Of course, this is an oversimplification: the entropy and enthalpy of a particular protein state do not remain constant over all temperatures. Rather, they vary in a way determined by the heat capacity (Cp), such that ΔG as a function of temperature is (1):
Unfortunately, for most proteins the temperature that favors unfolding lies below the freezing point of water, which makes this phenomenon difficult to study unless you do something unusual to your system. In 2004, Babu et al. (1) reported results from experiments that used reverse micelles to study the denaturation of ubiquitin at temperatures below freezing. By encapsulating a protein-water droplet in inverted micelles dissolved in pentane, it was possible to reduce the temperature to 243 K without causing freezing. These micelles also had the convenient property of tumbling quickly in the pentane, which allowed for reasonable NMR spectra even at these low temperatures. The appearance of the spectra they obtained indicated that the protein underwent a slow unfolding process with many different unfolded states, and also that the protein did not unfold in a cooperative fashion. Rather, it appeared that one contiguous region of the protein unfolded while the rest remained folded (the main helix was particularly stable).
This wasn’t expected, because ubiquitin apparently unfolds in a completely two-state manner when overheated. This being the case, what’s expected is for the protein to either be all folded or all unfolded, not some mixture of the two. However, cold does not affect all intramolecular contacts the same way. Lowering the temperature is expected to make hydrophobic interactions less favorable while not significantly affecting polar interactions like hydrogen bonds. This being the case, one might expect an α-helix to persist through a cold-denaturation transition, as happens in this case.
Something similar is observed in an upcoming paper in JACS from the Raleigh and Eliezer Labs (2), which approaches cold denaturation using a mutant form of the C-terminal domain of ribosomal protein L9. An isoleucine to alanine mutation at residue 98 of this domain doesn’t appear to significantly alter the structure, but it causes the protein to denature somewhere in the high teens. At 12 °C the unfolded state is about 80% of the visible population, and this is where Shan et al. performed their NMR experiments. They assigned the unfolded state using standard techniques and then decided to see what they could learn from the chemical shifts.
As I’ve mentioned before, the chemical shift of a nucleus depends on the probability distribution of the surrounding electrons, and therefore is sensitive to the strength, composition, and angles of the atom’s chemical bonds. Because the dihedral angles of the protein backbone are a good proxy for the secondary structure, one can use the chemical shifts of particular atoms to determine whether a given residue is in a helix or strand. When they performed this analysis, Shan et al. noticed two major differences between the native and cold-denatured states of the protein. The first was that the helix and strand propensities of the denatured protein were much lower than the folded form, as expected. In addition, however, they noticed that one loop of the protein had gained α-helical character. That is, it seemed like an α-helix had actually gotten longer as a result of the unfolding.
This doesn’t mean that denaturing the protein added secondary structure. The low values in the output from the algorithm Shan et al. used suggest that the secondary structure in this denatured state forms only transiently. However, the chemical shifts suggest, and other structural data appear to confirm, that this region of the protein has an increased propensity to inhabit a helical structure as a consequence of the unfolding.
These results emphasize the fact that the “unfolded state” isn’t as simple as it’s often described. Residual structure persists in unfolded states of many proteins, and unfolded ensembles of one protein generated through different means (heat, cold, pH, cosolutes) may not resemble each other. Unlike unfolding at high temperature, cold denaturation of ubiquitin appears to be non-cooperative. In both ubiquitin and L9, it appears that helices are robust to the unfolding process, persisting and even propagating as the protein denatures. While some of these features may be held in common between different kinds of denatured states, others may be unique to particular denaturation conditions. The lingering question is which of these unfolded ensembles best resembles the denatured state that exists under biological conditions, giving rise to misfolded states and their associated diseases.
(1) Babu, C., Hilser, V., & Wand, A. (2004). Direct access to the cooperative substructure of proteins and the protein ensemble via cold denaturation Nature Structural & Molecular Biology, 11 (4), 352-357 DOI: 10.1038/nsmb739
(2) Shan, B., McClendon, S., Rospigliosi, C., Eliezer, D., & Raleigh, D. (2010). The Cold Denatured State of the C-terminal Domain of Protein L9 Is Compact and Contains Both Native and Non-native Structure Journal of the American Chemical Society DOI: 10.1021/ja908104s