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

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

3.5.4 Ligand-Receptor Dynamics

Diamondoid structures can exhibit a stiffness and rigidity one or two orders of magnitude greater than that available in protein structures. In general, stiffer structures permit greater specificity because they enhance exclusion of non-target ligands based on van der Waals overlap forces (called steric hindrance) and allow narrower tolerances in distinguishing acceptable ligands.

In less-stiff protein-based receptors, each of the atoms is engaged in relatively large, rapid jiggling movements. Experimental and theoretical work has been done on the atomic fluctuations within the basic pancreatic trypsin molecule, a small enzyme with 58 amino acids and 454 heavy (non-hydrogen) atoms. This work established that fluctuations increase with distance from the center of the molecule, with the magnitude of RMS fluctuations ranging from ~0.04 nm for backbone atoms to ~0.15 nm for the ends of long side chains (roughly one atomic diameter), and an average of 0.069-0.076 nm per atom over the entire molecule.⁴⁰⁹ A similar experimental analysis of reduced cytochrome c, a common metabolic enzyme, shows that RMS fluctuations of each of the 103 amino acid residues in the molecule averages ~0.11 nm with lattice disorder (~0.05 nm) included, and fluctuations range from 0.09-0.16 nm (Fig. 3.10). Antibody core domain movements display RMS fluctuations of 0.04-0.19 nm.⁴¹² Hence it appears that the average atom within the typical protein receptor oscillates ~0.1 nm every ~10^-12 sec, although frequently residues with long side chains (e.g., arg, lys) have much higher RMS deviations than average.

By contrast, in stiff diamondoid-based receptors each of the atoms is locked in a rigid crystalline structure and thus is subject to thermal displacements approximately 10 times smaller. The RMS displacement for a quantum mechanical harmonic oscillator¹⁰ is given by:

{Eqn. 3.27}

where h = 1.055 x 10^-34 joule-sec, kT = 4.28 zJ at T = 310 K, and angular frequency w = (k_s/m_red)^1/2 rad/sec where k_s is mechanical stiffness and m_red is the reduced mass = m₁m₂/(m₁ + m₂). For C-C atoms (e.g., in the receptor body), k_s = 440 N/m, m₁ = m₂ = 2x10^-26 kg, thus w = 2.1 x 10¹⁴ rad/sec, so the RMS displacement of each atom is only ~0.005 nm every ~3 x 10^-14 sec. For C-H atoms (e.g., on the hydrogen passivated receptor surface), k_s = 460 N/m, m₁ = 2 x 10^-26 kg (C), and m₂ = 1.673 x 10^-27 kg (H), thus w = 5.5 x 10¹⁴ rad/sec, so the RMS displacement of each atom is ~0.008 nm every ~1 x 10^-14 sec. Similarly, at 310 K the RMS thermal displacement of a 1-nm wide, 10-nm long diamondoid rod is ~0.01 nm, including elastic and entropic contributions.¹⁰

The ratio of RMS displacements for protein/diamondoid receptors is ~10:1, so the minimum addressable volume (hence inverse maximum specificity) of a diamondoid receptor should be ~10³ smaller than for protein receptors, a ~30 zJ binding energy advantage for diamondoid receptors.

Last updated on 7 February 2003