Biology Reference
In-Depth Information
and also there are multiple types of molecules present at once. In addition, the
density of molecules is a ixed parameter on a living cell, while this could be
controlled and optimized when working with isolated molecules. Despite the
dificulties, researchers have stretched polymers on bacteria and were able to
determine elastic properties of these molecules on bacteria,
9-15
yeast cells
16,17
and fungal spores.
10,18-22
A summary of the common models is provided in
Table 13.1.
Summary of statistical mechanical models of polymer elasticity
Model
Expression
Fitting
parameters
Ref.
[
coth
(
Fl
k
)
-
kT
]
____
____
FJC
h
(
F
) =
L
c
kT
Fl
k
L
c
and
l
k
23 and 24
)
-
(
kT
)
[
1 +
(
Fl
k
F
]
____
______
____
Fl
k
L
c
κ
s
FJC+
h
(
F
) =
L
c
coth
kT
L
c
,
l
k
and
κ
s
23 and 24
[
h
]
kT
1
)
2
-
1
____
l
p
___
____________
4
__
WLC
F
(
h
) =
L
c
+
4
L
c
and
l
p
23-25
(
1 -
h
___
L
c
[
1
(
1 -
h
kT
F
)
2
+
h
F
φ
-
1
]
____
__
___
__
___
__
__
φ
WLC+
F
(
h
) =
l
p
4
L
c
+
L
c
-
4
L
c
,
l
p
and
φ
23 and 24
FJC is the freely jointed chain model, FJC+ is extensible freely jointed chain,
WLC is wormlike chain, WLC+ is extensible wormlike chain,
F
is pulling force,
h
the separation distance between the tip and the polymer,
L
c
the contour
length,
k
s
the Boltzmann constant,
T
temperature,
l
k
the segment length,
l
p
the
persistence length,
κ
the segment spring elasticity and
φ
the speciic stiffness
of the polymer.
The two most commonly used models to interpret polymer elasticity
measurements
are the freely jointed chain (FJC) and wormlike chain
(WLC) models and variations on these forms. The FJC model considers
that the polymer is composed of
l
k
,
connected by freely rotating pivots with equal probabilities for rotation in all
directions. Essentially, this model treats the polymer as an aggregate of many
independent segments.
26
The FJC cannot describe the chain if it is extended
to its full contour length, because this would mean the chain is ininitely rigid.
Also, this model considers only entropic effects and so the polymer cannot
become stretched beyond its contour length. To account for these limitations,
the FJC+ model was developed, known as the extensive freely jointed chain
model.
n
rigid segments, each of a Kuhn length,
24
The FJC+ model accounts for elastic deformations of bonds and
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