Free Energy Methodology

Thermodynamic perturbation as well as multiconfiguration thermodynamic integration are based on the generation of ensembles of configurations. Both techniques rely on the implementation of exact equations, and there is, a priori, no reason to expect one to provide better results than the other. The difference in results from the two techniques for the same mutation originates in the difficulty of adequate sampling. 

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This chapter summarizes most of the studies reported in the literature to date that use the free energy methodology to calculate relative solvation free energies with explicit solvent. In addition, the results are used to define the current scope and limitations of the methodology. 

Benoit Roux s group is using molecular dynamics (MD) simulations to elucidate the fundamental principles governing the transport of ions with a special interest in constructing detailed atomic models of the gramicidin channel.29 They also use MD simulations and free energy methodologies to study... 

One can also characterize the reactivity and selectivity of carbenes using the venerable Hammett ap linear free energy methodology. [5,39] Additions of CXY could be examined with a series of ring-substituted styrenes, ArCH=CH2. Relative reactivities could be obtained, with styrene itself as the standard olefin, and then log could be plotted against the appropriate a constant for each substituted styrene substrate. The slope of the resulting correlation is the Hammett p value for the carbene addition. 

Relative free energies determine important chemical quantities such as relative affinities of binding of ligands to receptor molecules, relative solubilities, relative electrode potentials of different substances, adsorption coefficients, and chemical potentials. Thermodynamic cycle free energy methodologies have become one of the most popular tools in the computational study of complex chemical systems. 

In the field of log P calculations, the free energy methodology was applied to the water/chloroform system using Monte Carlo simulations - and to water/carbon tetrachloride using molecular dynamics simulations. Because the computer resources necessary for such calculations appear enormous, only a few log P values for small organic compounds (methylamine, dimethylamine, methanol, ethanol, propanol, dimethyl ether, acetonitrile, acetic acid, methyl acetate, acetone) were examined even in organic solvents relatively simple to model. A major source of variation between experimental and calculated log P values may lie in the assumption of the immiscibility of the two solvent systems, an assumption which is not supported experimentally. 

Computer simulation has become a key scientific tool in the study of chemical and biochemical systems. Molecular modeling techniques are routinely being used in the study of a wide variety of chemical systems, such as proteins and DNA, and their interaction with potential pharmaceutical agents. The use of molecular simulations has become possible as a result of advances in theoretical and computational chemistry and the rapid development of cost-effective computing resources. Among the most popular tools in computer simulation studies of complex chemical systems are the thermodynamic cycle free energy methodologies. 

Warren GL, Patel S (2007) Hydration free energies of monovalent ions in transferable intermolecular potential four point fluctuating charge water an assessment of simulation methodology and force field performance and transferability. J Chem Phys 127(6) 064509... 

In the earlier sections, we have developed the theoretical framework for the FEP approach. In this section, we outline some specific methodologies built upon this framework to calculate the free energy differences associated with the transformation of a chemical species into a different one. This computational process is often called alchemical transformation because, in a sense, this is a realization of the inaccessible dream of the proverbial alchemist - to transmute matter. Yet, unlike lead, which was supposed to turn into gold in the alchemist s furnace, the potential energy function is sufficiently malleable in the hands of the computational chemist that it can be gently altered to transform one chemical system into another, slightly modified one. 

These examples show that for difficult cases, and especially when a prediction is being made, a large number of simulations may be necessary. Today, the continuing increase in computer power has made such multiple simulations possible in a reasonable time frame. Several other recent studies illustrate the scope of molecular dynamics free energy for molecular recognition problems they include studies of nucleic acids [13], proteins [14-16], and methodological studies of convergence and precision [17, 18]. Several recent reviews provide additional examples [19, 20]. 

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