is the distance between a pair of atoms.
is the - distance between residues and in the native state.
is the standard deviation, determining the width of the Gaussian function.
is the number of residues of the protein being considered.
The first term, , computes the unnormalized fraction of
- pair distances that are the same or similar
aligned structures. is the spatial
between residues and in protein a, and is the
between residues ' and ' in protein b. This term is restricted to
aligned positions, e.g., where is aligned to ' and is aligned
The remaining terms account for the residues in gaps. and are
residues in insertions in both proteins, respectively. and
the aligned residues on either side of the insertion in protein a. The
definition is analogous for and .
The normalization and the terms are computed as:
where is the number of aligned residues. is the number of residues appearing in gaps, and is sum of the number of insertions in protein ``a'', the number of insertions in protein ``b'' and the number of simultaneous insertions (referred to as bulges or c-gaps). is the number of c-gaps. Gap-to-gap contacts and intra-gap contacts do not enter into the computation, and terminal gaps are also ignored. is a slowly growing function of sequence separation of residues and , and this serves to stretch the spatial tolerance of similar contacts at larger sequence separations. ranges from 0 to 1 where refers to identical proteins. If there are no gaps in the alignment, then becomes , which is identical to the Q-measure described into the measure described before.