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

This article concerns the calculation of equilibria of ligand binding to mu ltiple sites in macromolecules in the presence of conformational flexibilit y and conformation-dependent interaction among the sites. A formulation of this problem is presented in which global conformational changes are distin guished 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 se paration of the conformational problem into global and local parts does not impose any loss of generality, although in practice it is necessary to res trict the number of global and local conformers. Because of the combinatori cs of binding and conformational states, the computational complexity of a problem having only local conformational flexibility grows exponentially wi th the number of sites and the number of locally flexible regions. An itera tive mobile clustering method for cutting off this exponential growth and o btaining approximate solutions with low computational cost is presented and tested. In this method, a binding site is selected, and a "cluster" of str ongly interacting sites is set up around it; within the cluster, the bindin g 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 anoth er (possibly overlapping) cluster is formed and the calculation is repeated . The procedure iterates through the list of sites in this way, using the r esults of previous iterations for the mean-field terms of current iteration s until a convergence criterion is met. The method is tested on a large set of randomly generated problems of varying size, whose geometries are chose n to have protein-like statistical properties. It is found that the method is accurate and rapid with the computational cost scaling linearly to quadr atically with the number of sites, except for a minority of cases in which large dusters occur by chance. The new method is more accurate than a Monte Carlo method, and may be faster or slower depending on the clustering crit eria and details of the macromolecule. (C) 1999 John Wiley & Sons, Inc.