Chemical-Monte Carlo/Molecular Dynamics (CMC/MD) is a new feature of AMBER 6.0. It permits a stochastic free energy calculation that, in contrast to GIBBS, allows the comparison of many (5- 10) similar species in a single calculation. CMC/MD calculations are carried out by a modified version of sander called sander.MC, just as LES calculations require the use of sander.LES. CMC/MD calculations have been used to optimize guests for hosts, rank the affinity of a family of ligands for a protein, and compare multiple side chains at a single position of a protein or peptide. CMC/MD is an extension of a method suggested by C.H. Bennett, and similar algorithms are commonly known as parameter hopping or extended ensemble algorithms.
In a CMC/MD calculation, there are two parts of the simulated system: the surroundings and the Monte Carlo region. For a CMC/MD calculation that compared the solvation free energies of a number of solutes, the surroundings would be the solvent water residues. The Monte Carlo region would consist of one copy of each solute of interest. At any point in time, one of these solute copies is treated as the real solute and interacts with the surroundings. The other (ghost) Monte Carlo residues are masked: the surroundings do not feel their influence. Molecular dynamics can be carried out on this system to generate a new set of coordinates for each residue. Occasionally, a trial move is explored which attempts to switch the identity of the real residue. A residue is chosen from the Monte Carlo region at random, and the energy change associated with making this the real residue is determined. This trial move to a new real residue is accepted or rejected based on this energy and the Metropolis Monte Carlo criteria:
As the simulation is carried out, each Monte Carlo residue becomes the real residue for varying lengths of time. A history is kept of the probability of sampling each residue, and if the simulation has converged, the relative free energies of any two residues may be determined by;
Just as with GIBBS, CMC/MD calculations can make use of a thermodynamic cycle to determine properties of chemical interest: relative solvation free energies, relative binding free energies, etc. However, in order to get efficient sampling between the Monte Carlo residues, they must not be too dissimilar; CMC/MD is best for comparing related families of compounds. While these compounds should be structurally related, they can have relatively different free energies. The discrete nature of the Monte Carlo sampling in CMC/MD makes it very straightforward to add biasing potentials to the Monte Carlo sampling. An adaptive procedure (adaptive CMC/MD) periodically re-adjusts biasing potentials over the course of a calculation to achieve optimal sampling between species with very different free energies.
Some references: