arXiv subjects

Fridtjof Brauns

Publications and source records attributed to Fridtjof Brauns.

At least 19 recordsLinked to original sources

arXiv2026

Feedback-controlled mechanics of tissue vertex model: emergent soft elasticity and active yielding

Biological tissues exhibit diverse mechanical and rheological behaviors during morphogenesis. While much is known about tissue phase transitions controlled by structural order and cell mechanics, key questions regarding how tissue-scale nematic order emerges from cell-scale processes and influences tissue rheology remain unclear. Here, we develop a minimal vertex model that incorporates a coupling between active forces generated by cytoskeletal fibers and their alignment with local elastic stress in solid epithelial tissues. Combining theory and simulations, we show that this feedback loop induces an isotropic--nematic transition, leading to an ordered solid state that exhibits soft elasticity. Further increasing activity drives collective self-yielding, that is the ability to spontaneously transition form elastic to plastic deformations, with tissue flows that are correlated across the entire system. We argue that this remarkable state, that we dub plastic nematic solid, is uniquely suited to facilitate active tissue remodeling during morphogenesis. It fundamentally differs from the well-studied fluid regime where macroscopic elastic stresses vanish and the velocity correlations remain short-ranged. Altogether, our theoretical results reveal a rich spectrum of tissue states jointly governed by activity and passive cell deformability, with important implications for understanding tissue mechanics and morphogenesis.

cond-mat.soft↗

arXiv2026

Pattern Formation in Bioconvection of Thiovulum in a Hele-Shaw Chamber

This paper is associated with a video winner of a 2025 American Physical Society's Division of Fluid Dynamics (DFD) Gallery of Fluid Motion Award for work presented at the DFD Gallery of Fluid Motion. The original video is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2025.GFM.V045. We investigate bioconvection in a colony of Thiovulum sp. ST bacteria, a recently isolated enrichment culture, confined within a Hele-Shaw chamber. Driven by chemotactic and gravitactic responses, the cells collectively develop striking emergent patterns and convection-like dynamics. Starting from a dense, homogeneous suspension, the swimming bacteria generate large-scale bioconvective flows within minutes. Although these flows resemble thermal convection, they arise in the absence of an imposed temperature gradient. Instead, they arise from the collective swimming of bacteria responding to oxygen gradients and gravity.

physics.flu-dyn↗

arXiv2026

Tissue shape from cell-scale active tensions

Connecting cell behavior to tissue shape and mechanics is a key challenge in the physics of morphogenesis. Cytoskeletal turnover precludes a fixed reference state, and tensions are actively generated independently of strain; so conventional elasticity theory is not applicable. Here, we study epithelia governed by quasi-static force balance between intracellular pressure and internal, active tensions. This makes the tissue a distributed hydrostatic skeleton. Our theory starts from a set of prescribed active tensions. It treats cell interfaces as force dipoles whose embedding in physical space - the physical cell configuration - is constrained by force balance. To solve this constraint problem geometrically, we represent the tensions as a triangulation dual to the cell tiling. This allows us to use (and extend) the mathematics of discrete conformal geometry to link tensions to cell and tissue shape. Adiabatic changes of tensions cause changes in the physical configuration. Thus, rather than fluidizing, tissues can deform - or "morph" - while resisting external forces like a solid. This constitutes a form of emergent elasticity, mediated by two geometric soft modes. Importantly, tissue-scale stress depends on cell shape, but is independent of microscopic tension anisotropy, with consequences for experimental stress measurements and modeling mechanosensitive feedback loops. Discrete conformal geometry also allows us to analyze how cellular tension dynamics drive cell rearrangement, required for large plastic deformation. The unified description of emergent elasticity of epithelial tissues and their plastic morphing, driven by adiabatic tension dynamics and cell rearrangement, provides a foundation to better understand the role of mechanics in morphogenesis. Furthermore, we highlight connections to the mechanics of other amorphous materials, such as granular media.

cond-mat.soft↗

arXiv2026

Emergent Elasticity and Quasiconformal Flow in Active Solids

A constitutive relation between stress and strain relative to a reference state is the basic assumption of elasticity theory. However, in living matter, force generation is governed by motor molecule activity, which does not depend on deformation relative to a reference. A different approach is needed to describe how cells sculpt tissues through local active forces. We develop a theory of two-dimensional continuum mechanics where the active stress configuration, rather than a reference shape, is the fundamental input. Motivated by the Active Tension Network model for epithelia, we encode motor-driven forces between cells in a Riemannian tension metric. We derive a stress-metric relation for the macroscopic stress that results from embedding the tension manifold into physical space (defining cell positions). Despite the absence of constitutive laws, a stress-free reference state and an effective stress-strain relation arise from the tension metric, making the system an effectively elastic active solid. Moving from statics to dynamics, our framework describes how an active solid can morph its shape through adiabatic dynamics of active stress. To capture large, plastic deformations through cell rearrangement, we introduce a second metric that geometrizes the cell network topology. Topological rearrangement appears as a continuous reparametrization of the tension manifold. This mathematical framework, based on Riemannian geometry, isothermal coordinates, and quasi-conformal flows, quantitatively predicts how local contractile activity determines large-scale shape and provides a principled continuum description of active plasticity. A companion paper validates the continuum analysis through coarse-graining of discrete cell networks. Our theory identifies a geometric origin of emergent elasticity and plasticity in living matter and, more broadly, in active and granular materials.

cond-mat.soft↗

arXiv2026

Proliferating Nematic That Collectively Senses an Anisotropic Substrate

Motivated by recent experiments on growing fibroblasts, we examine the development of nematic order in a colony of elongated cells proliferating on a nematic elastomer substrate. After sparse seeding, the cells divide and grow into locally ordered, but randomly oriented, domains that then interact with each other and the substrate. Global alignment with the substrate is only achieved above a critical density, suggesting a collective mechanism for the sensing of substrate anisotropy. The system jams at high density, where both reorientation and proliferation stop. Using a continuum model of a proliferating nematic liquid crystal, we examine the competition between growth-driven alignment and substrate-driven alignment in controlling the density and structure of the final jammed state. We propose that anisotropic traction forces and the tendency of cells to align perpendicular to the direction of density gradients act in concert to provide a mechanism for collective cell alignment.

cond-mat.soft↗

arXiv2025

Active assembly and non-reciprocal dynamics of elastic membranes

Equilibrium self-assembly and conventional materials processing techniques fall far short of mimicking dynamic self-actuating processes that are commonplace throughout biology. To bridge the gap between living and synthetic matter, we study adhesive non-thermal fibers immersed in an active fluid. Autonomous chaotic flows power non-equilibrium fiber dynamics, inducing their collisions, generating connections, and weaving a membrane-shaped elastic network. This active assembly generates a hierarchy of shapes, structures, and dynamical processes spanning nanometers to centimeters. Ultimately, it generates an active membrane that exhibits global limit cycles induced by a non-reciprocal coupling between the elastic membrane deformations and the alignment axis of the polar active fluid. Our work merges self-assembly with active matter, demonstrating self-processing materials wherein hierarchical life-like structures and dynamics emerge from an initially structureless suspension.

cond-mat.soft↗

arXiv2025

Active Solids: Topological Defect Self-Propulsion Without Flow

The self-propulsion of +1/2 topological defects is a hallmark of active nematic fluids, where the defects are advected by the flow field they themselves generate. In this paper we propose a minimal model for defect self-propulsion in a nematic active solid: a linear elastic medium with an embedded nematic texture that generates active stress and associated elastic strains. We show that such coupling gives rise to self-propelled +1/2 defects that move relative to the elastic medium by local remodeling of the nematic texture without advection. This mechanism is fundamentally different from the fluid case and can lead to unbinding of defect pairs and stabilization of +1 defects. Our findings might help explain how orientational order, of, for example, muscle fibers, is reconfigured during morphogenesis in solid-like tissues. The proposed mechanism may, for instance, control motility and merging of +1/2 defects, which play a crucial role in setting up the body axis during Hydra regeneration.

cond-mat.soft↗

arXiv2025

Topology and Kinetic Pathways of Colloidosome Assembly and Disassembly

Liquid shells, such as lipid vesicles and soap bubbles, are ubiquitous throughout biology, engineered matter, and everyday life. Their creation and disintegration are defined by a singularity that separates a topologically distinct extended liquid film from a boundary-free closed shell. Such topology-changing processes are essential for cellular transport and drug delivery. However, their studies are challenging because of the rapid dynamics and small length scale of conventional lipid vesicles. We develop fluid colloidosomes, micron-sized analogs of lipid vesicles. We study their stability close to their disk-to-sphere topological transition. Intrinsic colloidal length and time scales slow down the dynamics to reveal vesicle conformations in real time during their assembly and disassembly. Remarkably, the lowest-energy pathway by which a closed vesicle transforms into a disk involves a topologically distinct cylinder-like intermediate. These results reveal universal aspects of topological changes in all liquid shells and a robust platform for the encapsulation, transport, and delivery of nanosized cargoes.

cond-mat.soft↗

arXiv2024

The 2024 Motile Active Matter Roadmap

Activity and autonomous motion are fundamental aspects of many living and engineering systems. Here, the scale of biological agents covers a wide range, from nanomotors, cytoskeleton, and cells, to insects, fish, birds, and people. Inspired by biological active systems, various types of autonomous synthetic nano- and micromachines have been designed, which provide the basis for multifunctional, highly responsive, intelligent active materials. A major challenge for understanding and designing active matter is their inherent non-equilibrium nature due to persistent energy consumption, which invalidates equilibrium concepts such as free energy, detailed balance, and time-reversal symmetry. Furthermore, interactions in ensembles of active agents are often non-additive and non-reciprocal. An important aspect of biological agents is their ability to sense the environment, process this information, and adjust their motion accordingly. It is an important goal for the engineering of micro-robotic systems to achieve similar functionality. With many fundamental properties of motile active matter now reasonably well understood and under control, the ground is prepared for the study of physical aspects and mechanisms of motion in complex environments, of the behavior of systems with new physical features like chirality, of the development of novel micromachines and microbots, of the emergent collective behavior and swarming of intelligent self-propelled particles, and of particular features of microbial systems. The vast complexity of phenomena and mechanisms involved in the self-organization and dynamics of motile active matter poses major challenges, which can only be addressed by a truly interdisciplinary effort involving scientists from biology, chemistry, ecology, engineering, mathematics, and physics.

cond-mat.soft↗

arXiv2024

A Geometric Tension Dynamics Model of Epithelial Convergent Extension

Convergent extension of epithelial tissue is a key motif of animal morphogenesis. On a coarse scale, cell motion resembles laminar fluid flow; yet in contrast to a fluid, epithelial cells adhere to each other and maintain the tissue layer under actively generated internal tension. To resolve this apparent paradox, we formulate a model in which tissue flow in the tension-dominated regime occurs through adiabatic remodeling of force balance in the network of adherens junctions. We propose that the slow dynamics within the manifold of force-balanced configurations is driven by positive feedback on myosin-generated cytoskeletal tension. Shifting force balance within a tension network causes active cell rearrangements (T1 transitions) resulting in net tissue deformation oriented by initial tension anisotropy. Strikingly, we find that the total extent of tissue deformation depends on the initial cellular packing order. T1s degrade this order so that tissue flow is self-limiting. We explain these findings by showing that coordination of T1s depends on coherence in local tension configurations, quantified by a geometric order parameter in tension space. Our model reproduces the salient tissue- and cell-scale features of germ band elongation during Drosophila gastrulation, in particular the slowdown of tissue flow after approximately twofold longation concomitant with a loss of order in tension configurations. This suggests local cell geometry contains morphogenetic information and yields experimentally testable predictions. Defining biologically controlled active tension dynamics on the manifold of force-balanced states may provide a general approach to the description of morphogenetic flow.

physics.bio-ph↗

arXiv2024

A Mean-Field Model for Active Plastic Flow of Epithelial Tissue

Animal morphogenesis often involves significant shape changes of epithelial tissue sheets. Great progress has been made in understanding the underlying cellular driving forces and their coordination through biomechanical feedback loops. However, quantitative understanding of how cell-level dynamics translate into large-scale morphogenetic flows remains limited. A key challenge is finding the relevant macroscopic variables (order parameters) that retain the essential information about cell-scale structure. To address this challenge, we combine symmetry arguments with a stochastic mean-field model that accounts for the relevant microscopic dynamics. Complementary to previous work on the passive fluid- and solid-like properties of tissue, we focus on the role of actively generated internal stresses. Centrally, we use the timescale separation between elastic relaxation and morphogenetic dynamics to describe tissue shape change in quasi-static balance of forces within the tissue sheet. The resulting geometric structure - a triangulation in tension space dual to the polygonal cell tiling - proves ideal for developing a mean-field model. All parameters of the coarse-grained model are calculated from the underlying microscopic dynamics. Centrally, the model explains how active plastic flow driven by autonomous active cell rearrangements becomes self-limiting as previously observed in experiments and simulations. Additionally, the model quantitatively predicts tissue behavior when coupled with external fields, such as planar cell polarity and external forces. We show how such fields can sustain oriented active cell rearrangements and thus overcome the self-limited character of purely autonomous active plastic flow. These findings demonstrate how local self-organization and top-down genetic instruction together determine internally-driven tissue dynamics.

cond-mat.soft↗

arXiv2024

Learning a conserved mechanism for early neuroectoderm morphogenesis

Morphogenesis is the process whereby the body of an organism develops its target shape. The morphogen BMP is known to play a conserved role across bilaterian organisms in determining the dorsoventral (DV) axis. Yet, how BMP governs the spatio-temporal dynamics of cytoskeletal proteins driving morphogenetic flow remains an open question. Here, we use machine learning to mine a morphodynamic atlas of Drosophila development, and construct a mathematical model capable of predicting the coupled dynamics of myosin, E-cadherin, and morphogenetic flow. Mutant analysis shows that BMP sets the initial condition of this dynamical system according to the following signaling cascade: BMP establishes DV pair-rule-gene patterns that set-up an E-cadherin gradient which in turn creates a myosin gradient in the opposite direction through mechanochemical feedbacks. Using neural tube organoids, we argue that BMP, and the signaling cascade it triggers, prime the conserved dynamics of neuroectoderm morphogenesis from fly to humans.

physics.bio-ph↗

arXiv2024

Nonreciprocal pattern formation of conserved fields

In recent years, nonreciprocally coupled systems have received growing attention. Previous work has shown that the interplay of nonreciprocal coupling and Goldstone modes can drive the emergence of temporal order such as traveling waves. We show that these phenomena are generically found in a broad class of pattern-forming systems, including mass-conserving reaction--diffusion systems and viscoelastic active gels. All these systems share a characteristic dispersion relation that acquires a non-zero imaginary part at the edge of the band of unstable modes and exhibit a regime of propagating structures (traveling wave bands or droplets). We show that models for these systems can be mapped to a common "normal form" that can be seen as a spatially extended generalization of the FitzHugh--Nagumo model, providing a unifying dynamical-systems perspective. We show that the minimal nonreciprocal Cahn--Hilliard (NRCH) equations exhibit a surprisingly rich set of behaviors, including interrupted coarsening of traveling waves without selection of a preferred wavelength and transversal undulations of wave fronts in two dimensions. We show that the emergence of traveling waves and their speed are precisely predicted from the local dispersion relation at interfaces far away from the homogeneous steady state. Our work thus generalizes previously studied nonreciprocal phase transitions and shows that interfaces are the relevant collective excitations governing the rich dynamical patterns of conserved fields.

nlin.PS↗

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↗

arXiv2023

Patterning of morphogenetic anisotropy fields

Orientational order, encoded in anisotropic fields, plays an important role during the development of an organism. A striking example of this is the freshwater polyp Hydra, where topological defects in the muscle fiber orientation have been shown to localize to key features of the body plan. This body plan is organized by morphogen concentration gradients, raising the question how muscle fiber orientation, morphogen gradients and body shape interact. Here, we introduce a minimal model that couples nematic orientational order to the gradient of a morphogen field. We show that on a planar surface alignment to a radial concentration gradient can induce unbinding of topological defects, as observed during budding and tentacle formation in Hydra, and stabilize aster/vortex-like defects, as observed at a Hydra's mouth. On curved surfaces mimicking the morphologies of Hydra in various stages of development -- from spheroid to adult -- our model reproduces the experimentally observed reorganization of orientational order. Our results suggest how gradient alignment and curvature effects may work together to control orientational order during development and lays the foundations for future modeling efforts that will include the tissue mechanics that drive shape deformations.

physics.bio-ph↗

arXiv2022

Bridging scales in a multiscale pattern-forming system

Self-organized pattern formation is vital for many biological processes. Reaction-diffusion models have advanced our understanding of how biological systems develop spatial structures, starting from homogeneity. However, biological processes inherently involve multiple spatial and temporal scales and transition from one pattern to another over time, rather than progressing from homogeneity to a pattern. To deal with such multiscale systems, coarse-graining methods are needed that allow the dynamics to be reduced to the relevant degrees of freedom at large scales, but without losing information about the patterns at the small scales. Here, we present a semi-phenomenological approach which exploits mass-conservation in pattern formation, and enables to reconstruct information about patterns from the large-scale dynamics. The basic idea is to partition the domain into distinct regions (coarse-grain) and determine instantaneous dispersion relations in each region, which ultimately inform about local pattern-forming instabilities. We illustrate our approach by studying the Min system, a paradigmatic model for protein pattern formation. By performing simulations, we first show that the Min system produces multiscale patterns in a spatially heterogeneous geometry. This prediction is confirmed experimentally by in vitro reconstitution of the Min system. Using a recently developed theoretical framework for mass-conserving reaction-diffusion systems, we show that the spatiotemporal evolution of the total protein densities on large-scales reliably predicts the pattern-forming dynamics. Our approach provides an alternative and versatile theoretical framework for complex systems where analytical coarse-graining methods are not applicable, and can in principle be applied to a wide range of systems with an underlying conservation law.

physics.bio-ph↗

arXiv2021

Length Regulation Drives Self-Organization in Filament-Motor Mixtures

Cytoskeletal networks form complex intracellular structures. Here we investigate a minimal model for filament-motor mixtures in which motors act as depolymerases and thereby regulate filament length. Combining agent-based simulations and hydrodynamic equations, we show that resource-limited length regulation drives the formation of filament clusters despite the absence of mechanical interactions between filaments. Even though the orientation of individual remains fixed, collective filament orientation emerges in the clusters, aligned orthogonal to their interfaces.

physics.bio-ph↗

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↗