An exponential modeling algorithm is developed for protein structure comple
tion by X-ray crystallography and tested on experimental data from a 59-res
idue protein. An initial noisy difference Fourier map of missing residues o
f up to half of the protein is transformed by the algorithm into one that a
llows easy identification of the continuous tube of electron density associ
ated with that polypeptide chain. The method incorporates the paradigm of p
hase hypothesis generation and cross validation within an automated scheme.