Chemistry Reference
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(Figure 13.2A). As the distance between the tip and substrate increases with constant
velocity, extension of the molecule generates a restoring force that is measured from
the de
ection of a pre-calibrated cantilever. This system allows spatial manipulation
of less than a nanometer and can measure forces of only a few picoNewtons up to
hundreds of picoNewtons.
The resulting force-extension curve of a polyprotein has the characteristic appear-
ance of a saw-tooth pattern (Figure 13.2B). This pattern results from the sequential
extension and unfolding of the proteinmodules, which serves as a
fingerprint for the
individual single molecules. The peak force reached before an unfolding event
measures the mechanical stability of the protein module, while the spacing between
peaks is a measure of the increased contour length of the protein as it unfolds. The
saw-tooth pattern is described by the worm-like chain (WLC) model of polymer
elasticity, although it is unlikely that this simple polymer picture applies to proteins.
This model expresses the relationship between the force and extension of a protein
using two
fitting parameters: its persistence length (protein stiffness) and its contour
length (maximum end-to-end length).
Force-extension experiments have been used extensively in probing the mechani-
cal behavior of many different proteins and have begun to challenge some of the
simpli
ed thermodynamic descriptions of proteins obtained from bulk experiments
that are prevalent in the literature [1, 33, 34, 43
-
53]. However, force-extension
experiments lack the ability to accurately measure force-dependent parameters since
the force varies dynamically throughout the experiment. Computational studies have
served as an important guide to the experiments, and have made signi
cant
contributions to our understanding of protein folding [49, 54
-
62]. Nevertheless,
there was a need to develop an experimental tool which could probe force-dependent
parameters. The development of a new force spectroscopy technique in which the
force can be kept constant was crucial to gain real insight into the folding process in
proteins. Therefore, in this chapter, we have focused on the force-clamp technique
and highlighted some of the key breakthroughs it has allowed in our understanding
of the physics and chemistry of protein folding.
13.2.2
Force-clamp Spectroscopy
In force-clamp spectroscopy a single proteinmolecule is held at a constant stretching
force, such that the unfolding and refolding processes can be observed as a function
of time [28, 50]. The cantilever is kept at a constant de
ection (force) for a few seconds
with a feedback response time of 4
-
6ms. Stretching a polyprotein at a high constant
force results in a well-de
ned series of step increases in length, marking the
unfolding and extension of individual modules in the chain (Figure 13.2C). The
size of the observed steps is directly correlated to the number of amino acids released
by each unfolding event, which corresponds to 20 nm in the case of ubiquitin at a
constant force of 100 pN (Figure 13.3A). The observed staircase therefore serves as a
fingerprint of the single molecule. The cantilever picks up molecules at random
points on the surface, such that the number of modules in the chain,
N
, exposed to
