goodness of the fit to the experimental data was somewhat dependent on the step size,
Dn+ι - Dn , we used in our iteration procedure (Section 3.2.3). However, the general
direction of the fit was independent of step size. We analyzed the accuracy of our finite
element model using a resolution test whereby we increased the mesh density by many
orders of magnitude corresponding to an increase in the output tolerance from 10^5 to
10^8. This type of a test is commonly used as a measure of the accuracy of a finite
element model. The results were found to be independent of mesh density and are thus
convergent. Possible reasons for the step size dependence could be that the solutions of
the partial differential equation might be very sensitive to variations in initial conditions
and that such small changes might be propagating divergently with each step. More
detailed work will take into account such factors. Aside from that it is important to note
that this is the first attempt at interpreting AFM data by considering mobile lipid charge
regulation. The use of a continuum model in representing discrete structures and the use
of a Boltzmann relaxation to represent individual lipid motions is not ideal. However,
since the AFM tip is much larger than the individual lipid molecules, this approximation
is reasonable. In our analysis, we have varied the surface charge density of the entire lipid
surface at each iteration. Ideally, we would require a boundary condition that allows a
spatially varying surface charge. But, having multiple boundary conditions adds an
additional degree of complexity to the simulation and could be prone to propagation of
errors. In addition, the force signal is largely determined by the membrane region directly
below the tip, with variations in the potential elsewhere having little effect.
We have shown that mobile lipid charge regulation can be used to characterize short
range deviations from the expected electrostatics, over lipid surfaces. Recent theoretical
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