Deformation dynamics of cells, their membrane and nuclei

Abstract

The deformation and morphology change of cells are intimately involved in biological processes such as cell spreading, rounding, migration and division. For example, a hallmark of apoptotic or motile cells is the formation of membrane protrusions often referred to as cellular blebs. In addition, the nuclear envelope (NE) needs to undergo significant shape transformations during closed mitosis. Finally, it is commonly believed that the deformability of neurites, finger-like structures extending from the main body of neurons, plays an important role in the formation of the nervous network as well as the signal transmission among neural cells. However, fundamental questions like exactly how these deformation processes take place and the key physical factors governing them remain unclear. Aiming to address these outstanding issues, here we first developed a boundary integral model to track the shape evolution of the cell membrane during the blebbing process. We showed that, for a given weakened size of actin cortex, the intracellular pressure must be over a critical value for blebbing to occur. In addtion, a blebbing map, summarizing the essential physics involved, was also obtained which exhibits three distinct regimes: no bleb formation, bleb formed with a fixed width, and a growing bleb depending on the level of the intracellular pressure and the size of the initial weakened region. The interactions between blebs were also examined. Specifically, the volume that a second bleb can reach was found to heavily depend on its initial weakened size and the time lag with respect to the first bleb, all in quantitative agreement with experimental observations. Interestingly, we also showed that, as the strength of membrane-cortex adhesion increases, the possible coalescence of two neighboring blebs changes from smooth fusion to abrupt coalescence and no fusion at all eventually. The same boundary integral method was then used to study the morphology transformation of the nuclear envelope (NE) during closed mitosis. It was found that, due to the energy dissipation arising from viscous flow, a much larger poleward pressure is needed here (compared to that predicted from conventional energy minimization models) to induce the same deformation of the nuclear envelope. In addition, we showed that the morphology evolution of the NE, as well as its final shape, is insensitive to the bending rigidity of the NE, but mainly regulated by its membrane tension and the growth rate of the poleward pressure. Finally, we probe the viscoelastic properties of neurites by atomic force microscopy (AFM) indentation and subsequent finite element (FEM) simulations. Different loading modes (i.e. step, oscillating and ramp) were adopted and the apparent initial and long-term elastic modulus of neurites were found around 800 and 80 Pa, respectively. In addition, it was found that a minimum of three relaxation timescales (i.e. ~ 0.01, 0.1 and 1 seconds) are needed to fit all the experimental observations. We further demonstrated that these three characteristic relaxation times likely originate from thermal fluctuations of microtubules, membrane relaxation and cytosol viscosity, respectively.