Determining denaturation midpoints in multiprobe equilibrium protein folding experiments

Multiprobe equilibrium unfolding experiments in the downhill regime (i.e., maximal barrier < 3RT) can resolve the folding process with atomic resolution [Munoz ( 2002) Int. J. Quantum Chem. 90, 1522-1528]. Such information is extracted from hundreds of heterogeneous atomic equilibrium unfolding curves, which are characterized according to their denaturation midpoint (e.g., T-m for thermal denaturation). Using statistical methods, we analyze T-m accuracy when determined from the extremum of the derivative of the unfolding curve and from two-state fits under different sets of simulated experimental conditions. We develop simple procedures to discriminate between real unfolding heterogeneity at the atomic level and experimental uncertainty in the single T-m of conventional two-state folding. We apply these procedures to the recently published multiprobe NMR experiments of BBL [Sadqi et al. ( 2006) Nature 442, 317-321] and conclude that for the 122 single transition atomic unfolding curves reported for this protein the mean T-m accuracy is better than 1.8 K for both methods, compared to the 60 K spread in T-m determined experimentally. Importantly, we also find that when the pre- or posttransition baseline is incomplete, the two-state fits systematically drift the estimated T-m value toward the center of the experimental range. Therefore, the reported 60 K T-m spread in BBL is in fact, a lower limit. The derivative method is significantly less sensitive to this problem and thus is a better choice for multiprobe experiments with a broad T-m distribution. The results we obtain in this work lay the foundations for the quantitative analysis of future multiprobe unfolding experiments in fast-folding proteins.