Reconstruction of Macromolecular Envelopes From Crystal X-Ray Diffraction Amplitudes

The envelope problem in macromolecular x-ray crystallography involves determining the boundary of a molecule from measurements of amplitudes of x-rays diffracted from a crystalline specimen. This represents a highly underdetermined image reconstruction problem with a large number of degrees of freedom. We regularize the problem by applying binary and connectivity constraints to the image, and seek the solution using the method of iterated projections. However, since the constraints are highly non-convex, the usual methods of generalized projections are not effective. We use the difference map projection algorithm and show that this is effective with simulated diffraction data from a protein envelope