Technical Briefs

Effects of Virus Size and Cell Stiffness on Forces, Work, and Pressures Driving Membrane Invagination in a Receptor-Mediated Endocytosis

[+] Author and Article Information
Amit Gefen1

Department of Biomedical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israelgefen@eng.tau.ac.il

One zeptojoule is the work of a force of 1 pN over a distance of 1 nm.

In fact, at a finite temperature, a bond-breaking force is inextricably connected to the time of force application: Even a strong covalent bond will break under low forces if one waits long enough due to random Brownian kicks from the thermalized environment (3).


Corresponding author.

J Biomech Eng 132(8), 084501 (Jun 28, 2010) (4 pages) doi:10.1115/1.4001888 History: Received March 05, 2010; Revised May 22, 2010; Posted May 27, 2010; Published June 28, 2010; Online June 28, 2010

A continuum model based on the contact mechanics theory was developed and used for evaluating virus indentation forces at the early stage of membrane invagination, as well as the work of the virus indentation forces and virus-cell contact pressures in a receptor-mediated endocytosis, depending on the virus size and virus/cell stiffnesses. The model indicated that early virus indentation forces are in the order of 1–10 pN and for a given extent of virus engulfment, they increase linearly with the elastic modulus of the host cell and also with the square of the virus radius. The work of invagination at the initial phase of virus endocytosis is in the order of tens of zeptojoules and peak virus-cell contact pressures at this stage are in the order of hundreds of Pascals to several kPa. For a given extent of virus engulfment, peak and average contact pressures increase linearly with the elastic modulus of the host cell but interestingly, they are negligibly affected by the virus size. The present model may be useful in the fields of cellular biomechanics, virology and nanodrug delivery to evaluate mechanical factors during the early phase of membrane invagination.

Copyright © 2010 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

The virus-cell contact model. Receptor formation produces an equivalent virus indentation force F, which acts to deform the cell to an extent h=2αRv, where Rv is the radius of the virus and α is the engulfment index, which ranges between 0 and 1.

Grahic Jump Location
Figure 2

Model predictions of (a) virus indentation forces and (b) work of virus indentation forces for four viruses that are pathogenic to humans. Work of the yellow fever virus was below 1 zJ for all α≤0.1 and is, hence, not shown. The elastic modulus of the host cell was assumed to be 3 kPa for all virus simulation cases (11).

Grahic Jump Location
Figure 3

Model predictions of the contact pressure distribution at the virus-cell contact site for increasing extents of virus indentation into the host cell (α≤0.1). The elastic modulus of the host cell was assumed to be 3 kPa for all virus simulation cases (11).




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