Abstract
Many cell division processes have been conserved throughout evolution and are being revealed by studies on model organisms such as bacteria, yeasts, and protozoa. Cellular membrane constriction is one of these processes, observed almost universally during cell division. It happens similarly in all organisms through a mechanical pathway synchronized with the sequence of cytokinetic events in the cell interior. Arguably, such a mechanical process is mastered by the coordinated action of a constriction machinery fueled by biochemical energy in conjunction with the passive mechanics of the cellular membrane. Independently of the details of the constriction engine, the membrane component responds against deformation by minimizing the elastic energy at every constriction state following a pathway still unknown. In this paper, we address a theoretical study of the mechanics of membrane constriction in a simplified model that describes a homogeneous membrane vesicle in the regime where mechanical work due to osmotic pressure, surface tension, and bending energy are comparable. We develop a general method to find approximate analytical expressions for the main descriptors of a symmetrically constricted vesicle. Analytical solutions are obtained by combining a perturbative expansion for small deformations with a variational approach that was previously demonstrated valid at the reference state of an initially spherical vesicle at isotonic conditions. The analytic approximate results are compared with the exact solution obtained from numerical computations, getting a good agreement for all the computed quantities (energy, area, volume, constriction force). We analyze the effects of the spontaneous curvature, the surface tension and the osmotic pressure in these quantities, focusing especially on the constriction force. The more favorable conditions for vesicle constriction are determined, obtaining that smaller constriction forces are required for positive spontaneous curvatures, low or negative membrane tension and hypertonic media. Conditions for spontaneous constriction at a given constriction force are also determined. The implications of these results for biological cell division are discussed. This work contributes to a better quantitative understanding of the mechanical pathway of cellular division, and could assist the design of artificial divisomes in vesicle-based self-actuated microsystems obtained from synthetic biology approaches.
Highlights
The cell division cycle is a central process in biology, the essential mechanism whereby cells grow and duplicate (Carlson, 2007)
Far from being a passive element, the mechanics of the cellular plasma membrane is known to be physically, as well as biochemically, influenced by different transport processes, membrane biogenesis shuttled by lipid trafficking from the sites of metabolic synthesis to the cellular membranes (Blom et al, 2011), and stress-induced membrane remodeling occurred under the action of the cytokinetic machinery which, together with other passive skeletal structures, form the cellular divisome
We provide a minimal physical model for membrane constriction that considers either, impeded growth of membrane area characterized by positive membrane tension, which requests mechanical work to be exerted by the cytokinetic machinery (Lan et al, 2007; Lecuit and Lenne, 2007), or facilitated membrane growth characterized by negative membrane tension
Summary
The cell division cycle is a central process in biology, the essential mechanism whereby cells grow and duplicate (Carlson, 2007). Cytokinetic membrane remodeling is assumed to arise from a mechanical interplay between membrane tension, osmotic stresses and constriction forces exerted by the divisome These membrane stresses underlie subcellular force effectors, which are structurally and functionally coupled to dynamically adaptable plasma membrane, the extracellular medium and the cytoskeleton (Lecuit and Lenne, 2007). A quantitative insight on the membrane configurations that minimize the mechanical energy during cytokinesis is an important topic in cell biophysics (Lipowsky, 1991; Boal, 2012) Such membrane-focused rationale should allow us to compute the forces needed to divide the cell, providing a better understanding about the different routes of cell division in different organisms (Szostak et al, 2001; Chen, 2009; Budin and Szostak, 2011). The knowledge of these energies is especially interesting to know how the cell performs the large curvature deformations required for membrane constriction at the site of division
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