arXiv subjects

Benjamin Winkler

Publications and source records attributed to Benjamin Winkler.

3 recordsLinked to original sources

arXiv2026

A simple model for conserved intracellular dynamics exhibits multiscale pattern formation, traveling protein domains and arrested coarsening of lipid domains

We model the spatiotemporal dynamics of cellular protein concentrations relevant to cell polarity near membranes composed of different lipids. Therefore, we consider a three-variable continuum model for membrane-bound protein, cytosolic protein, and the local composition of a binary lipid membrane. The model contains two globally conserved quantities: the total protein content and the average fractions of the two lipid species. It combines a conserved reaction-diffusion model for the protein dynamics, undergoing an active phase separation, with a Cahn-Hilliard equation for lipid demixing. Linear stability analysis of the homogeneous steady state and direct numerical simulations show that the lipid dynamics undergoes classical phase separation, whereas the protein dynamics exhibits oscillatory phase separation for intermediate total protein contents, associated with a long-wavelength instability and traveling domains. In parameter regions where both instabilities are present, we find multiscale patterns with larger-scale traveling and rotating protein domains coexisting with smaller-scale stationary lipid domains. In this regime, traveling protein domains coexist with arrested coarsening of stationary lipid domains above a critical coupling. We further show that the main instabilities and phase diagram are well captured by an extension of a recently proposed conserved FitzHugh-Nagumo model for non-reciprocal pattern formation. The extended model consists of two non-reciprocally coupled Cahn-Hilliard equations with different interface tensions, reflecting the distinct physical properties of lipids and proteins. This also explains the observed asymmetry between static lipid patterns and traveling protein patterns.

cond-mat.soft↗

arXiv2023

Physical phase field model for phagocytosis

We propose and study a simple, physical model for phagocytosis, i.e. the active, actin-mediated uptake of micron-sized particles by biological cells. The cell is described by the phase field method and the driving mechanisms of uptake are actin ratcheting, modeled by a dynamic vector field, as well as cell-particle adhesion due to receptor-ligand binding. We first test the modeling framework for the symmetric situation of a spherical cell engulfing a fixed spherical particle. We then exemplify its versatility by studying various asymmetric situations like different particle shapes and orientations, as well as the simultaneous uptake of two particles. In addition, we perform a perturbation theory of a slightly modified model version in the symmetric setting, allowing to derive a reduced model, shedding light on the effective driving forces and being easier to solve. This work is meant as a first step in describing phagocytosis and we discuss several effects that are amenable to future modeling within the same framework.

cond-mat.soft↗

arXiv2015

Membrane tension feedback on shape and motility of eukaryotic cells

In the framework of a phase field model of a single cell crawling on a substrate, we investigate how the properties of the cell membrane affect the shape and motility of the cell. Since the membrane influences the cell dynamics on multiple levels and provides a nontrivial feedback, we consider the following fundamental interactions: (i) the reduction of the actin polymerization rate by membrane tension; (ii) area conservation of the cell's two-dimensional cross-section vs. conservation of its circumference (i.e. membrane inextensibility); and (iii) the contribution from the membrane's bending energy to the shape and integrity of the cell. As in experiments, we investigate two pertinent observables -- the cell's velocity and its aspect ratio. We find that the most important effect is the feedback of membrane tension on the actin polymerization. Bending rigidity has only minor effects, visible mostly in dynamic reshaping events, as exemplified by collisions of the cell with an obstacle.

cond-mat.soft↗