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

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

10.4.2.1 Transmembrane Siphonation and Ionic Disequilibration

A number of rigid diamondoid tubes with membrane-locking lipophilic external coatings and hydrophilic end rings may be inserted through the target cell membrane, preventing self-sealing of the breach (Section 9.4.5.6) and resulting in drainage of internal fluids and disruption of ionic balances, probably triggering apoptosis in eukaryotic cells after ~10⁴ sec.

What magnitude of siphonage may be required to achieve cell lethality? A cytosolic concentration of >~10⁴ Ca⁺⁺ ions/micron³ is believed to be toxic (Section 7.4.5.3) and there are ~10⁶ Ca⁺⁺ ions/micron³ present in blood plasma (Appendix B) or interstitial fluid, so replacing ~1% of cell volume (e.g., ~0.1 micron³ for a bacterium, ~80 micron³ for a tissue cell) with raw extracellular fluid should be lethal. Macrophages can ingest up to ~25% of their volume per hour,⁹⁹⁶ or ~10% of their volume in ~1000 sec, but the paramecium, a large protozoan, excretes through its contractive vacuole a quantity of water equal to 100% of its volume in 15-20 minutes,⁷⁵⁸ or ~10% in ~100 sec.

Conservatively assuming that a ~10% target cell volume influx of extracellular fluid in 1 sec will cause serious cell damage or induce apoptosis, the size and number of passive transmembrane siphons may be crudely estimated. Mean interstitial fluid pressure is ~0.0002 atm (Section 8.4.2). Thus from Eqn. 9.25, the total volume flow rate through water-bearing transmembrane tubes of length l_tube = 300 nm with pressure differential Dp ~ 0.0002 atm is 'V_HP = 4 x 10¹⁰ N_tube r_tube⁴ (m³/sec) for N_tube tubes each of inside radius r_tube. To exchange 10% of the volume of a ~2 micron diameter bacterium by siphonation with extracellular fluids in ~1 sec ('V_HP ~ 1 micron³/sec) requires one tube of radius r_tube ~ 70 nm. For a ~20 micron tissue cell, 'V_HP ~ 1000 micron³/sec which requires one tube of radius r_tube ~ 400 nm or 15 tubes of radius r_tube ~ 200 nm.

It is important that passive siphon tubes should be employed in minimum numbers and never be left unattended. They should be tethered to the nanorobot during use and retrieved after each use. Left unattended in the plasma membrane of a dying cell, diamondoid siphon tubes could become serious systemic poisons. For example, macrophages phagocytosing apoptotic siphon-studded cells would be unable to digest the tubes and might themselves become accidentally siphoned, or might pass the lethal tubes to other innocent cells in the liver, spleen, or elsewhere.

Death by siphonation may be hastened if the nanorobot actively pumps extracellular fluids (or cations directly) into the target cytosol. A pressure differential of ~1 atm applied along a simple bulk fluid injector with r_tube = 50 nm and l_tube = 300 nm gives 'V_HP ~ 1000 micron³/sec and draws ~76 pW of power during the transfer.

Artificial cytocidal cation inflows must surpass the net natural cellular outpumping rates of those cations. For instance, there are at least five known Ca⁺⁺ concentration-maintenance mechanisms in eukaryotic cells:

1. a cell membrane ATP-driven Ca⁺⁺ exporting pump,

2. a cell membrane 3Na⁺/Ca⁺⁺ exchange transporter,

3. a Ca⁺⁺ transporter into the mitochondria,

4. a 2Na⁺/Ca⁺⁺ exchange transporter into the mitochondria, and

5. an ATP-driven Ca⁺⁺ pump into the endoplasmic reticulum.³¹⁴⁶

What is the maximum natural outflow rate? Normal cytosolic Ca⁺⁺ concentration ranges from 60 ions/micron³ for a resting cell up to 3000 ions/micron³ for an activated cell (Section 7.4.5.3). From Eqn. 3.4, the diffusion-limited ion current through the surface of a 20-micron tissue cell is ~2 x 10⁷ ions/sec for a resting cell and ~10⁹ ions/sec for an activated cell. Taking the extracellular concentration of ~10⁶ Ca⁺⁺ ions/micron³ gives a minimum lethal extracellular bulk fluid inflow rate of ~1000 micron³/sec to defeat the maximum possible pumping rate of an activated 20-micron cell, consistent with the previous estimate. (The diffusion limit for a nanorobot pumping Ca⁺⁺ from the interstitial fluid into the cytosol is ~3 x 10¹¹ ions/sec, far higher than the maximum rate at which the cell can outpump.) Similarly, Na⁺/K⁺ transporters present in the eukaryotic membrane at 1000/micron², each device transporting 500 ions/sec (Section 3.4.1), move at most ~10⁹ ions/sec through the ~2400 micron² (Table 8.17) plasma membrane. The Na⁺/K⁺ pumping cost is ~16 zJ/ion (Section 3.4.1); devoting the entire 30 pW power budget of the typical cell (Section 6.5.1) to such pumping would allow the transport of ~2 x 10⁹ cations. Thus, >1000 molecular sorting rotors each operating at ~10⁶ ions/rotor-sec (Section 3.4.2) -- the entire array transporting >10⁹ ion/sec -- should allow an attacking nanorobot to defeat a cell's attempts to resist ionic disequilibration.

Last updated on 24 February 2003