Chemistry Reference
In-Depth Information
Figure 13.5 Power law distribution of unfolding
rates: a histogram of the most likely unfolding
rates for each polyprotein chain in the ensemble
plotted on a log-log plot. Beyond the peak, the
rates are distributed in a power law with a decay
coefficient
carry a larger error as the molecules often detach
from the cantilever at long times. The inset shows
the tentative energy landscape with multiple
energy minima in the native state ensemble,
which could give rise to such broad kinetics
according to the Trapp model for glasses [74].
g ΒΌ
1.8. The rates slower than the peak
Equation 13.2 to predict the most likely
as the maximum in the obtained
probability map. The maxima of the probability maps for all trajectories give rise to a
distribution of
a
,
N
) for the whole set of data (Figure 13.5).
We obtained a very broad distribution of unfolding rates that follows a power law
over more than two decades [27]. Such a broad distribution could not be explained by
the errors in the MLM or by the noise in the constant force. Rather, this result is
indicative of an unanticipated degree of complexity in the unfolding pathways of
ubiquitin, supporting the view that the energy landscape is muchmore complex than
was previously thought. It is the rare events that dominate the shape of the
distribution, which implies that only a large statistical ensemble of unfolding events
could reveal this complex physical picture.
P
max
(
a
13.4
Disordered Free Energy Landscape
The systems complex kinetics, as observed in the power law decay of the rate
constants, is a consequence of the underlying roughness of the free energy land-
scape [66]. Therefore, a plausible explanation for the observed heterogeneity is to
consider the diversity in the conformations within the native state ensemble [67, 68]
under a constant force. Thermal motion of the folded protein explores local
fluctuations in the secondary structure on an energy scale of a few k
B
T [29, 69],
where k
B
is the Boltzmann constant, which is crucial to the optimal functioning of the
protein [19]. Understanding these
fluctuations is therefore of fundamental biological
