Papers

Subcellular signaling pathways regulating, e.g., cell division or synaptic plasticity, are often modeled as dynamical networks of reactions satisfying the law of mass action. To remain physically grounded, these models must satisfy different physical conservation laws, such as conservation of energy. This gives rise to thermodynamic constraints formalized by the Wegscheider conditions, which ensure that the system is in detailed balance at thermodynamic equilibrium. Explicitly imposing Wegscheider conditions requires identifying cycles in the reaction network. This can become computationally cumbersome, especially in large, complex systems. Furthermore, even when these constraints are explicitly available, enforcing them requires choosing a reparameterization of the network, which may introduce asymmetries among the parameters and affect numerical conditioning. Moreover, this approach often causes inverse uncertainty quantification methods like Markov chain Monte Carlo (MCMC) to struggle. Instead of imposing Wegscheider conditions directly in the parameter space, we propose an approach for promoting physical consistency by penalizing parameters that violate detailed balance. We first illustrate the approach on a simple reaction network containing a single cycle. We show that parameter values inferred without thermodynamic constraints can reproduce the experimental data seemingly accurately, while substantially violating the Wegscheider condition. In contrast, the proposed approach preserves the agreement with the observed dynamics while yielding posterior samples that approximately satisfy the thermodynamic constraint. We further apply the approach to a model of PKA-calcineurin signaling in synaptic long-term depression, demonstrating its applicability to a more complex biochemical reaction network.

We improve upon our previous work using asymptotic analysis to characterize analytically the effective transport properties of a stochastic model for an ensemble of a cargo being pulled by two molecular motors walking on a microtubule. The governing equations are a system of stochastic differential equations with stochastic switching due to attachment and detachment kinetics of the molecular motors from the microtubule. Our model adopts a nonlinear tether which exerts no force when end-to-end distances are sufficiently small. This challenges some of the scale separation arguments from our previous work, and we modify the asymptotic analysis accordingly. In particular, spatial dynamics of the molecular motors may not always reach their quasi-stationary distribution within a particular attachment state. Rather, molecular motors tend to have a slack connection to the cargo for a while after they reattach, and we incorporate some first passage time analysis to determine if the tether becomes taut again. Through these and other modifications to the asymptotic analysis argument, the theoretical statistics for the run length, run time, and velocity of the motor-cargo ensemble can be brought into reasonable agreement with direct model simulations of two-motor ensembles consisting of kinesin-1 and kinesin-2. Additionally, we propose a new data fitting approach to obtain a double-exponential parameterization for the detachment rate of a motor as a function of the momentary force on its tether to the cargo, which is continuous at low load. Such a modified parameterization is needed to avoid artifacts in theoretical modeling of intracellular transport.

Tau and amyloid-$\beta$ (A$\beta$) deposits co-occur in Alzheimer's disease, and tau fibrils have recently been shown in vitro to catalyze A$\beta$ primary nucleation in a fold-specific manner. A two-compartment kinetic model is developed here, describing tau aggregation within the neuronal soma and A$\beta$ aggregation in the surrounding interstitium. The adjustable coupling parameter is the fraction f$_{acc}$ of somatic tau fibrillar material accessible to interstitial A$\beta$. Homotypic A$\beta$ secondary nucleation is restricted to the accessible surface of the consolidating plaque rather than scaling with total fibril mass, which preserves the in vitro calibration of the rate constant while preventing the surface term from growing without bound over decades. Three model predictions emerge. First, the model predicts that tau-catalyzed nucleation can increase the soluble A$\beta$ oligomer concentration and the number of A$\beta$ fibrillar species, by factors of 4.6 and 2.0, respectively, at complete accessibility, while leaving total A$\beta$ fibril mass and plaque volume unchanged, since in the absence of clearance these are fixed by the monomer supply; oligomer burden and visible plaque burden are therefore decoupled. Second, the predicted effect requires substantial accessibility: a 50 % increase in accumulated oligomer exposure needs f$_{acc}$ $\approx$ 0.035-0.15, which is difficult to reconcile with tangles enclosed by an intact neuronal membrane and points instead to neuronal lysis and the formation of extracellular ghost tangles. Third, physiologically relevant oligomer dissociation and proteolytic turnover each suppress accumulated exposure, by approximately three orders of magnitude and, at zero tau accessibility, about seventyfold, respectively, and remove the effect on a biological-age measure entirely.

Ultrasound is increasingly used to control biological cells, but its multiple physical effects, including radiation force, streaming, heating, and cavitation, require theoretical frameworks that can quantify their relative strengths. Here we develop a semi-analytical model to predict flow patterns and energy distributions of ultrasound-induced intracellular streaming. Cells are modeled as viscoelastic droplets immersed in a fluid with different viscoelastic properties. For this geometry, the momentum equation with an Oldroyd-B constitutive law is solved using a perturbation expansion commonly applied in acoustofluidics. The resulting equations for the different orders of the expansion are solved using partial wave expansion and explicit integration. We investigate our model for a range of parameters which is relevant both for synthetic polymer and for protein solutions. We find a series of flow reversals that we can connect to the distribution of energy into the different modes. We also consider density and compressibility contrasts, which shift these transitions and introduce new ones. Finally, we discuss the potential biological relevance of our mathematical results for cellular sensing and signaling.

Planar cell polarity is preceded by the clustering of polarity proteins into discrete, low-turnover membrane subdomains (puncta), yet the minimal interactions that nucleate puncta, set their number, and segregate opposite orientations remain unclear. We address these questions with a mass-conserving reaction-diffusion model in which two diffusible monomers bind reversibly across a cell-cell junction into trans-complexes of two orientations, with feedback entering only through concentration-dependent rates. Above a critical density, the uniform state undergoes a long-wavelength mass-redistribution instability rather than a finite-wavelength Turing bifurcation. The form of the feedback then selects between two morphologies: broad mesas fixed by a Maxwell construction under saturating feedback, and narrow mass-limited spikes under unbounded feedback. For spikes we obtain closed-form expressions exhibiting a clean separation of amplitude (mass and feedback), width (the complex diffusion length), and spacing (the monomer screening length). Within a fast-monomer reduction we prove, for any number and arrangement of puncta, that like-oriented arrays coarsen, so multiplicity is metastable and kinetically determined. The second monomer reservoir introduces a second screening length that rate-limits competition by the harmonic mean of the monomer diffusivities, and the spectrum of a punctum remains free of oscillatory ("blinking") instabilities throughout. Finally, sign-definite cross-modulation of turnover converts clustering into orientation sorting - the mutual exclusion of orientations along a single contact: mass redistribution sets puncta number, and the sign of the cross-coupling determines whether orientations segregate. Puncta number and orientation sorting are thus governed by mathematically separable ingredients.

Ion channels and pumps drive ion-selective currents through cell membranes at localized sites, yet a cell's electrical state is routinely summarized by a single transmembrane voltage. Combining theory and numerical simulations, we resolve the spatiotemporal dynamics of charge reorganization driven by a localized current on a spherical membrane vesicle. At early times, the response is insensitive to membrane geometry: as in the case of a flat membrane (arXiv:2407.11947; arXiv:2508.14001), the transmembrane voltage decays in a monopolar fashion, varying inversely with distance from the source, and crosses over to a dipolar tail that scales as the inverse cube of distance. Under sustained current, this monopolar response spreads outward from the source. Because the vesicle is closed, this response cannot persist indefinitely; once the monopolar front traverses the entire vesicle, the subsequent charging dynamics is dominated by a spatially uniform mode corresponding to capacitive charging of the membrane. We further decompose the bulk potentials into an electrostatic image-charge component that generates the bulk electric fields and a spatially uniform capacitive mode that can be represented as an equivalent circuit. We also derive a nonlocal cable equation governing the transmembrane voltage dynamics and show that the uniform mode is its long-time solution. This work provides a first-principles basis for the electrophysiological simplification of an electrotonically compact cell.

Self-organized spatial patterns are central to nonequilibrium physics and cell biology, yet locating instabilities in multi-component, reaction-diffusion networks remains challenging because standard eigenvalue analyses scale with the number of biochemical states and rely on reaction kinetics often poorly constrained by experiments. Exploiting the common mass-conserving structure of protein reaction kinetics and the fact that nonlinear feedback is typically confined to membrane reactions while lateral membrane diffusion is negligible, we develop a geometric classification that predicts stationary, and approximately also oscillatory, pattern-forming instabilities from reactive equilibria. The developed criteria reduce the stability analysis from the full component space to the space of conserved species. On this reduced space, slope matrices—describing the change of equilibrium cytosolic densities with respect to total species densities—govern onset. Based on densities in chemical equilibrium, this approach eliminates the requirement of comprehensive kinetic knowledge frequently lacking in experimental systems. Thus, a broad range of instabilities can be understood as mass-redistribution instabilities—self-amplifying mass redistribution caused by shifting local equilibria. We apply these criteria to models for the Escherichia coli Min system and the Caenorhabditis elegans polarity system and show that the reduction extends to the mixed-dimensional dynamics in systems coupling bulk cytosolic dynamics with membrane dynamics on the boundary. Together, these results provide an interpretable, broadly applicable, and experimentally accessible framework for diagnosing and designing pattern formation in multicomponent nonequilibrium systems on the basis of conservation laws.

Reproductive hormones regulate a wide range of physiological processes throughout the human lifespan. Estrogen, in particular, varies substantially across the menstrual cycle and is widely used in contraceptives and hormone replacement therapies. Despite its physiological importance, few experimental studies and even fewer mathematical models explicitly investigate how estrogen regulates smooth muscle function. As smooth muscle lines our blood vessels, airways, uterus, and several other organs, understanding how estrogen impacts smooth muscle is important to improving the understanding of sex differences in lifelong health. Here we extend an established mathematical model of smooth muscle cell calcium signalling to incorporate estrogen-dependent modulation of intracellular calcium transport pathways. Numerical simulations, global sensitivity analysis, and numerical bifurcation analysis are then used to quantify the influence of estrogen on intracellular calcium dynamics and the resulting steady-state and oscillatory behaviours. Our results demonstrate that physiologically relevant changes in estrogen shift intracellular calcium concentrations while leaving the underlying bifurcation structure and qualitative dynamics largely unchanged, suggesting that estrogen acts primarily as a quantitative modulator of smooth muscle calcium signalling. This work also serves to establish a foundation for future mechanistic models of hormone-dependent cell physiology.

Slow internal states reshape both the mean throughput and the temporal organization of a driven lattice gas. Exit-counting statistics reveal this effect in a finite open totally asymmetric simple exclusion process whose particles reversibly switch between active and paused states. Increasing pausing lowers the mean current smoothly, whereas the long-window Fano factor is strongly nonmonotonic. At the reference boundary rates, the maximum remains near a measured mean paused population \(N_p=L\rho_{\rm paused}\simeq1.5\)–\(2\) across lattice lengths L=50-500, while the corresponding pausing rate scales as \(k_p^{\rm max}\propto L^{-1}\). A minimal constant-birth, linear-death approximation translates an order-one collective crossover into this finite-size displacement and gives \(N_p^\star\simeq1.50\) in the independent-pause, strong-blocking limit. The simulations delimit this approximation: the pause number is overdispersed, and at fixed \(N_p\), slower unpausing increases both the correlation time and the noise amplitude. Residence-time and structural analyses further separate the relevant slow variables. The pause-free versus pause-containing residence-time scale tracks the fitted output-correlation time, whereas the noise amplitude follows fluctuations, rather than the mean size, of the largest particle cluster. Low-frequency output noise therefore identifies an intermittent finite-size regime shaped jointly by slow-defect kinetics and traffic-jam reorganization.

Excitable and oscillatory responses are widespread in cell signaling, but how these arise in the same system is unclear. We propose a minimal model of a saddle node bifurcation on an invariant circle, where slow fluctuations modulate transitions between excitable and oscillatory states, and noise drives excitability. Fitting the model to cell signaling data from embryonic stem cells reveals that these cells operate close to the bifurcation. Proximity to the bifurcation allows the cell to tune different dynamic states, suggesting a general principle for versatile cell signaling.

Cell adhesion to viscoelastic substrates is mediated by focal adhesions (FAs), which dynamically couple actomyosin contractility to the extracellular matrix. Although substrate stress relaxation is known to regulate adhesion stability and cell migration, a predictive physical framework linking viscoelasticity to force transmission and adhesion dynamics remains lacking. Here we review briefly what is known about the active wetting and de-wetting of FAs on viscoelastic substrates and synthesize existing experimental and theoretical work into a two-timescale physical framework to describe the phenomena reported. At short timescales, oscillatory actomyosin-driven displacements are transmitted through molecular clutches, leading to frequency-dependent energy transfer to the substrate. We show that this transfer is maximized at an optimal frequency set by a balance between elastic energy storage and viscous dissipation, establishing a resonance-like mechanism that selects both the effective FA stiffness and traction force amplitude. At longer timescales, this mechanically optimal state couples to adhesion remodelling through an effective surface tension, enabling FA growth and disassembly to be interpreted as active wetting and de-wetting processes. The model predicts that adhesion stability and steady-state size are controlled by substrate stiffness and viscoelastic timescales, as well as mechanosensitive feedback mediated by Piezo1-dependent calcium signalling.