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Maximum Entropy and CCP4

Chris Gilmore
Theoretical Crystallography Group
University of Glasgow

The maximum entropy (ME) phasing method has still not entered mainstream protein crystallography despite its successes [1-6]. In part this is undoubtedly due to a lack of a general-purpose computer program freely distributed within the protein crystallography community. CCP4 is therefore funding a one year programming post in which the MICE computer program developed by Chris Gilmore, Gerard Bricogne and Charles Carter will be adapted by Chris Gilmore and his group at Glasgow to become part of theCCP4 suite. It is proposed to include:

How will it be used?

It will be possible to compute a maximum entropy centroid map at any time where Fourier coefficients and some measure of their reliability are available are available. The user selects the reflections using acceptance criteria based on the agreement between observed and calculated structure factors and figures of merit from phasing procedures, and these are used as the starting point of a constrained entropy maximisation in which the amplitudes, their associated phases and any other crystallographic knowledge as listed above are used as constraints. In cases where traditional maps cannot quite be interpreted, this alone may push the structure over the edge into the realm of interpretability. The ME methodology is very good at dealing with low resolution data and situations where there are considerable measurement errors.

Strong reflection for which phase ambiguities exist at this point can be phased using phase permutation methods based on error correcting codes or incomplete factorial designs coupled with entropy maximation using the concepts of a phasing tree. This was used to great effect in solving the TrpRS structure. This step can also include the resolution of MIR/SIR phase ambiguities for subsets of strong reflections which are highly correlated with each other.

Ab initio phasing to determine heavy atom sites may be possible in favourable cases.

The User Interface

The program has a graphical user interface based on Tcl and the Tk toolkit and is fully integrated into CCP4 and its file structures. Wei Dong is carrying out this work at Glasgow University and we hope to have a beta release ready for distribution by Christmas. It is intended that the user need have no great understanding of the ME formalism, and that the software is simple to use.


  1. 'Entropy Maximisation Constrained by Solvent Flatness: A New Method for Macromolecular Phase Extension and Map Improvement', S.Xiang, C.W.Carter Jr., G.Bricogne, and C.J.Gilmore, Acta Cryst. (1993), D49, 193-212.
  2. '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.
  3. 'Entropy Maximisation Constrained by Solvent Flatness: Macromolecular Phase Extension and Refinement' C.W.Carter, S.Xiang, S.Doublié, G.Bricogne & C.J.Gilmore, Acta Cryst, (1993), A49, 48.
  4. ‘Overcoming Non-Isomorphism by Phase Permutation and Likelihood Scoring: Solution of the TrpRS Crystal Structure’ S. Doublié, S.Xiang, C.J.Gilmore, G.Bricogne & C.W.Carter Jnr. Acta Cryst. (1994), A50, 164-182.
  5. 'Maximum Entropy and Bayesian Statistics in Crystallography' C.J.Gilmore, Acta Cryst. (1996) A52, 561-589
  6. ‘A Multisolution Method of Phase Determination by Combined Maximisation of Entropy and Likelihood. VI The Use of Error-Correcting Codes as a Source of Phase Permutation and their Application to the Phase Problem in Powder, Electron and Macromolecular Crystallography’ C.J.Gilmore, W.Dong & G.Bricogne (1998), Acta Cryst. A, accepted for publication.

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