Molecular dynamics is routinely used to calculate free-energy changes associated with alchemical transformations. The free-energy differences can be used for many practical purposes such as drug screening, pKa calculations, and determining solvation energies, to mention but a few. Although the typical free-energy techniques (free-energy pertubartion and thermodynamic integration) are straight forward and deliver accurate free-energy changes, in many cases it may not be necessary to obtain accurate free-energy differences, but instead only the order of binding strength may be desired. For instance, one may want to determine which molecule out of several binds most strongly to a specific site in a protein for drug screening. For this type of comparison, it is necessary to know the free-energy changes of both removing the molecules from solvent and then binding to the host site. For two target molecules this would require four independent free-energy calculations.

To reduce the computational burden imposed by such calculations, it is desirable to couple binding and desolvation simulations of both target molecules. By coupling the manifolds of all end states it may then be possible to determine the most efficient binder directly from our simulation more efficiently. One method to couple the required states introduced by Kong and Brooks (J. Chem. Phys. 1996), is to first determine desolvation free-energies for each compound of interest and build these free-energies into a Hamiltonian that is then used to evaluate the preferential binding of the ligand. In the method of Kong and Brooks (Lambda-dynamics) the alchemical degree of freedom was treated as a dynamic variable, and forces applied to the lambda degree of freedom were used to determine the order of binding strength.

The general idea of building in desolvation energies into a competitive binding simulation has also been applied by Pitera and Kollman, but cast in a slightly different form. In the the chemical MC/MD method of Pitera and Kollman (J. Am. Chem. Soc. 1998), desolvation energies are first calculated. MD simulations are then run for a short period of time and periodically interrupted, and the question is asked whether a new ligand should replace the old ligand. The criteria for making the move is determined by the typical monte-carlo criteria, but the energy difference is augmented by the known desolvation energy differences. By this approach the simulation is analogs to an experimental binding competition experiment. Their approach can naturally be used for multiple possible ligands. In testing their methodthe binding strength for several ligands was tested for Rebek's "Tennis ball". The method quickly determined the correct order of binding, and with longer simulations delivered quantitative free-energy differences. In contrast to the continuous lambda-dynamics approach the MC/MD approach saves time by avoiding intermediate states, but may require longer simulations to get converged statistics due to possible low ligand exchange acceptance. Another method that uses a hybrid MC/MD protocol and coupled multiple free energy simulations is the work of Jarque and Tidor (J. Phys. Chem. B 1997).

In constrast to the MC/MD work of Pitera and Kollman this procedure required the simultaneous simulation of both environments, in this case the gas phase and solution, to evaluate the relative solvation energies of small molecules (methane/methanol). These simulations were periodically interrupted and a MC move was attempted. Instead of exchanging end states only however, intermediate states were attempted to improve the acceptance ratio. The acceptance criteria now was based on the combined energy difference from simulations in both environments. Another trick used by Jarque and Tidor to determine the most stable chemical state from both simulations was to use simulated annealing in the MC-move. This allowed very rapid determination of the most stable species (the species with the greatest solubility in aqueous solution).

The method of coupling MD to monte-carlo sampling of the alchemical degrees of freedom has been shown to be successful for small uncomplicated systems, and can provide a fast ordering of species stability. These methods generate an ensemble with MD and then use MC so sample the different energy surfaces generated by different ligands in the ensembles. It remains to be shown how this method would perform for more complicated systems, and systems with large energy differences between the end states. It is likely that for more complicated systems more traditional free-energy techniques may be superior due to low acceptance of exchange.