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Of relevance: A brief introduction to quantum chemistry This section is adapted from part 1.2.2. of O.S. Smart, "Simulation of a conformational rearrangement of the substrate in D-xylose Isomerase", University of London Ph.D. thesis (1991).
Bash, Field & Karplus (1987) have combined a semi-empirical quantum mechanical (AM1) treatment for a small part (about 20 non-hydrogen atoms) of a system with a molecular mechanics approach to the rest, adapting a method first used by Warshel & Levitt (1976). This allows for the treatment of chemical reactions in solution, and the method has since been applied to the enzymatic reaction of triose phosphate isomerase (Karplus et al. , 1992). Warshel and co-workers have made extensive use of a procedure which combines a valence bond quantum mechanical methodology with molecular mechanics - see Warshel (1991) for descriptions of many applications.
Another approach is based on Feynman path integral formulation of quantum dynamics. Examples of its use are the quantum simulation of ferrocytochrome c based on a conventional molecular mechanics force field (Zheng et al. , 1988) and the simulation of excess electrons in a hard sphere fluid and crystal (Baum & Cruzeiro-Hansson, 1990).
Simulations can also be made in which a only a small part of the protein is considered. This allows the representation of processes which could not be represented by a molecular mechanics potential (see next section), such as, chemical reactions or spectroscopic transitions. Arad et al. (1990) use AM1 (a semi-empirical quantum mechanics program see Dewar et al. , 1985) to simulate a reaction path for sulphur attack in the reaction mechanism of papain. The system is composed of 111 atoms, around the active site, taken from conformations derived energy minimization with a molecular mechanics potential. Penfield et al. (1985) use ab initio methods to examine the electronic structure of the blue copper site in plastocyanin and the hyperfine line splitting of the copper spectrum. They approximate the metal site by replacing the histidine residues with ammonia, cysteine with methanethiolate and methionine with dimethyl thioether -- representing the co-ordination site by 7 non-hydrogen atoms.
Bajorath et al. (1991) have shown how an enzyme (dihydrofolate reductase) perturbs the spatial electronic distribution of the substrate (folate) on binding. An alternate ab initio electronic structure technique was used (local density functional theory) allowing the 49 atoms of the substrate to be treated quantum mechanically in the coulomb field arising from partial charges assigned at each atomic position of the enzyme, co-enzyme and solvent molecules.