Biology Reference
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bond angles that are neglected in the non-elastic FJC model. The polymer
is modelled as consisting of
n
elastic springs, and a third itting parameter
(
κ
s
) is added to account for segment elasticity. Since an enthalpic term is
included, forces at large extensions can be described, and the polymer can
extend beyond its contour length. This may become signiicant during AFM
experiments, in which bonds are overstretched because of the design of the
experiment.
Another extremely common model for ideal stiff polymers is the WLC
model.
26
According to this model, the polymer chain is continuously curved
with a random direction for the curvature, according to the principle of self-
avoidance. This model accounts for chain stiffness in terms of the microscopic
persistence length,
l
p
. The bending energy of the curved chain gives rise
to energetic and enthalpic factors, and the chain cannot extend beyond its
contour length.
Finally, the extensible wormlike chain model (WLC+) is
considered, which adds the stiffness of the chain as a third itting parameter
to the WLC model.
26
Enthalphic stretching, in which the segment length can
continue to increase under stretching before the bond will break, has been
observed experimentally in the high force regime.
27
26
As an example, we tested the validity of different polymer models in
describing the characteristics of biopolymers present on an environmentally
isolated Gram-negative bacterium,
KT2442. Changing
the salt concentration of the buffer solution allowed us to observe changes
in polymer conformation, which could be captured with the various models.
9
The WLC model was unable to describe the biopolymers on
Pseudomonas
putida
, because
we predicted persistence lengths that were too small to be realistic. Both
the FJC and FJC+ models were generally applicable and gave good its with
FJC+ model deviated more from the experimental values. Therefore, our
comparisons are based on the application of the FJC model. We observed a
transition in the lexibility of the biopolymers (as estimated by
P. putida
l
k
values) as
the salt concentration increased from that of ultrapure water to 0.01 M KCl.
28
The Kuhn length increased from 0.15 nm to 1.0 nm as salt concentration
increased from that of ultrapure water to 0.01 M KCl.
9
These results showed
that the biopolymers on a bacterial surface have mechanical properties
similar to those of isolated polysaccharides. The Kuhn lengths have been
calculated for a number of bacteria and can vary by more than an order of
magnitude, from 0.15 nm (as we observed for
P. putida
) to 1.7 nm when the
FJC+ model was applied to a
Lactobacillus rhamnosus
GG (LGG) mutant.
29
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