Essentials of Computational Chemistry

12.6 CASE STUDY: BINDING OF BIOTIN ANALOGS TO AVIDIN 453
O
HN 1
2
3
HN
S 4
O
S
NH
5
NH
6
F
7
8
CO2
9
∆GS(1→2)
CO 2
∆Gbind,1
+ avidin E•S1
∆Gbind,2
+ avidin E•S2
∆GE•S(1→2)
Figure 12.6 Free-energy cycle associated with the binding of biotin and fluorobiotin analogs
to avidin. What issues arise in choosing a force field for explicit simulation of these systems?
What methods are better suited to computing the vertical legs of the cycle and what methods
the horizontal ones?
Note that since the free energies of the isolated components are computed using the
same geometries as are employed in computing the free energy of the complex, the internal
force-field energies cancel in computing a free energy of binding as
〈G〉bind =〈G〉complex −〈G〉biotin −〈G〉avidin
(12.33)
Only the force-field energy term associated with interactions between the biotin and avidin
fragments remains. This is added to the differential solvation free energies and differential
thermal terms to determine the full binding free energy.
To avoid the cost of multiple MD simulations, Eqs. (12.32) and (12.33) for fluorosubstituted
biotin analogs are also evaluated using geometries from the original MD
trajectory. The relevant hydrogen is simply replaced by a fluorine atom having the appropriate
bond length oriented along the original C–H bond axis. Thus, there is no relaxation
of the complex to relieve steric clashes if they are introduced. Again, the only forcefield
energy terms that survive in computing the free energy of binding are the interaction
energies between the biotin analog and the avidin. It is further assumed that the
entropy change computed for complexation with biotin remains the same for a fluorinated
biotin.
The results of this rapid fluorine scanning are that substitution at positions pro-R 6and
9andpro-S 7, 8, and 9 are all predicted to decrease binding by more than 4 kcal mol −1 ,
substitution at position pro-S 6 is predicted to decrease binding by about 2 kcal mol −1 ,
substitution at position pro-R 7 is predicted to have only a small unfavorable effect,
and substitution at position pro-R 8 is predicted to increase binding by a little less than
1 kcal mol −1 . The absolute free energy of binding for biotin itself with this method is
computed to be −18.8 kcal mol −1 , although the fluctuations in the ensemble average and