Free energy modeling

The literature/X-ray data was sparse (-1000), so the information content was amplified by generating vast numbers of alternative conformations (-10 ) with a 64-node Linux cluster. Typically, we were able to generate 1 distinct conformation per compound in an average of <1 per minute. At critical points during the drug discovery process, such as when new structural data was obtained, we retrained our free energy model to improve its performance. 

Potential Distribution Methods and Free Energy Models of Molecular Solutions... 

A first step toward quantum mechanical approximations for free energy calculations was made by Wigner and Kirkwood. A clear derivation of their method is given by Landau and Lifshitz [43]. They employ a plane-wave expansion to compute approximate canonical partition functions which then generate free energy models. The method produces an expansion of the free energy in powers of h. Here we just quote several of the results of their derivation. 

Fig. 11.1. The Helmholtz free energy as a function of /3 for the three free energy models of the harmonic oscillator. Here we have set h = uj = 1. The exact result is the solid line, the Feynman-Hibbs free energy is the upper dashed line, and the classical free energy is the lower dashed line. The classical and Feynman-Hibbs potentials bound the exact free energy, and the Feynman-Hibbs free energy becomes inaccurate as the quantum system drops into the ground state at low temperature...

They developed a continuum elastic-free energy model that suggests these observations can be explained as a first-order mechanical phase transition. In other recent work on steroids, Terech and co-workers reported the formation of nanotubes in single-component solutions of the elementary bile steroid derivative lithocholic acid, at alkaline pH,164 although these tubules do not show any chiral markings indicating helical aggregation. 

Cheng W. and Ganguly J. (1994). Some aspects of multicomponent excess free energy models with subregular binaries. Geochim. Cosmochim. Acta, 58 3763-3767. 

In this section, we describe a procedure by which a class of models for the ionic contribution to swelling can be tested. Our general approach is to assume that swelling forces due to ions are independent of and additive with other well known swelling forces such as polymer elasticity and polymer/solvent interaction. Thus we consider free energy models of form... 

Figure 26. Schematic representation of the nonequilibrium free energy model. LE and CT denote locally excited and charge transfer states respectively. From Ref. 82 with permission, from J. Phys. Chem. 92, 6801 (1988). Copyright 1988, American Chemical Society.

Gallicchio E, Linda Yu Zhang, Levy RM (2002) The SGB/NP Hydration Free Energy Model Based on the Surface Generalized Bom Solvent Reaction Field and Novel Nonpolar Hydration Free Energy Estimators. J. Comput. Chem. 23 517-529... 

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. 

Solubility of solids in supercritical fluids using equations of state - excess Gibbs free energy models. 

In principle, the parameters can be evaluated from minimal experimental data. If vapor-liquid equilibrium data at a series of compositions are available, the parameters in a given excess-free-energy model can be found by numerical regression techniques. The goodness of fit in each case depends on the suitability of the form of the equation. If a plot of GE/X X2RT versus X is nearly linear, use the Margules equation (see Section 3). If a plot of Xi X2RT/GE is linear, then use the Van Laar equation. If neither plot approaches linearity, apply the Wilson equation or some other model with more than two parameters. 

The Boltzmann factor in the denominator of this equation corresponds to coupling a distinguished molecule of component a to the solution. This result is reminiscent of local composition free energy models that are widely used to calculate fluid-phase equilibria for multicomponent mixtures of nonelectrolytes. We note that > 1 corresponds to less favorable interactions in the mixtures, and 1 as 1. 

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