arXiv subjects

Henrik Weyer

Publications and source records attributed to Henrik Weyer.

9 recordsLinked to original sources

arXiv2026

Classification of Intracellular Protein Patterns from Reactive Equilibria

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.

physics.bio-ph↗

arXiv2026

Active Model B$^-$ from Mass-Conserving Reaction-Diffusion Systems

We show that the late-time dynamics of a minimal three-component mass-conserving reaction--diffusion system reduce to a scalar active field theory, Active Model B$^-$ (AMB$^-$), in which a density-dependent interfacial coefficient $κ(ϕ)$ turns negative at high density. This drives a finite-wavelength instability and stabilises microphase-separated patterns, in contrast to the unbounded coarsening of two-component mass-conserving systems. Unlike Active Model B$^+$, AMB$^-$ retains a chemical potential that remains a state function, inherited from the underlying conservation law, but admits no equation of state for the pressure.

cond-mat.soft↗

arXiv2025

Pattern Formation Beyond Turing: Physical Principles of Mass-Conserving Reaction--Diffusion Systems

Intracellular protein patterns govern essential cellular functions by dynamically redistributing proteins between membrane-bound and cytosolic states, conserving their total numbers. This review presents a theoretical framework for understanding such patterns based on mass-conserving reaction--diffusion systems. The emergence, selection, and evolution of patterns are analyzed in terms of mass redistribution and interface motion, resulting in mesoscale laws of coarsening and wavelength selection. A geometric phase-space perspective provides a conceptual tool to link local reactive equilibria with global pattern dynamics through conserved mass fluxes. The Min protein system of \emph{Escherichia coli} provides a paradigmatic example, enabling direct comparison between theory and experiment. Successive model refinements capture both the robustness of pattern formation and the diversity of dynamic regimes observed \emph{in vivo} and \emph{in vitro}. The Min system thus illustrates how to extract predictive, multiscale theory from biochemical detail, providing a foundation for understanding pattern formation in more complex and synthetic systems.

physics.bio-ph↗

arXiv2025

Chemotaxis-induced phase separation

Chemotaxis allows single cells to self-organize at the population level, as classically described by Keller-Segel models. We show that chemotactic aggregation can be understood using a generalized Maxwell construction based on the balance of density fluxes and reactive turnover. This formulation implies that aggregates generically undergo coarsening, which is interrupted and reversed by cell growth and death. Together, both stable and spatiotemporally dynamic aggregates emerge. Our theory mechanistically links chemotactic self-organization to phase separation and reaction-diffusion patterns.

cond-mat.soft↗

arXiv2025

Coarsening dynamics of chemotactic aggregates

Auto-chemotaxis, the directed movement of cells along gradients in chemicals they secrete, is central to the formation of complex spatiotemporal patterns in biological systems. Since the introduction of the Keller--Segel model, numerous variants have been analyzed, revealing phenomena such as coarsening of aggregates, stable aggregate sizes, and spatiotemporally chaotic dynamics. Here, we consider general mass-conserving Keller--Segel models, that is, models without cell growth and death, and analyze the generic long-time dynamics of the chemotactic aggregates. Building on and extending our previous work, which demonstrated that chemotactic aggregation can be understood through a generalized Maxwell construction balancing density fluxes and reactive turnover, we use singular perturbation theory to derive the rates of mass competition between well-separated aggregates. We analyze how this mass-competition process drives coarsening in both diffusion- and reaction-limited regimes, with the diffusion-limited rate aligning with our previous quasi-steady-state analyses. Our results generalize earlier mathematical findings, demonstrating that coarsening is driven by self-amplifying mass transport and aggregate coalescence. Additionally, we provide a linear stability analysis of the lateral instability, predicting it through a nullcline-slope criterion that parallels the curvature criterion in spinodal decomposition. Overall, our findings suggest that chemotactic aggregates behave similarly to phase-separating droplets, providing a robust framework for understanding the coarse-grained dynamics of auto-chemotactic cell populations and a quantitative basis for comparing chemotactic coarsening to canonical non-equilibrium phase separation.

cond-mat.soft↗

arXiv2024

Deciphering the Interface Laws of Turing Mixtures and Foams

For cellular functions like division and polarization, protein pattern formation driven by NTPase cycles is a central spatial control strategy. Operating far from equilibrium, no general theory links microscopic reaction networks and parameters to the pattern type and dynamics. We discover a generic mechanism giving rise to an effective interfacial tension organizing the macroscopic structure of non-equilibrium steady-state patterns. Namely, maintaining protein-density interfaces by cyclic protein attachment and detachment produces curvature-dependent protein redistribution which straightens the interface. We develop a non-equilibrium Neumann angle law and Plateau vertex conditions for interface junctions and mesh patterns, thus introducing the concepts of ``Turing mixtures'' and ``Turing foams''. In contrast to liquid foams and mixtures, these non-equilibrium patterns can select an intrinsic wavelength by interrupting an equilibrium-like coarsening process. Data from in vitro experiments with the E. coli Min protein system verifies the vertex conditions and supports the wavelength dynamics. Our study uncovers interface laws with correspondence to thermodynamic relations that arise from distinct physical processes in active systems. It allows the design of specific pattern morphologies with potential applications as spatial control strategies in synthetic cells.

physics.bio-ph↗

arXiv2024

Coarsening and wavelength selection far from equilibrium: a unifying framework based on singular perturbation theory

Intracellular protein patterns are described by (nearly) mass-conserving reaction-diffusion systems. While these patterns initially form out of a homogeneous steady state due to the well-understood Turing instability, no general theory exists for the dynamics of fully nonlinear patterns. We develop a unifying theory for wavelength-selection dynamics in (nearly) mass-conserving two-component reaction-diffusion systems independent of the specific mathematical model chosen. This encompasses both the dynamics of the mesa- and peak-shaped patterns found in these systems. Our analysis uncovers a diffusion- and a reaction-limited regime of the dynamics, which provides a systematic link between the dynamics of mass-conserving reaction-diffusion systems and the Cahn-Hilliard as well as conserved Allen-Cahn equations, respectively. A stability threshold in the family of stationary patterns with different wavelengths predicts the wavelength selected for the final stationary pattern. At short wavelengths, self-amplifying mass transport between single pattern domains drives coarsening while at large wavelengths weak source terms that break strict mass conservation lead to an arrest of the coarsening process. The rate of mass competition between pattern domains is calculated analytically using singular perturbation theory, and rationalized in terms of the underlying physical processes. The resulting closed-form analytical expressions enable us to quantitatively predict the coarsening dynamics and the final pattern wavelength. We find excellent agreement of these expressions with numerical results. The systematic understanding of the length-scale dynamics of fully nonlinear patterns in two-component systems provided here builds the basis to reveal the mechanisms underlying wavelength selection in multi-component systems with potentially several conservation laws.

nlin.PS↗

arXiv2021

Wavelength selection by interrupted coarsening in reaction-diffusion systems

Wavelength selection in reaction--diffusion systems can be understood as a coarsening process that is interrupted by counteracting processes at certain wavelengths. We first show that coarsening in mass-conserving systems is driven by self-amplifying mass transport between neighboring high-density domains. We derive a general coarsening criterion and show that coarsening is generically uninterrupted in two-component systems that conserve mass. The theory is then generalized to study interrupted coarsening and anti-coarsening due to weakly-broken mass conservation, providing a general path to analyze wavelength selection in pattern formation far from equilibrium.

nlin.PS↗

arXiv2017

Resonant transport and near-field effects in photonic glasses

A fundamental quantity in multiple scattering is the transport mean free path the inverse of which describes the scattering strength of a sample. In this paper, we emphasize the importance of an appropriate description of the effective refractive index $n_{\mathrm{eff}}$ in multiple light scattering to accurately describe the light transport in dense photonic glasses. Using $n_{\mathrm{eff}}$ as calculated by the energy-density coherent potential approximation we are able to predict the transport mean free path of monodisperse photonic glasses. This model without any fit parameter is in qualitative agreement with numerical simulations and in fair quantitative agreement with spectrally resolved coherent backscattering measurements on new specially synthesized polystyrene photonic glasses. These materials exhibit resonant light scattering perturbed by strong near-field coupling, all captured within the model. Our model might be used to maximize the scattering strength of high index photonic glasses, which are a key in the search for Anderson localization of light in three dimensions.

cond-mat.dis-nn↗