© 1999 Robert A. Freitas Jr. All Rights Reserved.

Robert A. Freitas Jr., Nanomedicine, Volume I: Basic Capabilities, Landes Bioscience, Georgetown, TX, 1999

9.4.3.2.2 Plasma Membrane Shear Elasticity

A plasma membrane surface can deform by "shear" -- elongation in one dimension while narrowing in another dimension -- without bending or increasing surface area. If a deforming force normal to a plasma membrane surface is suddenly removed, the membrane surface will recover its normal unstressed shape in a characteristic time t_snapback = h_surface / m_shear ~ 0.1 sec,³¹⁷¹ where elastic shear modulus m_shear = 6.6 x 10^-6 N/m for the red cell plasma membrane at 298 K,³¹⁷² as determined experimentally, and the measured coefficient of surface viscosity h_surface ~ 10^-6 N-sec/m,³¹⁷¹ is the product of plasma membrane viscosity (~100 kg/m-sec for RBC; Table 9.4) and plasma membrane thickness (~8 nm for RBC), with measured h_surface = 0.6-1.2 x 10^-6 N-sec/m for the red cell plasma membrane.³⁷¹ (The change in elastic shear modulus with temperature is -6 x 10^-8 N/m-K.³¹⁷²) Shape recovery is dominated by plasma membrane viscosity, not cytoplasm viscosity, in some systems, particularly RBCs;³⁶² however, J. Hoh [personal communication, 1999] notes that this does not hold for all cells, and that for most cell types it is the cytoplasm that dominates the rheological properties, as experimentally measured, for example, by indentors or piezo controlled microplates.³⁶¹¹ The time required for a leukocyte to enter a capillary is ~1000-2000 times longer than the time required by red cells,⁸⁴⁶ suggesting t_snapback ~ 100 sec for white cells.

With nanorobot legswing frequency n_leg >> t_snapback^-1, a section of plasma membrane distorted by the passage of one nanorobot footpad may not be able to resume its fully relaxed state before the arrival of another footpad in the same spot as the first. If a traverse through a narrow passage of cell-rich tissue by large numbers of ambulating nanorobots is contemplated for a particular application, then footpad placements should be randomized as much as possible to avoid repeat-deformation grooving, rutting, or other persistent indentation features in the plasma membrane surface.

Last updated on 21 February 2003