Related papers: A coupled bulk-surface model for cell polarisation
Collective cell migration is a key driver of embryonic development, wound healing, and some types of cancer invasion. Here we provide a physical perspective of the mechanisms underlying collective cell migration. We begin with a catalogue…
We apply the cell merging method to a model shallow water problem with a permeable boundary. We use a cut cell approach which is more easily and systematically scalable with different shapes of boundaries. The novel cell merging method…
Blebs are cell protrusions generated by local membrane-cortex detachments followed by expansion of the plasma membrane. Blebs are formed by some migrating cells, for example primordial germ cells of the zebrafish. While blebs occur randomly…
A class of coupled cell-bulk ODE-PDE models is formulated and analyzed in a two-dimensional domain, which is relevant to studying quorum sensing behavior on thin substrates. In this model, spatially segregated dynamically active signaling…
We present a model, based on symmetry and geometry, for proteins. Using elementary ideas from mathematics and physics, we derive the geometries of discrete helices and sheets. We postulate a compatible solvent-mediated emergent pairwise…
This paper introduces novel bulk-surface splitting schemes of first and second order for the wave equation with kinetic and acoustic boundary conditions of semi-linear type. For kinetic boundary conditions, we propose a reinterpretation of…
In the modern theory of polarization, polarization itself is given by a geometric phase. In calculations for interacting systems the polarization and its variance are obtained from the polarization amplitude. We interpret this quantity as a…
Diffusion-driven patterns appear on curved surfaces in many settings, initiated by unstable modes of an underlying Laplacian operator. On a flat surface or perfect sphere, the patterns are degenerate, reflecting translational/rotational…
Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck scale, one of the many problems one has to face in this enterprise is to find the…
This paper introduces a novel approach for the construction of bulk--surface splitting schemes for semi-linear parabolic partial differential equations with dynamic boundary conditions. The proposed construction is based on a reformulation…
The evolution, regulation and sustenance of biological complexity is determined by protein-protein interaction network that is filled with dynamic events. Recent experimental evidences point out that clustering of proteins has a vital role…
Recent advances in microscopy and 3D reconstruction methods have allowed for characterization of cellular morphology in unprecedented detail, including the irregular geometries of intracellular subcompartments such as membrane-bound…
Understanding how fluctuations propagate across spatial scales is central to our understanding of inanimate matter from turbulence to critical phenomena. In contrast to physical systems, biological systems are organized into a hierarchy of…
Recently, we have used, pulsar polarisation datasets, on circular polarisation degree & linear polarisation position angle, to relate with well established theories, on ellipticity parameter and linear polarisation position angles, accrued…
The point-curvature model for membrane protein inclusions is shown to capture multibody interactions very well. Using this model, we find that the interplay between membrane tension and multibody interactions results in a collective…
Active Brownian particles (ABPs) serve as a minimal model of active matter systems. When ABPs are sufficiently persistent, they undergo a liquid-gas phase separation and, in the presence of obstacles, accumulate around them, forming a…
Cell adhesion proteins are transmembrane proteins that bind cells to their environment. These proteins typically cluster into disk-shaped or linear structures. Here we show that such clustering patterns spontaneously emerge when the protein…
Active-particle suspensions exhibit distinct polarization-density patterns in activity landscapes, even without anisotropic particle interactions. Such polarization without alignment forces is at work in motility-induced phase separation…
We review the theoretical analyses and simulations of the interactions between curvature-inducing proteins and biomembranes. Laterally isotropic proteins induce spherical budding, whereas anisotropic proteins, such as Bin/Amphiphysin/Rvs…
We present initial results regarding the existence, stability and interaction of linear and nonlinear vibrational modes in a system of two coupled, one dimensional lattices with unequal numbers of masses. The effects on these nonlinear…