The name is absent

Here ψ_aa is the unperturbed surface potential which is obtained from the simulation when
the tip is set very far away (200 nm) from the lipid surface. Using the same method as for
Equation 3.5, we modeled mobile lipid charge regulation using the above Boltzmann
relaxation equation. As shown in Figure 3.10, our mobile lipid charge regulation model
gives a good fit for the short range AFM data.

Figure 3.10: Data fit with the Boltzmann relaxation model of mobile lipid charge
regulation. The AFM data and the electrostatic simulation shown here is the same as in
Figure 3.2.

To make sure that lipid motion would result in a physically reasonable number of lipids
moving out within the time scale of our experiment, we did the following calculation.
Consider the 2-D Brownian motion that would occur in the top leaflet of the bilayer in the
absence of any velocity fields. The mean square displacement of an individual lipid
molecule would then be given by

(r²) = 4D√        (3.7)
40

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