The name is absent

mobile Iipid charge regulation was presented in the form of clear differences in the short
range behavior of mobile, fluid phase lipids when compared to immobile gel phase lipids,
in the presence of the AFM tip. The contrasting behavior of the mobile vs. immobile
surfaces observed in our experiments is also in good qualitative agreement with
theoretical predictions made by others (Figure 3.19) [26].

Figure 3.19: From Reference [26]. Theoretical prediction of a DNA-membrane
interaction for three different models of a membrane. The DNA was modeled as a
charged cylinder of length L and radius γq. βΩ is the grand potential and τ is the line
charge density and h is the distance from lipid surface to center of cylinder. In the above,
the quantity plotted on the у-axis is electrostatic interaction energy between the cylinder
and the surface and the quantity plotted on the x-axis is related to the DNA-membrane
separation, (mobile): the model membrane is composed of three types of mobile surface
groups: negatively charged, neutral and dissociable. (N-P): membrane charges result from
dissociation as in case I, but surface ions are immobile, (homogeneous): charges are
fixed, surface ions are immobile. In all three cases, the homogeneous surface charge
density far away from the DNA is equal and corresponds to an effective homogeneous
charge density of p_c= -1/4.8 nm² ( κ'' = 50 nm).

As with our data, the above figure shows long-range overlap and short-range deviations
in the mobile versus immobile theoretical surface charge models.

We computationally implemented the mobile lipid regulation with a model based on a
Boltzmann relaxation. The model resulted in an excellent short-range fit. While the

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