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This article concerns the calculation of equilibria of ligand binding to multiple sites in macromolecules in the presence of conformational flexibility and conformation-dependent interaction among the sites. A formulation of this problem is presented in which global conformational changes are distinguished from conformational changes that are confined to ‘‘locally flexible regions.’’ The formalism is quite general in that ligands of different types, multivalent binding sites, tautomeric binding sites, and sites that bind more than one type of ligand can be accommodated. Strictly speaking, the separation of the conformational problem into global and local parts does not impose any loss of generality, although in practice it is necessary to restrict the number of global and local conformers. Because of the combinatorics of binding and conformational states, the computational complexity of a problem having only local conformational flexibility grows exponentially with the number of sites and the number of locally flexible regions. An iterative mobile clustering method for cutting off this exponential growth and obtaining approximate solutions with low computational cost is presented and tested. In this method, a binding site is selected, and a ‘‘cluster’’ of strongly interacting sites is set up around it; within the cluster, the binding and conformational states are fully enumerated, whereas the influences of sites outside the cluster on the sites inside are treated by a mean field approximation. The procedure then moves to the next site around which another Correspondence to: D. Bashford; e-mail: bashford@scripps.edu Contractrgrant sponsor: National Institutes of Health Contractrgrant number: GM45607 ( ) Journal of Computational Chemistry, Vol. 20, No. 11, 1091]1111 1999 Q 1999 John Wiley & Sons, Inc. CCC 0192-8651 / 99 / 111091-21 SPASSOV AND BASHFORD Ž . possibly overlapping cluster is formed and the calculation is repeated. The procedure iterates through the list of sites in this way, using the results of previous iterations for the mean-field terms of current iterations until a convergence criterion is met. The method is tested on a large set of randomly generated problems of varying size, whose geometries are chosen to have protein-like statistical properties. It is found that the method is accurate and rapid with the computational cost scaling linearly to quadratically with the number of sites, except for a minority of cases in which large clusters occur by chance. The new method is more accurate than a Monte Carlo method, and may be faster or slower depending on the clustering criteria and details of the macromolecule. Q 1999 John Wiley & Sons, Inc. J Comput Chem 20: 1091]1111, 1999

j. comput. chem.

Multiple-site ligand binding to flexible macromolecules: Separation of global and local conformational change and an iterative mobile clustering approach