Statistical analysis of 3D localisation microscopy images for quantification of membrane protein distributions in a platelet clot model

We present the software platform 2CALM that allows for a comparative analysis of 3D localisation microscopy data representing protein distributions in two biological samples. The in-depth statistical analysis reveals differences between samples at the nanoscopic level using parameters such as cluster-density and -curvature. An automatic classification system combines multiplex and multi-level statistical approaches into one comprehensive parameter for similarity testing of the compared samples. We demonstrated the biological importance of 2CALM, comparing the protein distributions of CD41 and CD62p on activated platelets in a 3D artificial clot. Additionally, using 2CALM, we quantified the impact of the inflammatory cytokine interleukin-1β on platelet activation in clots. The platform is applicable to any other cell type and biological system and can provide new insights into biological and medical applications.


IL-1ß treatment
Platelets were incubated with 10 ng/mL of recombinant interleukin 1 beta (IL-1β, Sigma-Aldrich, Vienna, Austria) for 30 minutes at 22 °C. Subsequently, the platelets were centrifuged and resuspended in PBS.

Platelet clot formation
1x10 8 platelets were centrifuged at 500xg for 10 minutes to remove the anticoagulant storage solution from the concentrate. After resuspension in PBS, cells were gently mixed with 2.5 mg/mL fibrinogen (from bovine plasma, Sigma, Saint Louis, USA) and 0.2 U/mL thrombin (kind gift from LBI Trauma Care Vienna, Austria) in 40 mM CaCl2 and clots (20 µL contain 1x10 7 platelets) were pipetted onto either plain or collagen-coated glass. Clots were air-dried for 30 minutes at room temperature prior to fluorescence labelling.

Fluorescence microscopy and 3D dSTORM image acquisition
Images were acquired using a modified Olympus IX81 inverted epi-fluorescence microscope with an oil-immersion objective (PlanApo N 60x 1.42 NA, Olympus, Vienna, Austria). The sample was fixed on a XYZ piezo stage (PI Mars; P-562, Physical Instruments) with nanometer precision combined with a coarse mechanical stage with a travel range of 1 cm x 1 cm (Hybrid, JPK Instruments, Berlin, Germany). A tube lens with an additional magnification of 1.6 was used to achieve a final imaging magnification of 96 (corresponding to a pixel size in the image plane of 167 nm). Platelets were illuminated with a 642 nm laser light from a diode laser (Omicron-laserage Laserprodukte GmbH, Phoxx 642, Rodgau-Dudenhofen, Germany), a 532 nm laser light from a solid-state laser (diodepumped, Cobolt AB, Solna, Sweden), a 488 nm laser light from a solid-state laser (diode-pumped, Toptica Photonics, Graefelfing, Germany), and a 405 nm laser light from a diode laser (Insaneware, Gladbeck, Germany). The fluorescence signal was detected using an Andor iXonEM+ 897 (back-

3D dSTORM Imaging Protocol
Single-molecule photo-switching of the rhodamine dye Alexa Fluor 488 and the cyanine dye Alexa Fluor 647 was performed in a buffer optimized for both fluorophores in order to image both channels without the need for buffer exchange. The buffer containing OxEA, as described by Nahidiazar et al. [1], was applied to the cells immediately prior to the fluorescence microscopy measurements. For imaging, the sample was illuminated for 20 ms with 1.2 kW/cm 2 excitation intensity (647 nm) and 3.3 kW/cm 2 excitation intensity (488 nm) (both frame rates: 25 images/s), respectively. During camera readout, the sample was illuminated with a 405 nm laser light (10 ms at 100 W/cm 2 ) to recover fluorophores from the singlet ground state. The deformation characteristics introduced by the cylindrical lens are experimentally determined via a calibration step before each experiment using immobilized fluorescent diffraction-limited beads; this allows for determination of the axial position of a single-molecule from the deformation of its signal (3D dSTORM). Typically, we acquired 10 000 frames including approx. 75 000 -500 000 single-molecule signal events. Typically, singlemolecule signal levels of 1676 ± 1245 and 1263 ± 637 photons were derived for Alexa 647 and Alexa 488, respectively (illumination time = 20 ms). All illumination protocols were performed with custom-written acquisition software.

3D dSTORM fitting of single-molecules and visualization
The previously presented dSTORM analysis workflow [2]  The model is minimized using the Double Dogleg [4] algorithm. In the next step, the positional accuracy is calculated. The equations are based on the Thompson & Mortensen formulas [5], but were expanded to handle astigmatism as well as the axial accuracy [6]. In order to speed up the visualisation process, single molecules are sorted axially and drawn using false colours with a circle of pseudo-Gaussian decrease of the alpha colour channel.

Drift correction
The core of this algorithm is to determine a displacement vector ⃗ that minimizes the pairwise

Outlier filtering
Points are classified as core points or outlier points according to the following algorithm: Point is called a core point in cases when at least a number of points are located within the distance .
Distance is the given maximum radius of the neighbourhood. Thus, any point is directly accessible from , if point is within the distance  to the point . In general, a point is called reachable from the point , in case there is a path 1 , … , with 1 = and = ; where each +1 is directly reachable from . All points that are not reachable from any other point are classified as outliers. Hence, all points in a cluster (called primary clusters) are mutually 'density-connected' to each other; in case a point is reachable from any cluster point, it is also a part of the cluster [7][8][9][10][11].

Extraction of regions-of-interests in samples
To analyse isolated 3D clouds of points, regions-of-interests (ROIs) can be automatically extracted.
When the clouds of points are cumulated in regions within a single image, these regions can be combined to ROIs (accordingly cut out of the image). For ROI extraction from the samples, a DBSCAN algorithm is also used. In order to extract plausible regions, the factor should be increased to ~ 2.5 and the number of nearest neighbours ( ) should be minimal, i.e.

Simulation of random samples
Simulated samples with a random distribution have to reflect the statistical structure of the real sample. For this purpose, the simulated data set is generated in two stages: In the first stage, we split the real data sample into clusters with a diameter limited by a multiple (factor 2) of the cluster dimension and obtained via the maximum Ripley H function. Thus, the diameter is equal to twice the value of the cluster dimension at maximum Ripley H function value.
For these centroid sets, empirical probability distribution function (ECDF) of their locations in 3D space is determined. Further, for each cluster with a number of points greater than 5 the parameters for the Poisson distribution are estimated.
In the second stage, random 3D-positions of cluster-centroids using the empirical distribution of ECDF obtained in step 1 are generated. Hence, for each random centroid 3D-position, we assign a randomly selected (without repetition) index of the original cluster. Next, we generate new cluster points based on the estimated Poisson distribution for the assigned cluster index. The number of generated points is equalized to the number of points in the allocated original cluster by addition of noise points from a uniform distribution.