Protein Crystallography: Protein crystallography is especially difficult because diffraction is often quite weak and because the structures are so complex with resolution well below the atomic limit. Applications of the ME formalism in this field have included Avian pancreatic polypeptide, purple membrane using electron diffraction data, TrpRS and Trytophanyl-tRNA synthetase – all structures in which traditional direct methods do not work because of the complexity of the data and its resolution. In these cases the starting phasing were taken from MIR experiments. The method has been extended to membrane protein data with the ab initio solution of two membrane proteins in projection at ca. 9Å resolution, and Beef Liver Catalase at 6 Å.

• Extrapolating the resolution range of the observed structure factors. This is the determination of the reflection intensities which are not measured, but can be determined using maximum entropy techniques.
• The refinement of the protein envelope. The protein envelope is a very low resolution structure of the protein which defines the boundaries of the protein and the solvent. It can be obtained from a fragment of the structure and the observed reflections but it does not always have an accurate shape, therefore the boundaries of the envelope can be refined using maximum entropy techniques.
• Solution of protein structures using protein fragments and envelopes. If a fragment of a protein can be derived by what ever means, either the heavy atoms or a partial structure from direct methods, then this information can be used for the solution of the whole protein. This can be done by incorporting the most accurate phases of the fragment structure factors into a basis set, which are then used with maximum entropy to find the solution for the whole protein.
• The use of maximum entropy and envelopes being incorporated into the CCP4 program ACORN.

References for Protein crystallography

1. ‘Direct Methods in Protein Crystallography – Beef Liver Catalase in its Fully Hydrated Form at Room Temperature’ D.L.Dorset & C.J.Gilmore Acta Cryst. (1999), A55, 448-456.
2. 'Direct Methods in Protein Electron Crystallography: the Ab Initio Structure Determination of Two Membrane Proteins in Projection using Maximum Entropy and Likelihood’ C.J.Gilmore, W.V.Nicholson & D.L.Dorset, Acta Cryst. (1996), A52, 937-946.
3. 'Trytophanyl-tRNA synthetase crystal structure reveals an unexpected homology to tyrosyl-tRNA synthetase' S.Doublié, G. Bricogne, C.J.Gilmore, & C.W.Carter Jnr. Structure (1995), 3, 17-31.
4. 'Overcoming Non-Isomorphism by Phase Permutation with Likelihood Scoring: Solution of the TrpRS Crystal Structure' S.Doublié, S.Xiang, C.J.Gilmore, G.Bricogne, & C.W.Carter, Acta Cryst. (1994), A50, 164-182.
5. 'Entropy Maximisation Constrained by Solvent Flatness: A New Method for Macromolecular Phase Extension and Map Improvement', S.Xiang, C.W.Carter Jr., G.Bricogne, & C.J.Gilmore, Acta Cryst. (1993), D49, 193-212.
6. 'Phase Extension in Electron Crystallography Using the Maximum Entropy Method and its Application to Two-dimensional Purple Membrane Data from Halobacterium Halobium', C.J.Gilmore, K.Shankland & J.R.Fryer, Ultramicroscopy (1993), 49, 132-146.
7. 'A Multisolution Method of Phase Determination by Combined Maximisation of Entropy and Likelihood. V The Use of Likelihood as a Discriminator of Phase Sets Produced by the Saytan Program for a Small Protein' C.J.Gilmore, A.N.Henderson & G.Bricogne, Acta Cryst. (1991), A47, 842-847.