A theoretical model dealing with endocytosis, exocytosis and caveolae invagination, describing plasmalemma homeostasis during cell growth and division, was proposed. It considers transmembrane pressure, membrane tension and mechanosensitivity of membrane processes.

Description

1. A single cell was modeled as a mechanochemical set of plasmalemma, encapsulated cytoplasm and surrounding environment. It was assumed that membrane material can be delivered to the bilayer by exocytosis and unloaded by endocytosis. According to the model, locally flat membrane can invaginate forming bud-like caveolaes (C). Single cell volume can change due to the transport of water (WTr), small solute (STr), and endocytic (En) and exocytic (Ex) vesicles. The considered processes can be tension (t) sensitive. For simplicity the encapsulated volume as well as the excluded area of the membrane, occupied by membrane material of endocytic end exocytic vesicles, were not distinguished. Vesicle and the cell volume exceeding certain border limit were treated as incompressible. Additionally, the shape of the cell was assumed to be spherical, and characterized by time (t) dependent radius (R(t)).


2. We assumed that a cell initiates mitotic separation when its volume reaches a certain minimum, and the membrane tension is not higher than a certain critical value. During mitosis the cell rearranges its geometry forming a two-kernel peanut shape, made of a symmetrical pair of cut and joined spheres, with the centers separated by a distance (Z(t)), shorter than the diameter of the sphere.


3. The cell divides symmetrically when Z exceeds the distance 2R.

Figure: Dividing cell volume as a function of time.

Equations

where: t is time,

 is the hydraulic conductivity of the membrane,

 is excluded area of the cell membrane,

 is hydraulic pressure difference,

 is osmotic pressure difference,

 is the encapsulated volume of endocytic and exocytic vesicles,

 is the membrane excluded area of endocytic end exocytic vesicles,

 are the rates of endocytosis, exocytosis, budding and bud vanishing,

 is the number of buds (caveolaes).