Analysis of the ensemble of conformations ofD0
The ensemble of conformations generated by the replica-exchange
algorithm at 300K were further analyzed to characterizeD0 . The average Rg , of
value 2.19 ± 0.48 nm (cf. Fig. S11), was consistently larger than the
value 1.28 nm of the native conformation. The fact that the contact
probability between pairs of residues as a function of their distance
along the chain is a power law with an exponent ≈-1.8 (cf. Fig. S12)
suggests that the chain is, on average, in a coil state.
The average number of contacts is 60.6 ± 15.3 (cf. Fig. S13) and the
fraction qN of native contacts is low (≈ 0.018 ± 0.011).
To be noted the fraction qN of native contacts in the
denatured state is poorly correlated with the commonly employed RMSD
(cf. Fig. S14). In fact, the RMSD is a highly non-linear function of the
diversity between conformations in that it is very sensitive to
conformational changes between similar conformations and quite
insensitive to large conformational changes between dissimilar
conformations. Since the denatured state is expected to be
conformationally very heterogeneous, we compared pairs of conformations
using the fraction q of common contacts (and we compared a
conformation to the native one using the fractionqN of native contacts).
In Fig. 8(a) the distribution of common contacts q between
denatured conformations is plotted. Its average is 0.09 ± 0.08 but it
displays a tail up to 0.7. Not surprisingly, the denatured stateD0 thus appears conformationally very
heterogeneous. However, its average contact map (cf. Fig. 8(b)) displays
well-defined secondary structures that can reach a probability of 0.4
and also tertiary structures populated with probabilities up to 0.15.
Some of these structures are native-like and include the hairpin β1-β2,
the hairpin β4-β5, the hairpin β5-β6 and the terminal α-helix (cf. Fig.
8(c)). Non-native contacts (cf. Fig. 8(d)) include a set of alternative
structures in the region of the hairpin β4-β5, some fluctuating
structure around P63 and a small amount of tertiary contacts.