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Cellular membranes exhibit a large variety of shapes, strongly coupled to their function. Many biological processes involve dynamic reshaping of membranes, usually mediated by proteins. This interaction works both ways: while proteins…
In multicellular organisms, relations among parts and between parts and the whole are contextual and interdependent. These organisms and their cells are ontogenetically linked: an organism starts as a cell that divides producing…
The hydrodynamic theory of heterogeneous fluid membranes is extended to the case of a membrane adjacent to a solid substrate. We derive the coupling diffusion coefficients of pairs of membrane inclusions in the limit of large separation…
In order to describe two-dimensionally packed cells in epithelial tissues both mathematically and physically, there have been developed several sorts of geometrical models, such as the vertex model, the finite element model, the…
Predictive modeling of the evolutionary dynamics of cancer is a challenge issue in computational cancer biology. In this paper, we propose a general mathematical model framework for the evolutionary dynamics of cancer with plasticity and…
Active contributions to fluctuations are a direct consequence of metabolic energy consumption in living cells. Such metabolic processes continuously create active forces, which deform the membrane to control motility, proliferation as well…
The dynamics of a membrane coupled to an active fluid on top of a substrate is considered theoretically. It is assumed that the director field of the active fluid has rotational symmetry in the membrane plane. This situation is likely to be…
A motile cell, when stimulated, shows a dramatic increase in the activity of its membrane, manifested by the appearance of dynamic membrane structures such as lamellipodia, filopodia and membrane ruffles. The external stimulus turns on…
We study the dynamics of orientational phase ordering in fluid membranes. Through numerical simulation we find an unusually slow coarsening of topological texture, which is limited by subdiffusive propagation of membrane curvature. The…
Membrane computing is a well-established and successful research field which belongs to the more general area of molecular computing. Membrane computing aims at defining parallel and non-deterministic computing models, called membrane…
We present a general and systematic theory of non-equilibrium dynamics of multi-component fluid membranes, in general, and membranes containing transmembrane proteins, in particular. Developed based on a minimal number of principles of…
The quantitative understanding of membranes is still rooted in work performed in the 1970s by Helfrich and others, concerning amphiphilic bilayers. However, most biological membranes contain a wide variety of nonamphiphilic molecules too.…
A geometrically exact membrane formulation is presented that is based on curvilinear coordinates and isogeometric finite elements, and is suitable for both solid and liquid membranes. The curvilinear coordinate system is used to describe…
Many fundamental biological processes are dependent on cellular migration. Although the mechanical mechanisms of single-cell migration are relatively well understood, those underlying migration of multiple cells adhered to each other in a…
This work aims to describe a mathematical model and a numerical method to simulate a thin anisotropic composite membrane moving and deforming in 3D space under a dynamic load of an arbitrary time and space profile. The model and the method…
Biological membranes are host to proteins and molecules which may form domain-like structures resulting in spatially-varying material properties. Vesicles with such heterogeneous membranes can exhibit intricate shapes at equilibrium and…
How far is neuroepithelial cell proliferation in the developing central nervous system a deterministic process? Or, to put it in a more precise way, how accurately can it be described by a deterministic mathematical model? To provide tracks…
Measurements of lateral diffusion of proteins in a membrane typically assume that the movement of the protein occurs in a flat plane. Real membranes, however, are subject to thermal fluctuations, leading to movement of an inclusion into the…
Diffusion rates through a membrane can be asymmetric, if the diffusing particles are spatially extended and the pores in the membrane have asymmetric structure. This phenomenon is demonstrated here via a deterministic simulation of a…
Transmembrane ion flow through channel proteins undergoing density fluctuations may cause lateral gradients of the electrical potential across the membrane giving rise to electrophoresis of charged channels. A model for the dynamics of the…