In conjunction with Foresight Update 47
Volumetric Cellular Intrusiveness of Medical Nanorobots
By Robert A. Freitas Jr.
Research Scientist, Zyvex Corp.
|Robert A. Freitas Jr.|
Medical nanorobots on cytotherapeutic missions will often need to enter the living cell to perform repairs. Such missions may require the participation of many cooperating nanorobots, or perhaps just a few but relatively large nanorobots, per cell. And so the question logically arises: How many nanorobots can safely be crammed into a single living cell? There are at least two issues here. First, how much new foreign material can be added to a cell? Second, how much of a cell’s existing volume can be replaced with foreign material with no change in total cell volume? Since we can’t yet do direct experiments with medical nanorobots and living cells, no precise answer is possible. But we can estimate the maximum volume of foreign material that the intracellular compartment might safely accommodate by examining analogous instances of cellular intrusion.
We can start by considering cell membrane elasticity. How much can the cellular membrane stretch before it breaks? The introduction of foreign material into a cell may cause intracellular volume to expand. Assuming a spherical cell shape, the change in cell volume Δ Vcell from the original cell volume Vcell is related to the change in plasma membrane area Δ Acell of an unstretched membrane of area Acell by the relations Δ Vcell /Vcell ~ ((1 + Δ Acell/Acell)3/2 – 1) and Δ Acell/Acell = Tmemb / Kmemb, where Tmemb is the isotropic tension due to membrane expansion and the area compressibility modulus Kmemb = 0.378 N/m for erythrocyte plasma membrane at 310 K and Kmemb = 0.636 N/m for leukocyte plasma membrane (, Section 22.214.171.124.1). Taking a conservative lysis limit of Tmemb ~ 4 x 10-3 N/m for erythrocytes, then Δ Vcell /Vcell ~ 1.6% for red cells and ~0.9% for white cells. That’s not much stretch.
However, erythrocytes are not spheres but biconcave disks with a mean volume of 94 micron3 in isotonic solution (300 mosmol). Red cells absorb water in hypotonic solution, becoming spherical at 131 mosmol with a volume of 164 micron3, demonstrating a capacity for volumetric expansion of 74% without losing membrane integrity. Other cells may permit even more expansion. For example, taking Tmemb = 1.7 N/m and Kmemb = 1.3 N/m for TB/C3 hybridoma cells and Tmemb = 1.8 N/m and Kmemb = 1.2 N/m for NS1 myeloma cells , then Δ Vcell /Vcell ~ 250% for hybridomas and ~300% for myelomas. These estimates are crude at best because the lipid population of the plasma membrane is constantly changing and may enlarge or contract over time.
For more than four decades, microbiologists have routinely extracted from or inserted an entire nucleus into a cell using micropipettes without compromising cell viability. Such nuclear transplantation represents a volumetric change of Δ Vcell /Vcell ~ 3-4% for the typical 20-micron human tissue cell (, Table 8.17) but in the case of a human leukocyte would represent a volumetric change of Δ Vcell /Vcell ~ 18% for an eosinophil, 22% for a neutrophil, 26% for a monocyte, or 51% for a lymphocyte. Decades of laboratory practice have confirmed that at least ~10-10 ml/cell or ~100 micron3/cell of foreign material (representing perhaps 1-3% of cell volume) can be safely injected into a somatic cell without any significant effect on cell viability . Finally, we know that neutrophils increase volume by ~15% when stimulated in suspension, but rabbit neutrophils that migrate into the abdominal wall (cell size ~150 micron3) are +50% larger than those in the abdominal wall vasculature (~100 micron3) and human neutrophils induced by FMLP to migrate into collagen gels (~290 micron3) are 42% larger than those that did not migrate (~204 micron3) .
Another classic measure of tolerable volumetric intrusiveness in the context of medical nanorobots  is the amount of lipofuscin that can accumulate inside cells without ill effect. Lipofuscin consists of insoluble age-pigment lysosomal granules that collect in many of our cells, the accumulation starting as early in life as 11 years of age and rising with age, activity level and caloric intake, and varying with cell type. Clumps of these yellow-brown granules — typically 1-3 microns in diameter — may occupy up to 10% of the volume of heart muscle cells , and from 20% of brainstem neuron volume at age 20 to as much as 50% of cell volume by age 90 . Lipofuscin concentrations as high as 75% have been reported in Purkinje neurons of rats subjected to protein malnutrition . Elevated concentrations in heart cells appear not to increase the risk of heart attack and brain cell lipofuscin is not associated with any mental or motor abnormalities or other detrimental cellular function, although hereditary ceroid lipofuscinosis can lead to premature death. The fact that lipofuscin is an indigestible lipid peroxidation product that cannot be excreted but whose presence is usually not injurious to the cell argues strongly that cells can tolerate major volumetric replacements of protoplasm with artificial foreign bodies such as medical nanorobots while continuing to function normally. Other inert intracellular pigments are known along with a number of pathological intracellular storage diseases including Gaucher’s, Niemann-Pick, and Tay-Sachs. Noninert amyloid deposits average ~12% of pancreatic islet cell volume in patients with maturity onset diabetes .
Various particulate substances including microspheres and crystals have been introduced intracellularly to observe the effects on the cell. In one study , up to 500 polystyrene 0.26-micron beads were injected into a tissue cell and this 4.6 micron3 load did not affect the cell’s ability to transport the particles around inside as if they were tiny organelles or vesicles. A few micron3/cell of engineered nanoparticles are tolerated by living cells when employed as intracellular fluorescent reporters . Cholesterol crystals have been induced to grow inside living J774 mouse peritoneal macrophages, reaching a concentration of ~120 mg cholesterol/mg protein or ~2.4% intracellular crystals by volume  without lethality, though excessive intracellular crystallization (e.g., of drug molecules) can lead to problems such as acute renal failure and intracellular crystals have been found inside chondrocytes in certain crystal deposition diseases. A useful and simple experiment that could be done today would be to microinject various cell types with progressively larger loads of chemically inert diamond microparticles, noting the effect (if any) on cell motility, behavior, and metabolic function.
Interestingly, Pseudomonas stutzeri AG259, a species of bacterium isolated from silver mines, protects itself from the usual bactericidal effect of silver ions by sequestering triangular and hexagonal insoluble nanocrystals of Ag0 and Ag2S (believed to be acanthite, a stable crystalline form of silver sulfide) intracellularly in vacuole-like granules in the periplasmic space . In one photomicrograph, several crystals ranging from 90-200 nm in diameter are visible inside a living bacterial cell ~800 nm in diameter, suggesting a total inert particulate ~13% volumetric intrusiveness.
We can obtain yet another perspective on cellular intrusiveness by considering the phagocytes — specialized cells optimized for ingestion of foreign particles . Latex or polystyrene beads are among the most popular particles for phagocyte ingestion burden experiments. Guinea pig neutrophils can ingest up to 3.8% of cell volume in 3-micron polystyrene beads, but only 3.0% of cell volume of 0.3 micron beads. Peritoneal phagocytes from striped bass each ingested an average of four 3-micron latex beads during a 30-minute incubation time , giving a phagocytic capacity of ~64 micron3/phagocyte or ~4% of cell volume. Rabbit alveolar macrophages cultured in suspensions or on monolayers of latex particles internalized a maximum of 45 1-micron particles (45 micron3/cell or ~3% of cell volume) and 10 2-micron particles (~80 micron3/cell or ~5% of cell volume) at saturation . Another study of rat alveolar macrophages confirmed particle burdens exceeding 15 2-micron microspheres (~63 micron3 or ~4% of cell volume) . Murine bone-marrow macrophages that are only 13.8 microns in diameter can ingest IgG-opsonized beads up to 20 microns in diameter , representing an amazing ~200% of cell volume. Of course, phagocytes that eat too many latex microspheres develop impaired mobility, and some particles are highly toxic to phagocytes — just 0.05 µg of silica per 106 macrophages , or 0.002% of cell volume assuming 1166 micron3 per rat alveolar macrophage, is cytotoxic.
What about inorganic particles? Rat alveolar macrophages ingested at least ~1 micron3/cell of iron oxide particles (~0.1% of cell volume) without ill effect in one experiment , but another experiment  found up to 72 spherical 2.6-micron iron oxide particles (~663 micron3) had been nonfatally ingested by human alveolar macrophages each of mean volume 4990 micron3, a cell burden of ~13% foreign particles by volume. Murine macrophages suffer only ~10% mortality from ingesting up to 2500 alumina ceramic (sapphire) 0.6-micron particles, or ~10% of cell volume, although mortality rises to ~30% from ingesting a similar volume concentration of 2-micron particles . Micrographs of live mouse peritoneal macrophages  and human monocytes  that have been induced to ingest diamond dust particles up to 5 microns in diameter appear to have internalized particles amounting to 10-20% of their cell volume. A particle burden “overload criterion” (i.e., producing macrophage immobilization) of ~600 micron3 per rat alveolar macrophage (a ~50% cellular volumetric burden for 1166 micron3 cells) has been proposed by Oberdorster et al. .
Living cells are often seen swimming around inside larger living cells. Are there any obvious volumetric limits? Individual ~200 micron3 lymphocytes have been observed circulating for hours inside larger living cells (~3-5% volume fraction) with no evident ill effect, a phenomenon called emperipolesis (, Section 126.96.36.199). While neutrophils and macrophages are both found in mammalian lungs and neither cell phagocytoses the other in significant quantities, alveolar macrophages containing neutrophils have been observed. Neutrophils that have undergone apoptosis are taken up by macrophages, with mean uptake of 3 neutrophils per macrophage . Taking nonmigratory human neutrophils as 204 micron3 and human alveolar macrophages as 4990 micron3, the uptake represents ~12% of macrophage cell volume.
Cells may also harbor smaller pathogens which are usually volumetrically harmless to the host. Perhaps the best-known example is the case of the bacteriophage T4. A single Escherichia coli bacterium injected with a single T4 phage virion at 37oC in rich media lyses after 25-30 minutes, releasing 100-200 phage particles that have replicated themselves inside . Taking E. coli volume as 0.6 micron3 (, Section 10.4.2.5) and phage T4 volume as ~200,000 nm3, then the bacteriophage particle load on E. coli at lysis is 3-7% of bacterial cell volume. In human cells, the tuberculosis bacterium enters the alveolar macrophage, which transports the intruder into the blood, the lymphatic system, and elsewhere. Each ~1 micron3 bacillus that hitches a ride in this manner represents a volumetric intrusion of 0.02% of macrophage volume. Other intracellular microorganisms such as Listeria (~0.25 micron3) and Shigella (~2 micron3), once free in the cytoplasm, are propelled “harmlessly” through the cytosol via continuous cytoskeleton-linked actin polymerization (, Section 9.4.6). Macrophages infected with Listeria have been observed with ~2% of their volume co-opted by the microbes (~100 organisms) . While some motile intracellular parasites such as Tyzzer may cause disarrangement and depopulation of host cell organelles by the movement of their peritrichous flagella, other motile intracellular parasites such as the spotted fever-group rickettsiae  spread rapidly from cell to cell by actin-based movement but do not cause lysis of the host cell, and typhus-group rickettsiae  multiply in host cells to great numbers without profound damage (until cell lysis finally occurs) — providing a more positive intrusiveness benchmark for future medical nanorobots.
Copyright 2001 Robert A. Freitas Jr. All Rights Reserved
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