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

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

3.5.1 Physical Forces in Molecular Recognition

Covalent bonds, which occur when atoms share electrons, are the strongest bonds. Aside from metals and salts, most material objects are made of atoms held together by covalent bonds. The atoms comprising biological molecules like proteins, nucleic acids and lipids are strung together mostly by single, double, or triple covalent bonds, as are receptors and diamondoid nanomechanical structures. Interatomic bond strengths range from 181 zJ/bond for O-F up to 1785 zJ/bond for C-O.⁷⁶³ Covalent bond lengths range from 0.10-0.16 nm within CHON-atom molecules, giving a typical covalent bond rupture force of ~10 nN/bond.

But as Jean-Marie Lehn⁷⁶⁵ points out, "there is a chemistry beyond the molecule" -- noncovalent supramolecular chemistry (Section 2.3.2). The bonds employed in molecular recognition are weak noncovalent bonds. Noncovalent bonds are largely responsible for the secondary and higher order structure of macromolecules. On a per-bond basis, noncovalent bonds are 1-3 orders of magnitude weaker than covalent bonds. However, the possibility of combining within a limited area a great number of noncovalent bonds having complementary elements allows the formation of a large specific association whose affinity may be of the same order of magnitude as a covalent bond.⁴⁰¹ The high combinatorial diversity provided by many complementary elements allows numerous orthogonal specific associations, enabling self-assembly of many components; by comparison, covalent chemistry offers a poor diversity of reactivities. An additional advantage is that the formation of noncovalent bonds often is not hindered by high energy barriers. At least five types of noncovalent bonds may be distinguished: electrostatic, hydrogen, van der Waals, p aromatic, and hydrophobic.

1. Electrostatic Bond -- The electrostatic bond between two charged particles (e.g., the "salt bridge" in proteins) is a dipole interaction whose energy E_e is given by Coulomb's law as:

{Eqn. 3.20}

where e = 1.60 x 10^-19 coul (elementary charge), e₀ = 8.85 x 10^-12 farad/m (permittivity constant), Z₁ and Z₂ are the numbers of attractant charges, r is the distance between the charges, and k_e is the dielectric constant (74.3 for pure water at 310 K, usually reduced to ~40 in a hydrophobic environment). The bond is strengthened if the charges are in a hydrophobic environment. Conversely, the presence of electrolytes weakens the bond energy due to a shielding effect, given by K_dh, the Debye-Huckel reciprocal length parameter, which has a value of 1.25 nm^-1 for 0.15 M NaCl (~1% solution, ~human blood). Thus two unit charges separated by 0.3 nm produce an interaction energy of E_e = 19 zJ in a hydrophobic environment, 10 zJ in pure water, and 6.3 zJ in 1% salt water. Long-range electrostatic trapping has been observed in single-protein molecules at liquid-solid interfaces, raising the implication that the interaction of protein molecules with biological cell surfaces may be much more efficient than predicted by random diffusion.²¹⁴⁴

Most isolated amino acids in neutral solution are zwitterionic -- the molecule has no overall charge but carries both a negatively charged group (carboxyl, CO₂^­) and a positively charged group (amino, NH₃⁺). In proteins the individual amino acids are polymerized, giving a peptide backbone which is electrically neutral except for the ends of the chain. Most of the standard amino acids found in proteins have uncharged side chains, although histidine, lysine and arginine each have a positive charge at neutral pH and both glutamic and aspartic acids normally carry a negative charge.

2. Hydrogen Bond -- A second important noncovalent interaction is the hydrogen bond, a dipole formed when a hydrogen atom covalently bonded to an electronegative atom is shared with a second electronegative atom (typically an oxygen, nitrogen or fluorine atom), such that the proton may be approached very closely by an unshared pair of electrons. Hydrogen bonds are largely responsible for the unusual thermodynamic properties of water and ice, and the DNA double-helical and protein a-helical and b-structure conformations are extensively hydrogen bonded. Highest bonding energies occur when donor and acceptor atoms are 0.26-0.31 nm apart. Typical hydrogen bond strengths in proteins are 7-50 zJ.

3. Van der Waals Interaction -- A third important noncovalent force is van der Waals interactions (London dispersion forces).¹¹⁴⁹ There is an attractive component due to the induction of complementary partial charges or dipoles in the electron density of adjacent atoms when the electron orbitals of two atoms approach to a close distance. There is also a strongly repulsive component at shorter distances, when the electron orbitals of the adjacent atoms begin to overlap, commonly called steric hindrance. The van der Waals attractive bonding energy between two parallel plates of area A and separation z_sep is approximated by:

{Eqn. 3.21}

where the Hamaker constant H = 37 zJ for water, 66 zJ for glycerol, 340 zJ for diamond (Table 9.1). For A = 0.4 nm² (small molecule), z_sep = 0.3 nm, then E_vdW = 4 zJ (water) to 8 zJ (small organic molecules) -- close to the mean energy of a thermally excited harmonic oscillator, kT ~ 4.3 zJ at 310 K. While van der Waals bonds are individually very weak, they are also very numerous since they involve all pairs of neighboring atoms. For example, experimental analysis of an antigen molecule trapped in the anti-hen egg-white lysozyme monoclonal antibody Fv active binding site found 86 distinct interatomic contact points with antigen-antibody separations ranging from 0.25-0.46 nm, averaging 0.36 nm.⁴¹⁶ Since intermolecular dispersion forces act on all molecules, there are probably no ligands with MW > 400 daltons which cannot be receptored (Section 3.5.5). That is, van der Waals interactions ensure that virtually all molecules of nanomedical interest are theoretically bindable noncovalently.

4. Aromatic p Bonds -- A fourth type of interaction (p electron to p electron), called "aromatic" or "pi" bonding, occurs when two aromatic rings (conjugated p systems) approach each other with the plane of their aromatic rings overlapping, with successive p-bonded systems stacked like layers in a cake. This results in a noncovalent attractive force with a bond strength of ~40-50 zJ. (That is, the planes of conjugated p systems attract each other when superimposed.) p bond stacking forces contribute to nucleic acid stability at least as much as the hydrogen bonds between bases.⁴⁰¹

5. Hydrophobic Forces -- Finally, there are the strong hydrophobic forces, due entirely to solvent entropy changes. When two nonpolar residues approach each other, the surface area exposed to solvent is reduced, increasing the entropy of all the water present and decreasing the entropy of the residues, adding to the binding energy a hydrophobic free energy of ~17 zJ/nm² of contact surface area that was formerly exposed to water.⁴¹³

In designing an artificial binding site, the above forces may be combined to achieve the desired level of affinity and specificity for a given ligand. All forces are not equally useful in this regard, however. For example, hydrophobicity is the major factor in stabilizing protein-protein associations.⁴⁰² But hydrophobicity is almost entirely nonspecific, hence contributes little to ligand discrimination. By contrast, the proper formation of hydrogen bonds and van der Waals contacts require complementarity of the surfaces involved. Such surfaces must be able to pack closely together, creating many contact points, and charged atoms must be properly positioned to make electrostatic bonds. Thus van der Waals and polar interactions may contribute little to the dynamic stability of the ligand-receptor complex, but they do determine which molecular structures may recognize each other.⁴⁰² Other design elements of binding sites, such as directed channeling of substrates into the receptor,²⁰¹⁷ may also prove useful.

In analyzing molecular forces, note that at the nanoscale level, surface/surface, molecule/surface, and molecule/molecule interactions may feature very complicated behaviors. Nanodevices performing work may generate both thermodynamic and mechanical local nonequilibrium conditions, so calculations based on the general forms of interactions and on macroscopic expressions valid at equilibrium conditions should be taken only as basic estimates.

Last updated on 19 February 2003