Energy representation thermodynamic integration methods

The evaluation of the free energy is essential to quantitatively treat a chemical process in condensed phase. In this section, we review methods of free-energy calculation within the context of classical statistical mechanics. We start with the standard free-energy perturbation and thermodynamic integration methods. We then introduce the method of distribution functions in solution. The method of energy representation is described in its classical form in this section, and is combined with the QM/MM methodology in the next section. 

Recently, Kollman and coworkers calculated the effect of a methyl substitution on the a versus P carbon atom of the unnatural amino acid (S-2-amino-3-cyclopentylpropanoic acid) in position 133 on T4 lysozyme stability. The authors used AMBER 4.1 and compared the results obtained by thermodynamic integration method with the results obtained by newer methods. 2 5 The study determined that the methyl group substitution on the a carbon stabilizes T4 lysozyme by 1.8 kcal/mol, whereas the methyl substitution on the P carbon destabilizes the protein by 0.4 kcal/mol. The result is in good agreement with the less CPU-intensive method, pictorial representation of free energy changes (PROFEC). 

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