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by Robert A. Freitas Jr.

© Copyright 1998, Robert A. Freitas Jr.
All rights reserved.

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Chapter 3. Molecular Transport and Sortation

Chapt. 3 Table of Contents | Page 1 | Page 2 | Page 3 | Page 4


3.5.5 Diamondoid Receptor Design

Natural enzymes and antibodies are proteins folded into highly organized, preformed shapes that present a ready-made "keyhole" into which a target ligand will fit. The enzyme is folded in such a way as to create a region that has the correct molecular dimensions, the appropriate topology, and the optimal alignment of counterionic groups and hydrophobic regions to bind a specific target molecule. Tolerances in the active sites can be narrow enough to exclude one isomer of a diastereomeric pair. For example, D-amino acid oxidase will bind only D-amino acids, not L-amino acids.

These "keyholes" are extremely floppy, yet still achieve fair specificity. This is a consequence of "induced fit" in protein binding sites. That is, the interaction of the target molecule with an enzyme induces a conformational change in the enzyme, resulting in the formation of a strongly binding site and the repositioning of the appropriate amino acids to form the active site. The receptor flexes, balloons, hinges, or contracts by 0.05-1.0 nm in just the right places to maximize specificity as the selected ligand enters the site. In some cases such as O2 and CO binding by myoglobin, ligands enter the receptor through a series of temporary voids that appear and disappear in the receptor as ~10 picosec dynamic structural fluctuations [409]. Induced fit can reduce receptivity to undesired proteins that exploit relative geometry by bonding enough to bring portions of their surfaces into alignment with the same receptor sites that bind desired proteins. Folding transitions appear to be the most prevalent and to possess the most possibilities for adaptability or induced fit [1068].

For smaller molecules, it is likely that recognition processes will be relatively inefficient, time-consuming, and more difficult to engineer if they involve a good deal of rearrangement of the receptor's shape [382]. Thus there is considerable interest among chemists in designing artificial receptors that have their cavities already formed into the shape appropriate for the intended substrate [1057]. For instance, rigid-cavity "spherand" receptors are exceptionally efficient at binding metal ions [410], bowl-shaped molecules such as cryptaspherands, calixarenes, and carcerands can be lined with chemical groups along their walls and with charged groups along their rims to achieve high binding specificity [410-411, 1262], and container molecules with 0.2 -0.4 nm portals control entry to their interiors using "French door" and "sliding door" gates [417].

Ultimately, receptors will be designed to nanoscale precision and may be constructed using diamondoid materials [1199]. Electrostatic, hydrophobic, and hydrogen-bond forces will add immensely to artificial receptor specificity and are essential for binding small molecules. For example, using a 0.2-nm range in a saline environment, 10-40 charge contacts would be required to bind molecules of various sizes and concentrations using electrostatic force alone, which is ~0.5 charge/nm2 over the entire surface of a 60,000 dalton globular protein (vs. ~1 charge/nm2 for the surface of an isolated zwitterionic amino acid). Or, a 7 nm2 hydrophobic cavity having the exact folded shape of the target ligand generates ~120 zJ binding energy as the molecule stuffs itself into the cavity to exclude its surface from solvent water. (J. Soreff notes that such receptors may need to include solvent egress channels.)

But consider a theoretical receptor that employs van der Waals dispersion forces alone. Atoms comprising the typical protein/CHON target molecule in the human body have an average atomic mass of ~6 amu/atom and an average density of 1500 kg/m3, giving a mean molecular volume of ~6.7 x 10-30 m3 per atom in the target molecule. Assume for simplicity a spherical receptor surface that forms a negative image of the surface of the target molecule. The receptor surface lies ~1.5 x (minimum van der Waals contact distance) ~0.3 nm from the perimeter atoms of the target molecule, and completely encloses the target molecule (thus requiring at least one moving part). Table 3-6 shows that the theoretically available maximum binding energy Evdw, using only dispersion forces (from Eqn. 3.21), should be sufficient to adequately bind all but the smallest target molecules according to the criteria set forth in Section 3.5.2. (Proteins are actually ellipsoidal with a much larger surface area Ap = 0.111 MW2/3 nm2 [413] than if they were spherical1, so Table 3-6 figures are conservative for protein binding.) Dispersion forces alone can provide the minimum required binding energy of ~120 zJ with Ap ~6 nm2 of contact surface (MW > 400 daltons) at 0.3 nm mean range, and dispersion-force receptors can offer exceptionally high affinities for molecules >1000 atoms.


Table 3-6. Maximum Binding Energy Available in a Dispersion-Force Receptor
with 0.3-nm Contact Boundary for CHON Target Molecules of Various Sizes

Mean # of
Atoms in
Surface Area
of Target
Area of
  Maximum vdW
Binding Energy
10   60   0.80 nm2   2.6 nm2   0.39 nm3   16 zJ
102   600   3.7 nm2   6.9 nm2   1.7 nm3   72 zJ
103   6000   17 nm2   24 nm2   11 nm3   330 zJ
104   60,000   80 nm2   93 nm2   84 nm3   1600 zJ
105   600,000   370 nm2   400 nm2   740 nm3   7200 zJ


What about specificity? Given the ability to design diamondoid binding sites to at least localized <0.01 nm tolerances, chirality is readily detected and (purely as a design exercise) it may even be possible to distinguish diatomic nitrogen and oxygen on the basis of size alone. The molecular lengths (major axis) of N2 and O2 are 0.250 nm and 0.253 nm, but the molecular widths (minor axis) are 0.140 nm and 0.132 nm, respectively. (Diatomic molecules get longer and narrower at higher molecular weight.) Thus N2 is distinguishable from O2 on the basis of width (~0.01 nm). With a van der Waals energy well depth of 1.1-1.4 zJ for N2 and O2, in a tight receptor these gases are bound at an energy density corresponding to 3000-4000 atm of pressure.

1 The formula for Ap is valid for small and medium size monomeric proteins (50-320 residues). The ratio of actual protein surface area to the surface area of a smooth ellipsoid of equal volume increases with molecular weight, since larger proteins are more highly textured and aspherical in shape. For oligomers whose monomers have 330-840 residues, surface areas ~MW and are 20%-50% greater than those given by Ap.

Chapt. 3 Table of Contents


3.5.6 Minimum Feature Size and Positioning Accuracy

Maximum displacement measurement accuracy in nanoscale devices is ~0.01 nm (Section 4.3.1), and RMS thermal displacement in diamondoid bonds is ~0.01 nm at 310 K (Section 3.5.4). Thermal displacements in 10-nm long diamondoid rods are ~0.01 nm at a 1-nm rod width, ~0.02 nm at 0.5-nm width, and ~0.10 nm at 0.3-nm width [10]. However, it is possible to construct components to even narrower tolerances.

For instance, a single C-O bond inserted into a diamondoid rod in a collinear carbon chain extends rod length by 0.1402 nm, the C-O bond length. An adjacent rod into which an N-N bond is similarly inserted is extended by 0.1381 nm, the N-N bond length. By bonding these rods (aligned at one end) it is possible to build diamondoid structures having 0.002-nm features2 (at the other end), which at 310 K will nonetheless suffer thermal displacements of ~0.01 nm or more. Similarly tiny displacements can be induced in binding cavity surfaces by inserting a foreign atom deep inside the bulk diamondoid structure, causing dislocation strains that decline in magnitude at greater distances from the compositional disturbance.3

It is also possible to translate diamondoid components through a picometer step size [433], much smaller than the unavoidable RMS thermal displacements, using any of several methods; for example:

  1. Levers. Consider a 10-nm lever joined to a fixed bar by a pivot at one end, and driven axially by a ratchet interposed between lever and bar at the other end. Ratchet movements translate to smaller displacements at positions along the lever distant from the ratchet. Thus a follower rod attached to the lever 1 nm from the pivot and driven by a ratchet with 0.01-nm steps moves ~0.001 nm per ratchet step.
  2. Screws. Consider a 3-nm diameter cylindrical screw with a 1-nm pitch. Rotating the screw through a 0.01-nm circumferential displacement causes the screw to move laterally by ~0.001 nm, which may be transmitted elsewhere in the machine by an attached follower rod. Of course, nanoscale screws or gears are sensitive to the precise cancellation of the potentials and hence cannot be perfectly smooth and circular, producing some unavoidable "knobbiness" under load.
  3. Gear Trains. Consider a 32-nm diameter worm gear with 1-nm teeth. One rotation of the gear requires 100 rotations of the worm; hence a 0.1 nm displacement applied to the worm produces a 0.001 nm displacement in the gear. More efficient (and coaxial) compound planetary gear trains commonly employed in transmissions achieve displacement ratios up to 10,000:1, a hundred times better than the above example.
  4. Hydraulics. Consider a sealed, fluid-filled, tapered pipe. A piston 1000 nm2 in area is mounted at one end; another piston 10 nm2 in area lies at the other end. A displacement of 0.1 nm applied to the smaller piston produces a 0.001 nm displacement in the larger piston. (Here again the finite size of molecules may produce "knobby" performance as fluid particles slip from one stable configuration to the next.)
  5. Compression. Consider a rod upon which a compressive force of 100 nN/nm2 (near the maximum diamondoid strength) has been imposed. Affixed to the rod are two crossbars spaced 4 nm apart. If the force on the rod is increased to 101 nN/nm2, the gap between the crossbars compresses by ~0.001 nm.

2 For even finer feature control, the ground state atomic radius Ra depends on nuclear mass (mn), proton mass (mp) and electron mass (me) through the reduced mass of the electron µe = memn / (me + mn) ~ me (1 - 1/1836 Amass), or Ra ~ 1/µe, where Amass is nucleus mass number and mp/me = 1836. Thus, a 25-nm rod consisting of 162 planes of 12C atoms is ~0.1 picometer longer than a 162-plane rod of 13C atoms; a single ground-state deuterium atom is measured as ~0.4 picometer smaller than a hydrogen atom. SQUIDs and x-ray interferometers have been used to measure displacements of 10-7 nm, or ~1% of the nuclear diameter [445].

3 J. Soreff points out that such strain fields have components at various spatial frequencies, and that at high spatial frequencies there is much design freedom but the effects decay exponentially with a short characteristic length, hence design choices are not spread uniformly throughout the constraint space but rather are clustered. As a result, it may not be possible to achieve a 0.01-nm designed receptor topography simultaneously everywhere across an entire binding surface, nor may it be possible via surface binding alone to distinguish molecules which differ only deep in their interiors.

Chapt. 3 Table of Contents


3.5.7 Receptor Configurations

Many different useful receptor configurations may be readily envisioned, of which the following brief descriptions are but a small sample. Note that most large target molecules of nanomedical interest are proteins which are probably floppy enough to permit entry into reasonably open multiply-concave rigid receptor structures; if not, hinges are easily added to the receptor design. Imprint Model

Molecular imprinting [421-422] is an existing technique in which a cocktail of functionalized monomers interacts reversibly with a target molecule using only noncovalent forces. The complex is then cross-linked and polymerized in a casting procedure, leaving behind a polymer with recognition sites complementary to the target molecule in both shape and functionality (Figure 3-11). Each such site constitutes an induced molecular "memory," capable of selectively binding the target species. In one experiment involving an amino acid derivative target, one artificial binding site per (3.8 nm)3 polymer block was created, only slightly larger than the (2.7 nm)3 sorting rotor receptors described by Drexler [10] (Section 3.4.2). Chiral separations, enzymatic transition state activity, and high receptor affinities up to Kd ~ 10-7 have been demonstrated, with specificity against closely competing ligands up to (delta)Kd ~ 10-2 (~20 zJ).


Imprint Model

Figure 3-11. Imprint Model for
Creating Artificial Molecular Receptors
redrawn from Ansell, Ramstrom and Mosbach [422])

Several difficulties with this approach from a diamondoid engineering perspective include:

  1. A sample of the target molecule is required to make each mold,
  2. it is currently unknown how to prepare diamondoid castings, and
  3. once the imprint has been taken, the site cannot easily be further modified. Solid Mosaic Model

In the solid mosaic receptor model, the precise shape and charge distribution of the target molecule is already known. Working from this information, a set of diamondoid components could be fabricated which, when fitted together like a Chinese puzzle box, create a solid object having a cavity in the precise shape of the optimum negative image of the target molecule (Figure 3-12A). The mosaic may contain point charges, voids, stressed surfaces, or dislocations to achieve fine positional control. Mosaic components may be as small as individual atoms, so this model is conceptually similar to 3D printing or raster-scan techniques in which the desired cavity formation is constructed atom by atom inside a nanofactory (Figure 3-12B; Chapter 19). This model, like the imprint model, cannot easily be reconfigured once it has been constructed because each of the many unique parts may contribute to the entire structure.


Multiform Block Design

Figure 3-12A. 2-D Schematic Representation of a 3-D Solid
Mosaic Model Artificial Receptor: Multiform Block Design


Raster Scan Design

Figure 3-12B. 2-D Schematic Representation of a 3-D Solid
Mosaic Model Artificial Receptor: Raster Scan Design

M. Reza Ghadiri has designed a protein mosaic model using cyclic peptides that assemble spontaneously into nanotubes of predefined diameter; incorporation of hydrophobic amino acid side chains on the outside of these tubes leads to spontaneous insertion into bilayers, allowing the tubes to function as transmembrane ion channels [428]. Other examples of mosaic model receptors are mesoporous silica filters with functionalized organic monolayers forming 5.5-nm sieve-like pores [693], and zeolites and zeolite-like molecular sieves. Zeolites are artificial crystal structures with precise and uniform 0.4-1.5 nm internal void arrays which can also be used as shape-selective catalysts able to favor one product over another that differs in size by as little as 0.03 nm, such as p-xylene and o-xylene [430]. Rational de novo computational design of artificial zeolite templates [431-432, 934] and crystal engineering [695, 948] has begun. Tomographic Model

In the tomographic receptor model, the receptor engineer again starts with a known target molecule topography and designs a series of thin planar sections which, when stacked together in the correct order (using positionally-coded docking pins) and bonded, create a solid object containing the desired optimum binding cavity (Figure 3-13). As in the mosaic model, point charges or dislocations in each planar segment can be used to manipulate cavity features and dimensions to precise tolerances. Unlike the mosaic model, a tomographic receptor can be reconfigured by partial disassembly and replacement of specific planar segments, each of which contributes only locally to the total receptor structure. Hybrid or modular artificial enzymes [651,692] and two-dimensional sheetlike hydrogen-bonded networks [695] are crude analogies in current research.


Tomographic Model

Figure 3-13. Schematic Representation of Tomographic Model
for a Reconfigurable Artificial Receptor Pin Cushion Model

The pin cushion receptor, suggested independently by K.E. Drexler [personal communication, 1996], is a hemispheroidal or hemiellipsoidal shell through which a number of rods protrude, each of which may be moved radially (Figure 3-14). When inserted through the shell to varying depths, the endpoints of the rods define a negative image surface which may be made to mirror the topography and charge distribution of a known target molecule. Rods may be tipped with positive, negative or no charge, or they may terminate in any number of functionalized surface segments designed to optimally match parts of the target molecule shape. Other configurations such as a rectangular box, hinged plates with protruding rods, counterrotating rollers, or time-varying rod positioners are readily conceivable. Pin cushion receptors are easily reconfigured to bind different target molecules, hence may be regarded as fully programmable "universal" binding sites. The principal difficulty with the pin cushion receptor is its excessive size (compared to other receptor models) and its greater complexity (since each rod must be controllable individually).


Pin Cushion Model

Figure 3-14. Pin Cushion Model for a
Reconfigurable Artificial Molecular Receptor
(planar cutaway section omitting sensors and drive mechaniisms)

Pin cushion receptors can also be used to discover the shapes of unknown molecules (Section 3.5.8): A target molecule is placed in the central cavity with all rods fully retracted, and the rods are slowly slid forward using nanopistons with force reflection feedback, until all pistons register zero force, indicating balance between attractive and repulsive van der Waals interactions, at which point all rod positions are recorded. Rods of differing end tip charge may then be tested for additional attractive potential. The final result is a precise mapping of the target molecule, which data may be stored or transmitted elsewhere for future use. Construction Costs

The active binding site of a receptor consisting of (2.7 nm)3 ~ 19 nm3 of structural atoms and constructed with 0.001-nm feature sizes in theory requires information from 2 x 1010 voxels (volume pixels) for complete description. However, there are only Natom ~ 1000 atoms involved in the structure and their locations cannot be arbitrarily chosen. Atomic scale (~0.1 nm) resolution would require ~19,000 voxels; each voxel minimally requires an index number (~log2 (19,000) ~14 bits), an atomic identifier (~log2 (92) ~7 bits), and a charge identifier (~log2 (3) ~2 bits), for a total of 23 bits/voxel which gives 4 x 105 bits/receptor at atomic scale resolution. Drexler [10] estimates the number of configurational options per atom Nopt ~ 150; hence a description of the receptor could require as few as Natom log2 (Nopt) ~ 7 x 103 bits.4 Assuming energy dissipation of ~3 zJ/bit for rod logic register reading [10, 420] or ~kT ln (2) (Eqn. 7.1), then each time the receptor description is retrieved, stored or processed may require a minimum energy dissipation of ~104-106 zJ. Reversible computing may reduce this energy requirement by a factor of 10-100 or more (Section 10.X.X). Construction of a receptor containing ~1000 atoms using the nanomanipulator arm mentioned in Section 3.4.3 requires ~10-2 sec and consumes ~0.001 picojoule of mechanical energy. Receptor Durability

Receptor durability is difficult to estimate ab initio. Molecularly imprinted polymer sites can be stored at least several years without loss of performance, but these receptors have only been tested to <~100 cycles of use without any detectable loss of memory [422]. The lifetime in vivo for metabolic enzymes often exceeds ~105 sec (~1 day) [172], and taste cell receptors survive ~106 sec (~2 weeks) [423], which suggests operational lifetimes for natural receptors on the order of 107-1012 cycles despite the relative fragility of protein structures. Diamondoid structures should be even more durable because of their superior physical strength, their affirmative forcible ejection of bound ligands each cycle, and because of their high resistance to chemical degradation thus reducing susceptibility to poisoning.

4 Higher level descriptions may allow considerable additional information compaction, as for instance where a 30-bit word indexes a single receptor structure stored in a library containing perhaps 109 distinct designs.

Chapt. 3 Table of Contents


3.5.8 Ligand-Receptor Mapping

To achieve a fully general-purpose receptor capability in nanomedical systems, two classes of analytic function are essential.

First, presented with an arbitrary molecule, the system or user must be able to infer from the molecule's structure the shape and electronic configuration of an optimal receptor geometry that will efficiently bind it, with a particular affinity and specificity (as a design specification). This discovery procedure may involve a process akin to molecular imprinting (Section, fluorescent dye affinity matching on testing chips (Chapter 20), structure-activity relationships (SAR) by NMR techniques [424], or pin cushion receptor mapping (Section

Second, presented with an arbitrary protein-built binding site embedded in living tissue, the system or user must be able to infer the molecule(s) which the given receptor could bind, and to compute the affinity and specificity of that activity. This capability may require a rather diverse steric toolkit. Biological receptors are constructed in one of ~500-1000 distinct shapes or "domains," such as the well-known Y-shaped antibody immunoglobulin domain (~100 residues) and other assorted clefts, folds, kringles and coils. Several hundred distinct fold families are known, though it is believed there are only ~20 major domain types [414].

One mapping technique would employ a series of rodlike probes inserted into the receptor cavity like a pick gun or other lockpicking tool: After physically securing the receptor, the first crude probes quickly map the cavity to nanometer scale. Based on this preliminary information, subsequent probes having ever-finer discrimination chart smaller features as well as charge distributions by inserting a predetermined set of test rods with functionalized tips in a standard sequence, to rapidly prune the huge configurational space down to a single unique electrophysical shape using the minimum possible number of tests. (A 1 nm3 volume of multi-element diamondoid receptor structure has ~10148 possible distinct configurations, by one conservative estimate [10], requiring at least 492 binary tests to eliminate all but one configuration. Antibody domains contain ~1050 possible configurations, requiring 166 binary tests.) Cavity Stuffer, a software package comprising an experimental design tool to investigate automated cram-packing of predefined cavities using randomly branched polymers, is a preliminary effort in this general direction [425], although the algorithmic task of discovering an unknown receptor contour may be considerably more challenging.

Another approach to receptor mapping would be the reversible chemical or mechanical denaturation of the receptor protein followed by precise nondestructive amino acid sequencing (Chapter 20), from which tertiary structure and activity could then be computationally inferred. Algorithms to perform such computations are the subject of intense current research interest [952]. Even imperfect tertiary structure predictions should greatly reduce the search space, so that only a partial residue sequencing may be necessary for unambiguous identification from a library of possible proteins. Once the target ligand structure has been inferred, the subsequent design and manufacture of receptor-specific agonists and antagonists (including catalysts and cofactors, activators and inhibitors, promotors and repressors) should be comparatively easy.

Chapt. 3 Table of Contents


3.5.9 Large Molecule Binding, Sorting and Transport

Is there any size limit for target molecules to be transported? Natural receptors have already been found for large molecules including low-density lipoproteins (LDLs) > 1,000,000 daltons [426] and high-density lipoproteins (HDLs) [1038].

The methods described in earlier sections can be adapted for binding large molecules (>1000 atoms; Figure 3-15), including molecules far wider than the binding device itself (e.g. ~200-nm diameter virus particles and larger). Making a binding site for a large molecule should be physically easier (albeit computationally more challenging) than making a binding site for a small molecule because of the greatly increased area of interaction. For example, a binding energy of 400 zJ may be realized by creating a dispersion-force binding area covering only ~25% of the surface of a 10,000-atom target molecule (Table 3-6) or a mere ~0.02% of a 200-nm virus particle.


Protein Dimensions

Figure 3-15. Relative Dimensions of
Some Typical Proteins (Mol. Wt. in daltons)

This makes possible the concept of binding pads -- small surfaces with dimples (concave or convex), each dimple consisting of precisely-placed nanometer-scale features that are complementary to specific patches on the surface of the large target molecule. (Specificity is lost for portions of the molecule outside the particular patches.) Each dimple could effectively grasp the side of the large molecule without having to fully enclose it -- a capability useful in nanorobot foot pads during cell walking and anchoring (Section 9.4.X.X), in handles for nanociliary or nanomanipulator transport functions (Section 9.3.2), and for chemotactic sensing (Section 4.2.6). (For example, macrophage receptors for LDLs employ a "pad" consisting of three globular cysteine-rich domains [426].) The large compliance of target protein molecule subunits should prove curative for any misalignment problems caused by cumulative small errors in bond lengths across large diamondoid receptor structures.

Rather than using sorting rotors, which become unwieldy when large molecule binding pockets must be used, the shuttle pump illustrated schematically in Figure 3-16 may provide reasonably efficient large molecule sortation and transport. The shuttle pump consists of a diamondoid tube within which a receptor ring moves between iris diaphragms at either end (shuttling mechanism not shown). The receptor ring is constructed as two or more binding pad segments. For molecule pickup, the ring is pressed together, forming an annular binding region for the target large molecule, which binds and is shuttled to the other side. The receptor ring is then fragmented, destroying binding affinity and unlocking the target molecule, which escapes via diffusion. The shuttle returns to the pickup side, the receptor is pressed together again, and the cycle repeats. A biocompatible solvent environment is maintained during large-protein manipulation tasks.


Large-Molecule Shuttle Pump

Larger version, 777 x 551 pixels, 35K

Figure 3-16. Schematic of Large-Molecule Shuttle Pump
using Fragmentable Binding Ring and Iris Diaphragms

Assuming a roughly spherical large molecule and laminar fluid flow at 1 atm forcing pressure (Section 9.2.7), a 10-nm diameter molecule moves through a 20-nm long pump (~10-20 kg, ~106 atoms) in ~10-6 sec at ~0.02 m/sec, consuming ~0.02 picowatts during transfer. A 200-nm virus-size target molecule moves through a 400-nm long pump (~10-17 kg, ~109 atoms) in ~10-2 sec at ~60 microns/sec, consuming ~10-16 watts during transfer; at ~0.0002 atm, release time is diffusion limited. The transfer force exerted on a 10-nm molecule is ~1 pN, ~600 pN on a 200-nm virion; a binding energy of 400 zJ at a 0.2-nm contact distance gives a binding force of ~2300 pN, sufficient to hold a particle of either size firmly during transport and release.

J. Soreff points out that as protein size increases, so does the energy available for local minima in the binding. Desired proteins may become stuck in incorrect positions, or undesired proteins may become partially adhered to a receptor. Besides designing to minimize these possibilities, using a multireceptor cascade with different combinations of binding patches at each stage should allow complete exclusion of undesired large-molecule species.

Chapt. 3 Table of Contents | Page 1 | Page 2 | Page 3 | Page 4


© Copyright 1998, Robert A. Freitas Jr. All rights reserved.