Biology Reference
In-Depth Information
11.3.3.2 Energy landscape roughness
Given the combination of the various types of interactions (van der Waals,
electrostatic, etc.), the energy landscape of biological bonds has been described
as being rugged and composed of multiple hierarchical barriers and local
minima. Zwanzig theoretically showed that the intrinsic dissociation lifetime
increased importantly in a rough energy landscape.
The pioneer works by
Frauenfelder showed that the energy landscape of haemoglobin presented a
hierarchy of conformational states.
73
The theory developed by Zwanzig was
recently adapted to describe the effect of energy landscape roughness on
single-molecule force spectroscopy measurements.
74
The authors proposed
an approach to calculate the roughness amplitude by measuring the dynamic
force spectra of molecular interactions at various temperatures. Assuming a
Gaussian distribution of roughness amplitudes independent of the position
along the reaction coordinate, they showed that a constant term proportional
to the squared roughness amplitude (
ε
) appeared in the expression of the
most probable rupture force [Eq. (11.6)]. Equating the most probable rupture
forces at two different temperatures they derived an expression for
ε
.
75
Nevo
and coworkers adapted the approach to take into account possible variations
with temperature of the potential width, obtaining an extended expression
for
ε
.
75
In the same work, the authors experimentally tested the theory for the
irst time in the unbinding of the nuclear transport receptor importin
76
B
and
GTPase Ran,
. Since then,
the energy landscape roughness of different systems has been determined.
The unfolding of the actin cross-linking protein ilamin
76
inding an unexpectedly high value of
ε
~ 5.7
k
B
T
77
yielded a value of
ε
~ 4
from unfolding measurements of
the transmembrane helices of bacteriorhodopsin.
k
B
T
, while it ranged from ~4 to ~7
k
B
T
Unbinding measurements
on the well-studied streptavidin-biotin complex revealed two roughness
values of ~5.5 and 7.5
78
along the dissociation pathway, corresponding
to the inner and outer transition barriers, respectively.
k
B
T
The similar values
of roughness observed in such different systems suggests a common origin,
perhaps because of the oversimpliication of a three-dimensional (3D) energy
landscape to a single dimension.
34
11.3.3.3 Catch bonds
We have described biological bonds in a simplistic way by assuming an energy
landscape with a single reaction coordinate being, thus, unidimensional.
However, receptor-ligand complexes are complex structures in which
proteins can undergo conformational changes that may vary their binding
state. Not only energy landscapes present multiple barriers or rough
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