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

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

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 Self-assembling capsules or "container molecules" made of hydrogen-bonded subunits, capable of limited molecular recognition, have been synthesized.^2143,2336 A designed receptor for creatinine was demonstrated in 1995,²²² and in 1998, K. Suslick and colleagues²⁷¹⁴ designed metalloporphyrin-dendrimeric artificial receptors that can bind straight, skinny molecules but block out bent or fat molecules. Container molecules with 0.2-0.4 nm portals control entry to their interiors using "French door" and "sliding door" gates⁴¹⁷ and hinges.²⁵⁴⁸ Active binding sites for small simple molecules such as NO,^2912,2913 CO,³²²⁸ and C₂H₄²⁹¹⁴ are well-known.

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.

But consider a theoretical receptor that employs van der Waals dispersion forces alone. Atoms comprising the typical protein or 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 E_vdW, 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 A_p = 0.111 MW^2/3 nm²,⁴¹³ than if they were spherical,* so Table 3.6 figures are conservative for protein binding; proteins typically have a ~60-85% interior packing density.³²¹¹) Dispersion forces alone can provide the minimum required binding energy of ~120 zJ with A_p ~ 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.

* The formula for A_p 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 A_p.

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.

Last updated on 7 February 2003