Statistical coil model of the unfolded state: Resolving the reconciliation problem

Abstract

An unfolded state ensemble is generated by using a self-avoiding statistical coil model that is based on backbone conformational frequencies in a coil library, a subset of the Protein Data Bank. The model reproduces two apparently contradicting behaviors observed in the chemically denatured state for a variety of proteins, random coil scaling of the radius of gyration and the presence of significant amounts of local backbone structure (NMR residual dipolar couplings). The most stretched members of our unfolded ensemble dominate the residual dipolar coupling signal, whereas the uniformity of the sign of the couplings follows from the preponderance of polyproline II and ␤ conformers in the coil library. Agreement with the NMR data substantially improves when the backbone conformational preferences include correlations arising from the chemical and conformational identity of neighboring residues. Although the unfolded ensembles match the experimental observables, they do not display evidence of nativelike topology. By providing an accurate representation of the unfolded state, our statistical coil model can be used to improve thermodynamic and kinetic modeling of protein folding. denatured state ͉ protein folding ͉ residual dipolar coupling ͉ nearest neighbor ͉ radius of gyration D enatured proteins are the initial state for mechanistic and thermodynamic studies of folding. The recent resurgence of interest in the unfolded state is partly motivated by the development of NMR methods that are capable of providing site-resolved structural information (1-7). These measurements indicate that unfolded proteins have far richer structural diversity than earlier believed, possibly even encoding the native topology (1,(8)(9)(10)(11).These works seem at odds with the classic studies by Tanford et al. (12,13), who demonstrated by using hydrodynamic methods that the global dimensions of denatured proteins exhibit the size dependence expected for self-avoiding ''random coil'' polymers. More recent measurements of the radius of gyration, R g , using small-angle scattering methods exhibit the same random coil scaling behavior with length R g ϰ N 0.585 (8,14). These observations are consistent with denatured proteins being random coils in good solvent conditions (15). This finding leads to the so-called ''reconciliation problem'' between the random coil scaling behavior and the presence of significant amounts of local structure in unfolded state (14, 16).However, Rose and Fitzkee (17) demonstrate that even a ''deliberately extreme'' model of chains composed of native-like segments connected by flexible residues also can reproduce random coil scaling behavior. Hence, the recapitulation of the scaling behavior provides only a weak test for any unfolded state model. Nevertheless, spectroscopic measurements, such as circular dichroism, indicate that most unfolded states, particularly chemicaldenatured proteins (8,13,18), have little secondary structure. Accordingly, the unrealistic native-like segment model is ruled out. More exacting...

The hydrodynamic and conformational properties of denatured proteins in dilute solutions

“…[11][12][13] solution, 23 and a constant value of (R G /N 1/2 ) RIS calculated for the rotational-isomeric-state model in the limit of large N. 24 It may be seen that the experimental values of R G /N 1/2 are about equal to H0.7(R G /N 1/2 ) STAT . Thus, if (R G /N 1/2 ) STAT is presumed to be an accurate measure of R G /N 1/2 for the chain without any intramolecular association producing ring structures, g ¼ R 2 G /(R 2 G ) LIN % 0.7, larger than the value g ¼ 1/2 expected for a pure ring-shaped polymer.…”

Accurate Random Coil Chemical Shifts from an Analysis of Loop Regions in Native States of Proteins

“…18,19 In conclusion, we suggest that increasingly accurate random coil chemical shift scales will be obtained through approaches of the type that we have presented here by exploiting the continuous growth of databases of protein structures and chemical shifts, which will enable progressively more sophisticated functions to be parametrized. …”

Protein folding: Then and now

“…To reconcile the seemingly controversial properties of denatured proteins -the random coil scaling of their sizes and the presence of residual native structures -several computational works have recently been reported [203][204][205][206][207]. Fitzkee and Rose [206] reproduced the random coil scaling exponent using a denatured protein model with fixed secondary structure elements for a set of proteins.…”

“…Tran et al [204,207] constructed the protein denatured state ensemble at atomic resolution in the excluded volume limit. Jha et al [205] built the denatured state using a statistical coil library. Both the Pappu and Sosnick groups found that the putative denatured state ensemble features transient local structures such as turns, strand, and helices.…”

“…Previous computational studies [203][204][205]207] suggest that the residual structures in the denatured state are limited to short-range elements, which only extend approximately seven to ten residues. The correlated fluctuation of residual structures diminishes quickly along the sequence and long-range contact formation is purely governed by the random diffusion of peptide chains.…”