Chemistry Reference
In-Depth Information
were folding is successful. These force-clamp experiments have provided evidence
that the probability of observing a folding event as well as its duration is strongly force
dependent. Additionally, it should be noted that even under the same experimental
conditions different folding trajectories are observed. For example, in Figure 13.7B,
three distinct folding trajectories are shown for the polyprotein ubiquitin which have
been unfolded and then quenched to the same force. In the majority of cases the
protein fails to fold on the timescale of the experiments (blue trace), while in
some cases the protein attempts to fold (green trace). Only in a small percentage
of cases is the protein observed to fold (red trace). Therefore the application of force
greatly reduces the folding probability of the protein on the timescale of the
experiment.
To observe the force dependency of protein folding we grouped the experimental
data frommany force quench experiments at the longest range of contour lengths, for
which the effect of force is most evident (150 to 200 nm). We observed that the
duration of the folding collapse is exponentially dependent on the quench force
(Figure 13.7C), as observed in the unfolding process (Figure 13.3C). An Arrhenius
term can again be
fit by the data to model a two-state process with a single folding
energy barrier in the reaction coordinate of the end-to-end length [63]. The distance to
the folded transition state,
8.2 Å, is a distance comparable to the length-scales
expected for long range hydrophobic forces [92] which are widely believed to play a
crucial role in protein folding [93]. It should be noted that his length is considerably
longer than that in the unfolding process (
D
x
f
¼
1.7 Å).
Another important difference between the unfolding and the refolding process is
that the modules unfold stochastically, independently of one another, while the
contraction in the protein length during folding appears cooperative between the
modules. This asymmetry has been the topic of much debate in the literature,
suggesting protein aggregation [40] or entropic masking [39]. Aggregation was ruled
out by the second unfolding of the same modules in response to the second pull [41].
Entropic masking of stepwise folding was rejected by the fact that the folding
trajectories scale with the number of modules in the chain
D
x
u
¼
[42]. In other words,
a singlemodule refolding trajectory has the same end-to-end length pro
N
le as a chain
of modules multiplied by
. We can therefore consider the different stages in folding
as being present for any number of modules in the chain and compare them with
theories for even single monomer proteins.
N
13.5.2
Developing a Model for Protein Folding
Many theoretical models have been developed which attempt to explain the pathways
of protein folding [54, 84
91]. The generally acceptedmodel for folding of proteins in
the bulk is a two-state picture, in which intermediates are only rarely encountered
under speci
c folding conditions. These data predict the height of the energy barrier
to folding and the structures associated with the energy minima in this simple
landscape deduced from point mutation experiments. They also predict the relative
position of the transition state and since the reaction coordinate is not known this
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