Mesoscopic models of lipid bilayers and bilayers with embedded ...

3.4 Surface tension in lipid bilayers 35
Area compressibility
From the dependence of the area per lipid on the surface tension, the bilayer area
compressibility can be calculated. The bilayer area compressibility KA is defined as
[77]
Integrating equation 3.21 we have
KA = A
γ = KA ln A
∂γ
. (3.21)
∂A
Ao
(3.22)
where Ao is the area at the free energy minimum, i.e. at zero surface tension. Expanding
equation 3.22 around Ao we obtain a linear dependence of γ on A
γ ≈ KA
(A − Ao). (3.23)
Ao
In simulation, the area compressibility can be calculated from the above equation,
either by fixing the area of the bilayer and computing the corresponding surface tension,
or by imposing the surface tension and calculating the area. In this study we
use the latter method. If the area is taken as the dependent variable, then, from 3.23,
we have
A = Ao
γ + Ao
(3.24)
KA
To fit the area as function of γ using equation 3.24, we used two approaches. The
first one consists in computing the area at different values of imposed surface tension,
in the regime were the area dependence on surface tension is linear. We found
the behavior of the average projected area per lipid to be linear in the applied surface
tension for values of the tension in the range γ=[-0.5,1.5]. The second method
consists in considering the spontaneous fluctuations at equilibrium, of both the area
and the measured surface tension, in a tensionless bilayer, as computed in the histogram
shown in figure 3.6(b). The results of both fitting methods are in very good
agreement: in both cases we find KAR 2 c/kBT=20.8 from the slope of the fitted lines.
Also, a value of 1.66 R 2 c is found as the intercept, which is the same value of the area
at zero surface tension, Ao, as directly measured from the simulation at γ = 0.
Using Rc=6.4633 ˚A and taking kBT as room temperature, i.e. kBT = 4.14 10 −21 J, we
can convert the area compressibility into physical units, resulting in KA ≈ 210 mN/m.
This value is comparable to the value of the compressibility equal to 300 mN/m found
by Lindahl and Edholm [77] in atomistic MD simulations of lipid bilayers, and to
the values measured by micropipette aspiration experiments which, for saturated
phosphatidylcholine bilayers in the fluid phase, are also in the range 230-240 mN/m
[78].