Essentials of Computational Chemistry

454 12 EXPLICIT MODELS FOR CONDENSED PHASES
the possible error in the entropy calculation are sufficiently large to make the good agreement
with the experimental value quoted above seem potentially slightly misleading.
Irrespective of the accuracy of the absolute binding free energies, the major goal of the
scanning is to identify possible substitutions meriting further study by a more accurate
methodology. First, as a check on the assumptions of the model, binding free energies
for two substituted cases were computed from Eqs. (12.32) and (12.33) but using MD
trajectories generated for the proper complexes. The results were sufficiently close to those
obtained using the unsubstituted trajectory that no concerns were generated. Then, full
FEP calculations using TI and explicit solvent were carried out mutating biotin into 8Rfluoroavidin
and 8S-fluoroavidin, i.e., computing the vertical legs in Figure 12.6 (mutations
were run in both the backward and forward directions). For the 8R-fluoro analog, the
binding free energy was computed to be 1.5 kcal mol −1 stronger than biotin, in reasonable
agreement with the fluorine scanning value of 0.9 kcal mol −1 .
There are a few technical details in this paper that are rather more ill-defined than
ideal for a ‘canned’ strategy – the description above of the fluorine scanning procedure
glosses over some of the finer details associated with evaluating binding free energies
for the substituted analogs. Nevertheless, this paper presents an interesting comparison
of more and less time-consuming models for estimating differential binding free energies
from explicit simulation. The joint application of explicit solvent and continuum solvent
methodologies for biomolecular studies seems destined to increase in frequency.
Extensions of this case study are available for the interested reader. First, Dixon et al.
(2002) have expanded the analysis presented above to include consideration of methylated
biotin analogs and in the process developed a graphical approach for visualizing free energy
changes. In addition, Lazaridis, Masunov, and Gandolfo (2002) have also considered the
binding free energies of various ligands, including biotin and biotin analogs, to avidin and
streptavidin. These authors decompose results from MD simulations with implicit solvation
into ligand/enzyme interaction energies, reorganization energies, and entropy changes, and
they conclude that the most difficult component to predict with acceptable precision is
the reorganization energy of the macromolecule. The results from all three of these studies
have important implications for docking models in general, and in particular for models that
employ static ligand and/or receptor structures to improve efficiency, and thereby ignore
relaxation energetics.
Bibliography and Suggested Additional Reading
Blondel, A. 2004. ‘Ensemble Variance in Free Energy Calculations by Thermodynamic Integration:
Theory, Optimal “Alchemical” Path, and Practical Solution’, J. Comput. Chem., 25, 985.
Brooks, C. L., III and Case, D. A. 1993. ‘Simulations of Peptide Conformational Dynamics and Thermodynamics’
Chem. Rev. 93, 2487.
Boresch, S. 2002. ‘The Role of Bonded Energy Terms in Free Energy Simulations – Insights from
Analytical Results’, Mol. Sim., 28, 13.
Frenkel, D. and Smit, B. 1996. Understanding Molecular Simulation, Academic Press: New York.
Jensen, F. 1999. Introduction to Computational Chemistry, Wiley: Chichester.
Kollman, P. 1993. ‘Free Energy Calculations: Applications to Chemical and Biochemical Phenomena’,
Chem. Rev., 93, 2395.