Giant unilamellar vesicles (GUVs) and supported lipid bilayers (SLBs) are synthetic model systems widely used in biophysical studies of lipid membranes. Phase separation behaviors of lipid species in these two model systems differ due to the lipid-substrate interactions that are present only for SLBs. Therefore, GUVs are believed to resemble natural cell membranes more closely, and a very large body of literature focuses on applying nanocharacterization techniques to quantify phase separation on GUVs. However, one important technique, atomic force microscopy (AFM), has not yet been used successfully to study phase separation on GUVs. In the present study, we report that in binary systems, certain phase domains on GUVs retain their original shapes and patterns after the GUVs rupture on glass surfaces. This enabled AFM experiments on phase domains from binary GUVs containing 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC) and either 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) or 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC). These DLPC/DSPC and DLPC/DPPC GUVs both presented two different gel phases, one of which (bright phase) included a relatively high concentration of DiI-C 20 but excluded Bodipy-HPC, and the other of which (dark phase) excluded both probes. The bright phases are of interest because they seem to stabilize dark phases against coalescence. Results suggested that the gel phases labeled by DiI-C 20 in the DLPC/DSPC membrane, which surround the dark gel phase, is an extra layer of membrane, indicating a highly curved structure that might stabilize the interior dark domains. This phenomenon was not found in the DLPC/DPPC membrane. These results show the utility of AFM on collapsed GUVs, and suggest a possible mechanism for stabilization of lipid domains.

Analysis of fluctuations arising as fluorescent particles pass through a focused laser beam has enabled quantitative characterization of molecular kinetic processes. The mathematical frameworks of both fluorescence correlation spectroscopy (FCS) and photon counting histogram (PCH) analysis, which can measure these fluctuations, assume an infinite Gaussian beam, which prevents their application to particles within domains bounded at the nanoscale. We therefore derived general forms of FCS and PCH for bounded systems. The finite domain form of FCS differs from the classical form in its boundary and initial conditions and requires development of a new Fourier space solution for fitting data. Our finite-domain FCS predicts simulated data accurately and reduces to a previous model for the special case of molecules confined by two boundaries under Gaussian beams. Our approach enables estimation of the concentration of diffusing fluorophores within a finite domain for the first time. The method opens the possibility of quantification of kinetics in several systems for which this has never been possible, including in the one-dimensional lipid tubules discussed in Part 2 of this paper. Statement of Significance:Methods based on fluorescence measurements of molecular concentration fluctuations, including Fluorescence Correlation Spectroscopy and Photon Count Histogram analysis, are widely used to determine rates of diffusion, chemical reaction and sizes of molecular aggregates. Typically, the range over which the molecules can diffuse is large compared to the size of the focused laser beam that excites the fluorescence. This work extends these measurements to systems that are comparable in size to the excitation laser beam. This extends the application of these methods to very small samples such as the interior of bacterial cells or the diffusion of molecules along individual macromolecules such as DNA.