  The folding rates of two-state proteins have been found to correlate with
simple measures of native-state topology. The most prominent among these
measures is the relative contact order (CO), which is the average CO or
'localness' of all contacts in the native protein structure, divided by the
chain length. Here, we test whether such measures can be generalized to capture
the effect of chain crosslinks on the folding rate. Crosslinks change the chain
connectivity and therefore also the localness of some of the the native
contacts. These changes in localness can be taken into account by the
graph-theoretical concept of effective contact order (ECO). The relative ECO,
however, the natural extension of the relative CO for proteins with crosslinks,
overestimates the changes in the folding rates caused by crosslinks. We suggest
here a novel measure of native-state topology, the relative logCO, and its
natural extension, the relative logECO. The relative logCO is the average value
for the logarithm of the CO of all contacts, divided by the logarithm of the
chain length. The relative log(E)CO reproduces the folding rates of a set of 26
two-state proteins without crosslinks with essentially the same high
correlation coefficient as the relative CO. In addition, it also captures the
folding rates of 8 two-state proteins with crosslinks.
