Determining denaturation midpoints in multiprobe equilibrium protein folding experiments.

Multiprobe equilibrium unfolding experiments in the downhill regime (i.e., maximal barrier < 3 RT) 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.