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

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

9.4.3.1 Ambulatory Contact Event

Stripped to its fundamentals, the act of ambulation requires that a mobile surface (e.g., a footpad) is brought into adhesive contact with a fixed surface to be traversed. After the contact event has occurred, the point of adhesion becomes a fulcrum allowing mechanical leverage to be applied against the fixed surface, thus permitting forward motion of a mass attached to a lever. The mobile surface may then be detached from the fixed surface and the cycle repeated.

Consider a footpad approaching the extracellular surface of a cell. The footpad first encounters 5-8 nm thick strands of the circumcellular glycocalyx at a number density of ~10⁵ strands/micron², typically at a distance of 10-100 nm from the plasma membrane surface (see Section 8.5.3.2). A reversible binding site embedded in the footpad contact area (Section 4.2.8) can recognize glycocalyx chains unique to specific cell types or tissues, or more generally any glycoprotein chain, and then securely bind to such chain until mechanically released. If cell-type specificity is not an important design requirement, then a simple reversible mechanical grappling system may be employed. Each carbohydrate chain may be up to 100-200 nm in length, so a footpad adhering to a cell surface in this fashion may experience up to ~100 nm of horizontal or vertical free play in its anchorage. This can seriously degrade the efficiency of motive levers (e.g., nanorobot legs) <~1 micron in length, and can make ambulatory locomotion nearly impossible for motive levers <~100 nm in length. (If the footpad adheres to many chains, free play is substantially reduced.)

Alternatively, footpads may employ spikelike structures and glycophobic coatings to penetrate the glycocalyx without injuring it. At 10-20 nm above the plasma membrane surface, these footpad structures will encounter the extracellular polar regions of integral proteins that are embedded in the cellular plasma membrane. Integral proteins, typically ~100,000 daltons, are present in RBCs at a number density of ~10⁵/micron²; however, ~100 different integral protein types are present, reducing the number density of any one common type (e.g., red cell glycophorins) to 10³-10⁴/micron². Free-floating integral proteins (constituting 20%-70% of the total number¹⁴³⁵) exhibit considerable lateral diffusion but can provide adequate anchorage if the dwell time is brief enough. Transmembrane proteins are often immobilized by links to protein networks located near the cytoplasmic side of the plasma membrane, possibly reducing free play to ~20-30 nm, although many transmembrane proteins are required to be unattached to the internal cytoskeleton, permitting them to circulate so they can mediate multi-receptor signal transduction.

Penetrating still further to the plasma membrane surface, reversibly-hydrophilic footpads may bind with the polar phospholipid heads of the ~650 dalton molecules comprising the lipid bilayer, with number density ~2.5 x 10⁶/micron² in each of the two layers. (The erythrocyte plasma membrane contains well over 100 different lipid species,¹⁴³⁰ in much lesser concentrations.) Adjacent phospholipid molecules generally are not bound covalently, so individual molecules may be extracted from the lipid bilayer with a modest vertical force (taking ~10 zJ/nm² interlipid hydrophobic binding energy (Section 3.5.1) and lipid-lipid contact area ~4 nm²/lipid divided by single-layer extraction distance ~4 nm implies a single-lipid, single-layer extraction force F_lipid ~ 10 pN, comparable to the estimate by Evans¹⁴¹⁵) and hence provide relatively weak anchorage in the vertical direction. Although such anchorage may suffice in many applications, artificial amphipathic transmembrane anchored structures (Section 9.4.3.3) can provide an even more secure bond for locomotion and parking.

After the contact event has occurred, the adhesion structure is used as a fulcrum to apply mechanical leverage against the cell plasma membrane surface, giving rise to tensile or shear forces at the point of attachment. How large are these forces?* As a minimal estimate, we assume that each transmembrane protein is anchored to the internal cytoskeleton by only a single actin microfilament. An actin microfilament has a failure strength of ~2.2 x 10⁶ N/m² (Table 9.3) and a cross-sectional area of ~30 nm² (Section 8.5.3.11), thus requiring a tearing force of ~108 pN for detachment.³⁶² A glycoprotein molecule consisting primarily of a chain of C-C covalent bonds may have a rupture strength on the order of ~10,000 pN (Section 3.5.1).

* J. Hoh emphasizes that a large thermal contribution exists for forces in the piconewton range; the smaller the force, the larger the time-dependent contribution. Normal biomolecular interactions, such as antibody-antigen interactions at >~100 pN, have finite lifetimes and will unbind on a timescale of hours or days in the absence of any force. Even a very small loading force may shift the unbinding timescale significantly downward. As a result, the binding forces for nanorobot footpads will be critically linked to the speed at which the nanorobot is moving. Hoh believes these variations in force may span orders of magnitude; additional research on nanorobot footpad mechanics is clearly needed.

When mechanical leverage is applied against the cell surface, plasma membrane components feel a force in the direction opposite to the direction of travel of the ambulating nanorobot. Since the plasma membrane is a fluid, components within the membrane may be free to slip backwards, reducing traction. For simplicity of analysis, consider a spherical nanorobot of radius R_nano that inserts a spherical footpad of radius R_foot into a lipid bilayer membrane, at the end of each of N_leg legs each of a width that is small in comparison with R_foot (so that the contribution from the legs may be ignored). The viscosity of the plasma membrane that resists the backward movement of the footpad is approximately h_membrane ~ 10 kg/m-sec and the viscosity of the extracellular fluid is h_extra ~ 10^-3 kg/m-sec (Table 9.4). The nanorobot ambulates across the cell surface through the extracellular fluid at a velocity v_nano against a "headwind" of v_headwind (the fluid speed relative to plasma membrane surface), during which movement the footpad slips backwards at a velocity v_foot. Equating the forces on the nanorobot and the footpad from Eqn. 9.73 gives:

{Eqn. 9.79}

where the coefficient of traction k_traction = h_membrane R_foot / h_extra R_nano. Taking N_leg = 2, R_nano = 1 micron and R_foot = 10 nm, then k_traction = 200. Thus with v_headwind = 0, the footpads of a bipedal nanorobot traveling forward at v_nano = 1 cm/sec slip backward within the lipid bilayer membrane at only v_foot = 50 microns/sec. This process is functionally similar to the tracked system modeled by kinesin microtubule transport (Section 9.4.6) wherein productive steps are directed by protein-protein interaction affinities.

Repeated application of physical forces across a cell surface may activate mechanical signal transduction pathways mediated by specific transmembrane proteins such as the integrins and cadherins (Sections 8.5.2.2 and 8.5.3.11). These signals can trigger major changes in cell behavior and in cellular protein expression. Microfilaments readily transduce 0.01-2 Hz mechanical signals throughout the cell.¹²⁰² In 1998, it was not yet known whether much higher frequencies, such as might be employed in cytoambulation, also induce a significant cellular response, except, of course, in specialized mechanoreceptor cells such as the cochlear stereocilia.^3597,3598 Footpad target proteins, motions, and operating frequencies should be selected with the objective of minimizing mechanical signal transduction effects.

Last updated on 21 February 2003