Microbivores: Artificial Mechanical Phagocytes
using Digest and Discharge Protocol

Nanomedicine offers the prospect of powerful new tools for the treatment of human diseases and the improvement of human biological systems using molecular nanotechnology. This paper presents a theoretical nanorobot scaling study for artificial mechanical phagocytes of microscopic size, called "microbivores," whose primary function is to destroy microbiological pathogens found in the human bloodstream using a digest and discharge protocol. The microbivore is an oblate spheroidal nanomedical device measuring 3.4 microns in diameter along its major axis and 2.0 microns in diameter along its minor axis, consisting of 610 billion precisely arranged structural atoms in a gross geometric volume of 12.1 micron³. The device may consume up to 200 pW of continuous power while completely digesting trapped microbes at a maximum throughput of 2 micron³ of organic material per 30-second cycle. Microbivores are up to ~1000 times faster-acting than either natural or antibiotic-assisted biological phagocytic defenses, and are ~80 times more efficient as phagocytic agents than macrophages, in terms of volume/sec digested per unit volume of phagocytic agent.

OUTLINE

1. Introduction

After a basic overview of current approaches to sepsis and septicemia that defines the medical challenge, the basic microbivore scaling design is presented, followed by a brief analysis of the phagocytic activity and pharmacokinetics of bloodborne nanorobotic microbivores. As a scaling study, this paper serves mainly to demonstrate that all systems required for mechanical phagocytosis could fit into the stated volumes and could apply the necessary forces and perform all essential functions within the given power limits and time allotments. This scaling study is neither a complete design nor a formal design proposal.
 
 

2. Sepsis and Septicemia

Septicemia may be caused by several different classes of pathogenic organisms, most commonly identified as bacteria (bacteremia; Section 2.1), viruses (viremia; Section 2.2), fungi (fungemia; Section 2.3), parasites (parasitemia; Section 2.4) and rickettsiae (rickettsemia; Section 2.4).

2.1 Bacteremia

Still, it is not unusual to find a few bacteria in blood. Normal activities like chewing, brushing or flossing teeth causes movement of teeth in their sockets, infusing a burst of commensal oral microbes into the bloodstream [7]. Bacteria can enter the blood via an injury to the skin, the lining of the mouth or gums, or from gingivitis or other minor infections in the skin and elsewhere [8]. Bacteremias from a focus of infection are usually intermittent, while those from vascular system infection tend to be continuous [7], such as endocarditis or embolism from heart valve vegetations in subacute bacterial endocarditis (SBE), sometimes leading to infectious mycotic (e.g., Staphylococcus aureus) aneurysms.

Bacteria can also enter the blood during surgical, dental, or other medical procedures [8] such as the insertion of I.V. lines (providing fluids, nutrition or medications), cystoscopy (a viewing tube inserted to examine the bladder), colonoscopy (a viewing tube inserted to view the colon), or heart valve replacement with a prosthetic (thankfully now rare, due to heavy preoperative dosing with cefazolin). Such bacteria are normally removed by circulating leukocytes (along with the fixed reticuloendothelial cells in the spleen, liver, and lungs), but a few species of bacteria are unusually virulent and can overwhelm the natural defenses. The CDC estimates that ~25,000 U.S. patients die each year from bacterial sepsis [9]. Worldwide, there are ~1.5 million cases of sepsis and ~0.5 million deaths from sepsis annually. Antibiotics can fight sepsis, pressors can relieve hypotension from sepsis, volume replacement and I.V. albumin or HESPAN (hetastarch) can offset hypovolemia, but until recently there have been no pharmacological agents approved to fight the complications of coagulation and inflammation due to bacterial endotoxin (Section 4.4.2) (which can still lead to a mortality rate of 30%-50% [10]) although antiendotoxin peptides [242] and anti-LPS monoclonal antibodies [243] are being investigated for this purpose.

2.1.1 Gram-positive Bacteremia and Current Therapy

The recommended duration of therapy even for uncomplicated cases of S. aureus bacteremia arising from a removable source is 2-9 grams/day of antibiotics given I.V. for 2 weeks [11], after which 5% of patients still relapse, usually with endocarditis. Endocarditis accompanying bacteremic pneumonia in years past might require a treatment regimen of penicillin G potassium in the quantity of 24 million units/day, representing 15 grams/day dissolved in a minimum I.V. infusate volume of 24 ml/day, for 4 weeks [11, 12]; the current most aggressive treatment is 0.5-2 gm/day vancomycin orally for 7-10 days [12], often together with 1-4 gm/day ceftriaxone and possibly also a similar dose of teichoplanin (antibiotics of last resort, due to potential toxicity).

2.1.2 Gram-negative Bacteremia and Current Therapy

Treatment for brucellosis involves gram/day intramuscular streptomycin injections (use generally curtailed; side effect is deafness) plus an oral 1-2 gram/day multiple-antibiotic regimen lasting 3 weeks [11], and longer courses of therapy lasting several months may be required to cure relapses [11]. Doses up to 12 gm/day of Ancef (cefazolin) have been used for severe septicemia [12]. Acute enterobacteremia may require enormous daily treatment doses of penicillin G, typically 20-80 million units or 12.5-50 grams/day, administered I.V. [12]. Evolving antibiotic resistance is an increasing problem, particularly vancomycin-resistant enterococcus, which is developing at an alarming rate among immunocompromised hospitalized patients (but often responds to 1-4 gm/day of erythromycin for 1-2 weeks).

2.1.3 Phage Therapy

With the relatively recent realization that phages have a very narrow host range [27], success rates of 80-95% have been reported [23] and interest in phage therapy as an alternative to antibiotics is reawakening [25]. For example, 10⁶ E. coli bacteria injected intramuscularly into mice killed all of the animals (100% mortality), but the simultaneous injection of 10⁴ phage virions specifically selected against the K1 capsule antigen of that bacterial strain of E. coli completely prevented death (0% mortality) [17]. Soothill [19] found that a dose of 1.2 ×10⁷ virions of a bacteriophage targeted against a virulent strain of Pseudomonas aeruginosa protected half of the mice who were challenged with 5 LD50 of the bacterium; as few as 100 virions of another phage specifically targeted against a virulent strain of Acinetobacter baumanii protected mice challenged with 5 LD50 (10⁸ CFU)^* of the pathogen. Interestingly, an oncolytic virus has recently been reported [31].

One practical difficulty with phage therapy is that even in the absence of an immune response, intravenous therapeutic phage particles are rapidly eliminated from circulation by the reticuloendothelial system (RES), largely by sequestration in the spleen [16]. But Merril et al [27] found that splenic capture could be greatly eliminated by the serial passage of phage through the circulations of mice to isolate mutants that resist sequestration. This selection process results in the modification of the nature of the phage surface proteins, via a double-charge change from acidic to basic which is achieved by replacing glutamic acid (- charge) with lysine (+ charge) at the solvent-exposed surface of the phage virion [27]. The mutant virions display 13,000-fold to 16,000-fold greater capacity to evade RES entrapment 24 hours post-injection as compared to the original phage [27]. But one concern is that since evasion of entrapment allows increased virulence for most pathogens, widespread use of such modified virus could make possible species jumping of the altered phage genes, especially if the virion is RNA-based and has a high mutation rate. Nanorobotic agents entirely avoid this risk.

2.1.4 Bacterial Shape, Size, and Intravenous LD50

The intravenous median lethal dose (LD50) for 50% of hosts inoculated with various bacteremic microorganisms ranges widely from 1-10⁹ CFU/gm (Table 2), but the central range appears to be 0.1-100 ×10⁶ CFU/ml assuming a ~1 gm/cm³ density for biological materials.

2.2 Viremia

In cases of blood plasma viremia, virion particle counts range from 1/ml to 0.35 ×10⁶/ml for HIV in humans [54-56], with a mean of 25/ml for asymptomatic patients; viral loads for simian immunodeficiency virus (SIV) in monkeys may be much higher, 2-200 ×10⁶/ml of blood [57]. Hepatitis C (HCV) [58] infectious viral loads (at ~10^-18 gm/virion) are considered low at 0.2-1 × 10⁶/ml, medium at 1-5 ×10⁶/ml, high at 5-25 ×10⁶/ml, and very high at >25 ×10⁶/ml. Hepatitis G (HGV) [59] viral loads in symptomatic patients are 0.16-5.1 ×10⁶/ml. TT virus (TTV) [60] loads in HIV patients may exceed >0.35 ×10⁶/ml. Thus the typical blood particle burdens in viremia are much the same as in bacteremia, roughly 0.1-100 ×10⁶/ml. Viral infections can be very difficult to eradicate pharmaceutically, as most treatments are virustatic, not virucidal. For example, acute treatment of herpesvirus requires 2 grams/day of acyclovir, with chronic suppressive therapy for recurrent disease requiring 0.8 grams/day for up to 12 months [12].

2.3 Fungemia

Patients with catheter-related fungemia due to fungus counts of Malassezia furfur at 50-1000 CFU/ml required antibiotic treatment [66], and catheter-related Rhodotorula (red yeast) infected patients with colony counts in the 100-1000 CFU/ml range required antifungal therapy [67]. Human bloodstream fungal infections thus appear to range from 1-1000 CFU/ml. Disseminated (systemic) candidiasis is effectively managed with 0.2 gm/day of fluconazole for at least 4 weeks [12]. Coccidioides immitis fungal infection is treated with ~0.02 gm/day (~200 ml/day I.V. drip solution via Ommaya reservoir into the brain ventricles) of amphotericin B for up to 9-11 months [12] (very toxic, with overdose leading to cardio-respiratory arrest; typically dosed as total cumulative). Respiratory fungal histoplasmosis (Histoplasma capulatum) may be treated with oral doses of itraconazole at 0.2-0.5 gm/day for a minimum of 3 months [12].

2.4 Parasitemia and Rickettsemia

Rickettsia are rod-shaped or coccoid gram-negative obligate intracellular parasites ~0.25 microns in diameter that in humans grow principally in endothelial cells of small blood vessels, producing vasculitis, cell necrosis, vessel thrombosis, skin rashes and organ dysfunctions [73]. The infection is characterized by repetitive cycles of bloodborne organisms, or rickettsemia. For example, in cattle the number of pathogens in the blood varies between a low of 100/ml and a peak of 1-10 ×10⁶/ml over 6-8 week intervals; in each cycle, the blood count slowly rises over 10-14 days and then declines precipitously [74]. However, most of these parasites are found in the red cells, and the organism's appearance in the blood plasma is incidental to its activity. Plasma titers for free R. rickettsii organisms in the blood of human patients with Rocky Mountain spotted fever averaged 5-16 parasites/ml in treated patients who survived, and 1000 parasites/ml in the postmortem plasma of one patient with untreated fatal fulminant fever [75]. Antibiotic therapy has reduced the death rate from 20% to about 7%, with death usually occurring when treatment is delayed [8].
 
 

3. Microbivore Scaling Analysis and Baseline Design

The microbivore is an oblate spheroidal nanomedical device consisting of 610 billion precisely arranged structural atoms plus another 150 billion mostly gas or water molecules when fully loaded (Section 3.2.5). The nanorobot measures 3.4 microns in diameter along its major axis and 2.0 microns in diameter along its minor axis, thus ensuring ready passage through even the narrowest of human capillaries (~4 microns in diameter [1]). Its gross geometric volume of 12.1056 micron³ includes two normally empty internal materials processing chambers totalling 4 micron³ in displaced volume. The device may consume up to 200 pW of continuous power while in operation and can completely digest trapped microbes at a maximum throughput of 2 micron³ per 30-second cycle, large enough to internalize almost all relevant microbes in a single gulp. As in previous designs [2], to help ensure high reliability the system presented here has tenfold redundancy in all major components, excluding only the largest passive structural elements.

During each cycle of operation, the target bacterium is bound to the surface of the microbivore via species-specific reversible binding sites [1]. Telescoping robotic grapples emerge from silos in the device surface, establish secure anchorage to the microbe's plasma membrane, then transport the pathogen to the ingestion port at the front of the device where the cell is internalized into a morcellation chamber. After sufficient mechanical mincing, the morcellated remains are pistoned into a digestion chamber where a preprogrammed sequence of engineered enzymes are successively injected and extracted, reducing the morcellate primarily to monoresidue amino acids, mononucleotides, glycerol, free fatty acids and simple sugars, which are then harmlessly discharged into the environment through an exhaust port at the rear of the device, completing the cycle.

This "digest and discharge" protocol [1] is conceptually similar to the internalization and digestion process practiced by natural phagocytes, but the artificial process should be much faster and cleaner. For example, it is well-known that macrophages release biologically active compounds such as muramyl peptides during bacteriophagy [76], whereas well-designed microbivores need only release biologically inactive effluent.

3.1 Primary Phagocytic Systems

3.1.1 Reversible Microbial Binding Sites

Additionally, all bacteria of a given species express numerous unique proteins in their outermost coat. A complete review is beyond the scope of this paper, but a few representative examples can be cited. Each single-celled Staphylococcus aureus organism displays binding sites for human vitronectin on its surface, including 260 copies/cell representing high-affinity sites and 5,240 copies/cell representing moderate-affinity sites [86]. The plasmid-specified major outer membrane protein TraTp of Escherichia coli is normally present in 21,000 copies/cell at the cell surface [87]. Streptococcus pyogenes (strain 6414) has 11,600 copies/cell of surface binding sites to human collagen [88]; another receptor protein specific to type II collagen (among the dozens of collagen types) are found in 30,000 copies/cell on the surface of each Staphylococcus aureus (strain Cowan 1) cell with equilibrium constant K_d = 10^-7 M [89]. (Researchers found that the same bacterial receptor would also specifically respond to synthetic collagenlike analogs containing the peptide sequences (Pro-Gly-Pro)_n, (Pro-Pro-Gly)₁₀, and (Pro-OH-Pro-Gly)₁₀ [89].) If the microbivore must distinguish among ~500 different bacterial species or strains, then each bacterial cell type may be uniquely identified using as few as log₂(500) ~ 9 binary antigenic markers [1].

Assuming that nine species-specific bacterial coat ligands are sufficient to uniquely identify an encountered bacterium as belonging to the target species or strain, and that ~10⁴ copies of each of the nine ligands are present on a bacterial surface of area ~10 micron², then the mean distance between each ligand of the same type is 31.6 nm. A square array of 200 adjacent ligand receptors on the nanorobot surface, with each ligand or receptor active site ~5 nm² in area (e.g., antibody-antigen complexes typically show contact interfaces of 6-9 nm², involving 14-21 residues on each side [90-92]), would on average overlap one such ligand that is resident in a bacterial surface pressed against it. If there are 100 such arrays uniformly distributed over the entire nanorobot surface, then a randomly chosen mutual contact area of only 1% of the nanorobot surface suffices to ensure that there is at least one array overlapping a unique ligand on the bacterial surface during a collision. Of course, the probability of binding, even given mutual contact, is not unity, but perhaps only ~10% (e.g., N_encounter ~ 10 [1]). However, this factor is almost completely offset because there are nine equivalent array sets -- one set for each of the nine unique bacterial ligands -- and recognition and binding of any one of the nine unique ligands will suffice to bind the bacterium securely to the nanorobot.

Since array members need not be adjacent, the actual physical configuration on the microbivore surface is a bit different. The binding sites are modeled after the narrowband chemical sensor described in Nanomedicine [1], Figure 4.2. Each 3×3 receptor block consists of nine 7 nm × 7 nm receptor sites, one for each of the nine species-specific bacterial coat ligands. There are 20,000 of these 3×3 receptor blocks distributed uniformly across the microbivore surface. Each 3×3 receptor block measures 21 nm × 21 nm ×10 nm. A single receptor, if bound to a ligand, may provide a binding force of 40-160 pN [1], probably larger than the largest plausible in sanguo dislodgement force of ~100 pN [1] and thus gripping the bacterium reasonably securely. The recognition event can be consumated in t_meas ~ 30 microsec, according to Eqn. 8.5 from Nanomedicine [1]. As an operational procedure, once any one of the nine key ligands has been detected, all of the remaining unoccupied receptors for that ligand in other receptor blocks can be deactivated, and so on until all nine ligands have been individually confirmed -- a combination lock whose completion triggers bacteriocide. Interestingly, during phagocytosis by macrophages most injected particles are recognized by more than one receptor; these receptors are capable of cross-talk and synergy, and phagocytic receptors can both activate and inhibit each other's function [247].

Microbial binding is energetically favored; if binding energy is ~240 zJ per microbial ligand [1] (1 zeptojoule (zJ) = 10^-21 J), then the power requirement for debinding a set of 9 occupied receptors in ~100 microsec is only ~0.02 pW.

3.1.2 Telescoping Grapples

Each telescoping grapple is housed beneath a self-cleaning irising cover mechanism that hides a vertical silo measuring 50 nm in diameter and 300 nm in depth, sufficient to accommodate elevator mechanisms needed to raise the grapple to full extension or to lower it into its fully stowed position. At a 1 mm/sec elevator velocity, the transition requires 0.25 millisec at a Stokes drag power cost (operating in human blood plasma) of 0.0008 pW, or 0.008 pW for 10 grapples maximally extended simultaneously [1]. The elevator mechanism consists of compressed nitrogen gas rotored into or out of the subgrapple chamber volume from a small high-pressure sealed reservoir, a pneumatic piston providing the requisite extension or retraction force. A grapple-distension force of ~100 pN applied for a distance of 250 nm could be provided by 25 atm gas pressure in a minimum subgrapple chamber volume of 10⁴ nm³, involving the importation of ~6000 gas molecules. Removal of these ~6000 gas molecules from a maximum subgrapple chamber volume of 10⁵ nm³ provides a ~1 atm pressure differential and a maximum grapple-retraction force of ~100 pN; cables or other mechanisms may assist in retraction if more force is needed.  The aperture of the irising silo cover can be controlled to continuously match the width of the protruding grapple, greatly reducing the intrusion of foreign biomolecules into the silo.

Each grapple is terminated with a reversible footpad ~20 nm in diameter. In the case of gram-positive bacteria, a footpad may consist of 100 close-packed lipophilic binding sites targeted to plasma membrane surface lipid molecules, providing a secure 100 pN anchorage between the nanorobot and the bacterium assuming a single-lipid extraction force of ~1 pN [1]. In the case of gram-negative bacteria, a footpad with binding sites for ~3 murein-linked covalently attached transmembrane protein molecules would provide a secure 120-480 pN anchorage, assuming 40-160 pN/molecule and ~9 such molecules per 1000 nm² of microbial surface (Section 3.1.1). In either case, undesired adhesions with bacterial slime must be avoided. The footpad tool is rotated into, or out of, an exposed position from behind a protective cowling, using countercoiled internal pull cables.

The tiniest bacterium to be digested may be ~200 nm in diameter (Section 2.1.4), but the smallest virus can be only ~16 nm wide (Section 2.2). Since the work envelopes of adjacent grapples picking particles bound to the hull surface extend 150 nm toward each other from either side, the maximum center-to-center intergrapple separation that permits the ciliary transport of 16 nm objects is ~300 nm. This requires 1 grapple per 0.09 micron² of nanorobot surface, for a total of 277 grapple silos uniformly distributed over the entire 26.885 micron² microbivore outer hull, excluding the two 1-micron² port doors. (One or more grapple-containing bridges across the annular exhaust port aperture (Section 3.1.4) may be necessary if it is desired to transport targets <200 nm in diameter from the circular DC exhaust port island to the main grapple field of the microbivore, allowing subsequent transport to the ingestion port inlet; such bridges are not included in the present design.) During transport, a bacterium of more typical size such as a 0.4 micron × 2 micron P. aeruginosa bacillus may be supported by up to 9 grapples simultaneously. A somewhat larger E. coli bacterium would be supported by up to 12 grapples.

After telescoping grapples are securely anchored to the captive bacterium, the receptor blocks are debonded from the microbial surface, leaving the grapples free to maneuver the pathogen as required. Grapple force sensors inform the onboard computer of the captive microbe's footprint size and orientation. The grapples then execute a ciliary transport protocol in which adjacent manipulators move forward and backward countercyclically, alternately binding and releasing the bacterium, with new grapples along the path ahead emerging from their silos as necessary and unused grapples in the path behind being stowed. Manipulator arrays, ciliary arrays (MEMS), and Intelligent Motion Surfaces are related precursor (and currently available) technologies (reviewed in Section 9.3.4 of Nanomedicine [1]).

Rodlike organisms are first repositioned to align their major axis perpendicular to a great circle plane containing both the device center point and the ingestion port at the front of the device. This keeps the organism traveling over surfaces having the largest possible radius of curvature during transport, thus minimizing any forces necessary to bend the bacterium as it follows the curved microbivore surface. A cylindrical bacterium of length L_tube and bending stiffness k_tube is bent by a force F into a circle segment having radius of curvature R_curve ~ (k_tubeL_tube² / 2 F) for small deflections. For the bacillus P. aeruginosa, L_tube ~ 2 microns and tube radius is ~0.2 microns; the elastic modulus is 2.5 ×10⁷ N/m² for the 3-nm thick hydrated sacculus [97], giving k_tube ~ 4 ×10^-4 N/m using Eqn. 9.50 from Nanomedicine [1]. To bend the microbe to the semimajor axis of the microbivore (R_curve = 1.7 microns) requires F ~ 470 pN, or F ~ 800 pN for the semiminor axis (R_curve = 1 micron), both of which are substantial bending forces in comparison to the nominal single-grapple anchorage force of 100-500 pN/footpad. Thus it is desirable to bend the bacterium as little as possible during transport. Bending forces may be minimized by adjusting grapple lengths to hold the bacillus farther from the microbivore surface near the endpoints of the footprint, and closer to the microbivore surface near the center of the footprint.

Organisms of all shapes are conveyed toward the ingestion port via cyclical ciliary cycling motions. At a transport velocity of 1 mm/sec, a microbe captured at the greatest possible distance from the ingestion port (~3 microns) is moved to the vicinity of the ingestion port in ~3 millisec. The Stokes law energy cost of transporting an E. coli bacterium through blood plasma side-on at 1 mm/sec is 0.01 pW, so transport power is dominated by mechanical losses in the grapples, a total of ~0.06 pW if 10 grapples are operated simultaneously.

Because the ingestion port is slightly recessed into the body of the nanorobot ellipsoid at the equator, the approaching bacterium must be carried around an inlet rim having a considerably smaller radius of curvature than the main body of the microbivore. The inlet rim is essential in this design and provides needed mechanical control from inlet-wall grapples as the microbe is fed into the ingestion port. From simple geometry, if one grapple is fully extended to length L = L_grap and the adjacent grapple is almost fully retracted to length L ~ 0, then the bacillus can be conveyed around an inlet rim curve of radius R_rim with zero bending if the distance between the adjacent grapples is no more than d_max ~ 2 R_rim sin^-1 (L_grap / 2 R_rim)^½ ~ 0.39 microns, taking L_grap = 250 nm and R_rim ~ 0.25 microns at the inlet rim. This requires at least 1 grapple per d_max² ~ 0.15 micron² of nanorobot surface near the ingestion port, comfortably lower in number density than the 0.09 micron²/grapple elsewhere on the hull. Nevertheless, to ensure full control of the transported object near the ingestion port an additional 23 grapple silos are non-uniformly distributed over the 10% of microbivore surface nearest the ingestion port, sufficient to raise the mean number density to 0.05 micron²/grapple in that region. Thus there are a total of 300 grapple silos embedded in the entire microbivore outer hull, excluding the area covered by the two 1-micron² port doors.

3.1.3 Ingestion Port and Morcellation Chamber

Opening the ingestion port door allows entry into the morcellation chamber (MC), a cylindrical chamber 2 microns in length and the same interior elliptical cross-section as the port door, giving a total open volume of 2 micron³ which is large enough to hold one intact microorganism because most sepsis-related bacteria are <2 micron³ in volume (Table 1). Recessed into the MC walls are 10 diamondoid cutting blades (possibly multisegmented), each ~2 micron long, ~0.25 micron wide, and 10 nm thick with a 1 nm cutting edge, giving ~0.050 micron³ of blades (~0.005 micron³/blade). Following the analysis of nano-morcellation systems described elsewhere [1], to mince material having Young's modulus ~10⁸ N/m² using one blade at a time (reserving the other 9 blades as replacements or to provide alternative chopping geometries) requires the application of ~100 nN/chop, consuming up to ~100 pW during a process in which the blade reciprocates at 50 Hz and travels at ~60 micron/sec, making 20 cuts in a total mincing time of 400 millisec. (Bacterial walls include a 3-6 nm thick hydrated sacculus [97] and include a cross-linked peptidoglycan (murein) mesh [95-97] with strands spaced ~1.3 nm apart [98].) The resulting morcellate should consist largely of organic chunks ~3-10 nm in diameter [1]. An intriguing alternative configuration is a diamondoid sieve or dragnet that could be pulled repeatedly through the MC, analogous to pushing the microbe forcibly through a strainer; other possible fragmentation techniques such as sonication appear to require too much onboard acoustic energy to be feasible (e.g., power intensities of ~10⁶ pW/micron² [1]).

Although complex mechanical assemblages may dissipate 10⁹ W/m³, mechanomechanical and electromechanical transducers are generally very efficient, dissipating 10¹²-10¹⁶ W/m³ during mechanical energy transmission [1, 93]. Conservatively assuming that the nanomotors needed to drive the chopping blade may dissipate ~10¹⁰ W/m³, then a ~0.01 micron³ drive motor is required to operate the blade; we allocate a total of 0.1 micron³ for multiple drive motors, thus providing tenfold redundancy. Another 0.1 micron³ is allocated for blade housings. A diamondoid MC wall ~10 nm thick (materials volume ~0.073 micron³) allows the MC to withstand internal pressures >1000 atm, far higher than the natural internal microbial pressurization of 3-5 atm [99]. (Bacterial rigidity is regulated by turgor pressure [100].)

Once microbial mincing is complete, the morcellate must be removed to the digestion chamber (Section 3.1.4) using an ejection piston. A 20-nm thick piston pusher plate driven by a 2 micron long, 10 nm thick pusher cable (energized by the chopping blade motor coupled through a mechanical transmission gearbox) comprises ~0.02 micron³ of device volume. This piston moves forward at ~20 microns/sec, applying ~1 atm of pressure to push morcellate of viscosity ~100 kg/m-sec through a 1 micron² gated annular aperture for a chamber length of 2 microns, emptying the MC in ~100 millisec with a Poiseuille fluid flow power dissipation [1] of ~2 pW. Interestingly, the energy dissipation rate required to disrupt the plasma membrane of ~95% of all animal cells transported in forced turbulent capillary flows is on the order of 10⁸-10⁹ W/m³ [101], corresponding to a mechanical power input of 100-1000 pW into a 1 micron³ chamber volume. The annular MC/DC interchamber door must be opened before activating the MC ejection piston; its size and power specifications are similar to those of the annular DC exhaust port door (Section 3.1.4.4).

The MC ejection piston also is used initially to draw the microbe into the MC in a controlled manner. By slowly pulling a vacuum after the ingestion port door has opened, the piston can apply ~1 atm of negative pressure over the ~1 micron² leading surface of the bacterium, or up to ~100 nN of force. The Poiseuille flow of a microorganism of viscosity ~1000 kg/m-sec through a 1 micron² aperture with a 1 atm pressure differential into a chamber 2 microns in length dissipates 0.2 pW as the bacterium is drawn into the chamber at a speed of 2 microns/sec, thus requiring ~1 second for complete internalization of 2 micron³ of ingesta.

3.1.4 Digestion Chamber and Exhaust Port

If the morcellate consists of organic chunks ~3-10 nm in diameter (Section 3.1.3), enzymes directed against specific bond types may attack these bonds only if they are exposed on the outermost surface of each chunk. Considering for simplicity only proteinaceous chunks, and given that the average amino acid has a molecular weight of 141.1 daltons and a molecular volume of V_res ~ 0.49 nm³, then a chunk of volume V_chunk may be regarded as having N_layer successive surface layers where V_chunk ~ V_res (1 + 2N_layer)³. Taking V_chunk^1/3 = 10.2 nm for the largest pieces implies a chunk comprised of 2197 residues and having N_layer ~ 6 layers that must be processed sequentially, like peeling an onion one skin at a time. Thus the entire enzyme suite must be shuttled in and out of the DC six times, with one "layer" of all chunks being processed during each of the six subcycles.

3.1.4.1 Artificial Enzyme Suite

To prevent self-digestion during storage and use, each artificial peptidase is engineered so that the class of residue it is designed to attack is not exposed on its own external physical surface [112] -- that is, each artificial enzyme minimally exhibits strong autolysis resistance [110-116], with an ideal objective of near-zero autolysis. (A few natural enzymes retain full post-autolysis functionality [117].) Another significant design constraint is that natural bacterial enzymes already present in the morcellate (e.g., elastase produced by P. aeruginosa [118]) must have negligible activity against any of the microbivore's artificial enzymes. Since the target microbe's enzyme inventory is known in advance, the microbivore enzyme suite can be tailored to deal with any unusually troublesome bacterial enzymes, and optimal pH in the DC can be actively managed (see below).

Ensuring biological digestive universality while allowing the enzyme engineer sufficient diversity of available protein building blocks requires a minimum of two pre-activated artificial enzymes that attack specific peptide bonds in each of the seven major amino acid classes -- acidic (Asn, Asp, Gln, Glu), aliphatic (Ala, Gly, Ile, Leu, Val), aromatic/hydrophobic (His, Phe, Trp, Tyr), basic (Arg, His, Lys), hydroxylic (Ser, Thr, Tyr), imino (Pro), and sulfur (Cys, Met). The present design thus includes a requirement for 14 artificial endopeptidases, plus 2 broad-spectrum artificial tripeptidase [119] and dipeptidase [120] if needed to complete the digestion of potentially bioactive tripeptides and dipeptides to free amino acids.

Enzymes capable of degrading nucleic acid polymers are classified as deoxyribonucleases (specificity for DNA) or ribonucleases (specifically hydrolyzing RNA), or as exonucleases (hydrolyzing a nucleotide only when present at a strand terminus, moving in only one direction, either 3'®5' or 5'®3') or endonucleases (cleaving internal phosphodiester bonds to produce either 3'-hydroxyl and 5'-phosphoryl termini or 5'-hydroxyl and 3'-phosphoryl termini) [105]. Some endonucleases can hydrolyze both strands of a double-stranded molecule, others attack only one strand of a double-stranded molecule, while still others cleave only single-stranded molecules. Restriction endonucleases recognize specific DNA sequences -- for example, Hpa I recognizes a specific double-strand 6-base sequence (GTTAAC/CAATTG) and selectively cleaves both strands of the double strand in the middle at the TA/AT bond, producing an unreactive molecular "blunt end" [105]. There are ten distinct dinucleotide bond combinations (AA, AC, AG, AT, CC, CG, CT, GG, GT, and TT), which suggests that 10 artificial endonucleases may suffice, plus 2 general-purpose dinucleases to complete the digestion to mononucleotides, for a total of 12 artificial polynucleotidases.

Additional engineered enzymes (not included in the present design) may be needed to digest bacteriophages that may be resident inside certain bacteria. To avoid digestion by bacterial restriction enzymes, phages often employ unusual molecular substitutions involving 2,6-diaminopurine, 6-methyladenine, 8-azaguanine, 5-hydroxymethyl uracil, 5-methylcytosine, 5-hydroxymethylcytosine, and others [121]. For example, B. subtilis phage DNA replaces thymine with hydroxymethyluracil and uracil; S-2L cyanophage replaces adenine by 2-aminoadenine (2,6-diaminopurine); SPO1, SP82G, and Phi-e substitute hydroxymethyl dUTP for dTTP in the phage DNA up to 20%; PBS1 and PBS2 phages substitute uracil for thymine; T-even (T2/T4/T6) phage DNA replaces dCMP by hydroxymethylcytosine which is then further glycosylated, rendering the phage DNA resistant to host restriction; and in phage Mu DNA, a unique glycinamide moiety modifies about 15% of the adenine residues [121]. Given our complete future knowledge of phage genomes and the bacteria they are likely to inhabit, a comprehensive phage digestive strategy can be planned and installed in advance, during microbivore design and construction. This problem is not considered serious in the case of standard antibiotic therapy.

Free adenosine (a mononucleotide) is involved in the regulation of coronary blood flow [122], and certain free nucleotides have been shown to exhibit minor physiological action on lymphocytes [123] and T cells [124] in animal models, so additional nucleotidases, phosphatidases and nucleosidases may be added if necessary to reduce free mononucleotides to phosphoric acid, sugars, and purine/pyrimidine bases prior to discharge from the nanorobot. However, such additional enzymes are not included in the present microbivore design because nucleotidase is naturally present in normal human serum [125-129] and at elevated serum levels in many disease conditions [129-133].

Microbial lipids may be digested by analogs of pancreatic lipase (e.g., steapsin) or lipoprotein lipase which hydrolyze polyacylglycerols (mostly glycosyl diacylglycerols in bacteria) containing fatty acid chains into free fatty acids and glycerol, by cholesterol esterase that hydrolyzes cholesteryl esters into free cholesterol (although cholesterol and other sterols are relatively rare in microorganisms [134-136]), by phospholipase that attacks phospholipids producing glycerol, fatty acids, phosphoric acid, and perhaps choline [105], or by sphingolipidases [137] or ceramidases [138] that hydrolyze the sphingolipids found in some bacteria, resulting in mostly glycerol and saturated (in bacteria) free fatty acids in the final digesta. Acyloxyacyl hydrolase removes the secondary (acyloxyacyl-linked) fatty acyl chains from the lipid A region of bacterial lipopolysaccharides (LPS endotoxin), thereby detoxifying the molecules [139]. The present microbivore design assumes a requirement for 5 artificial lipases.

Microbial carbohydrates may be digested by an amylase that hydrolyzes starch and glycogen, and by a selection of oligosaccharidases (e.g., maltase, sucrase-isomaltase) and disaccharidases or saccharases (e.g., lactase, invertase, sucrase, trehalase) to complete the digestion to monosaccharides [105]. (Lactase also has a second active site for splitting glycosylceramides [105].) The present design assumes a requirement for 4 artificial carbohydrases in the microbivore enzyme suite.

Finally, simple anions or cations may be required for pH management of the morcellate, and 25% of all enzymes contain tightly bound metal ions or require them for activity [105], most commonly Mg⁺⁺, Mn⁺⁺, Ca⁺⁺, or K⁺; certain low-bioavailability but essential cofactors such as iron and copper might also need to be actively managed. It might also be necessary in some cases to inject and extract small quantities of superoxide dismutase, catalase and chelating agents such as metallothionein, ferritin, or transferrin to control potentially damaging concentrations of superoxides and metals in the morcellate, or small quantities of other specialized enzymes analogous to heme oxygenase, biliverdin reductase and beta-glucuronidases to digest bacterial porphyrins [244], enzymes [245] to cleave bacterial rhodopsins, and so forth, but a full analysis of these factors is beyond the scope of this paper. The present design assumes a requirement for 3 additional chemical species of this type, to be manipulated simultaneously with the artificial enzymes as previously described.

Full digestion of the morcellate, constituting one complete digestion cycle, is thus presumed to require six subcycles of activity, with each subcycle involving the serial injection and extraction of 40 different enzymes or enzyme-related molecules (i.e., 40 sub-subcycles per subcycle), one after the other, for a total of 240 enzyme sub-subcycles. Interestingly, intracellular lysosomes are known to contain ~40 digestive enzymes capable of degrading all major classes of biological macromolecules -- including at least 5 phosphatases, 4 proteases, 2 nucleases, 6 lipases, 12 glycosidases, and an arylsulfatase [140, 141].

3.1.4.2 Digestion Cycle Time

3.1.4.2.1 Speed of Enzymatic Action

However, for most of the digestion cycle the DC environment consists of a relatively small number of temporarily resident enzyme molecules floating in a sea of plentiful substrate. Zubay [142] notes that in this situation, the speed of enzymatic action is considerably slower and k_cat, also known as the enzyme turnover number, is the most relevant measure of enzyme catalytic activity.  Table 3 shows that for peptidases, k_cat ranges from ~10^-1 sec^-1 to ~10⁵ sec^-1, while for other enzymes the range is even wider, from ~10^-1 sec^-1 to ~10⁸ sec^-1. In the present scaling study, the mean k_cat for all artificial engineered enzymes used in the microbivore enzyme suite, measured against representative substrates, is taken as a midrange value (for all enzymes) of ~10⁴ sec^-1 at physiological temperatures (~37°C).

Note that the diffusion time required by an enzyme molecule of radius 3.47 nm at 37°C in a plasma-like fluid of viscosity ~10^-3 kg/m-sec (for molecular diffusion) to achieve an RMS displacement equivalent to the ~0.5 micron clearance between the DC and MC chamber walls is ~2 millisec (<< t_enz), according to Eqn. 3.1 from Nanomedicine [1], so the enzyme action during each sub-subcycle is not seriously diffusion-limited. (The diffusion constant for a ~72 kDa fusion protein in unmorcellated intact E. coli cytoplasm is ~7.7 ×10^-12 m²/sec [163], giving a diffusion time across 0.5 microns of ~16 millisec, according to Eqn. 9.80 from Nanomedicine [1].)

3.1.4.2.2 Speed of Enzyme-Transport Rotors

What is the value of k_rotor during enzyme extraction? The injection of 10⁴ enzyme molecules into the 2 micron³ digestion chamber produces an enzyme concentration of ~10^-5 M (~5 ×10^-6 molecules/nm³), giving an initial rotor rate k_r(1) ~ 10,000 molecules/rotor-sec for the first enzyme molecule that is extracted from the DC by a rotor; k_r(2) ~ 9,999 molecules/rotor-sec for the second molecule extracted; and so forth. At the end of enzyme extraction, the last enzyme molecule present in the DC represents a concentration of ~10^-9 M (~5 ×10^-10 molecules/nm³), giving a final rotor rate k_r(10,000 = n_enz) ~ 1 molecule/rotor-sec for the last enzyme molecule that is extracted from the DC by a rotor. The first molecule to be extracted takes (1/k_r(1)) = 100 microsec for one rotor to extract, whereas the last molecule to be extracted takes (1/k_r(10,000 = n_enz)) = 1 sec for a rotor to extract. For the entire extraction process, the average number of rotor-sec per molecule required to empty the DC of n_enz enzyme molecules approximates the sum of the harmonic series (1/k_r(1)) + (1/k_r(2)) + ... + (1/k_r(n_enz)) divided by the number of molecules, or k_rotor^-1 ~ (gamma + ln(n_enz)) / n_enz = 0.978756 ×10^-3 rotor-sec/molecule, where Euler's constant gamma ~ 0.577215... and n_enz >> 1. Hence the net transport rate for all n_enz molecules is k_rotor ~ n_enz / (gamma + ln(n_enz)) ~ 10³ molecules/rotor-sec for n_enz = 10⁴ enzyme molecules, and taking t_extract = 50 millisec, then n_rotor = n_enz / (t_extractk_rotor) = 200 rotors.

However, increasing n_rotor to 2000 rotors to provide tenfold redundancy, while holding t_extract constant, reduces the required k_rotor by a factor of 10 -- e.g., to k_r(10,000) ~ 0.1 molecule/rotor-sec. According to Section 3.2.2 of Nanomedicine [1], the diffusion current to a rotor of face area 200 nm² (equivalent circular radius ~8 nm), taking the enzyme diffusion coefficient as ~7 ×10^-11 m²/sec at 37°C, is ~2 molecules/sec when the enzyme concentration is 10^-9 M at the rotor/digesta interface as the last enzyme molecule is being extracted. This is now more than an order of magnitude larger than the k_r(10,000) ~ 0.1 molecule/rotor-sec requirement, so enzyme rotors are operating well within the diffusion limit for these devices. After extraction of all enzymes, the rotors for that enzyme are stowed with the rotor blank space exposed, thus protecting stored enzymes from contact with a potentially degradative intrachamber environment.

Increasing n_rotor to 2000 rotors per enzyme species also permits the elimination of enzyme storage tanks and associated support structures, because 2 ×10⁴ enzyme molecules can be stored in 2000 rotors each having 10 enzyme receptor sites per rotor. If the rotors are turned at 1 kHz, the entire enzyme inventory is injected into the DC in ~1 rotor rotation time, giving t_inject ~ 1 millisec.

3.1.4.3 Summary of Digestion Systems

There is one set of 2000 enzyme-transport rotors for each of the 40 enzyme species transported, hence there are 80,000 enzyme-transport rotors protruding into the DC. These rotors have a total face area of 16 micron², somewhat more than the ~10 micron² cylindrical DC sidewall area, thus require some slight rotor invagination into the DC volume. The rotors occupy a total onboard volume of 0.4 micron³ with an additional 0.1 micron³ allocated for drive mechanisms, housings, and other rotor-related support, for a total 0.5 micron³ enzyme-transport rotor volume allocation. If the binding energy of each enzyme receptor is ~240 zJ [1], then the total energy cost to eject 10⁴ enzyme molecules from their rotors is ~0.0024 pJ, representing a mean power requirement of 2.4 pW when injection is performed over t_inject ~ 1 millisec. Rotor drag power during extraction is negligible, so full-cycle power consumption averages ~0.024 pW.

Note that bond hydrolysis is often thermodynamically favored, evolving a free energy of hydrolysis E_hydrol ~ -4 zJ/bond to -14 zJ/bond for breaking peptide bonds [164, 165], -21 zJ/bond to -46 zJ/bond for glycosides and sugars [165], and -15 zJ/bond to -103 zJ/bond for various organophosphate bonds [165, 166]. Hence the scission of N_bondx ~ 5 ×10⁶ bonds/sub-subcycle during a time t_ssc ~ 101 millisec/sub-subcycle produces a continuous digestive waste heat of P_digest = E_hydrolN_bondx / t_ssc~ 0.2-5 pW per nanorobot, but most likely <1 pW for typical microbial compositions.

It is well-known that protein components of the cell membrane are continually removed and replaced, with the turnover rate in the unprotected cellular environment varying for different proteins but averaging a half-life of ~200,000 sec or ~ 2 days [140, 141]. However, each enzyme spends a total time of 0.306 sec per digestion cycle (Table 6) exposed to the morcellate or intermediate digesta, which suggests useful enzyme suite lifetimes of at least 10⁴-10⁵ digestion cycles (e.g., mission lifetimes >3-30 days assuming continuous digestive activity) conservatively may be expected. In typical clinical deployments to combat acute bacteremia, each microbivore will experience at most 1-10 digestion cycles during the entire mission. Additionally, artificial enzymes that are deployed in relatively nondegradative controlled intrananorobotic environments might be expected to survive perhaps an order of magnitude longer than natural enzymes in the wild. This increased survivability, coupled with the tenfold redundancy of all critical onboard systems including the artificial enzymes and their transport mechanisms, suggests that extended microbivore missions lasting many months in duration might be feasible.

3.1.4.4 Ejection Piston and Exhaust Port

An annular exhaust port door must be opened prior to activation of the ejection piston to allow the digesta to escape. The exhaust port door is an oval-shaped irising mechanism [1] with an annular elliptical aperture measuring 0.721 microns × 1.227 microns along the inside curve and 1.108 microns × 1.884 microns along the outside curve in vertical plane projection, providing a 1.161 micron² aperture in the hull surface when fully open. Assuming 0.5 micron² of contact surfaces sliding ~1 micron at 1 cm/sec, power dissipation is ~3 pW during the 0.1 millisec door opening or closing time.

3.2 Microbivore Support Systems

3.2.1 Power Supply and Fuel Buffer Tankage

The microbivore is initially charged with glucose and compressed oxygen (stored in sapphire-walled tankage), and thereafter absorbs its ongoing requirements directly from the bloodstream. Assuming 50% energy conversion efficiency and a 200 pW continuous power production requirement, each glucose and oxygen molecule that are consumed produce 2382.5 zJ or 397.1 zJ, respectively [1], indicating a peak burn rate of 8.4 ×10⁷ molecules/sec of glucose and 50 ×10⁷ molecules/sec of O₂.

The minimum glucose concentration in normal adult human blood is 2.3 ×10^-3 molecules/nm³ [1]. From Eqns. 3.4 and 4.7 in Nanomedicine [1], the required glucose current may be supplied by 13 receptor sites on the device surface at the diffusion limit, assuming device radius ~1 micron and receptor radius ~1 nm. However, at the minimum bloodstream concentration a conventional molecular sorting rotor transports ~10⁶ molecules/rotor-sec, so a minimum of 84 rotors are required to provide the required maximum flow. The present design employs 100 glucose rotors for each of the ten independent powerplants. A small number of glucose rotors could also be positioned for uptake inside the digestion chamber, allowing the scavenging of any microbe-derived glucose before the digesta is expelled; however, this facility is not included in the current design.

The minimum free molecular oxygen concentration in normal adult human blood is 3.0 ×10^-5 molecules/nm³ in venous blood and 7.3 ×10^-5 molecules/nm³ in arterial blood [1]. From Eqns. 3.4 and 4.7 in Nanomedicine [1], the required oxygen current may be supplied at the diffusion limit by ~1200 receptor sites on the device surface, while in arterial blood; by ~2000 receptor sites assuming an average 50%/50% arterial/venous environment during one complete circulation; or by ~6200 receptor sites in venous blood alone. However, at blood plasma oxygen concentrations a conventional molecular sorting rotor transports ~10⁵ molecules/rotor-sec, so a minimum of ~5000 rotors are required to provide the required maximum flow. The present design employs 7500 oxygen rotors for each of the ten independent powerplants, thus retaining full tenfold redundancy throughout.

Waste products from oxyglucose power generation include water and carbon dioxide. There are 50 ×10⁷ molecules/sec of each waste species produced, which may be ejected from the nanorobot using 500 standard sorting rotors for each species, assuming a transport rate of ~10⁶ molecules/rotor-sec. The present design thus employs 500 rotors each for H₂O and for CO₂, for each of the ten independent powerplants. However, in an emergency these wastes could alternatively be bulk-vented to the external environment without harmful effect -- the effervescence limit for point releases of bulk CO₂ in arterial plasma is ~70 ×10⁷ molecules/sec [1].

The microbivore design thus includes 86,000 small-molecule sorting rotors for energy-molecule transport with full tenfold redundancy, occupying a total of ~8.6 micron² of microbivore surface area and 0.103 micron³ of microbivore volume. Energy dissipation by the rotor system, if operated at the maximum 200 pW production rate, is 16 pW assuming the transfer of 158.4 ×10⁷ molecules/sec at an energy cost of ~10 zJ/molecule (net energy cost after compression energy recovery) [1]. On the microbivore surface, the energy-molecule transport rotors are arranged as compactly as possible into ten lune-shaped sectors (one for each of the ten powerplants) running from front to back (i.e., from ingestion port to exhaust port), with 8600 rotors/lune.

Onboard oxyglucose fuel tanks are scaled to provide a buffer supply of ~one-half circulation time or one digestion cycle time (~30 sec) of peak device energy requirement. Assuming a 50% aqueous solution of glucose in the glucose storage tank and a molecular volume of 0.191 nm³/molecule for glucose molecules [1], then the required glucose tank volume is 0.962 micron³ to hold a buffer supply of 252 ×10⁷ molecules of glucose fuel. Adding ~0.038 micron³ for 5-nm thick diamondoid walls and other support structure gives a 1.0 micron³ microbivore volume requirement for the glucose buffer tank. Assuming oxygen storage at 1000 atm (0.0791 nm³/molecule [1]), the 30-sec buffer supply of 1500 ×10⁷ oxygen molecules at 200 pW peak powerplant output requires an oxygen tank of volume 1.187 micron³. A spherical pressure tank requires a diamondoid wall thickness of >3.3 nm to avoid bursting; the present design assumes 10 nm thick tank walls. Adding ~0.055 micron³ for tank material volume and 0.058 micron³ for other support structure gives a 1.3 micron³ microbivore volume requirement for the oxygen buffer tank.

Diamondoid mechanical cables may transmit internal mechanical energy at power densities of ~6 ×10¹² W/m³ [1]. Therefore a single cable that can transmit the entire microbivore power output of 200 pW may have a volume of ~3 ×10^-5 micron³, or ~5 ×10^-5 micron³ including sheathing. To connect every powerplant with each of its 9 neighbors via power cables, permitting rapid load sharing among any pair of powerplants inside the device, requires 45 power cables; assuming 1000 internal power cables to accommodate additional power distribution tasks and for redundancy, total power cable volume is 0.05 micron³. By varying the cable rotation rate, the same power cables can simultaneously be used to convey necessary internal operational information including sensor data traffic and control signals from the computers.

3.2.2 Sensors

Acoustic communication sensors mounted within the nanorobot hull permit the microbivore to receive external instructions from the attending physician during the course of in vivo activities. Assuming (21 nm)³ pressure transducers [2], then 1000 of these transducers displace ~0.01 micron³ of device volume and 0.44 micron² of device surface area, producing a small net power input to the device of ~10^-4 pW when driven by continuous 0.1-atm pulses [2].

An internal temperature sensor capable of detecting 0.3°C temperature change [1] may have a volume of (~46 nm)³ ~ 10^-4 micron³; positioning ten such sensors near each of the 10 independent powerplants for redundancy implies a total internal temperature sensor volume of ~0.01 micron³. An additional 0.03 micron³ of unspecified internal sensors are included in the microbivore design, bringing the total for all sensors to 0.15 micron³.

3.2.3 Onboard Computers