Some published indices like those listed ahead can be obtained from the previously described using other aggregation_operator procedure to transform the vector of residue indices to a single value for the protein or a particular group:
Long range order (LRO) is defined by the quotient between the total number of contacts of the protein and its whole number of residues (Gromiha and Selvaraj, 2001).
Where i and j are two residues whose Ca-Ca distance is less equal than 8Å and nr is the total number of residues in a protein.
This descriptor can be calculated with ProtDCal averaging the number of contacts over the protein (using the aggregation_operator procedure arithmetic mean, Ar), using .
Absolute contact order (Abs_CO) was originally defined by Ivankov (Ivankov et al., 2003) as:
ProtDCal can estimates such descriptor as the summation (the aggregation_operator procedure N1, distance 1 of Minkosky) of the weighted residue-wise relative contact order for each residue of the protein, using .
The total contact distance was originally defined as:
where nr is the number of amino acid residues of a protein, nc is the number of contacts (Zhou and Zhou, 2002).
The original global TCD can be obtained averaging (using the aggregation_operator procedure arithmetic mean, Ar) all the obtained residue-wise values using .
Gromiha, M.M., and Selvaraj, S., 2001. Comparison between long-range interactions and contact order in determining the folding rate of two-state proteins: application of long-range order to folding rate prediction. J. Mol. Biol. 310, 27-32.
Ivankov, D.N., Garbuzynskiy, S.O., Alm, E., Plaxco, K.W., Baker, D., and Finkelstein, A.V., 2003. Contact order revisited: Influence of protein size on the folding rate. Protein Sci. 12, 2057-2062.
Zhou, H., and Zhou, Y., 2002. Folding Rate Prediction Using Total Contact Distance. Biophysical Journal 82, 458-463.