  It has been observed that the topology of the native state is an important
determinant of protein folding kinetics and there is a significant correlation
between folding rate and relative contact order (RCO) in two-state small
single-domain proteins. However, as a pure topological property, RCO does not
take into account residue interactions that also play an important role in
folding kinetics. Using the inter-residue statistical contact potentials, we
introduce weight into the residue network of contacts, and therefore define a
weighted RCO. Using the weighted RCO, we can capture the folding kinetics of
proteins having the same topology, but different sequence information. By
constructing essential sub-networks based on the strength of the pairwise
interactions, we are able to deduce the features of sequences redundant for
folding events. We perform an analysis on 48 two-state proteins and the
ultrafast-folding proteins, as well as mutants of the protein CI2, protein G,
and protein L. Our results indicate that (i) both the weighted RCO of original
residue network and that of essential sub-networks have significant
correlations with the folding rate like RCO; (ii) the folding rate is
critically dependent on the hydrophobic interactions for two-state folding; and
(iii) the sub-networks distinguish the folding rate differences of the mutants
and reveal the folding preferences of proteins.
