Absolute free energy

Fig. 11.9 Thermodynamic cycle used to calculate absolute free energies [Jorgensen et al. 1988].

Umbrella sampling can give free-energy differences, but not absolute free energies Usually done in NPT—isothermal/isobaric ensembles, including a water box... 

WL Jorgensen, JK Buckner, S Boudon, J Tirado-Rives. Efficient computation of absolute free energies of binding by computer simulations. Application to the methane dimer m water. J Chem Phys 89 3742-3746, 1988. 

Computing the absolute free energy A is in general a difficult task. For the same reasons the absolute entropy cannot be computed except in special cases. However, entropy differences can be computed. Indeed, using finite differences, we can approximate... 

Srinivisan, J. Volobuev, Y. L. Mielke, S. L. Truhlar, D. G., Parallel Fourier path-integral Monte Carlo calculations of absolute free energies and chemical equilibria, Comput. Phys. Commun. 2000, 128, 446-464... 

It still remains that the pervasive use of the expression absolute free energy in the literature requires that this concept be clarified in the case of protein-ligand... 

Dixit, S. B. Chipot, C., Can absolute free energies of association be estimated from molecular mechanical simulations The biotin-streptavidin system revisited, J. Phys. Chem. A 2001,105, 9795-9799. 

In other words, to calculate G we must be able to determine a converged value of (and its higher moments), in contrast to AG, which is derived from . converges much more slowly than , which makes calculation of the absolute free energy impractical in most cases. 

That said, for select systems it is possible to attempt to calculate an absolute free energy. This can be done by running two FEP or TI simulations and summing the results.44 For example, to calculate the absolute free energy of binding of a substrate to an enzyme, we perform the following simulations ... 

Table 1. Absolute free energy of netropsin binding to [d(CGCGAATTGCGC)]2...

In Eqs. (25) and (26), the summations are over the incremental steps in going from X to Y in the gas phase or in solution. The Hj are the intermediate Hamiltonians (or force fields in a classical treatment). Thus, Hi=0,gas = Hx,gas, Hi=Njgas = HY,gas, etc. It is of course desirable that the molecules X and Y be structurally similar, so that the perturbation of X that produces Y be small. Another option is to let Y be composed of noninteracting dummy) atoms,75 so that its free energy of solvation is zero. Then Eq. (24) gives the absolute free energy of solvation of X ... 

Table 11.3 Absolute free energies of solvation (kcal mol ) and chloroform/water partition coefficients (logio units) for nucleic acid bases at the SM5.4/AM1 Icvcf ...

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