CHARMM Element doc/pdetail.doc 1.1#File: PDETAIL, Node: Top, Up: (chmdoc/perturb.doc), Next: Introduction Details about TSM Free Energy Calculations* Menu: * Introduction:: What will be covered.* Theory and Methodology:: General discussion.* Practice:: How to do it.#File: PDETAIL, Node: Introduction, Up: Top, Next: Theory and Methodology, Previous: Top Introduction For a good overview of free energy simulation methods, the follow-ing references are suggested: M. Mezei and D. L. Beveridge, in Annals ofthe New York Academy of Sciences, chapter titled "Free Energy Simulations",482 (1986) 1; T. P. Straatsma, PhD dissertation, "Free Energy Evaluationby Molecular Dynamics Simulations", University of Groningen, Netherlands(1987) and S. H. Fleischman and C. L. Brooks III, "Thermodynamics ofAqueous Solvation: Solution Properties of Alchohols and Alkanes", J.Chem. Phys., 87, (1987) p. 3029, D. J. Tobias and C. L. Brooks III,J. Chem. Phys., 89, (1988) 5115-5127, and D.J. Tobias, "The Formation and Stability of Protein Folding Initiation Structures", Ph.D. dissertationCarnegie Mellon University (1991). In the previous nodes we have generally referred to this area ofmolecular simulation as a "perturbation" theory. Actually, none of thetechniques used are actually perturbation methods. The relationshipsused for computing the relative free energy differences are all exact inthe statistical mechanical sense. The use of the term perturbation inthis context arises from the fact that in the pre-number crunchingsupercomputer days, various series expansions were derived from theseequations and were in fact perturbation theories. The name thermodynamicintegration might be used, however common practice has been to apply itto only one particular formulation (and furthermore not put that underthe rubric of thermodynamic perturbation). Finally, the use of the name"free energy simulations" is another misonomer for two reasons: 1) we cancalculate the temperature derivative thermodynamic properties as well(Delta E and Delta S) and the one thing we can't get is absolute freeenergies (as van Gunsterin has pointed out , Mother Nature doesn'tintegrate all over phase space either). In fact, we generally are limitedto calculating relative changes in free energies, i.e. Delta Delta A's. In thermodynamic perturbation theory, a system with the potential energy function U0 is perturbed to one with the potential function U1, and the resulting free energy difference is calculated asA1 - A0 = -kT ln < exp[ -(1/kT)*(U1 - U0)] >where k is Boltzmann's constant, T is temperature (degrees K), and A0 and A1 are the excess Helmholtz free energies of systems 0 and 1, respectively. Two methods of thermodynamic perturbation are implemented in CHARMM: 1) Chemical perturbation, where the perturbation being considered is a change in the system's potential function parameters and topology,e.g., CH3OH is "mutated" to CH3CH3, and 2) Internal coordinate perturbation, where the perturbation represents a variation in configuration, and the potential function remains the same for the perturbed and unperturbed systems.Each of these is discussed separately below.#File: PDETAIL, Node: Theory and Methodology, Up: Top, Next: Practice, Previous: Introduction THEORY AND METHODOLOGY* Menu:* Chemical:: Chemical Perturbation Theory and Methodology* Internal:: Internal Coordinate Perturbation Theory and Methodology* References:: Some References on Thermodynamic Perturbation#File: PDETAIL, Node: Chemical, Up: Theory and Methodology, Next: Internal, Previous: Theory and Methodology Chemical Perturbation If you have read either (Fleischman and Brooks, 1987) or(Straatsma, 1987) or any of the McCammon or Kollman perturbation (oops!that word again) papers, then you have seen the standard schpiel on whygetting Delta A's (or Delta G's) of solvation or drug/enzyme binding,among other processes is so difficult and that if one is satisfied withrelative changes in free energies it is computationally more tractable to"trans-mutate" various parts of a system in a way that is usuallyphysically unreasonable but computationally feasible andthermodynamically equivalent to that obtained from the physical process.Read some of the aforementioned references if this doesn't ring a bell. So that's what we are doing - calculating relative changes infree energies (Delta Delta A) for solvation and small molecule/enzymebinding, among other things. In the rest of this node, we will discuss alittle bit of the theory (you're better off reading the papers) and lotabout the actual how-to-do-it in our implementation. Subsequent nodesdiscuss the actual implementation and some issues to consider whenattempting this type of calculation. The Hamiltonian There are three basic techniques for calculating relative changesin free energy and their temperature derivative properties: 1) theso-called "perturbation" approach 2) "Thermodynamic Integration" (TI) 3)and the somewhat dubious "slow-growth" technique (which is actually astep-child of the TI method). In all of the methods we use a hybrid hamiltonian, N N H(lambda) = H + (1 - lambda) H + lambda H . o R P where: H = "Environment" part of the Hamiltoniano H = "Reactant" part of the Hamiltonian R H = "Product" part of the Hamiltonian P lambda = coupling parameter (extent of transformation) N = integer exponent The various terms will be explained shortly. First, a bit aboutour Weltanshauung viz. free energy simulations. The system is dividedinto four sets of atoms: 1) The reactant atoms 2) the product atoms 3)the colo atoms and 4) the environment atoms. The reactant and productatoms are those that are actually being changed. The colo atoms (shortfor co-located charge) are those in which only the charge changes