Geometric invariant core for the V(L) and V(H) domains of immunoglobulin molecules

A new algorithmic method for identifying a geometric invariant of protein structures, termed geometrical core, is developed. The method used the matrix of C(alpha)-C(alpha) distances and does not require the usual superposition of structures. The result of applying the algorithm to 53 immunoglobulin structures led to the identification of two geometrical core sets of C(alpha) atoms positions for the V(L) and V(H) domains. Based on these geometric invariants a preferred coordinate system for the immunoglobulin family is constructed which serves as a basis for structural prediction. The X-ray atom coordinates for all available immunoglobulin structures are transformed to the preferred coordinate system. An affine symmetry between the V(L) and V(H) domains is defined and computed for each of the 53 immunoglobulin structures.