The size, shape, and dynamics of cellular blebs

A cellular bleb grows when a portion of the cell membrane detaches from the underlying cortex under the influence of a cytoplasmic pressure. We develop a quantitative model for the growth and dynamics of these objects in a simple two-dimensional setting. In particular, we first find the minimum cytoplasmic pressure and minimum unsupported membrane length for a stationary bleb to nucleate and grow as a function of the membrane-cortex adhesion. We next show how a bleb may travel around the periphery of the cell when the cytoplasmic pressure varies in space and time in a prescribed way and find that the traveling speed is governed by the speed of the pressure change induced by local cortical contraction while the shape of the traveling bleb is governed by the speed of cortical healing. Finally, we relax the assumption that the pressure change is prescribed and couple it hydrodynamically to the cortical contraction and membrane deformation. By quantifying the phase space of bleb formation and dynamics, our framework serves to delineate the range and scope of bleb-associated cell motility. Copyright c © EPLA, 2012 Introduction. – Blebs are protrusions of a cell membrane driven by local variations in intracellular pressure induced by contractility and are commonly seen in many types of cells. Blebbing is closely related to an elementary mechanical process —the formation of a blister in a thin film adherent to a substrate, but also rather different in that it involves a number of active processes: active (and regulated) contractile stresses that drive the process, as well as active mechanisms associated with bleb healing via forces at the boundary. Cellular blebbing is an important mechanism contributing to apoptosis, cytokinesis, and cell motility in normal and pathological/cancer cells [1–6]. In the context of motility, recent experiments [7,8] on various cell types show that blebs arise as a result of homogenous intracellular pressure change coupled with a global contraction of the entire cytoskeleton. It has been further suggested that bleb protrusions can cooperate with lamellipodium-based protrusions to power cell motility [2,5], and cells can switch between different motility modes depending on their environment [4,6,9,10]. Thus the focus on actin (a)E-mail: [email protected] (corresponding author) polymerization-driven protrusions in lamellipodia and filopodia on cell motility must be complemented by considerations of contractility/pressure induced blebbing before one can determine the relative contributions of these modes for whole cell motility. Understanding blebbing quantitatively is a first step in this process. While there have been some previous theoretical studies [11,12] on aspects of blebbing such as for formation time or growth, here we focus on a synthetic approach that accounts for the nucleation, expansion, retraction, and large scale movements of blebs, with the aim of providing a qualitative theory presented as a series of phase diagrams. A bleb is nucleated when the local hydrostatic pressure generated by cortical contraction causes the cell membrane to detach from the cortex. Cytoplasmic pressure and flow then drive the expansion of a bleb. This is accommodated by further delamination of the cell membrane from the cortex, flow of lipid into the bleb through the bleb neck, and unwrinkling of excess folded membrane. Eventually, the bleb expansion slows down as the driving contractile pressure is relieved, and the actin cortex starts to reform underneath the bleb membrane and the bleb heals. In non-motile cells, myosin-driven