Chemistry Reference
In-Depth Information
relative position is dimensionless. It should be noted that the trajectory of a protein
that folds after chemical denaturation involves changes in the end-to-end length of
only a couple of nanometers, very close to the radius of gyration of the native state. For
example, in the presence of 5M urea, small angle X-ray scattering has shown that a
protein chains radius of gyration expands from
16 to 35 Å, an expansion of only
2.1 nm [94]. A further study revealed the high persistence of native-like topology in a
denatured protein in 8M urea [95]. Therefore, force quench experiments monitor
folding trajectories over much longer length-scales, exploring new regions of the
folding landscape.
Since themechanical and thermal/chemical studies of protein folding involve very
different endpoints they are not directly comparable. At present a number of physical
models exist which attempt to explain the folding timescales observed in thermal
denaturation experiments. For example, multipathway folding mechanisms, discov-
ered using minimal protein models in conjunction with scaling arguments, have
been used to obtain timescales for protein folding [91]. These scaling laws have been
derived for proteins in bulk solution which have undergone a temperature pertur-
bation. While we would expect that similar phenomena may be at work in a
mechanically perturbed system, we anticipate that the timescales predicted using
these scaling laws will be incorrect. There is therefore a need to develop physical
models which consider force as a perturbation in the unfolding and subsequent
refolding of proteins.
Nonetheless, it is interesting to compare the relative timescales of the distinct
stages observed in the force quench folding trajectory (Figure 13.6) with that of the
scaling laws discovered usingminimal proteinmodels [91]. The predicted timescales
describe the stages of folding as a function of the number of amino acids, formulated
in analogy with the principles of polymer physics together with an imposed directed
search for native contacts. According to thismodel there are two distinct mechanisms
by which proteins reach the native state [91]. The first route is a direct pathway which
involves a speci c collapse followed by a direct pathway or nucleation to a native state
conformation. The alternative route or the indirect route involves three key stages,
each with a particular timescale. These scaling laws can now be compared with
experimental protein folding trajectories for the
first time.
The first stage in the force-clamp folding trajectory of the polyprotein ubiquitin
(Figure 13.6) is observed to have a timescale of
10ms. According to entropic
recoil [91] this stage is the non-speci c collapse of the protein to a compact
conformation on a timescale
t NSC given by
/ h
a
g
N 2
t
ð
13
:
4
Þ
NSC
where
h
is the viscosity of the solution, a is the persistence length of the protein,
g
is
the surface tension and
is the number of amino acids in the protein. For the protein
ubiquitin in aqueous solution this predicts
N
is which is too fast to be
detected by the 10-ms time resolution of the force-clamp technique. It is clear that the
non-speci c collapse of the protein is the fastest stage in the folding trajectory
(Figure 13.6), in agreement with the scaling laws predictions. According to this
t NSC ¼
0.032
m
 
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