where a(k) is the score of AFP k itself, determined by its RMSD and length with long AFPs rewarded and large RMSDs penalized; is the score of introducing a connection between AFP m and AFP k, defined by a function of the compatibility of the AFPs and the mis-matched regions and/or gaps created by the connection of the two AFPs; T(k) is the number of twists required to connect the chain of AFPs leading up to S(k).
The FATCAT (chaining) score is the best of all S(k) in the alignment graph.
The FATCAT similarity score is computed as
where cs is the FATCAT chaining score; L is the number of equivalent positions in the alignment; RMSD is the overall RMSD between two the structures when one structure is rearranged at the positions where twists are detected by FATCAT; N is the number of blocks in the alignment (number of twists + 1).
The p-value of s is then computed as
where the location and the scale parameter of the extreme value distribution of FATCAT similarity scores of unrelated structures were determined by empirical simulation. For more details about FATCAT significance calculation and examples illustrating its possible biological interpretations, please see the original publication.
The length of the alignment (including gaps)
The number of equivalent positions in the alignment
The root mean square deviation (RMSD) of aligned Cα atoms of the input structures, with one input structure rearranged if flexibility is detected (by introducing twists in the alignment).