Chemistry Reference
In-Depth Information
Figure 13.3 Unfolding of a ubiquitin polyprotein
at a constant stretching force. (A) A typical length
versus time recording (red trace) obtained by
stretching a ubiquitin polyprotein at a constant
force of 110 pN. The polyprotein elongates in
steps of 20 nm, marking the unfolding of
individual ubiquitins in the chain. The dwell time
(
several trajectories such as those in B, at each of
the three forces shown, gives the overall
probability of unfolding as a function of time
(black traces), independent of protein length.
The blue lines correspond to single exponential
fits with unfolding time constants of
7.7 s
1
at 140 pN, 1.9 s
1
at 120 pN and 0.4 s
1
at
100 pN, respectively. (D) The unfolding rate
depends exponentially on the stretching force.
A semi-logarithmic plot of the unfolding rate,
a
u
¼
t
k
) of each unfolding event of order k
(numbered 1
D
7 in this example) can be
accurately measured. (B) Unfolding trajectories
over time for protein chains of different lengths,
N, at constant force. In a stochastic process, the
dwell times on average depend on the total
number of modules in the chain and on the order
k in the sequence. (C) Averaging and normalizing
-
a
u
,
as a function of the stretching force F is shown.
A fit to the data using an Arrhenius term [63],
where a
u
(F) ¼a
0
exp (FDx/k
B
T), gives values of
the unfolding rate at zero force, a
0
¼0.015 s
1
and Dx ¼1.7 Å.
force can be anything up to the engineered protein length (
12), resulting in a
number of unfolding trajectories (Figure 13.3B). An ensemble of such trajectories
allows for accurate investigation of the force and time dependency of protein
unfolding, independent of the length of the chain.
Averaging a few unfolding trajectories provides a measure of the unfolding
probability as a function of time for each stretching force (Figure 13.3C) which can
be approximated by a single exponential
fit analogous to bulk measurements.
Moreover, the linear relationship observed in the semi-logarithmic plot of the unfold-
N¼
