In Situ Characterization of Bak Clusters Responsible for Cell Death Using Single Molecule Localization Microscopy

Apoptosis plays a pivotal role in development and tissue homeostasis in multicellular organisms. Clustering of Bak proteins on the mitochondrial outer membrane is responsible for the induction of apoptosis by evoking a release of pro-apoptotic proteins from mitochondria into cytosol. However, how the protein cluster permeabilizes the mitochondrial membrane remains unclear because elucidation of the cluster characteristics such as size and protein density has been hampered by the diffraction-limited resolution of light microscopy. Here, we describe an approach to quantitatively characterize Bak clusters in situ based on single molecule localization. We showed that Bak proteins form densely packed clusters at the nanoscale on mitochondria during apoptosis. Quantitative analysis based on the localization of each Bak protein revealed that the density of Bak protein is uniform among clusters although the cluster size is highly heterogeneous. Our approach provides unprecedented information on the size and protein density of Bak clusters possibly critical for the permeabilization and is applicable for the analysis of different cluster formations.

where δij = 1 if δij < r, otherwise 0. [S1] Therein, A represents the area of the analyzed region, n stands for the number of points, r denotes the analyzed spatial scale and δij is the distance between two points i and j. K(r) represents the normalized number of points encircled by concentric circle with radius r centered on each point. This function, which scales with circle area, was then transformed into the Lfunction such that the scaling is linear with radius r.
Here, L(r) equals to r at all r for completely random distribution of points. We therefore plotted L(r) -r as a function of r such that a random distribution results in L(r) -r = 0 for all r. L(r) -r has positive values for a given r at which the distribution is more clustered than a random distribution. Points at the edge of the analyzed region were weighted to negate edge-related effects 37 . We calculated 99% confidence intervals by simulating 500 spatially random distributions with the same mean molecular density as the data region.
To objectively identify Bak clusters, we performed cluster analysis using an existing algorithm, density-based spatial clustering of application with noise (DBSCAN). DBSCAN is often used for data mining and spatial pattern analysis 14,18 . Identification of Bak clusters with DBSCAN is based on the density distribution of Bak molecules in a dataset obtained in a PALM experiment. Bak localizations with greater than MinPts neighbors within a radius ε are connected to their neighbors. These connected localizations are regarded as clustered. Bak localizations that are not connected to any other localizations are regarded as be non-clustered noise.
There are two parameters in DBSCAN: ε and MinPts. Because the mean molecular densities in healthy cells were comparable in mEos3-Bak and mEos3-BakΔN ( Supplementary   Fig. 4d), it was possible to meaningfully use the same values of the parameters for these datasets. We chose ε of 20 nm, which corresponds to the mean localization precision. MinPts should be sufficiently large to separate them from noise, but it should not be too large as to overlook a part of clusters. We determined MinPts based on datasets in healthy cells which were not considered to contain any physiological Bak clusters and found that MinPts = 13 provided the best result in this regard. Finally, we defined the localizations identified with DBSCAN as a cluster containing a minimum number of 18 Bak molecules, which was previously shown with a biochemical study 3 .
Cluster characterization. After identifying Bak clusters with DBSCAN, we examined a set of different parameters to characterize Bak clusters. The following quantitative characterizations were performed using the list of Bak localization coordinates and not the rendered PALM images 38 . The radius of each cluster, Rg, was calculated as the radius of gyration of all localizations within the cluster.
Therein, N stands for the number of localizations belonging to each cluster, ri (xi, yi) is the coordinate of each localization within a cluster, and rc (xc, yc) is the coordinate of the center of mass. The measurement of R g is based on two-dimensional (2D) projection of threedimensional (3D) cluster. The relationship between Rg and radius of 3D cluster, R, is given by, where zi and zc represent the coordinate along z axis of each localization and the center of mass, respectively. Eq. S4 shows the degree of underestimation in the measurement of cluster radius attributable to the 2D projection. Assuming that the variances of cluster size along the x, y, and z axes are comparable, we underestimate the radius approximately by 20%.
The fractal dimension, Df, was defined as where N denotes the number of localizations belonging to each cluster, a represents the radius of a Bak molecule, and k is the structural coefficient 19 . The scattered plot of N with Rg in logarithmic fashion was fitted by a linear model to obtain the slope, which corresponds to Df.
Local molecular densities were measured by counting the number of localizations within a square with a side of 20 nm.