimulus formulation; (V) mechanosensitive gating and a dimensionally consistent cytosol-store calcium model with extracellular influx; and (VI) a phenomenological mechanical-memory state. We formally derive that the single-platelet stochastic dynamics and the continuum population balance form a Fokker-Planck pair, with the spatially varying diffusivity handled by an explicit drift correction. ResultsThe framework yields a family of mechanochemical dimensionless groups delineating priming regimes. Its central prediction is reformulated as a falsifiable, history-sensitive signature: in a conditioning-test protocol, a low-tension conditioning block charges the memory state, and a fixed sub-threshold test pulse then reports a delay-dependent calcium facilitation that decays on the memory time{tau} m and is distinguishable from no-memory gating, channel adaptation, and residual-calcium priming. We show explicitly that the previously proposed pulsatile-versus-monotone contrast is a nonlinear convexity/thresholding effect of the gating nonlinearity--its difference-in-differences is approximately zero-- and is therefore not a valid test of memory; the conditioning-test signature is. A second prediction links RBC stiffening to reduced near-wall delivery and captured-platelet calcium response, upstream of intrinsic platelet signalling. ConclusionsThe framework provides a dimensionally consistent, mechanistically grounded and hypothesis-generating description linking hemodynamic forcing to mechanosensitive calcium entry. It demonstrates how history-dependent platelet priming may arise from a phenomenological sensitisation state and proposes a conditioning-test protocol for comparison against adhesive, channel and intracellular-store persistence. The framework is calibratable rather than validated, and the quantitative outputs shown use representative uncalibrated parameters.

Mechanical properties of biological tissues, driven by passive and active forces, play a vital role in several processes ranging from development to cancer metastasis. However, the dynamical responses of cells in tissues, subject to mechanical deformations such as shear and the associated rheological properties, are not well characterized. Here, we use three-dimensional agent-based models for normal and cancer tissues to investigate their responses to simple shear as a function of cell stiffness and stochastic active forces. In the normal epithelium, with uniform strength of active force, the yield stress as a function of shear rate follows the Herschel-Bulkley form over a range of cell volume fraction. Strikingly, the shear rate dependence and the elasticity-dependent changes in the yield stress fall on master curves upon suitable scaling. To model cancer-like behavior, a certain fraction (Np) of cells was chosen to have enhanced activity and decreased stiffness. As Np increases, the extent of collective cell movement decreases, transitioning from affine (collective) to non-affine (individualistic) movement, a finding that is in accord with imaging experiments. Simulations of a model of a stiff solid tumor, with radius Rs embedded in normal tissue, show that as Rs increases, the yield stress increases. Interestingly, the cells migrate collectively as Rs increases. A Gaussian Mixture Model (GMM) and a mean field theory quantitatively account for the simulation as well as experimental results on cancerous, non-cancerous, and a mixture of these two types. The combined theoretical and experimental study establishes that heterogeneity in stiffness and activity determines non-affine movements in normal and cancer tissues.

The high energy-efficiency of life is hard to understand only with classical physics. Many efforts have been made to study its mechanism based on quantum mechanics; the progress is nevertheless slow due to lack of experimental evidence with living cells. Here, combining experiments on cells, tissues and mitochondria with a theoretical model, we demonstrate a quantum state of mitochondria, which can be employed to modulate ATP production in living cells. We found an anomalous 71.0-THz oscillation mode only in living cells and tissues, which is highly determined by intact structure of mitochondria, and cannot be assigned to any specific molecules. Based on experimental data, a quantum model of light-matter coupling was introduced to trace the origin of this mode. Our calculations suggest a quantum superposition state of functional mitochondrion that forms by the coupling of light and lipid CH2 bonds in functional cristae, and induces a splitting of the intrinsic CH2 vibration mode of 87 THz to two levels at 71 THz and 103 THz, respectively. The former can be observed only in living cells and tissues; whereas the latter falls in the range (90-110 THz) of biomolecular and water vibrations, thus indistinguishable. Additional experiments revealed this mitochondrial quantum state able to serve as an efficient channel to modulate ATP production. Our findings provide a quantum mechanics view for understanding living cells, and it will be interesting to further explore whether such quantum state could act as a channel for energy metabolism, and even information transmission in life.

A classical study found no excitation transfer when isolated cardiomyocytes were placed side by side, whereas a recent paper reported action potential transfer in carrdiomyocytes placed end to end. We use nanoscale numerical simulations based on the full Poisson-Nernst-Planck equations to investigate whether these apparently opposing observations can be explained by the different geometrical configurations. The computations show that in the end-to-end configuration, ephaptic coupling occurs when the intercellular cleft is sufficiently narrow and a sufficiently large fraction of the sodium channels is localized at the intercalated disc. Coupling is strengthened when the sodium channels are concentrated in fewer clusters and when ionic diffusion within the cleft is reduced. Under these conditions, excitation transfer occurs on a timescale consistent with rapid cell-to-cell activation. Conduction depends biphasically on cleft width and terminates abruptly beyond a critical width. Localization of potassium channels at the intercalated disc has only a moderate effect, whereas gap junctions substantially improve conduction and reduce the relative contribution of ephaptic coupling. In the side-by-side configuration, excitation transfer does not occur under physiological conditions and requires highly flattened cells, minimal separation, and unrealistically strong sodium-channel clustering. The different outcomes of the side-by-side and end-to-end experiments can therefore be explained by the fundamentally different geometrical conditions for ephaptic coupling.

The relatively long flagella of spermatozoa from insects, birds, and octopuses display double waves, characterized by two superimposed helical waves. The prevalance of these highly organized waveforms across diverse taxa and distinct flagellar architectures hints at shared underlying physics, motivating a model of the flagellum as an elastic filament immersed in a viscous fluid, actively driven by a single set of internal bending moment waves. Simulations of a clamped filament show that it can buckle under its own activity into whirling and flapping states. A multiple-scales analysis of the elastohydrodynamic equations reveals how nonlinear interactions between fast undulations generate an effective compression driving buckling, and connects wave-driven buckling to classical follower-force instabilities. Extending the model to a swimming spermatozoon, the same instability produces double waves. Parameter estimates across species show that most observed double waves lie within the regime where buckling is permitted, supporting self-buckling as a generic physical mechanism for double waves.

We investigate the dynamics of the spread of the infection due to a phage- during the range expansion of an E coli colony. We find a rich panoply of spatio-temporal dynamics at large colony-level length scales, arising due to the interplay of mechanical forces, growth and viral infection dynamics at smaller cellular length scales. Strikingly, the phages "surf" the front of the growing bacterial colony by hitchhiking on E coli that are advected due to the growth of bacteria in the colony, resulting in an anisotropic spread of the phages. We identify microscopic processes - of the phage release during lysis (occurring on short millisecond timescales at length scales close to that of a single bacterium) and local nematic alignment of the rod-like E coli bacteria (occurring on timescales comparable to the bacterial growth rate and the length scales of a few bacterial cells) - that enhance the advective effects driving the hitchhiking behavior. Combining our experiments with a mathematical model, we explain the multiple spatio-temporal dynamical regimes - from the coexistence of uninfected bacteria, resistant (lysogenic) cells and phages, to fixed points where the entire population turns resistant or remains uninfected. Our work broaches a new frontier in the investigation of eco-evolutionary processes arising from the mechanical and ecological forces due to the interactions between viruses and their hosts.

Epithelial monolayers are the foundation of many mammalian organs and have a significant impact on numerous biological processes, including the secretion of cytokines, absorption of waste products and barrier function. During organ development epithelia are subject to many external forces due to the growth of the surrounding tissues. They exhibit complex responses to such forces, with deformation occurring on short timescales (seconds), and relaxation and remodelling occurring on longer timescales (minutes or hours). Existing mathematical and computational models do not typically account for subcellular remodelling, assuming instead that the response to an applied force or strain acts on a single timescale. In this paper we extend an off-lattice, cell-centre modelling framework to account for subcellular and tissue remodelling by introducing a Dynamic Reference Frame (DRF). The DRF provides a discrete, cell-based analogue of morpho-elasticity: it decouples the evolution of each cell's mechanical reference configuration from its instantaneous deformation, providing a phenomenological description of subcellular remodelling processes - cytoskeletal reorganisation, myosin turnover and adhesion bond remodelling - at the cellular scale. Using this extended multicellular model, we reproduce multiscale responses to external mechanical forces, including creep and stress relaxation experiments, and demonstrate that the history of applied deformation influences tissue recovery upon release. Additionally we identify and quantify where and how these multiscale responses occur. The resulting framework allows for more detailed descriptions and analyses of the development and function of biological tissues.

Wound repair is an important mechanism to preserve tissue integrity in organisms after injury. However, why different tissues exhibit different mechanisms to repair wounds is a long-standing question that remains unanswered. In this work, we theoretically explore the role of the purse string, an actomyosin contractile cable used by tissues to close small wounds. Does the tissue 3D geometry influence the efficiency of the purse string in driving wound closure? Using a 3D biophysical model, we study in silico tissues with the same cell volumes but different aspect ratios, ranging from squamous to thick and tall tissues. The model predicts that taller cells are easily deformed by the purse string. In contrast, very squamous cells require a very strong purse string that might demand additional cellular mechanisms to close the gap. These findings establish a theoretical framework to predict the optimal biophysical mechanisms of wound healing in different tissues. Graphical abstractCells of different aspect ratios can be observed in a range of organisms with different function and mechanics. The wound healing efficiency of the purse string increases with the cell aspect ratio in our theoretical exploration. O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=135 SRC="FIGDIR/small/743165v1_ufig1.gif" ALT="Figure 1"> View larger version (23K): org.highwire.dtl.DTLVardef@d44ab0org.highwire.dtl.DTLVardef@1737cbaorg.highwire.dtl.DTLVardef@101b5d4org.highwire.dtl.DTLVardef@1487f26_HPS_FORMAT_FIGEXP M_FIG C_FIG

We develop a general geometrical framework for growth processes in which the growth rate depends exponentially on the number of active growth-supporting components. The framework separates the fraction of active components from the size of the accessible component space, allowing qualitatively different growth laws to arise from the same underlying construction. Bacterial population growth provides an example of a fixed-size component space controlled primarily by activation and deactivation, whereas examples such as human population growth or speciation provide an expanding component space in which interactions between individuals promote further growth. This motivates a Replicative geometrical law, dX/dt= X exp({beta} X^{gamma}), whose exponent characterizes the scaling of the effective growth-supporting component space and is tested against historical human-population regimes and eukaryotic lineage-through-time data. For innovation indicators such as patents and arXiv manuscript submissions, where an existing item need not itself reproduce, the same construction motivates a Direct Geometrical production law without the prefactor X. The framework therefore provides a common description of fixed and expanding component spaces while distinguishing Replicative from Direct Geometrical growth.

Structural network representations of metastatic dissemination typically focus on static topology without resolving transport dynamics, relaxation timescales, or steady-state behaviour. Here, we formulate a discrete Markovian transport model on a directed higher-order network with transition rates derived from qualitative clinical affinity classes. By constructing a non-Hermitian row-stochastic transfer operator, we characterise the relaxation dynamics through its spectral decomposition. The system exhibits a fast-mixing regime characterised by a spectral gap of {gamma} {approx} 0.67, corresponding to a characteristic relaxation timescale of {tau} {approx} 1.49 discrete steps, with the influence of the primary tumour origin progressively attenuated during dissemination. Convergence towards a non-equilibrium steady state (NESS) is accompanied by a reduction in Shannon entropy, concentrating probability mass within specific topological sinks. This spectral relaxation delineates two distinct dynamical regimes: early transient dissemination (n < {tau}), dominated by local organ-specific transition probabilities (organotropism), and the asymptotic regime (n > {tau}), determined increasingly by the global transport architecture of the network. Comparison with independent clinical and autopsy observations across 21 primary tumours and 23 target organs indicates that the predicted stationary distribution is consistent with the observed hierarchy of metastatic organ involvement.

Background: Tuberculosis remains a persistent infectious disease whose control is complicated by latent infection, delayed treatment, incomplete recovery, reinfection, and continuing transmission from infectious individuals. Although treatment is central to tuberculosis management, it is frequently represented only as a transition parameter in mathematical models rather than as a separate epidemiological state. In this study, treatment was therefore incorporated explicitly as an independent compartment so that its influence on transmission, recovery, disease-induced mortality, and long-term disease persistence could be evaluated. Methods: A deterministic nonlinear compartmental model was formulated by dividing the total population into susceptible, exposed, actively infected, treated, and recovered classes. Reinfection of recovered individuals, progression from latent infection to active disease, movement of infectious individuals into treatment, treatment-associated recovery, natural mortality, and disease-induced mortality were included. Positivity and boundedness of the solutions were examined to establish biological validity. The basic reproduction number, R0, was derived through the next-generation matrix approach. Disease-free and endemic equilibria were determined, and their local and conditional global stability properties were investigated using Jacobian analysis, the Routh-Hurwitz criterion, center manifold theory, Lyapunov functions, and LaSalles invariance principle. Normalized sensitivity indices, Latin hypercube sampling, partial rank correlation coefficients, and numerical simulations were also applied. Results: The disease-free equilibrium was shown to be locally asymptotically stable when ,R0<1 whereas sustained transmission and a unique endemic equilibrium were associated with R0>1. Under the stated reduced-model assumptions, stability of the endemic equilibrium was established. Transmission-related parameters were identified as the strongest positive contributors to disease persistence. In contrast, treatment and recovery parameters were found to reduce the reproduction number and infectious burden. Numerical simulations indicated that stronger treatment implementation and reduced transmission opportunities produced substantial reductions in active tuberculosis cases. Conclusion: Treatment was shown to function as both a clinical pathway and an epidemiological control mechanism. The proposed framework may support the design of treatment-centered strategies for reducing tuberculosis prevalence and preventing long-term endemic persistence.

Classical neuronal cable theory relies on quasi-static electric field approximations and neglects magnetic induction, Lorentz force coupling, and transient electromagnetic currents, limiting its ability to fully characterize action potential propagation within geometrically branched axons and dendrites. This work develops a coupled Maxwell-electromagnetic cable framework by integrating finite-difference time-domain (FDTD) solutions of Maxwells equations with extended Hodgkin-Huxley and Fitzhugh-Nagumo membrane dynamics, incorporating magnetic gating perturbations, electromagnetic trans-membrane currents IEM, and nanoscale quantum corrections for thin neural segments. Controlled propagation experiments are designed to quantify deviations from standard cable predictions across asymmetric and symmetric axonal bifurcation geometries. Numerical results demonstrate that inductive magnetic effects lower the critical branch radius for junction conduction failure and break symmetric action potential invasion in geometrically identical child branches under external transverse magnetic fields. An electromagnetic corrected geometric ratio GREM is proposed to revise impedance-matching conditions at branch points, accounting for size-dependent axial current imbalance induced by magnetic and displacement currents. Parent axon conduction velocity deviates substantially from the canonical [Formula] scaling law when electromagnetic feedback and quantum charge distributions are included, triggering early signal blockage at large cable diameters. Collectively, this study establishes that quasi-static cable models underestimate electromagnetic corrections to propagation speed, waveform shape, and bifurcation transmission fidelity; the coupled Maxwell-cable framework provides a comprehensive multi-physics tool for modeling electrodynamic signal behavior in complex neuronal architectures.

We show that the p53-Mdm2 gene interaction can be understood as a form of antithetic feedback, but with mixed feedback loops. In particular, we show that this viewpoint sheds light on the emergence and robustness properties of p53's oscillatory behaviour, as observed experimentally.

AO_SCPLOWBSTRACTC_SCPLOWCellular automata and graph reaction-diffusion systems encode local spatial interactions in different mathematical forms. We develop a cochain-operator calculus for these two settings. Over a finite field Fq, every local rule on a finite neighborhood has a unique reduced polynomial representative. On an oriented line, the coboundary and endpoint maps recover the left and right shifts. Our main theorem shows that these operators, together with linear operations, constant cochains, and the degree-zero cup product, generate every finite-radius polynomial cellular automaton. Explicit formulas for Rules 30, 110, and 22 show how reflection-invariant linear coupling, directed transport, and nonlinear neighbor interactions enter the calculus. On a general graph, d*d is the unweighted combinatorial Laplacian and enters a graph reaction- diffusion recurrence. Over [R], the term - Dd*d with D [&ge;] 0 admits the usual diffusion interpretation; over Fq, the corresponding expression defines modular coupling without an intrinsic order. In the morphogenetic examples, we therefore distinguish pattern-generating dynamics from finite-state observation and use the Betti numbers of active induced subcomplexes to summarize observed patterns. This yields a common algebraic representation without identifying real-valued diffusion with finite-field dynamics.

Despite lacking a dedicated structural function, brain tissue is exposed to severe mechanical loading during accidents and trauma, with potentially permanent or lethal consequences. Therefore, characterizing its mechanical behavior assumes particular importance for designing protective equipment, planning surgeries, and training neurosurgeons, tasks that often rely on physical brain replicas made from phantom materials. Although the mechanics of brain tissue has been extensively studied, the selection of suitable phantom materials still relies on simplified metrics that fail to capture the highly nonlinear and rate-dependent behavior of the brain. In this work, we characterize the mechanical response at low-to-medium strain rates of common synthetic brain phantom materials, including Sylgard 527, Ecoflex Gel, and a composite hydrogel, and establish rigorous comparisons with porcine brain tissue as a benchmark. To this end, we employ a multi-step stress relaxation protocol under both uniaxial extension and compression across two different strain rates, introduce thermodynamic metrics, and perform comparisons based on rigorous statistical analysis. In particular, we isolate the thermodynamic equilibrium stress-strain curves, representing the baseline material's response, from rate-dependent dissipative inelastic effects, relatable to viscoelastic and poroelastic mechanisms. Our results provide a thorough comparison, revealing critical limitations in existing simulant materials and highlighting significant space for developing improved brain surrogates. The comprehensive dataset collected can also support the calibration of constitutive models, enhancing the predictive accuracy of numerical simulations involving brain tissue and its surrogates. More broadly, this study highlights the need to move beyond simplistic, scalar-metric-based comparisons of mechanical responses across materials.