Linear-response free energy method

We present and analyze the most important simplified free energy methods, emphasizing their connection to more-rigorous methods and the underlying theoretical framework. The simplified methods can all be superficially defined by their use of just one or two simulations to compare two systems, as opposed to many simulations along a complete connecting pathway. More importantly, the use of just one or two simulations implies a common approximation of a near-linear response of the system to a perturbation. Another important theme for simplified methods is the use, in many cases, of an implicit description of solvent usually a continuum dielectric model, often supplemented by a simple description of hydrophobic effects [11]. 

We now turn to the problem of proton binding to proteins, an important area for simplified free energy methods. The linear response formalism earlier underlies most of the methods used today. It leads directly to one of the more useful practical methods, the so-called LRA, or linear response approximation method [59], presented here. 

Carlson, H. A., Jorgensen, W. L. An extended linear response method for determining free energies of hydration. J. Phys. Chem. 99 (1995) 10667-10673... 

Appendix 11.3 Expansion of Zwanzig Expression for the Free Energy Difference for the Linear Response Method... 

Carlson H A and W L Jorgensen 1995. An Extended Linear Response Method for Determining Free Energies of Hydration. Journal of Physical Chemistry 99 10667-10673. 

X Chen, A Tropsha. A generalized linear response method Application to the hydration free energy calculations. J Comput Chem 20 749-759, 1999. 

The first version of the LIE method employed the linear response approximation to estimate the electrostatic part of the solvation/binding free energies. The linear response result for this component of the solvation... 

The procedure adopted to portray the scope and utility of a linear free-energy relationship for aromatic substitution involves first a determination of the p-values for the reactions. These parameters are evaluated by plotting the values of log (k/ka) for a series of substituted benzenes against the values based on the solvolysis studies (Section IV, B). The resultant slope of the line is p, the reaction constant. The procedure is then reversed to assess the reliability and validity of the Extended Selectivity Treatment. In this approach the log ( K/ H) observations for a single substituent are plotted against p for a variety of reactions. This method assays the linear or non-linear response of each substituent to variations in the selectivity of the reagents and conditions. Unfortunately, insufficient data are available to allow the assignment of p for many reactions. It is more practical in these cases to adopt the Selectivity Factor S as a substitute for p and revert to the more empirical Selectivity Treatment for an examination of the behavior of the substituents. 

---