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

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

9.4.6 In Cyto Locomotion

Once inside a cell, a motile nanorobot must navigate a cluttered and highly viscous cytomatrix-rich environment (Section 8.5.3). (When microscopic iron particles are introduced into the cytoplasm, they move erratically (rather than smoothly) under the influence of external magnetic fields.⁹³⁸) Any of the methods described for cytoambulation (Section 9.4.3), histonatation (Section 9.4.4), or cytopenetration (Section 9.4.5) may also be employed in modified form within the cell. From Eqn. 9.65 and the data in Table 9.4, and assuming a top speed of v ~ 10 microns/sec (Section 9.4.4.2), then the Reynolds number of an L ~ 1 micron object inside a red blood cell (a nucleus-free floppy bag filled with hemoglobin solution) is N_R ~ 10^-6. For a nanorobot inside a free leukocyte, N_R ~ 10^-9; inside an E. coli bacterium, N_R ~ 10^-11, taking the higher viscosity into account.

There are many natural transport mechanisms inside cytomatrix-rich cells which may serve as analogs for in cyto nanorobot locomotion. For example, vesicles and granules ~100 nm in diameter or larger are carried at a peak speed of up to ~2 microns/sec (although mean unloaded kinesin motor speed is usually 0.5-0.8 microns/sec) on the back of a 60-nm kinesin transport molecule (Fig. 9.32) that takes 8-nm ATP-powered steps along microtubule tracks running throughout the cell^{1535,1536,3202-3204} with a stall force of 5-7 pN;^3201,3202 typically kinesin takes ~100 steps along a microtubule, then lets go. Nanorobots could be designed to brachiate along these tracks as well. Inside giant amoebas, mitochondria measuring 1-3 microns in length are carried along microtubules at speeds up to 10 microns/sec,⁴⁵³ and the pseudopods of fibroblasts (and amoebas) can also extend at ~10 microns/sec.¹²⁵² Faster speeds may be possible for well-designed nanorobots, but an upper limit of ~10 microns/sec through fluid-rich intracellular clear channels seems reasonably conservative.

It is well-known that several pathogenic bacterial species, once free in the cytoplasm of a human cell, propel themselves through the cytosol using a continuous actin polymerization process that takes place at one pole of the bacterium.¹⁰¹² Actin assembly is visible as a tail of polymerized F-actin that remains stationary in the cytosol while the bacterium moves ahead. The polymerizing tail rectifies the random thermal motions of the bacterium, preventing it from diffusing backwards while permitting forward diffusion; thus the tail doesn't actually "push" the bacterium forward.¹²⁰³ Actin-based motility is mediated by a single bacterial protein -- ActA (610 amino acids) in Listeria and IcsA/VirG (120,000 daltons) in Shigella -- localized in the polar regions of the bacterium.¹⁰¹² Actin microfilaments (and tubulin) typically self-assemble at ~0.11 micron/sec;⁹⁴² actin polymerization gives a stall force of ~10 pN per fiber, sufficient to drive a 1-micron object at ~1.5 micron/sec against a ~1 pN load in free fluid cytoplasm.¹²⁰³ This probably defines the top speed for actin-based bacterial mobility.

To progress through dense cytomatrical regions, motile nanorobots of similar size to bacteria must cut or detach cross-bridged cytoskeletal elements lying across the path ahead, then attempt to reattach or reconstruct those elements after the nanorobot has passed through the breach, because these elements lack sufficient elasticity (and grid sizes are too small) to be pushed completely out of the way. Such cytoskeletal elements will most commonly include intermediate filaments and actin-based microfilaments. This procedure is crudely analogous to the process employed by fibroblasts transiting the ECM during wound repair. Fibroblast movement into cross-linked fibrin blood clots or tightly woven ECM requires an active proteolytic system that cleaves a pathway for migration; known enzymes serving this purpose include plasminogen activator, interstitial collagenase (MMP-1), the 72 kilodalton gelatinase A (MMP-2), and stromelysin (MMP-3).¹⁵³⁷

For an average filament grid size of L_grid ~ 100 nm for the cortical actin cytogel¹²⁰³ and a nanorobot of radius R_nano ~ 1 micron, a minimum of two long diagonal cuts each of length 2 R_nano (simplistically, making four triangular flaps) to allow passage requires N_cut = 4 R_nano / L_grid = 40 transected grid segments in order to advance a distance L_grid, or n_cut = 4 R_nano v_nano / L_grid² = 400 cuts (or reattachments) per second at v_nano ~ 1 micron/sec. This compares favorably with the n_brach ~ 500 Hz estimated earlier for a manipulator arm used for ECM brachiation, where chemopositional validation is required at every step (Section 9.4.4.2), and is well below the n_detach ~ 10 KHz estimated for intercellular passage where such validation is not required (Section 9.4.4.3). An important additional design issue for in cyto brachiation systems is to minimize accidental mechanical signal transduction into the nucleus, which may trigger unwanted cytological responses.

Power requirements for intracellular mobility are typically modest but vary widely, depending mainly upon velocity, the type of cell, and the path chosen. In highly fluidic clear channels, viscosity should more closely resemble that of the red cell interior (h ~ 10^-2 kg/m-sec), so from Eqn. 9.74 and taking R_nano = 1 micron and v_nano ~ 10 microns/sec, then P_nano/e% ~ (0.00002 pW)/e% for pure cytonatation. Nanorobots traversing pathways through filament-rich regions of the cell will experience much higher effective viscosities, on the order of h ~ 10-1000 kg/m-sec (Table 9.4), but will also travel more slowly (e.g., v_nano ~ 1 micron/sec), giving a viscous resistance power requirement for the nanorobot body of P_nano/e% ~ (0.0002-0.02 pW)/e%, from Eqn. 9.74. A telescoping manipulator arm measuring 500 nm in length, performing the filament cuts and joins at n_cut ~ n_join ~ 400 Hz with ~2.5 microns of tool-tip travel per cycle, moves at a tip speed of ~1 mm/sec, producing ~0.025 pW of mechanical losses under no-load conditions (Section 9.3.1.4); there are at least two operational arms, one fore and one (or more) aft. Multiple arms may be needed in a dense filament network. Another ~0.025 pW is required to overcome the viscous resistance against each moving arm (using Eqn. 9.75), giving a total power cost of 0.1-0.3 pW for transfilamentary intracellular locomotion at v_nano ~ 1 micron/sec assuming locomotive efficiency e% = 0.10 (10%).

Some of the difficulties and limitations of in nucleo locomotion have already been mentioned in Sections 8.5.4.7 and 9.4.5.7. The most important constraint is to observe a maximum speed limit that avoids mechanical chromatin damage. Although a 500 kilodalton protein would diffuse from one side of a 5-8 micron nucleus to the other in only ~5-6 sec (~1 micron/sec average), normal chromosomal movements during interphase have been estimated by observing the motions of individual centromeres, typically 0.002-0.003 microns/sec,¹⁵²⁹ and peak chromosome transport speeds during mitosis are ~0.1 micron/sec.¹⁴⁶³ A strict in nucleo speed limit of ~0.1 micron/sec on all nanorobot bodies and most exposed appendages appears prudent. A force limit of ~50 pN for intranuclear locomotion should also be observed (Section 8.5.4.7) -- a 1-micron nanorobot picking its way through a filament-rich medium of net viscosity ~10 kg/m-sec requires the application of ~20 pN to overcome viscous drag at a travel speed of ~0.1 micron/sec.

Last updated on 21 February 2003