arXiv subjects

Andreas Buttenschön

Publications and source records attributed to Andreas Buttenschön.

10 recordsLinked to original sources

arXiv2026

Clustering versus sorting: a mass-conserving reaction-diffusion model of planar polarity puncta

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.

q-bio.SC↗

arXiv2026

Directional bias of a single polarized cell under confinement

Chiral patterns have been observed in various processes from swirling bacterial colonies to tissue morphogenesis and cytoskeletal organization, yet the physical mechanisms underlying chiral cell motion remain poorly understood. Motivated by experiments demonstrating directional bias in the circular motion of confined cells, we use the tools of dynamical systems analysis with computer simulations to identify minimal intrinsic and extrinsic mechanisms capable of generating persistent biased migration. The dynamical systems framework reveals a common organizing principle: directional bias emerges through changes in the stability and/or basins of attraction of the clockwise and counter-clockwise motility states. We find four distinct routes to such bias. First, intrinsic torque in a polarized cytoskeleton can be spatially integrated to produce biased circular motion. Second, anisotropic cell-substrate friction can generate directional preference when reduced friction along the polarity axis is coupled to a directional offset. Third, a chiral wall-alignment response can also produce a persistent directional preference. Finally, substrate patterns that break mirror symmetry, such as dextral or sinistral ridges and troughs, can likewise bias rotational direction. Together, these mechanisms yield distinct, testable predictions and suggest a unifying lens for experimental interrogation of cellular chirality and the design of synthetic systems with programmable chiral motion.

physics.bio-ph↗

arXiv2026

Competing forces of polarization and adhesion generate directional migration bias in a minimal model

Left-right axis specification establishes embryonic laterality through asymmetric signaling cascades originating at the cellular scale. We previously reported the presence of a directionality bias in confined pairs of endothelial (and fibroblast) cells exhibiting persistent circular motion, with cytoskeletal contractility modulating the direction. The relative simplicity of the experimental setup makes it a perfect testing ground for the physical forces that could endow this system with a tunable directional migration bias. We model self-propelling biological cells migrating in response to confinement, polarity, and pairwise repulsive forces. Our framework reproduces three key experimental observations: spontaneous coherent circular movement of confined cell pairs, emergence of directional bias when cells have asymmetric properties, and contractility-modulated switching of the rotation direction. Two key assumptions are required: an internal torque arising from cytoskeletal organization (previously observed in other cellular systems), and an asymmetric polarity response between cells, which introduces a difference in how quickly each cell reorients its migration direction. New experiments on daughter cell pairs support this asymmetry requirement in cellular properties. Tuning the polarity response timescale (or strength) relative to centering forces from confinement and cell-cell adhesion can amplify or reverse the directional migration bias.

q-bio.CB↗

arXiv2026

Support Graph Preconditioners for Off-Lattice Cell-Based Models

Off-lattice agent-based models (or cell-based models) of multicellular systems are increasingly used to create in-silico models of in-vitro and in-vivo experimental setups of cells and tissues, such as cancer spheroids, neural crest cell migration, and liver lobules. These applications, which simulate thousands to millions of cells, require robust and efficient numerical methods. At their core, these models necessitate the solution of a large friction-dominated equation of motion, resulting in a sparse, symmetric, and positive definite matrix equation. The conjugate gradient method is employed to solve this problem, but this requires a good preconditioner for optimal performance. In this study, we develop a graph-based preconditioning strategy that can be easily implemented in such agent-based models. Our approach centers on extending support graph preconditioners to block-structured matrices. We prove asymptotic bounds on the condition number of these preconditioned friction matrices. We then benchmark the conjugate gradient method with our support graph preconditioners and compare its performance to other common preconditioning strategies.

math.NA↗

arXiv2024

How cells stay together; a mechanism for maintenance of a robust cluster explored by local and nonlocal continuum models

Formation of organs and specialized tissues in embryonic development requires migration of cells to specific targets. In some instances, such cells migrate as a robust cluster. We here explore a recent local approximation of nonlocal continuum models by Falcó, Baker, and Carrillo (2023). We apply their theoretical results by specifying biologically-based cell-cell interactions, showing how such cell communication results in an effective attraction-repulsion Morse potential. We then explore the clustering instability, the existence and size of the cluster, and its stability. We also extend their work by investigating the accuracy of the local approximation relative to the full nonlocal model.

q-bio.CB↗

arXiv2020

Bridging from single to collective cell migration: A review of models and links to experiments

Mathematical and computational models can assist in gaining an understanding of cell behavior at many levels of organization. Here, we review models in the literature that focus on eukaryotic cell motility at 3 size scales: intracellular signaling that regulates cell shape and movement, single cell motility, and collective cell behavior from a few cells to tissues. We survey recent literature to summarize distinct computational methods (phase-field, polygonal, Cellular Potts, and spherical cells). We discuss models that bridge between levels of organization, and describe levels of detail, both biochemical and geometric, included in the models. We also highlight links between models and experiments. We find that models that span the 3 levels are still in the minority.

q-bio.CB↗

arXiv2020

Adhesion-driven patterns in a calcium-dependent model of cancer cell movement

Cancer cells exhibit increased motility and proliferation, which are instrumental in the formation of tumours and metastases. These pathological changes can be traced back to malfunctions of cellular signalling pathways, and calcium signalling plays a prominent role in these. We formulate a new model for cancer cell movement which for the first time explicitly accounts for the dependence of cell proliferation and cell-cell adhesion on calcium. At the heart of our work is a non-linear, integro-differential (non-local) equation for cancer cell movement, accounting for cell diffusion, advection and proliferation. We also employ an established model of cellular calcium signalling with a rich dynamical repertoire that includes experimentally observed periodic wave trains and solitary pulses. The cancer cell density exhibits travelling fronts and complex spatial patterns arising from an adhesion-driven instability (ADI). We show how the different calcium signals and variations in the strengths of cell-cell attraction and repulsion shape the emergent cellular aggregation patterns, which are a key component of the metastatic process. Performing a linear stability analysis, we identify parameter regions corresponding to ADI. These regions are confirmed by numerical simulations, which also reveal different types of aggregation patterns and these patterns are significantly affected by \ca. Our study demonstrates that the maximal cell density decreases with calcium concentration, while the frequencies of the calcium oscillations and the cell density oscillations are approximately equal in many cases. Furthermore, as the calcium levels increase the speed of the travelling fronts increases, which is related to a higher cancer invasion potential. These novel insights provide a step forward in the design of new cancer treatments that may rely on controlling the dynamics of cellular calcium.

q-bio.CB↗

arXiv2020

Non-Local Cell Adhesion Models: Steady States and Bifurcations

In this manuscript, we consider the modelling of cellular adhesions, which is a key interaction between biological cells. Continuum models of the diffusion-advection-reaction type have long been used in tissue modelling. In 2006, Armstrong, Painter, and Sherratt proposed an extension to take adhesion effects into account. The resulting equation is a non-local advection-diffusion equation. While immensely successful in applications, the development of mathematical theory pertaining to steady states and pattern formation is lacking. The mathematical analysis of the non-local adhesion model is challenging. In this monograph, we contribute to the analysis of steady states and their bifurcation structure. The importance of steady-states is that these are the patterns observed in nature and tissues (e.g. cell-sorting experiments). In the case of periodic boundary conditions, we combine global bifurcation results pioneered by Rabinowitz, equivariant bifurcation theory, and the mathematical properties (maximum principle) of the non-local term to obtain a global bifurcation result for the branches of non-trivial solutions.

math.AP↗

arXiv2019

Cell size, mechanical tension, and GTPase signaling in the Single Cell

Cell polarization requires redistribution of specific proteins to the nascent front and back of a eukarytotic cell. Among these proteins are Rac and Rho, members of the small GTPase family that regulate the actin cytoskeleton. Rac promotes actin assembly and protrusion of the front edge, whereas Rho activates myosin-driven contraction at the back. Mathematical models of cell polarization at many levels of detail have appeared. One of the simplest based on "wave-pinning", consists of a pair of reaction-diffusion equations for a single GTPase. Mathematical analysis of wave-pinning so far is largely restricted to static domains in one spatial dimension. Here we extend the analysis to cells that change in size, showing that both shrinking and growing cells can lose polarity. We further consider the feedback between mechanical tension, GTPase activation, and cell deformation in both static, growing, shrinking, and moving cells. Special cases (spatially uniform cell chemistry, absence or presence of mechanical feedback) are analyzed, and the full model is explored by simulations in 1D. We find a variety of novel behaviors, including "dilution-induced" oscillations of Rac activity and cell size, as well as gain or loss of polarization and motility in the model cell.

q-bio.CB↗

arXiv2019

Nonlocal Adhesion Models for Microorganisms on Bounded Domains

In 2006 Armstrong, Painter and Sherratt formulated a non-local differential equation model for cell-cell adhesion. For the one dimensional case we derive various types of adhesive, repulsive, and no-flux boundary bonditions. We prove local and global existence and uniqueness for the resulting integro-differential equations. In numerical simulations we consider adhesive, repulsive and neutral boundary conditions and we show that the solutions mimic known behavior of fluid adhesion to boundaries. In addition, we observe interior pattern formation due to cell-cell adhesion.

math.AP↗