Free energy computation

Frenkel D 1986 Free-energy computation and first-order phase transitions Moiecuiar Dynamics Simuiation of Statisticai Mechanicai Systems ed G Ciccotti and W G Hoover (Amsterdam North-Holland) pp 151-88... 

The Gibbs free energy (computed in the harmonic approximation) were converted from the 1 atm standard state into the standard state of molar concentration (ideal mixture at 1 molL-1 and 1 atm). 

The activation free energies computed both in the gas phase and in aqueous solution (Table 2.6) suggest that the generation of an alkylating QM (QM-NI) becomes a much easier process, passing from the protonated quaternary ammonium salt NI to its zwitterionic form NI. ... 

Fig. 4.2. Free energy computation using constraint forces. It may be difficult to sample the surface (x) = using a constrained simulation because of the presence of energy barriers separating different reaction pathways. Left a barrier is shown in the middle of the pathway from reactant A to product B. Right two barriers are shown at B...

Fig. 4.8. Free energy computation using ABF and a constrained simulation. Reprinted with permission from Darve et al. 2001 [28], Copyright 2001, American Institute of Physics...

Shirts, M. R. Pande, V. S., Comparison of efficiency and bias of free energies computed by exponential averaging. The Bennett acceptance ratio and thermodynamic integration, J. Chem. Phys. 2005,122, 144107... 

Frenkel, D., Free-energy computation and first-order phase transitions. In Molecular Dynamics Simulations of Statistical Mechanical Systems. Proceedings of the Enrico Fermi Summer School, Varenna, 1985 (Amsterdam, 1986), Ciccotti, G. Hoover, W. G., Eds., North-Holland, pp. 151-188... 

Two concepts are helpful in understanding and characterizing relative free energy computational errors phase space relationships and probability distribution functions of perturbations. 

Figure 4.3 Correlation between the solvation free energy computed using solvent adapted or gas phase geometries.

Keywords binding free energy computational mutagenesis empirical functions fully atomistic... 

So far, the several reported studies in which free energy computations have been applied to the mechanism of OMP decarboxylation have not produced an answer to the question of where the rate acceleration provided by ODCase comes from. 

The enzyme mechanism, however, remains elusive. Quantum mechanical models generally disfavor C6-protonation, but 02, 04, and C5-protonation mechanisms remain possibilities. Free energy computations also appear to indicate that C5-protonation is a feasible mechanism, as is direct decarboxylation without preprotonation O-protonation mechanisms have yet to be explored with these methods. Controversy remains, however, as to the roles of ground state destabilization, transition state stabilization, and dynamic effects. Because free energy models do take into account the entire enzyme active site, a comprehensive study of the relative energetics of pre-protonation and concerted protonation-decarboxylation at 02, 04, and C5 should be undertaken with such methods. In addition, quantum mechanical isotope effects are also likely to figure prominently in the ultimate identification of the operative ODCase mechanism. 

TABLE 1.2 Mean Unsigned Error (kcal mol ) for the Solvation Free Energies Computed with DUferent Methods"... 

Frenkel, D., "Free-energy computations and first-order phase transitions", in G. Cicotti and W.G. Hoover, Molecular Dynamics Simulations of Statistical Mechanical Systems, Proceeding of the International School of Physics "Enrico Fermi", course 97, Elsevier, 1986. 

This equation shows that the excess Gibbs free energy computed from a cubic EOS of the van der Waals type and the one-fluid mixing rules contains three contributions. The first, which is the Flory free-volume term, comes from the hard core repulsion terms and is completely entropic in nature. The second term is very similar to the excess free-energy term in the regular solution theory, and the third term is similar to a term that appears in augmented regular solution theory. Consequently, one is led... 

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