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Where Di is the lateral diffusion constant of the lipid and t is the time. The AFM tip speed
is 2240 nm∕s. In our mobile lipid model, we calculate our modified force values in steps
of 0.5 run. At the above speed, it takes approximately 250 μs to move that distance.
Using Equation 3.7, and taking
Di = 4.2 x 10^12 m2∕s for DOPC [87], we find that the root
mean square displacement is approximately 100 run. The force on the AFM is mostly
influenced by the region of lipid under the tip. Given that the AFM tip is also on the order
of 100 run, the lipid motion is of a time scale and length scale accessible to the AFM.
Furthermore, the minimum change in surface charge density seen in the between steps of
our simulation is also on the order of a few tens of individual lipid charges. Thus, in
terms of the lateral mobility of the lipids and the AFM ,s ability to detect them, our
mobile lipid simulation is physically reasonable.

3.3.4 Comparing mobile lipid charge regulation on gel and fluid phase lipids

As a further demonstration of the importance of mobile lipid charge regulation in the
analysis of Iipid-AFM force curve data, we have harnessed the large mobility differences
between gel and fluid phase lipid species. The individual molecules of a lipid in gel phase
are quite rigid and stationary in comparison to those of the fluid phase lipid. If we
consider structurally similar (i.e. having the same tail groups) gel and fluid lipid patches
of similar surface charge density, tip induced mobile lipid charge regulation would be
more prominent over fluid phase lipid patches. Thus, the force curves over fluid patches

41



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