A PDE model for bleb formation and interaction with linker proteins

Abstract

The aim of this paper is to further develop mathematical models for bleb formation in cells, including cell-membrane interactions with linker proteins. This leads to nonlinear reaction-diffusion equations on a surface coupled to fluid dynamics in the bulk. We provide a detailed mathematical analysis and investigate some singular limits of the model, connecting it to previous literature. Moreover, we provide numerical simulations in different scenarios, confirming that the model can reproduce experimental results on bleb initation. Cell blebbing, Surface PDEs, Fluid-Structure Interaction, Free Boundary Problems. T for the symmetrised gradient. The set of k-times, k ≥ 0, weak differentiable, X-valued functions, where X is a vector space, on some open set Ω ⊆ R 3 is H k (Ω, X). We will also employ the subspaces of mean-value-free functions:of functions with time-constant mean value:T ∈ [0, ∞), of solenoidals functions:, and the traces of solenoidal functions:

A Diffuse Interface Model for Cell Blebbing Including Membrane-Cortex Coupling with Linker Dynamics

“…for ϑ 1 has been used in [40] as a continuous interpolation. Going from sharp to diffuse, we only need to introduce a weight under the integral ˆΓ ω (x, y, ν Σ ) r(x, y) dH 2 (y) −→ ˆΩ δ ε [φ] ω (x, y, ν ψ ) r(x, y) dL 3 (y).…”

“…In this work, we do not deal with this phase in the process of cell blebbing: our model targets the process after bleb site selection and is aimed at investigating the mechanics of bleb formation. Previous works on this topic are, e.g., [23,36,35,5,4,34,40]. Lim et al [23] present a onedimensional model focusing on bending and surface energy of the membrane and include another important energy for the influence of so-called linker proteins (see below) that also play a role in the development of membrane protrusions.…”

A Finite Element Method for a Fourth Order Surface Equation With Application to the Onset of Cell Blebbing

“…Thanks to the regularity assumption (35), the properties of the Ritz projection (Lemma 3.4), and the properties of the lift (Lemma 3.2) error bounds for the projection errors are straightforward:…”

“…The assumption of a constant k l , which corresponds to a homogeneous linker, is a simplification. The cell usually is able to control the density and, thus, the local effective linker strength by its biochemistry [35]. We briefly report on a way to account for membranebound biochemistry in section 5.5.…”

3D Computational Modeling of Bleb Initiation Dynamics

“…Although this model included membrane-cortex adhesion dynamics, the membrane was assumed to be axisymmetric and the cortex was fixed in space. A model of bleb expansion that included reaction-diffusion of membrane-cortex adhesion proteins with limited membrane deformation was presented in [24]. Lastly, a full 3D model of bleb expansion with a viscous fluid cytoplasm (an extension of the model in [7]) was presented in [25] to illustrate a numerical method for computing forces on an elastic shell using the immersed boundary method [26].…”