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well characterized [22, 23] and it is known that silicon nitride surfaces carry possess a net
negative charge in water at physiological pH (ph = 7). Thus the electrostatic interaction
between charged lipid surfaces and charged silicon nitride AFM tips is interpreted in
terms of the electric double layer force. Theoretical considerations show that if two
surfaces with constant surface charge density approach each in an electrolyte, the
pressure and hence the double layer force between them approaches infinity [24].

In reality, when two such charged surfaces approach contact, the counterions are forced
to readsorb onto their original surface sites. Thus, as their separation approaches zero the
surface charge density also reduces, i.e., it becomes a function of surface separation. This
is known as charge regulation. The effect of charge regulation is always to reduce the
effective repulsion below that calculated on the assumption of constant surface
charge[24].

1.7 Charge regulation at lipid interfaces

In lipids, the above mentioned form of charge regulation occurs when counterions bind to
the headgroups of the lipids and form a stem layer which results in a reduction in the
membrane surface charge density [25]. Another form of charge regulation that is unique
to lipids also exists. Unlike most other surfaces, individual lipid molecules in bilayers,
and hence the surface charges they carry, posses lateral mobility. Thus, lipids are able to
rearrange themselves in response to the presence of an approaching charged surface so as
to minimize the interaction energy. This phenomenon is known as mobile lipid charge
regulation [26] and is thought to be important in biological macroion-lipid interactions.

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