Differential detection algorithm

The optical images were first bicubically interpolated five times in size by adding additional pixels as weighted averages to the nearest 4-by-4 neighborhoods. The interpolation procedure did not add additional information to the quantification, but served the purpose of making the image smoother. The image size represented by each pixel size was determined by dividing the physical dimension of the pixel in the sCMOS imager (6.5 μm, Hamamatsu Flash 4.0) with the optical zoom and digital interpolation in the system. An ROI with a typical size of 100 × 100 interpolated pixels (2.2 μm x 2.2 μm) was selected at one location at the cell edge and split into two halves, one inside (I₁) and one outside (I₂). For calibrating the response of normalized differential intensity with displacement, the ROI was shifted by a certain number of pixels in the direction perpendicular to the edge (Figure S1). Normalized differential intensity, (I₁-I₂)/(I₁+I₂), vs. pixel shift (displacement) showed a typical “S” shape (Figure S1). Within a certain range (marked between two dashed lines in Figure S1d, ~500 nm), the differential intensity change is linearly proportional to the pixel shift (displacement). The slope of the linear region was determined, and used as the calibration factor to determine the membrane displacement with the differential detection algorithm (Figure S1e). For all the measurements performed in this work, the membrane displacement was small (less than few tens of nanometer) and well within the linear region (Figure 2d).

For both HEK293T cells and hippocampal neurons, cell edges were manually identified, and the local membrane displacement was determined using the procedure described above. Note that the differential detection algorithm is insensitive to the accuracy of edge identification as long as the edge falls within the ROI, and the displacement is within the linear rage (~500 nm) as shown in Figure S1e. After the displacement at one location we quantified, the ROI was automatically shifted to an adjacent location, and the procedure was repeated until the displacement along the edge of the entire cell was determined. In the case of HEK293T cells, the ROI was shifted every 10 degrees to the centroid of the cell (average ~1.7 μm/step along the edge for 10 μm cell in radius). For neurons, the ROI was shifted every 64 interpolated pixels along the boundary (~1.4 μm/step for 60x zoom). It took about 5 mins to complete the analysis of one cell with the method, which can be further optimized in the future.

Edge tracking of cells was reported to detect membrane flickering via tracking the derivative of the intensity profile across a cell edge.⁴² Rather than tracking the derivative, we determined the intensity difference between two regions. Because the intensity in each region was integrated over many pixels, our approach minimized pixel noise (shot noise). We further normalized the intensity difference (I₁-I₂) by the total intensity (I₁+I₂) to remove the common noise from the light source, allowing imaging of the sub-nanometer membrane displacement in neurons.