Biomedical Engineering Reference
In-Depth Information
Fig. 5.1
A vertically sus-
pended spring with an equi-
librium length L extends to
its new length L
Extended
Equilibrium
+
ξ
due to a
load W [kg] suspended at the
bottom of the spring
L
ξ
F
=−
k
ξ,
(5.2)
where
F
is the restoring force exerted by the material, and
k
is the force constant
(spring constant in the case of a spring). If
ξ
L
, the spring behaves as a harmonic
oscillator. Here,
F
and
ξ
are measured using the conventional units of force (newtons)
and linear dimension (meters), respectively.
The associated energy stored in the spring following the Eq.
5.2
is given by
1
2
k
ξ
2
U
=
.
(5.3)
One of the important conditions of Hooke's law is that the body returns to its
equilibrium state instantaneously as soon as the suspended weight is removed, which
means that in the case of the above-mentioned spring, it will regain its original length
L
soon after the weight
W
is taken away from its attachment point.
Does the lipid membrane behave like a spring which can be extended or deformed
without breaking its molecular organization or specific structure? Does the membrane
return to its original length and shape once the membrane extending or deforming
force is withdrawn? Does the membrane follow Hooke's law; represented either by
therestoringforceF(seeEq.
5.2
) or elastic energy
U
(see Eq.
5.3
)? These are some
intriguing questions, which membrane biophysicists have been trying to answer dur-
ing over almost a half-century since the publication of the famous paper by Helfrich
on the elastic behavior of the lipid membrane [
37
]. Various groups of researchers
have attempted to address the bilayer's elastic problems using different techniques
which will be discussed later in this chapter. However, first we wish to mention a
generally accepted fact about lipid membranes which states that they form liquid
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