Geometric invariant core for the V-L and VH domains of immunoglobulin molecules

A new algorithmic method for identifying a geometric invariant of protein s tructures, termed geometrical core, is developed, The method used the matri x of C-alpha-C-alpha distances and does not require the usual superposition of structures. The result of applying the algorithm to 53 immunoglobulin s tructures 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 inva riants a preferred coordinate system for the immunoglobulin family is const ructed which serves as a basis for structural prediction. The X-ray atom co ordinates for all available immunoglobulin structures are transformed to th e preferred coordinate system. An affine symmetry between the V-L and V-H d omains is defined and computed for each of the 53 immunoglobulin structures .