Essentials of Computational Chemistry

452 12 EXPLICIT MODELS FOR CONDENSED PHASES
of such a situation might be the aqueous coordination sphere surrounding a highly charged
metal cation. In that case, the electrostriction of the first shell makes the water molecules more
ligand-like than solvent-like, and their explicit inclusion in the solute complex is entirely
warranted.
12.6 Case Study: Binding of Biotin Analogs to Avidin
Synopsis of Kuhn and Kollman (2000) ‘A Ligand That Is Predicted to Bind Better to Avidin
than Biotin: Insights from Computational Fluorine Scanning’.
One of the strongest known interactions between a biopolymer and a small-molecule
substrate is that between the protein avidin and D-(+)-biotin, the structure of which is
shown in Figure 12.6. The binding energy for this complex has been measured to be
−20.8 kcal mol −1 . While this represents an extraordinarily strong interaction, Kuhn and
Kollman suggested that it might be possible to make it still stronger by replacing one or
more hydrogen atoms on the biotin framework with fluorine atoms. Fluorine is roughly
isosteric with hydrogen (i.e., the C–F and C–H bond lengths have roughly similar lengths
and F and H have similar covalent radii), but is considerably more hydrophobic. Thus,
if a region of the binding pocket interacts with biotin via non-polar interactions, and is
adequately shaped to accommodate the very slightly larger fluorine atom, decreased aqueous
solvation of the fluorinated analog would be expected to increase the binding free energy
(note that the lower polarizability of fluorine compared to alkyl hydrogen also suggests the
favorable dispersion interactions between the biotin analog and the protein will be reduced,
but this is generally a smaller effect than enhanced hydrophobicity in the absence of steric
constraints).
Kuhn and Kollman pursue several different algorithmic approaches to estimating the
binding free energies of different fluorobiotins. The fastest approach, which they refer to
as fluorine scanning, involves a combination of explicit and implicit solvation models to
compute the horizontal legs of the free-energy cycle in Figure 12.6. First, an MD trajectory
of the avidin–biotin complex is obtained under standard MD conditions, including explicit
solvent and using periodic boundary conditions.
The trajectory is then ‘post-processed’ to determine absolute free energies in solution for
biotin, avidin, and the avidin–biotin complex. This process begins by stripping the water
from the trajectory, and then computing absolute free energy as
〈G〉 =〈EMM + Gsolv〉−TS (12.32)
where EMM is the force-field energy, Gsolv is computed from a continuum solvation
model (in this case a finite difference Poisson–Boltzmann (FDPB) model with hydrophobic
atomic surface tensions), and the expectation value is taken over the snapshots of the
MD trajectory. Evaluations of Eq. (12.32) for isolated biotin and avidin are carried out
using the same snapshots as those for the complex, i.e., using those geometries found
in the complex, but only the atoms of the individual component are retained. The solute
entropies S are determined from the usual statistical mechanical formulae (Section 10.3)
with the vibrational frequencies being determined from normal mode analysis of each solute
optimized separately using a distance-dependent dielectric constant to mimic the effects of
solvation.