Nanomedicine, Volume I: Basic Capabilities

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

Robert A. Freitas Jr., Nanomedicine, Volume I: Basic Capabilities, Landes Bioscience, Georgetown, TX, 1999 Plasma Membrane Areal Expansion Elasticity

A nanorobot with a footpad of width Lfoot = 10 nm that applies a pressure of Pnano = 10 pN / Lfoot2 across a span Lfoot of plasma membrane surface (and normal to it) creates an isotropic tension of T ~ Pnano Lfoot = 1 x 10-3 N/m within the membrane, causing the plasma membrane under the nanorobot to expand uniformly without shearing or bending. For comparison, the tension required to smooth out the thermal undulations or "Brownian motion" of the outer membrane of artificial phospholipid vesicles 10-20 microns in diameter (typical cell size) was determined experimentally to be 0.01-0.1 x 10-3 N/m.368 At the other extreme, osmotically swollen red cells will instantaneously lyse* at a plasma membrane tension of Tlyse = 10-20 x 10-3 N/m1415,1421 or at an elastic modulus with respect to area dilation of Tlyse / hcell ~ 3 x 106 N/m2,1422 where red cell wall thickness hcell = 8 nm.

* T ~ 6 x 10-3 N/m produces red cell plasma membrane lysis after ~10 sec; time of lysis is a stochastic function that increases to ~120 days (maximum red cell lifetime) at T ~ 3-4 x 10-3 N/m.1415

The relative area expansion of the plasma membrane under the nanorobot footpad is DA / A = T / K,1415 where the experimentally-determined area compressibility modulus is K = 0.45 N/m for red cell plasma membrane at 298 K1412,1413,3171,3172 (change in area compressibility modulus with temperature is 6 x 10-3 N/m-K)3172; K = 1.7 N/m for certain cholesterol-lipid mixtures.1414 This gives DA / A ~ 0.2% or 0.06% for the nanorobot footpad of size Lfoot described above (2%-4% areal expansion produces lysis1415), or a mean linear strain of e = (DA / A)1/2 ~ 0.04 (4%) or 0.02 (2%). For e << 1, the footpad depresses the surface by Dx ~ Lfoot (e/2)1/2 ~ 1.5 nm into the red cell's interior. This deflection represents only ~15% of lipid bilayer membrane thickness and must be considered modest in most circumstances. For leukocyte plasma membranes, measured K = 0.636 N/m.846

The design of cytoambulation mechanisms should attempt to minimize the activation of sodium-ion (and many other) stretch-activated channels -- gated transmembrane channels that are activated by simply stretching the plasma membrane, or by tension or stress development in cytoskeletal elements associated with the cell membrane.362,1506 Such channels have already been implicated in the maintenance of cell volume.491,1416 Biochemical transduction of mechanical strain has also been investigated in bone cells during normal loading. Linear strains of e < 0.05% were nonstimulative; those between 0.05%-0.15% maintained normal bone mass, and strains of e > 0.15% stimulated osteoblasts to increase bone mass.1417-1419 Linear strains >1% induced osteoblasts to alter morphology, becoming fibroblast-like,1420 and red cells lyse at e >~ 20%.362 A limit of DA / A ~ 0.05% for a 10 nm footpad on a red cell surface would give an estimate of ~2 pN for the activation threshold. However, a force of 1 pN across a protein stretch sensor of cross-sectional area ~1 nm2 represents an energy density of 106 joules/m3, or 10 zJ (~2 kT) for a ~10 nm3 sensor volume, which is probably close to the limit for biological force detection consistent with earlier estimates of nanosensor detection limits (Section 4.4.1).

From these comparisons, it appears that a biological response, stimulated by plasma membrane areal expansion due to the passage of nanorobot footpads across the cell surface employing forces typical in cytoambulation (e.g., ~20 pN; Section, cannot be ruled out. However, in 1998 it was not yet known how efficiently mechanical pressures cycled at 10-100 KHz are transduced by plasma membrane stretch sensors, since most mechanical cell stimulation experiments have been conducted at frequencies between 0.05-5 Hz.* Energy coupling may be poor due to a large mechanical impedance mismatch. Looser glycocalyx anchorages also could minimize stretch activation effects.

* Specifically: 0.05 Hz,3599 0.1 Hz,3600 0.25 Hz,3601 0.33Hz,3600,3602 0.5 Hz,3603-3604 1 Hz,3604-3609 1.67 Hz,3609 2 Hz,3604 and 5 Hz.3610


Last updated on 21 February 2003