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
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 220.127.116.11) 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 18.104.22.168) 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 ltube = 300 nm with pressure differential Dp ~ 0.0002 atm is 'VHP = 4 x 1010 Ntube rtube4 (m3/sec) for Ntube tubes each of inside radius rtube. To exchange 10% of the volume of a ~2 micron diameter bacterium by siphonation with extracellular fluids in ~1 sec ('VHP ~ 1 micron3/sec) requires one tube of radius rtube ~ 70 nm. For a ~20 micron tissue cell, 'VHP ~ 1000 micron3/sec which requires one tube of radius rtube ~ 400 nm or 15 tubes of radius rtube ~ 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 rtube = 50 nm and ltube = 300 nm gives 'VHP ~ 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 22.214.171.124). 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