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observations available using single-molecule spectroscopy have a power that should
not be underestimated.
The group that studied GCN4 also pursued studies of single molecules freely
diffusing in solution [82], and they found distributions in line with expectations. In
their case, the interconversion time between folded and unfolded states was shorter
than the observation time, so they were able to use correlation analysis to probe the
time scales of interconversion. For CI2, the time scales for unfolding and refolding
were longer than the observation time so that folded and unfolded populations were
well separated.
These initial experiments on protein folding helped form our opinion that new
experiments in single-molecule fluorescence spectroscopy should in general be rst
approached with measurements on freely diffusing molecules. Such measurements
are easier to initiate and optimize than immobilized experiments. Problems with the
biological system working at the single-molecule level and with uorophores
attached are easier to address without the additional complications of immobiliza-
tion. Long time trajectories are sacri ced initially, but can be added later.
Wemade two additional observations in our initial experiments with CI2. First, the
width of the distribution in energy transfer ef ciency E is wider than what we
predicted based on shot noise. Second, the average distance between donor and
acceptor of the unfolded subpopulation decreases with decreasing denaturant; this
result was not very strong, but was outside the noise levels. Schuler et al. performed
similar single-molecule experiments on another protein, cold shock protein from
Thermotogamaritima (CspTm) [81]. Most importantly, they compared the width of the
distribution in E found in their CspTm experiments with controls using polyproline
(approximating a rigid rod). They found that the widths of the E distributions from
CspTm were identical to widths found using polyproline, indicating that the wide E
distributions must originate from experimental noise rather than from structural
changes in the protein, contradicting our initial speculations. Based on this and the
measurement time per protein of (
s), they were able to conclude that the
fluctuations of unfoldedCspTmmust be averaged out in less than 100
100
m
s. This in turn
allowed them to conclude that the free energy barrier between folded and unfolded
proteins must be greater than 2 k B T.
Schuler et al. also saw a decrease in the size of the unfolded proteinwith decreasing
denaturant similar to that seen with CI2. The decrease in size was more dramatic in
the case of CspTm. They explained this shift in terms of a continuous expansion of the
unfolded protein with increasing denaturant, although this expansion does not t
completely with the expectation that the unfolded state would continue to expand
with increasing denaturant. The next two sections describe two subsequent papers
that focused on elucidating the nature of the unfolded state in more native-like
conditions.
m
9.4.1.4 Single-molecule Protein Folding under Non-equilibrium Conditions
Lipman et al. [83] coupled a laminar flow mixer with the single-molecule measure-
ments in solution to trigger refolding of CspTm. They were able tomonitor E for both
the folded and unfolded subpopulations after diluting the denaturant to native
 
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