4.4 Generation and characterization of micrometer-sized protruded
4.4.1 Influence of the substrate dimension on the determination of
Over the last years, it became evident that cells regulate processes such as endo-and exocytosis or cell movement not only by the complex interplay of protein-protein and protein-protein-membrane interactions but also by changing their membrane tension.[42, 137] The applicability of protruded pore-spanning membranes as a model system with tunable curvature for the analysis of membrane-protein interactions has been shown (Section 4.3). Binding of ENTH to PIP2-containing membranes was imaged by fluorescence microscopy and the growth of protruded pore-spanning membranes has been attributed to a local decrease of the lateral membrane tension.[150]
Membrane tension of protruded pore-spanning membranes is calculated applying a Young-Laplace behavior as a function of the applied osmolarity gradient and the geometry of pores and protruded pore-spanning membranes. The height of protruded pore-spanning membranes on substrates with nanometer-sized pores has been measured and a lateral membrane tension of 1.4±0.7 mN/m
was calculated (Section 4.2). A large distribution of the heights of protruded pore-spanning membranes on nanometer-sized pores after application of large osmolarity gradients has been measured (Figure 4.10). This might be caused by a breakdown of the osmolarity gradient between bulk solution and pore interior or by deviations in shape of the protruded pore-spanning membranes from the ideal spherical cap geometry which was used for the calculation of the lateral membrane tension. Therefore, the aim was to create a „tension sensor“ of protruded pore-spanning membranes which do not exceed the pore radius in height or radius to improve the accuracy of the „tension sensor“. The constrain of a maximum height of the protruded pore-spanning membranes equal to pore radius ensures a spherical cap geometry. The osmolarity gradient required to protrude a planar pore-spanning membrane until its height is equal to the pore radius was relatively small (≈10 mOsmol/L) for the porous substrates used. A breakdown of the osmolarity gradient between pore interior and bulk solution is therefore unlikely.
The changes in membrane height resulting from different membrane tensions depend on the applied osmolarity gradient (∆O), the absolute osmolarity of the buffer used during spreading of the GUVs (Ocavity,0) and the geometry of the pores. Porous substrates were available with a pore depth of 8 µm and with pore radii of 1.75 µm, 2.25 µm and 2.75 µm. To evaluate the optimal pore geometry, to be able to determine the lateral membrane tension of protruded pore-spanning membranes with high accuracy, the theoretical membrane height of pore-spanning membranes on pores with a radius of 1.75 µm (Figure 4.14 A), 2.25 µm (Figure 4.14 B) and 2.75 µm (Figure 4.14 C) was simulated for three different lateral tensions, a pore depth of 8 µm and an osmolarity during PSM formation ofOcavity,0=100 mOsmol/L. The height of the protruded pore-spanning membranes was experimentally measured by imaging ofz-stacks of PSMs by means of confocal fluorescence microscopy. Since conventional confocal fluorescence microscopy has a finite axial resolution, typically in the range of 500 nm, larger heights of the pore-spanning membranes would result in a higher accuracy of the determination of the lateral membrane tension.[151, 152]Otherwise small deviations in membrane height would result in large relative errors of the PSM height.
Even though the relative error of the protruded pore-spanning membranes is reduced by large pore radii, differences in membrane height, originating from different lateral tensions, decrease with increasing pore radius. This reduces the accuracy of the determination of the lateral membrane tension as small deviations
in membrane height translate into large changes in lateral membrane tension.
Therefore, pores with a radius of 1.75 µm were selected as they have the broadest spacing of the membrane heights simulated for three different membrane tensions (Figure 4.14 A-C).
Figure 4.14:Calculated height of pore-spanning membranes on pores with a depth of 8 µm as a function of the applied osmolarity gradient, simulated for three different membrane tensions (0.2 mN/m, 2 mN/m and 5 mN/m) and osmolarities used for PSM formation.
A-C: Heights of PSMs simulated for pore radii of 1.75 µm (A), 2.25 µm (B) and 2.75 µm (C), a pore depth of 8 µm and an osmolarity inside the pore during spreading of the GUVs of Ocavity,0=100 mOsmol/L. The separation of the membrane heights resulting from different lateral tensions decreases with increasing pore radius. D-F: Heights of PSMs simulated for a pore radius of 1.75 µm and different osmolarities during spreading of the GUVs of Ocavity,0=50 mOsmol/L (D),Ocavity,0=100 mOsmol/L (E) andOcavity,0=200 mOsmol/L (F).
The separation of the membrane heights resulting from different lateral tensions decreases with increasing osmolarity during spreading of the GUVs. The height of the PSMs equal to pore radius is marked by the dotted green line.
The influence of the osmolarity inside the pores during spreading of GUVs and the formation of pore-spanning membranes for the selected pore geometry with pore radii of 1.75 µm and a pore depth of 8 µm was then analyzed (Figure 4.14 D-F).
Simulating the heights of protruded pore-spanning membranes with three different
lateral membrane tensions and osmolarities during GUV spreading (Ocavity,0: 50 mOsmol/L, 100 mOsmol/L and 200 mOsmol/L) revealed that the spacing of the membrane height resulting from different lateral membrane tensions decreases with increasing osmolarity inside the pores (Figure 4.14 D-F). The largest spacings of membrane heights originating from different membrane tensions were calculated for an osmolarity during PSM formation of Ocavity,0 =50 mOsmol/L. However, the critical osmolarity gradient when the height of the protruded pore-spanning membrane equals the pore radius decreases with decreasing pore radius. Since the height of the pore-spanning membrane is non-linearly dependent on the applied osmolarity gradient and the lateral membrane tension (equation 4.7), a preferentially large number of data points is required for an accurate fitting of the data yielding the lateral membrane tension. A minimum of five data points was defined to be required for fitting the data. A minimal separation of 2 mOsmol/L between two data points was chosen as the osmolarity could be measured with an accuracy of±1 mOsmol/L. Therefore, to be able to fit equation 4.7 to minimal five osmolarity gradients the height of the pore-spanning membrane must not exceed the pore radius when applying an osmolarity gradient of 10 mOsmol/L.
For an osmolarity of 50 mOsmol/L protruded pore-spanning membranes exceed the pore radius in height when applying osmolarity gradients larger than 7 to 8 mOsmol/L preventing to measure the previously defined minimum of five osmolarity gradients with a spacing of 2 mOsmol/L. Additionally, small uncertain-ties of the osmolarity gradient would result in large changes of membrane height further decreasing the accuracy of the determined lateral tension. Therefore, an osmolarity of 100 mOsmol/L was chosen for PSM formation to achieve a compromise between highest sensitivity and minimized uncertainties from the determination of osmolarities or protrusion heights.