The name is absent

(C₀), the area per lipid (A), and the binding constant of the electrolyte cation to the PS
headgroup (K). Note that the solid line in Figure 2.4 is not a fit, but rather the result of
this model for C₀ = 0.47 mM, A = 0.7 nm², and K = 1 M^¹ [9]. In the numerical
simulations, charge regulation was not included in the boundary condition [25] since a
simple constant field boundary condition was applied evenly to the entire sample surface.
This method of analysis is not exact since the presence of the tip locally alters the surface
potential, thus requiring a boundary condition that allows a spatially varying surface
field. In addition, two other charge regulation mechanisms were not considered. The
effect of the surface potential on protonation of the PS headgroup was not included since
the pK of the headgroup is 2, very much lower than the pH of the buffer [55]. More
significantly, not included was a charge regulation mechanism specific to lipid
membranes that takes into account the high level of mobility of the charged lipids [26].
Unlike an inorganic surface, charged headgroups in a fluid lipid membrane can move and
redistribute in response to a potential. Calculations of this effect find that it can be
significant for cases such as DNA bound to a cationic membrane. Chapter 3 will show
that the constant charge density boundary condition model described in this chapter
deviates divergently from the data in the short-range (< 1 Debye length) regime and that
mobile lipid charge regulation needs to be accounted for in order to characterize this
observed short-range deviation.

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