Lipid Bilayer Thickness Measured by Quantitative DIC Reveals Phase Transitions and Effects of Substrate Hydrophilicity

Quantitative differential interference contrast microscopy is demonstrated here as a label-free method, which is able to image and measure the thickness of lipid bilayers with 0.1 nm precision. We investigate the influence of the substrate on the thickness of fluid-phase 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC)-supported lipid bilayers and find a thinning of up to 10%, depending on substrate hydrophilicity, local bilayer coverage, and ionic strength of the medium. With fluorescently labeled lipid bilayers, we also observe changes in the bilayer thickness depending on the choice of fluorophore. Furthermore, liquid-ordered domains in bilayers, formed from DOPC, cholesterol, and sphingomyelin, are measured, and the corresponding thickness change between the liquid-ordered and liquid-disordered phases is accurately determined. Again, the thickness difference is found to be dependent on the presence of the fluorophore label, highlighting the need for quantitative label-free techniques.

qDIC phase images resulting from Wiener deconvolution [1] tend to suffer from stripe-like artefacts running parallel to the shear direction, as can be seen in Fig. S1. They are the results of the fact that only the phase gradient in one direction is measured, and not the phase itself, and thus information about the gradient orthogonal to the DIC shear direction is missing. For the analysis of bilayer steps, this is not problematic, as it is sufficient to take phase profiles close to parallel to the shear, and fitting with the function Eq.(1) of the main paper which includes a linear slope to accommodate the long-range artefacts resulting from the integration. However, the stripes affect the visibility of low contrast objects such as S o or L o domains in the qDIC phase images.
These artefacts can be reduced using a global minimisation method, varying the qDIC phase image to minimise not purely the deviation between measured and simulated DIC contrast, but the sum of this deviation, and the magnitude of the gradient, elevated to a power α and multiplied with a weight λ. For a power between zero and one, small gradients carry a higher penalty, resulting in qDIC phase images with flat regions connected by steps, consistent with the bilayer structure. The power and the weight have to be chosen suitably to provide a small minimum step height while still flattening regions dominated by measurement noise. This method, inspired by Koos et al. [2], and described in detail in [3], is implemented in MATLAB R2015a, and for clarity most images in the main body of the paper have been processed in this way. focal drift of a similar scale was observed due to, for example, thermal drift between image acquisition. To determine the effect of this undesired defocus on the retrieved step heights, the same region of interest was imaged multiple times at different defocus. A total of ten line profiles were taken in each image, with the positions of the line profiles kept constant between images. The number of profiles used is much smaller than used for the mean thicknesses reported in the manuscript, but is sufficient to observe significant systematic changes with defocus.
The resulting mean thickness as function of defocus is shown in Fig. S2. The error bars for the mean values at different degrees of defocus overlap, indicating that the mean bilayer thickness was not significantly affected over the range of axial positions studied. It can also be seen that the changes in mean thickness with defocus are effectively random, so defocus is not expected to bias the mean values towards higher or lower thicknesses. A small degree of focal drift across the field of view was therefore deemed permissible. It should be pointed out that the extremes of defocus explored here are easily visible in the images, and in practise the sample would have been refocussed before taking data. The width of the function fitted to the data (the c parameter in Eq.(1)) was increasing with defocus (see Fig. S3), as expected.

MEASUREMENTS
For many measurements, the polariser had to be calibrated manually. This was done by adjusting the polariser until the mean number of counts detected by the camera matched the expected value calculated from Eq.(S1).
In Eq.(S1), N 0 is the number of counts detected when the polariser angle is 90°, corresponding to an excitation polarisation parallel to the DIC analyser, ensuring that the camera was not being saturated. N BG is the average number of dark counts of the camera, which is measured by taking the average number of counts when the light from the objective is directed away from the camera to the eyepiece. The same region was imaged three times at a nominal polariser angle of 12.9°with the calibration of the polariser redone each time.
Multiple line profiles were taken at the same positions in the three images. The resulting average thicknesses were (3.75 ± 0.04)nm, (3.72 ± 0.05)nm and (3.77 ± 0.05)nm, equal within the experimental precision.

S4. EFFECT OF DIC IMAGE AVERAGING ON PHASE MEASUREMENTS
Due to the small levels of DIC contrast generated by lipid bilayers, individual frames result in a noise only a few times below the bilayer step signal. To reduce the noise, the DIC images were averaged over N frames taken at each polariser orientation. Increasing N reduces the random noise in the images, while also correspondingly increasing the variations of the sample during the measurement time, e.g. due to drift, or bilayer motion.
It was therefore important to determine an appropriate number of frame averages to take during imaging. To this end, a single region of interest was imaged and 1000 individual frames were taken over about 100 seconds, first for positive and then for negative phase offset. The qDIC phase was then determined using I + and I − averaged over subsets of 1, 10, 100 and 1000 frames, resulting in the images shown in Fig. S4. A reduction of the image noise with increasing N is observed.
In order to determine the resulting effect on the retrieved bilayer thickness, the qDIC   ground gradient parameter, d, equal to the set values within the error. When converted to a thickness value, the error on the phase step value a becomes 0.045 nm. This is of a comparable scale to the experimentally measured errors, indicating that glass noise accounts for most of the observed distribution in thickness values. The slightly larger size of the error in the mock data compared to the real experimental data is likely due to the fact that when taking steps from real data, phase profiles which deviate significantly from the expected step-like shape are excluded, thus the most noisy data is filtered out manually before analysis.
To quantify the roughness of the glass, the spatial standard deviation of the glass surface measurements was taken, without the addition of the mock step function. To exclude the effects of local gradients which are accounted for in our fit function (and thus wouldn't affect our measurements), a linear fit was made to each line profile, and the gradient and offset subtracted before taking the standard deviation. The standard deviation of all our glass phase measurements (a total of 21,424 points) was 0.204 ± 0.002 mrad. This is equivalent to a thickness variation of 0.161 ± 0.002 nm using the DOPC refractive index of 1.445, or 0.097 ± 0.001 nm using the glass refractive index of 1.5171.

S6. BILAYER COVERAGE
In spin-coated SLBs, the degree of bilayer coverage can vary considerably between different fields of view. Examples are shown in Fig. S7. The degree of coverage is quantified either using the threshold tool in ImageJ on the fluorescence images to set all pixels covered by lipid to 1 and all uncovered pixels to 0, and measuring then mean image intensity, or by using the ImageJ polygonal selection tool for manual area measurements.
In the case of the bilayer patches, the local coverage is very low, with usually only a couple of bilayer patches visible within a single field of view. The bilayer patches have sizes typically on the order of 10 -20 µm, as shown in Fig. S9. While in some cases the patches may be linked by small stretches of lipid, generally they are unconnected.

S7. ABSOLUTE VALUES OF NORMALISED DATA
The average bilayer thicknesses presented in normalised form the in Table 1 in the main text are presented in Table SIII Table 1 are marked in italics. Entries are ordered from oldest to newest date of data acquisition.

S8. DOMAIN THICKNESS AND AREA DATA
As part of our discussion of the L o domain thickness in the main text, it is mentioned that we find no evidence of significant thickness differences between domains. The distribution we observe for both labelled and unlabelled samples is shown in Fig. S10. Additionally, we find no correlation between domain area and thickness. We present the data in Fig. S11 for both labelled and unlabelled samples. It can be seen that there is no clear relationship between area and thickness, within the measurement error.   Table   SIV.
It is important to note that while we attribute the reduced optical thickness difference in the unlabelled samples compared to the labelled samples to a change of interaction with the substrate, the optical thickness difference in the first bilayer without labelling remains affected by the substrate interaction (see Table 2), and thus can be different to the one in the second bilayer. We find for example that reducing hydrophilicity increases both the L d and L o phase thickness in the first bilayer, as shown in Fig. 7   with the substrate.