Adiabatic switching and thermodynamic integration 321∆Ab∆A 1
∆A 2
∆A 3
E
I
H O 2
Fig. 8.1Two thermodynamic pathways for the calculation of the binding free energy of an
enzyme E and inhibitor I. According the figure, ∆Ab= ∆A 1 + ∆A 2 + ∆A 3.
the expensive water–water interactions have been removed. Although the desolvation
and solvation parts of the cycle are still expensive to carry out, they are considerably
more straightforward than direct binding in solution (see Problem 8.8). The method
shown in Fig. 8.1 is known as the “double decoupling method” (Gilsonet al., 1997;
Deng and Roux, 2009).
As with free energy perturbation theory, the thermodynamic integration approach
can be implemented easily. An immediate disadvantage of the method,however, is
the same as applies to eqn. (8.1.7): in order to perform the numerical integration,
it is necessary to perform many simulations of a system at physically uninteresting
intermediate values ofλwhere the potentialU(r 1 ,...,rN,λ) is, itself, unphysical. Only
λ= 0,1 correspond to actual physical states, and ultimately we can onlyattach
physical meaning to the free energy difference ∆AAB=A(N,V,T,1)−A(N,V,T,0).
Nevertheless, the intermediate averages must be accurately calculated in order for the
integration to yield a correct result. The approach in the next section attempts to
reduce the time spent in such unphysical intermediate states, thereby focusing the
sampling in the important regionsλ= 0,1.