Instability and critical pulling rate of tethers in tether extension process using a mathematical model

A.H. Karimi, M. Rahimi, S. Ziaei-Rad and H.R. Mirdamadi 

Mechanics of Soft Materials, Volume 2, Issue 1, February 2020, 2

ABSTRACT

Cells and organelles are enclosed by a biological membrane called the lipid bilayer membrane. These membranes appear in a variety of complex shapes under certain conditions of the surrounding environment. Shape transformation of lipid bilayers is involved in many cellular processes to perform essential functions. Hence, dynamic behavior of lipid bilayer membranes is one of the important subjects of researches in the last decades. Among different shape transformations of biomembranes, formation of tubes and tethers is quite common in cells and between cells. Tubular networks of the Golgi apparatus and the smooth part of the endoplasmic reticulum and tubes involving cell-cell adhesion are clear examples of formation of tubes. Most of these shape transformations in the cell are carried out by the action of motor proteins of cytoskeleton. In this paper, a mathematical model based on the mechanical properties of fluid bilayer membranes is utilized to study the dynamic behavior of the tether extension process. The dynamic pulling force of the tether extracted by a constant pulling rate is obtained as a function of tether length. The effect of the pulling rates on the dynamic pulling force and shape transformation of bilayer membrane is investigated. By increasing the pulling rate, pearling occurred in the tether. For a specific value of pulling rate called the critical pulling rate, the dynamic pulling force tends to zero and the tether becomes unstable. The effect of material parameters on the critical pulling rate of tethers is also investigated.

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