Predicting antibody hypervariable loop conformation. I. Ensembles of random conformations for ringlike structures

Abstract

One approach to finding the conformation of minimum energy for a complicated molecule is to perform energy minimization, perhaps coupled to more exhaustive search procedures such as dynamics or Monte Carlo sampling, from many starting conformation. Where there are geometric constraints on the conformations, as in a ring molecule, or a variable loop starting and ending in known constant regions of one of a series of homologous proteins, rapidly generating many such starting conformations, all satisfying the constraints, has been a problem in the past. We have devised an algorithm, which we call random tweak, which performs this task in the context of a torsional description of a molecule, and have used it to model the backbones of the six CDRs (complementarity determining regions) of the immunoglobulin MCPC603. These range in size from 5 to 19 residues, and have from 8 to 36 variable dihedral angles. Ensembles of 100 properly closed backbone structures for each CDR were generated under several conditions of van der Waals screening internally and against the rest of the molecule, and ensembles of 1000 were generated for selected CDRs. These structure “libraries” reveal how the geometry at the base of a CDR and the topography of the surrounding protein surface restrict the region of space that a given CDR can occupy. In accord with simple notions of chain molecule statistics, the more highly extended a CDR at its base, the more similar the possible structures and the fewer that are necessary to span the conformational space. Energy minimization and molecular dynamics studies (reported elsewhere) using these libraries to furnish starting conformations show that, as the number of residues in a CDR goes from five to nine, the number of randomly generated structures necessary to ensure that low‐lying energetic minima, such as the native conformation, will be found several times goes from a few tens to a few hundred. Some of the spatial features of an ensemble of random conformations are implicit in the histogram of the rms atomic displacements calculated for all the pairs in the ensemble. The random tweak method is carried out by setting each dihederal angle on the main chain of the variable fragment to a random value, then using an iterated linearized Lagrange multiplier technique to enforce the geometric constraints with the minimal conformational perturbation. The time required for the algorithm is linear in fragment length, and the resulting ability of the method to handle large loops makes it especially applicable to the modeling of homologous proteins. In most cases, hundreds of acceptable structures could be generated in a few hours on a VAX 11/780. Where van der Waals screening against fixed atoms need not be performed, as for isolated ring molecules, generation times go down by an order of magnitude or more.