Thermodynamic cycle perturbation method

In 1984 (2), the thermodynamic cycle-perturbation method was introduced to help compare the binding affinity of a group of similar inhibitors. This method is based on constructing a thermodynamic cycle relating two binding processes ... 

Figure 6 Thermodynamic cycle—perturbation method for a host interacting with two different guest molecules.

One approach is the thermodynamic cycle-perturbation method that allows one to eompare the relative binding affinity of a number of similar ligands. This approaeh reeognizes the difficulty in simulating the absolute binding affinity AG between a ligand and its receptor ... 

The general formalism for thermodynamic simulation methods follows from early work by Zwanzig [33], and provides a tool for the computation of thermodynamic properties, AA, AE and AS, as well as barriers for chemical processes occurring on long timescales [34]. These methods take on several guises in present implementations. The two approaches which we will describe are termed thermodynamic cycle perturbation theory (TP) [35] and thermodynamic integration (TI) [36]. Both of the methods are based on the definition of a hybrid Hamiltonian which represents some mixture of the initial state (1) and final state (2) of the system [37]. If /.represents the coordinate describing the pathway used to interconvert the two systems, then the hybrid Hamiltonian may be defined by [35, 37]. 

Whilst this Chapter is primarily concerned with the methods of determining the free energies of tautomeric or ionisation equilibria via computer simulation of free energy differences, many of the issues raised relate also to the determination of other molecular properties upon which behaviour of the molecule within the body may depend, such as the redox potential or the partition coefficient.6 In the next section, we shall give a brief explanation of the methods used to calculate these free energy differences -namely the use of a thermodynamic cycle in conjunction with ab initio and free energy perturbation (FEP) methods. This enables an explicit representation of the solvent environment to be used. In depth descriptions of the various simulation protocols, or the accuracy limiting factors of the simulations and methods of validation, have not been included. These are... 

The free energy perturbation calculations on mutation of the central statine residue of pepstatin to its dehydroxy and other derivatives were carried out using the window method. The crystal structure reported by Suguna et al.l4 l5was used for these calculations. In most simulations, the mutations were achieved either in 101 or 51 windows with 0.4 ps of equilibration and 0.4 ps of data collection at each window. The calculation for each mutation was repeated in water to determine the difference in the free energies of solvation and to complete the thermodynamic cycle. 

Considerable use has been made of the thermodynamic perturbation and thermodynamic integration methods in biochemical modelling, calculating the relative Gibbs energies of binding of inhibitors of biological macromolecules (e.g. proteins) with the aid of suitable thermodynamic cycles. Some applications to materials are described by Alfe et al. [11]. 

Relative ligand binding in solution of different ligands Si and S2 to a receptor site or enzyme E can be estimated by the free energy perturbation method, using the principle of the thermodynamic cycle (Fig. 3), in which all processes are run with explicit inclusion of water. 

Further developments of these ideas took place in computational structural biology, where nonphysical local transformations were implemented within the framework of thermodynamic cycles. These nonphysical transformations were introduced in 1981 by Warshel, who studied ionization in acidic residues in proteins pK calculations). Although the cycle included nonphysical transformations, they were not carried out by the perturbation technique. A year later Warshel used the perturbation method together with umbrella sampling to study the solvation free energy contribution to an electron transfer reaction coordinate, using two spheres for donor and acceptor in water the perturbation, however, was performed along a physical path. Warshel also modeled some enzymatic reactions that involve nonphysical processes. ... 

Differences in binding energies of similar Hgands, A and B, differing only by a few atoms, can be precisely calculated by the free-energy perturbation method (see O Fig- 4.1). A thermodynamic cycle is constructed, where the horizontal free energies are determined experimentally... 

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