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

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

8.5.3.12 Cytonavigational Issues

Cytonavigational requirements are strongly mission-driven. A nonexhaustive list of mission classes might include:

1. examination or modification of the plasma membrane or cell cortex, including chemical testing for toxins or poisons in cell receptors and transport channels;

2. cytosolic chemical or pathogenic assay, chemical injection or extraction, or other selective cytosolic modification;

3. biocellular messaging or eavesdropping using chemical, mechanical, or other means;

4. organelle counting, dimensional measuring, and general cytocartography;

5. circumorganelle chemical assay;

6. organelle-specific surface membrane analysis or intraplasmic chemical assay;

7. dynamic functional or structural testing of cellular components;

8. sampling, diagnosis, chemoinjection, replacement or repair operations to be performed upon an individual organelle or cytocomponent located at a specific cellular physical address;

9. cytoassembly or structural editing;

10. establishment of direct functional control over some or all of normal cellular functions, including metabolism, secretion, and mitotic cycling;

11. comprehensive cellular reconstruction;

12. long-term cytoplasmic materials or equipment storage;

13. sentinel or cytodefensive functions; or

14. activities involving the nucleus (Section 8.5.4). Each of these mission classes has very specific, and often quite different, navigational requirements.

Medical nanorobots can certainly undertake many useful tasks without physically entering the cell, relying solely upon diffusion, transport via cellular pumps, endocytosis and pinocytosis, or even nanoinjectors or manipulator appendages inserted through the plasma membrane (Section 9.4.5) while the nanorobot remains securely anchored outside the cell. However, it is well-known that motile entities are capable of entering and navigating the interiors of living cells for long periods of time without ill effect. For example, one description⁸⁴⁸ from early microscopic investigations included the following observation: "...lymphocytes entered the cells and circulated inside them for hours at a time. This odd relationship of lymphocytes to other cells, sometimes moving around them, sometimes entering them, they termed 'emperipolesis'." (Emperipolesis^3286-3293 is a rarely observed and still poorly understood phenomenon that may only occur in pathological conditions.) Micron-scale bacterial pathogens that invade nonphagocytic cells, once free in the cytoplasm, are propelled "harmlessly" through the cytosol via continuous cytoskeleton-linked actin polymerization¹⁰¹² (Section 9.4.6). While delivery of treatment "packages" to extracellular spaces may be an early use of medical nanorobotics, subsequent development will allow nanorobots to enter and operate inside the cell. Ultimate applications would permit delicate sensing and repair of DNA or organelles (Chapter 21).

The interior of a cell is a unique and intuitively unfamiliar environment. Figure 8.36, drawn primarily for conceptual clarity, erroneously makes the cell appear spacious and relatively empty. In reality, cellular components are fairly closely packed. Even though cells may consist of up to 70% water, only some of this is bulk water and the cytosol more closely resembles a proteinaceous crystal (Section 8.5.3.3). The mean separation of adjacent organelles (of all types) is <1 micron, roughly the size of the nanorobot itself. Forward travel is further impeded by the presence of a dense cytoskeletal network. This includes sheetlike ~30 nm meshes of microfilaments intertwined and bonded with peripheral proteins comprising the cell cortex, plus additional three-dimensional networks of intermediate filaments (~100 nm mesh) and microtubules (~300 nm mesh) throughout the body of the cell (Fig. 8.44). There may be only a few multi-micron-scale "freely swimmable" spaces for nanorobots within the cell.

A medical nanorobot bears about the same size relationship to a cell as a human body bears to a swimming pool. Consider this fanciful analogy to a common macroscale experience, imagining a "nanorobot" of roughly human size: The subsurface robot does not find itself traversing a large swimming pool of water, encountering an occasional submerged obstacle. Rather, it finds itself crawling through a swimming pool mostly filled with thick-skinned water balloons separated by its own width, or slightly less, of fluid. The water balloons are of many different sizes and shapes but average an equivalent volume as the nanorobot itself, with almost all of the balloons embedded in and loosely tethered to a dense three-dimensional multilevel webbing of threads, strings, cords, and 1-cm gauge ropes arranged in a progressive semirandom 1-10 cm mesh. To employ a slightly different and even more imprecise metaphor, navigating the interior of a cell may more closely resemble hacking through a dense jungle than strolling in an open garden.

Given the tight spacing of the multilevel cytoskeletal webbing, it will be almost impossible for a micron-scale medical nanorobot to enter cells and freely navigate therein without disrupting the cytoskeletal framework that lies across its path. Some disruption cannot be avoided even if useful nanodevices or their extensible appendages can be metamorphically compressed as narrow as ~100 nm in width (Section 5.3.1.2). However, cytoskeletal disruption can be minimized by employing active and continuous breach-sealing polymerization protocols during passage (Section 9.4.6). The nanorobot must also avoid applying excessive forces to the cytoskeleton, as these forces could transmit mechanically-mediated signal cascades into the nucleus and activate unwanted stress responses via regulated genetic circuits.¹⁹⁵⁶ Some details regarding cytopenetration (Section 9.4.5), in cyto locomotion (Section 9.4.6), and biocompatible nanorobot surfaces³²³⁴ (Chapter 15) are presented elsewhere.

How can a nanorobot determine its intracellular position? If a high-resolution microtransponder network (Section 8.3.3) has been installed in the surrounding tissue, in vivo nanorobots can acoustically fix their cytographic position to within ~3 microns, although a gigahertz acoustic chirp system may allow localized accuracies as close as ~100 nm in some cases (Section 8.5.4.7). A 3-micron grid size divides a 20-micron cell volume into ~300 distinguishable voxels with each voxel encompassing an average of ~10 individual major organelles.

Because of the close spacing of cellular organelles, a micron-scale nanorobot typically may be in direct physical contact with at least one organelle at all times. The nanorobot can uniquely identify any organelle type based on membrane composition, intraplasmic biochemistry, or physical structure, and can also estimate which additional organelles may be in the neighborhood based on peri-organelle chemogradients. In the case of the nucleus or the ER, where there may be only one organelle of that type per cell, organelle detection provides relative positional localization in the radial dimension (although the ER has multiple layers). In the angular dimensions, and in the case of multiple organelles, cytoskeletal network topology provides additional positional and orientational cues. The circumnuclear ring of intermediate filaments and the microtubule-organizing centers (MTOCs) have already been mentioned. Center-to-periphery orientation is readily established by comparing the net polarity of the local microtubule array with a previously assembled gross map of cellular microtubular topology.

Dead reckoning (Section 8.3.1) may also be used to estimate transit positions and to create internal maps accurate to ~100 nm, the typical internodal separation of the junctions of the intermediate fibers (the most persistent component of the cytoskeletal network). The mean separation of cytoplasmic free ribosomes is also ~100 nm. However, even positional localization as crude as ~1 micron resolution will uniquely locate all individual major organelles within the cytoplasm. This may be sufficient for most purposes, since random hydrodynamic flows induced by thermal fluctuations inside a cell have velocities of ~10 microns/sec in a time range of ~10 millisec with a characteristic length of ~1 micron.¹⁰⁶⁹

A volumetric cytographic map using (100 nm)³ voxels requires 8 million 8-bit voxels or ~64 megabits of memory. A 1 micron³ nanorobot moving at ~1 micron/sec would require ~8000 sec to volumetrically survey the entire interior of a 20-micron cell using an efficient nonoverlapping scanning pattern, or ~300 sec to scan a region having the same volume as the nucleus. A volumetric map would allow computation of the shortest path to the plasma membrane in order to exit the cell quickly and with minimum disruption. Such maps might help the nanorobot to identify the axodendritic polarity of a neuron, locate the nucleus or a specific part of a membrane -- for instance, a part of the membrane that is connected via intercellular junctions to adjacent cells, or which is adjacent to bone or digestive juices. Volumetric maps could also allow the nanorobot to return to the exact site of unwanted natural deposits (e.g., lipofuscin) or to sites where foreign objects are lodged, although long-term map stability is problemmatical.

The cytoplasmic membranes present inside a 20-micron tissue cell have a total surface area of ~180,000 micron², plus another ~280,000 micron² of cytoskeletal fiber surfaces (Table 8.17). Assuming 8-bit pixels, the totality of internal cellular surfaces could be instantaneously described using 1 micron² pixels with a 4 megabit map, or with (100 nm)² pixels using a 400 megabit map (requiring ~0.02 micron³ of hydrofluorocarbon memory tape). However, high-resolution cytographic surface survey maps are not as useful because of their short half-lives. Membrane lipids and transmembrane protein molecules have lateral diffusion speeds (Section 8.5.3.2) averaging ~3 microns/sec and ~0.02 micron/sec, respectively; giving a 0.3-50 sec half-life for a 1 micron² resolution surface map. Surface folds and other gross morphological features on the nuclear envelope, the endoplasmic reticulum and the Golgi complex may have half lives of ~10³-10⁵ sec, so maps of these features may have modest operational utility but still will have minimal archival utility. In any case, many malfunctions in these three organelles may require biochemical rather than mechanical interventions (Chapter 21).

For multiple-copy organelles, statistical sampling to acquire census data may provide the most useful information. Semipermanent structures such as mitochondria may be examined one by one to measure size and number density, to verify biochemical composition, and to test functionality. If a population of N cellular objects is independently and randomly sampled one by one by a population of N_nano in cyto nanorobots, taking a time t_exam for each examination, then the probability that any one object has not yet been examined after n selections is p_x = (1 - N^-1)^{(n Nnano)}, the total examination time T = n t_exam / N_nano, and the average number of times the same object is examined n_po = n N_nano / N. For a cell containing N = 1000 mitochondria, mean travel distance between these organelles is X_travel ~ 2 microns in a 20-micron cell, or t_travel ~ 2 sec travel time at a travel speed of ~1 micron/sec. Conservatively taking t_exam ~ 10 sec, then reducing the probability of nonexamination of any mitochondrion to p_x = N^-1 = 0.1% requires n ~ 7,000 examinations or an average of n_po = 7 examinations per mitochondrion, and requires T = 70,000 sec ~ 19 hours to complete all the examinations using a single in cyto nanorobot (N_nano = 1). A census sampling that reaches only p_x = 50% completeness requires just n ~ 700 examinations, n_po = 0.7 examinations per mitochondrion and T = 7000 sec ~ 2 hours using one nanorobot. An n_po ~ 1% sampling of a population of 10⁶ cytoplasmic free ribosomes requires n = 10,000 examinations and T ~ 10,000 sec ~ 3 hours assuming t_exam ~ 1 sec (t_travel ~ 0.2 sec) for a single in cyto nanorobot. These times compare well even against the rapid multiplication rate of proliferating tissue cells (e.g., human embryonal cells, ~24 hours). Post-examination individual target object tagging (e.g., using anchored messenger molecules) without physical sequestration reduces t_exam only slightly but does not reduce t_travel, hence has no significant impact on T. Note that successive mitochondrial samplings will generally be independent if X_travel (~2 microns) >> DX_diffuse; from Eqn. 3.1, mitochondrial diffusion displacement is of order DX_diffuse ~ 20 nm, taking t = t_exam ~ 10 sec, R ~ 1 micron, and h ~ 10 kg/m-sec (in cyto, at 310 K; Table 9.4), hence the independence condition is usually satisfied.

Last updated on 20 February 2003