Measure the folding-to-glass temperature ratio of a real protein
In plain words
Energy landscape theory says a protein folds reliably only if the pull toward its native shape beats the roughness of its energy surface, meaning the many traps a chain can fall into. The roughness has been estimated at a few times the thermal energy, but the ratio of two temperatures that decides foldability has not been measured for a natural protein.
Precise statement
In the random-energy model of folding (Bryngelson and Wolynes), foldability requires $T_f/T_g > 1$, where $T_f$ is the folding temperature and $T_g = dE / \sqrt{2 k_B S_0}$ the glass temperature set by the energy spread dE of non-native states and their configurational entropy $S_0$; theoretical estimates for small natural proteins are of order 1.5 to 2 (approximate). Determine both dE and S_0 for the same natural protein from experiment (roughness estimates of approximately $4 \text{ to } 5\,k_B T$ exist; Milanesi and co-workers, 2012), and compute $T_f/T_g$ with error bars.
What would settle it
Temperature-dependent measurement of configurational diffusion or transition-path dynamics on one protein, analyzed with the random-energy model to yield dE, $S_0$ and $T_f/T_g$.