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spontaneous contraction of the protein down to the folded end-to-end length
corresponds to the folding trajectory of the mechanically unfolded polyprotein. To
con rm that the protein has folded, we again raise the force to 110 pN and the
polyprotein again unfolds to its initial unfolded length in steps of 20 nm
(Figure 13.6A).
The folding trajectories we observe can be divided into four distinct regions,
marked by abrupt changes in the slope of the collapse (Figure 13.6A). Furthermore,
we have determined that the collapse time of a protein is highly dependent on
the quenching force [28]. Figure 13.7A illustrates the variation in trajectories for the
polyprotein ubiquitin when quenched from a high force (trajectory 1), where the
protein fails to fold on the timescale of an experiment, to a low force (trajectory 5)
Figure 13.7 Complexity of the folding energy
landscape. (A) The folding pathway of ubiquitin at
a number of different quench forces is directly
measured by force-clamp spectroscopy. The end-
to-end length of a protein is shown as a function of
time. As the force is quenched to lower forces
(trajectories 1
(B) The folding pathway is probabilistic. The three
folding trajectories shown begin from the same
initial conditions and are quenched to the same
force, however very different trajectories are
clearly observed. The blue trace illustrates a
protein which failed to fold on the timescale of the
experiment, the green trace shows a proteinwhich
attempted to fold while the red trace shows a
successfully folded protein. (C) Average folding
times are exponentially dependent on the quench
force with a
5 where trajectory 1 corresponds
to a high quench force of 50 pN while trajectory 5
corresponds to a lower quench force of 23 pN),
the time taken to refold becomes smaller on
average. At a high quench force (1
-
100 s 1 and
2) the protein
may fail to fold on the timescale of the experiment.
a 0 ¼
D
x f ¼
8.2 Å, using an
-
Arrhenius term [63].
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