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@@ -44,20 +44,66 @@ The functionality to perform and visualize these alignments can of course be use
 
 ### Combinatorial Extension (CE)
 
-The Combinatorial Extension (CE) algorithm was originally developed by [Shindyalov and Bourne in 1998](http://peds.oxfordjournals.org/content/11/9/739.short). 
+The Combinatorial Extension (CE) algorithm was originally developed by
+[Shindyalov and Bourne in
+1998](http://peds.oxfordjournals.org/content/11/9/739.short).
+It works by identifying segments of the two proteins with similar local
+structure, and then combining those to try to align the most residues possible
+while keeping the overall RMSD of the superposition low.
+
+CE is a rigid-body alignment algorithm, which means that the structures being
+compared are kept fixed during superpositon. In some cases it may be desirable
+to break large proteins up into domains prior to aligning them (by manually
+inputing a subrange, using the [SCOP or CATH databases](externaldb.md), or by
+decomposing the protein automatically using the [Protein Domain
+Parser](http://www.biojava.org/docs/api/org/biojava/bio/structure/domain/LocalProteinDomainParser.html)
+algorithm).
 
 ### Combinatorial Extension with Circular Permutation (CE-CP)
 
-This is a new variation of CE that can detect circular permutations in proteins. @sbliven &amp; @andreasprlic , unpublished
+CE and FATCAT both assume that aligned residues occur in the same order in both
+proteins (e.g. they are both *sequence-order dependent* algorithms). In proteins
+related by a circular permutation, the N-terminal part of one protein is related
+to the C-terminal part of the other, and vice versa. CE-CP allows circularly
+permuted proteins to be compared.  For more information on circular
+permutations, see the
+[wikipedia](http://en.wikipedia.org/wiki/Circular_permutation_in_proteins) or
+[Molecule of the
+Month](http://www.pdb.org/pdb/101/motm.do?momID=124&evtc=Suggest&evta=Moleculeof%20the%20Month&evtl=TopBar)
+articles.
+
+
+For proteins without a circular permutation, CE-CP results look very similar to
+CE results (with perhaps some minor differences and a slightly longer
+calculation time). If a circular permutation is found, the two halves of the
+proteins will be shown in different colors:
+
+![Concanavalin A (yellow & orange) aligned with Pea Leptin (blue and cyan)](img/3cna.A_2pel.A_cecp.png)
+
+CE-CP was developed by Spencer E. Bliven, Philip E. Bourne, and Andreas Prli&#263;.
 
 ### FATCAT - rigid
 
-This is a Java implementation of the original FATCAT algorithm. [Yuzhen Ye &amp; Adam Godzik in 2003] (http://bioinformatics.oxfordjournals.org/content/19/suppl_2/ii246.abstract)
+This is a Java implementation of the original FATCAT algorithm by [Yuzhen Ye
+&amp; Adam Godzik in
+2003](http://bioinformatics.oxfordjournals.org/content/19/suppl_2/ii246.abstract).
+It performs similarly to CE for most proteins. The 'rigid' flavor uses a
+rigid-body superposition and only considers alignments with matching sequence
+order.
 
 ### FATCAT - flexible
 
-Just as FATCAT - rigid, a Java implementation of the original FATCAT algorithm.
+FATCAT-flexible introduces 'twists' between different parts of the proteins
+which are superimposed independently. This is ideal for proteins which undergo
+large conformational shifts, where a global superposition cannot capture the
+underlying similarity between domains. For instance, the structures of
+calmodulin with and without calcium bound can be much better aligned with
+FATCAT-flexible than with one of the rigid alignment algorithms. The downside of
+this is that it can lead to additional false positives in unrelated structures.
+
+![(Left) Rigid and (Right) flexible alignments of
+calmodulin](img/1cfd_1cll_fatcat.png)
 
 ## Acknowledgements
 
-Thanks to P. Bourne, Yuzhen Ye and A. Godzik for granting permission to freely use and redistribute their algorithms.
+Thanks to P. Bourne, Yuzhen Ye and A. Godzik for granting permission to freely use and redistribute their algorithms.