arXiv subjects

Nikolas H. Claussen

Publications and source records attributed to Nikolas H. Claussen.

4 recordsLinked to original sources

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↗

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↗