Free energy difference calculations

Mitchell M J and J A McCammon 1991. Free Energy Difference Calculations by Thermodynamic Integration Difficulties in Obtaining a Precise Value. Journal of Computational Chemistry 12 271-275. 

M. J. Mitchell and J. A. McCammon, Free energy difference calculations by... 

A hybrid approach of the extended scaled particle theory (SPT) and the Poisson-Boltzmann (PB) equation for the solvation free energy of non-polar and polar solutes has been proposed by us. This new method is applied for the hydration free energy of the protein, avian pancreatic polypeptide (36 residues). The contributions form the cavity formation and the attractive interaction between the solute and the solvent to the solvation free energy compensate each other. The electrostatic conffibution is much larger than other terms in this hyelration free energy, because hydrophilic residues are ionized in water. This work is the first step toward further applications of our new method to free energy difference calculation appeared in the stability analysis of protein. 

The average free energy difference calculated from the two independent simulations of columns 2 and 3, with the standard error of the mean. The sign of this value corresponds to the Cys->Ser mutation. 

As Table 1.1 shows, fluorine is the second smallest element, with size approximately 20% larger than the smallest element, hydrogen. Table 1.2 summarizes four steric parameters for various elements and groups (i) Taft steric parameters Es [44], (ii) revised Taft steric parameters E [45], (iii) Charton steric parameters o [46], and (iv) A values [47], The steric parameters, Es, E, and u are determined on the basis of relative acid-catalyzed esterification rates, while the A values are derived from the Gibbs free energy difference calculated from the ratios of axial and equatorial conformers of monosubstituted cyclohexanes by NMR. 

Mitchell, M.J., McCammon, J.A. Free-energy difference calculations by thermodynamic integration—difficulties in obtaining a precise value. J. Comput. Chem. 1991,12, 271-5. 

If X and Y do not overlap in phase space then the value of the free energy difference calculated using Equation (11.6) will not be very accurate, because we will not adequately sample the phase space of Y when simulating X. This problem arises when the energy difference between the two states is much larger than k T - 3tx > bT- How then... 

Thermodynamic integration is a method for free energy difference calculations based on some thermodynamic relationship for the derivative of the free energy with respect to the quantity X in which the two states differ. Simple integration of this derivative then gives the free energy difference AF between the two states, described by X = 0 and X = 1. Examples of these thermodynamic relationships are the volume derivative of the Helmholtz free energy. 

The creation or annihilation of atoms in a molecular system (e.g., in the dual topology description just discussed) is frequently applied in free energy difference calculations. Although such a process is conceptually identical to other mutations, in practice the treatment of dummy atoms in a free energy difference calculation necessitates further approximations, which cause additional problems. 

An analysis of the effect of sampling errors on free energy difference calculations has demonstrated a definite relation between the calculated error... 

The practical details of free energy difference calculations depend on the particular system and the particular mutation that is studied. For example, determining the potential of mean force between two small molecules in solvent clearly demands a simulation strategy different from that applied to the calculation of the free energy difference between two stereoisomers of an enzyme-bound inhibitor. 

This section reviews a number of practical issues and indicates some of the choices that must be made to perform free energy difference calculations. 

The sensitivity analysis approach has also been shown to be useful for studying error propagations due to the use of nonoptimal parameters in biomolecular simulations and for examining how error cancellations may occur in free energy difference calculations. The sensitivity analysis approach can also suggest how potential functions could be simplified and how the parameters of these functions can be effectively refined. 

Here AG elec is the electrostatic free energy difference calculated using Eq. 3 with the static X-ray structure, and X is the "reorganization energy" associated... 

The finite difference thermodynamic integration combines the thermodynamic perturbation and integration methods. The value of the integrands at the integration points is determined by thermodynamic perturbation. In certain cases this approach has been shown to lead to faster convergence of the free energy difference calculation. 

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