2.1.

Sample Preparation

The tests of the platform were performed on the postmortem routine brain tissue samples. A list of test sample sources is presented in Table 1.

Table 1

Source of test—samples (Nerve Clinic Linz, Department of Pathology and Neuropathology)

2.2.

Antibodies

Astrocyte labeling: The astrocytes were marked with an anti-GFAP mouse anti-human monoclonal IgG antibody labeled with Alexa Fluor^® 488 (Molecular Probes^®, Vienna, Austria).

${\mathrm{HT}}_{1\mathrm{A}}$ receptor labeling: The ${\mathrm{HT}}_{1\mathrm{A}}$ receptors were marked with an anti-HTR1A rabbit anti-human antibody (LS-B970/27181, Lifespan BioSciences Inc., Seattle) This antibody turned out to be best suited for immunohistochemistry experiments and is also used at the Nerve Clinic Linz (LNK) for neural standard screening.

Anti-HTR1A antibody was labeled via a N-hydroxysuccinimid (NHS)-ester bond with Atto655 (Attotec, Attotec. Labeling protocol, Siegen, Germany).

Seventy-five microliters of $1\mathrm{mg}/\mathrm{ml}$ HTR1A (dissolved in PBS buffer and 2% sucrose) were diluted with a 0.2-M sodium bicarbonate buffer at a pH of 8.4. Thereafter, 1 μl of $0.25\mathrm{mg}/\mathrm{ml}$ Atto655 dimethylsulfoxid (DMSO) solution was added to adjust a labeling ratio of $\sim 1.8$. The reaction mixture was incubated for 1 h at room temperature. To separate the labeled HTR1A antibodies from free dyes, a PD-10 Sephadex^® G-25m column (GE Healthcare, Pittsburgh) was used. The labeling solution was purified via a PD-10 purification column in PBS buffer. To concentrate the labeled antibody, the eluate was pelleted (Thermo, Multifuge 1S-R, HERAEUS, Thermo Scientific, Vienna, Austria). The solution was split into three aliquots and stored at $-20°\mathrm{C}$.

2.3.

Setup and Imaging

The images were taken on a modified Olympus IX81 inverted microscope. The samples were illuminated through an Olympus UApo N 100×/1.49 NA oil objective with two diode lasers at 642-nm (Omicron Laserage Laserprodukte GmbH—Phoxx^® 642, Rodgau-Dudenhofen, Germany) and 491-nm wavelength (Cobolt Calypso 100™, Solna, Sweden). The signal acquisition was carried out on an Andor iXonEM + 897 (back-illuminated) EMCCD (16-μm pixel size).

Used filter sets:

The experiments were performed using excitation powers of 3.35 and $0.025\mathrm{kW}/{\mathrm{cm}}^2$ at 642 and 491 nm, respectively. The samples were illuminated for 10 ms (642 nm) and 5 ms (491 nm) with 40 ms delay time. The illumination protocols were timed with a custom-made LabView^®-based control software.

2.4.

Image Preprocessing

The requirement of multicolor imaging presents additional challenges for tissue imaging and analysis. Given the low signal-to-noise ratio of single-molecule images, we have chosen a detection method based on the isotropic undecimated wavelet transform (IUWT).^24,25 Wavelet thresholding offers a robust solution for the detection of small bright features, for example, detection of subcellular structures labeled by fluorescent dyes. Since a fluorescent dye can be considered as a point light source, its image is the point-spread function of the optical system that can be approximated by a 2-D Gaussian shape. The typical noise model is photon count noise, following a Poisson distribution, and an additive Gaussian read-out noise:

For an EMCCD camera, the model including the effect of the multiplier can be approximated²⁶ by the equation:

To deal with heterogeneity of the image noise, a variance-stabilizing transform is applied prior to the IUWT. The implementation of IUWT is based on the binomial filter $h=[1,4,6,4,1]/16$ as scaling function and the “à trous” algorithm.^25,27 The wavelet coefficients are computed as the difference between two successive scales. The wavelet coefficients of the finest resolution are discarded as noise. The remaining coefficients are threshold based on the control of false discovery rate as proposed in Ref. 28. The pixels considered significantly across scales are the result of the single-molecule detection step.

Subsequently, the detected molecules’ position was determined with subpixel accuracy by least square fitting of a 2-D Gaussian function in the neighborhood of the detected significant pixels. An estimation of the localization accuracy was also calculated.^29,30

2.5.

Single-Molecule Analysis

Commonly, the position determination for image reconstruction is only limited by the single-molecule signal and the local background noise (see Thompson/Mortensen formula).^29,31 The fixation and epitope-retrieval protocols used guarantee good single-molecule detection. However, this assumption can be inaccurate, if, for example, the setup exhibits an intrinsic error in position determination. In order to consider this additional dynamic offset in the estimation of the position accuracy (PA), we assumed a bound fluorescent antibody as mobile and calculated the PA via error of the mean square displacement (MSD). The position deviation was described by MSD error estimation for a single trajectory using Qian formula^30,32,33

In our approach, the calculated PA via MSD (offset of the MSD plot) is global (${\mathrm{PA}}_g$), averaged over all single-molecule signals detected over all frames, and describes the smallest localization radius in the image. To characterize the smallest possible localization accuracy of our setup, glass bound and sparsely distributed Atto655-labeled antibodies were used. The estimated PA was determined to be $22.2\mp 3.9\mathrm{nm}$ (approximately two to three times larger than the size of an antibody³⁴). This value defines the resolution limit for the dSTORM images. Local position accuracies (${\mathrm{PA}}_l$) for individual single molecules were determined via standard deviation of the peak position over all illuminated frames within the maximal search radius of ${\mathrm{PA}}_g$. For the image reconstruction, the mean values of all point coordinates detected within ${\mathrm{PA}}_g$ were used. In comparison, the calculated Thompson PA reaches a value of 11 nm (minimum); however, it does not take into account the setup properties.

2.6.

Image Sector Alignment

Due to the heterogeneous laser profile and variations in setup adjustment in the particular experiments, the images analyzed at single molecule show a nonregular density profile along the $y$-axis (heterogeneous illumination). Therefore, for comparison of two sample images, it is necessary to choose the nearly homogenous illuminated sectors from both images. To ensure that both images have the same size, we first calculated the normalized molecule density distribution along the $y$-axis of an image. The normalized molecule density for a given $y$-value is the ratio of the density of molecules in an image segment with a length [0, $x_{\max }$] and a width $y\pm \mathrm{\Delta }$ to the molecule density of the whole image (total number of molecules/image surfaces). The estimated density profile along the $y$-axis is then approximated with a one-dimensional Gauss function. The width of a segment is determined as width of the Gauss function at 50% of its maximal value (typically 140 to 200 pixels). An example of sector determination is presented in Fig. 1.

Fig. 1

(a) Empirical density distribution and a Gauss fit of molecule density along the $y$-axis of an image. (b) Selected sector of an image.

2.7.

Clustering-Based Spatial Analysis of Image

In order to determine the spatial distribution pattern of receptors, we need to find characteristic parameters or image features, which will help us to quantify changes between the images. Classical spatial analysis uses the changes of selected spatial parameters, which take place when the distance scale (observation scale) is made to vary. The most popular method, proposed by Ripley (known as Ripley K- and L-functions),³⁵ describes the characteristics of the point groups (clusters) at many distance scales. For given maximal distance between points in cluster $d$, the Ripley’s $L(d)$ function is estimated as

Fig. 2

Ripley’s L-functions (distance $d$ in pixel) for cryopreserved (${\mathrm{L}}_1$) and paraffin-fixed (${\mathrm{L}}_2$) images of a healthy brain tissue. Both samples show statistically significant clustering dissimilarity to complete spatial randomness (CSR) distribution at smaller distances and significant dispersion at larger distance. However, similarity between both samples (${\mathrm{L}}_1$ and ${\mathrm{L}}_2$) is very high ($p$-value of Kolmogorov–Smirnov two-sample nonparametric test is equal to 0.96).

Therefore, we propose a novel approach for spatial analysis based on clustering of preselected image sectors and cluster profiling. In our case, the Ripley’s L-function is only used for establishing the significant interval of distance scale (cluster maximal size) $d_{\min }$ to $d_{\max }$ (Fig. 2).

The selected sector of points (single molecules) can be clustered in nonoverlapping clusters $C(d)$ with a cluster dimension less or equal to a given value $d[d\in (d_{\min },d_{\max })]$. The dimension $d$ of cluster (cluster size) is the maximal distance between points within the cluster. For fast clustering of a given sector of image, we use the hierarchical agglomerative clustering (HAC) method with complete link.³³ HAC clusters are established by cutting the dendrogram at a desired level so that each connected component (subclusters) forms a new cluster. The linkage between two clusters is achieved by complete linkage. This method is well suited for our consideration, because it takes into account the “similarity” between clusters based on the “outermost” points [the least distance-similar (Ref. 33)] in clusters. The two clusters with a minimal complete linkage are merged in a new one. For a given distance $d$, HAC algorithm generates a lot of nonoverlapping clusters so that the dimension (size) of each cluster is less or equal $d$. The clusters represent stochastic distribution of points in selected sector, scaled into a cluster set. For each cluster, we defined local characteristics (features) which describe the spatial structure of a sector more accurately than with the standard spatial analysis method.

2.7.1.

Spatial properties of cluster

Each cluster $c(d)\in C(d)$ can be characterized by the following local features:

• 1. Single fluorophore intensity determines the number of detected single fluorophores (or molecules). The cluster fluorophore ratio $\mathrm{fluor}[c(d)]$ is the proportion of fluorophore number per cluster to total number of fluorophores in the whole image sector. In an ideal case, where every antibody carries only one fluorophore and is imaged only once, the number of antibody-labeled receptors would be directly described by $\mathrm{fluor}[c(d)]$.

• 2. The relative density of cluster $\mathrm{dens}[c(d)]$ is the proportion of cluster density to the mean density of the complete image sector under consideration. The cluster density is determined as number of points (molecules) within a cluster per cluster area. The cluster area is calculated as the sum of the area inside the circle located at any point of the cluster with a radius equal to half the distance to its first nearest neighbor.

• 3. Cluster eccentricity: The best suited eccentricity definition for our analysis is based on central moments of points within a cluster.³⁵ As a measure of eccentricity, we took the proportion $\mathrm{ecc}[C(d)]=v_1/v_2$, where $v_1$ and $v_2$ are the eigenvalues of the symmetric $2\times 2$ matrix M of central moments of cluster points. Such a measure is an invariant with respect to location, rotation, translation, and scaling of cluster. The eccentricity of a round-shaped cluster is equal to 1, and the eccentricity of a line-shaped cluster is equal to 0.

• 4. To determine the relationship between the cluster and the bulk fluorescent structure of the image, the skeleton representation of the bulk image sector is prepared.^37,38 The cluster distance-to-skeleton ratio $\mathrm{dist}[c(d)]$ is the proportion of the distance of the cluster centroid (mean position of points in the cluster) to the skeleton and of the mean distance of all points to the skeleton within an image sector. This representation of relationship between the clusters and the structure of the bulk fluorescent image enables additionally a more precise analysis of concentration and density of receptors surrounding, for example, glia structures.

An example of clustering and cluster features is presented in Fig. 3.

Fig. 3

Cluster and cluster features for cryopreserved sample images of a healthy brain tissue. (a) Image sector and clustering result for cluster max-size $d=18\text{pixels}$. (b) Skeleton of bulk fluorescence image (a) (glia tissue) and localized molecules (dots). (c) Mean value of clusters eccentricity ($y$-axis) and clusters distance-to-skeleton ($z$-axis) as function of cluster size ($x$-axis) for $d$ from 1 to 35 pixels (light gray). For comparison, the clustering results for randomly located points on the same image are represented by the black. The eccentricity and distance-to-skeleton of randomly located points are almost constant for all cluster sizes. (d) Mean values of relative cluster density ($y$-axis) and cluster distance-to-skeleton ($z$-axis) as function of cluster size ($x$-axis) for $d$ from 1 to 35 pixels (light gray). Black represents the same features for randomly located points. The mean density of cluster and mean distance-to-skeleton is almost constant, too.

We gathered information about cluster properties in the aforementioned manner and compared the resulting data with cluster features extracted from randomly located points on the same image. The average eccentricity of the clusters changes from an almost circular shape to the shape of an elongated ellipse with increasing mean distance-to-skeleton and cluster size. A similar behavior was observed for changes in the density of the clusters. The average density of the cluster decreases with the increase of the average distance-to-skeleton and with the increase in the size of clusters. In contrast, the average eccentricity and average density of clusters for randomly located points is almost constant for all cluster sizes.

2.8.

Spatial Comparison of Image Sectors from Two Samples

In order to characterize and compare the spatial distribution of single receptors between two image sectors of two samples, we applied the features described above for spatial analysis. For each cluster set, we used $C(d)$ derived from two sample images and computed the empirical feature distributions $\mathrm{fluor}(d)$, $\mathrm{dens}(d)$, $\mathrm{ecc}(d)$, and $\mathrm{dist}(d)$ for each distance $d$ from the test interval $[d_{\min },d_{\max }]$, respectively. Next, for a pair of such distributions (e.g., ${\mathrm{dens}}^1(d)$—first sample and ${\mathrm{dens}}^2(d)$—second sample) and for a $d$ obtained from the clustering process of the first and second samples, we made two null hypotheses:

These distributions can be compared with the Kolmogorov–Smirnov two sample nonparametric test or with the Wilcoxon rank sum test.^39–41 We tested both hypotheses at the standard 5% significance level using a two-sample Kolmogorov–Smirnov test. The Kolmogorov–Smirnov test calculates the $p$-value $pv(d)$ between two empirical distributions for a given maximum size of clusters $d$. It is sensitive to differences between the empirical cumulative distribution functions of the two samples. The test rejects the null hypothesis (at the 5% significance level), if $pv(d)<0.05$ [where $pv(d)=p{v}_{\text{equal}}(d)$ for test of hypothesis I and $pv(d)=p{v}_{\text{large}}(d)$ for test of hypothesis II]. Additionally, we apply a 2-D and two-sample Kolmogorov–Smirnov test.⁴² This test compares a pair of 2-D distributions using Fasano and Franceschini’s generalization of the Kolmogorov–Smirnov test.⁴² The test of null hypothesis II can be applied to identify differences between samples, but only for selected spatial features of a cluster, for example the receptor–density distribution.

The test of null hypothesis I is used to define the similarity coefficient between two samples. The similarity coefficient is the mean of the weighted sum of the $pv(d)$ values for the different cluster features like $\mathrm{fluor}(d)$ and pairwise features like [$\mathrm{dens}(d)$, $\mathrm{dist}(d)$] and [$\mathrm{ecc}(d)$, $\mathrm{dist}(d)$] [throughout the range of cluster size ($d$)]. The weighted sum of the $pv(d)$ is called aggregated $p$-value $p{v}_{\mathrm{agg}}(d)$.

To estimate the similarity or dissimilarity between two images, it is sufficient to compare these three $p$-values $pv(d)$ on the interval $[d_{\min },d_{\max }]$. The analysis of the presented images by using the Ripley’s L-function revealed an appearance of statistically significant clustering dissimilarity, when compared with a complete spatial randomness (CSR) distribution usually in the distance interval of $[d_{\min },d_{\max }]=[1,\sim 35]\text{pixels}$. This interval was chosen for the further estimation and comparison of $p{v}_{\text{large}}$-value functions. To exemplify the method described above, a comparison of two brain tissue images is presented in Fig. 4.

Fig. 4

(a) Image of a cryopreserved healthy brain tissue. (b) Image of a paraffin-fixed healthy brain tissue. (c) Comparison between (a) and (b) samples—$p{v}_{\mathrm{agg}}(d)$ of cluster features distributions with similarity $\text{coefficient}=0.234$ [gray zone shows minimal and maximal values of aggregated $pv(d)$]. (d) Image of a cryopreserved healthy brain tissue. (e) Image of a brain tissue of patient with depressive disease. (f) Comparison between (d) and (e) samples—$p{v}_{\mathrm{agg}}(d)$ of cluster features distributions (similarity $\text{coefficient}=0.029$).

3.1.

STORM Imaging

For dSTORM-imaging of serotonin receptor clusters on glial and nerve cells, the sample preparation methods and the illumination conditions had to be adapted. All measurements were performed on $\sim 3\text{-}\mu \text{m}$ thin brain slices. To reduce autofluorescence and light scattering for two-color imaging, we used a total internal reflection fluorescence (TIRF) microscopy derived⁴³ highly inclined and laminated optical (HILO) sheet illumination configuration.^44,45 In this configuration, a laser beam is tilted through a single objective and leads to the illumination in only a thin intersection of the focal plane. The method is, however, not related to the wide-field imaging technique HiLo.^46,47

The target proteins were labeled with commercially available antibodies marked with Alexa488 or Atto655 fluorophores (Attotec, Siegen, Germany). In case of the polyclonal anti-serotonin receptor antibody (Lifespan BioSciences Inc., Seattle), the labeling was performed via covalent amino fluorophore conjugation, and for the specific recognition of the glia, a monoclonal Alexa488-conjugated antibody (Molecular Probes, Vienna, Austria) against GFAP was used. We aimed to have a labeling ratio of 1.8 fluorophores per antibody, which guarantees that a relatively high amount of antibodies are labeled with just a single fluorophore and at the same time leads to a low abundance of blank antibodies. Due to this stochastic-labeling method, an exact quantification of the protein number within a serotonin receptor cluster is not possible. However, to guarantee the comparability of the samples measured in this work, all tissues are incubated with antibodies labeled in the same batch. Estimating more accurate numbers of serotonin receptors will require a labeling ration of one fluorophore per antibody and a detection system in which every fluorophore will only be imaged once. Moreover, the receptor recognition is also restricted to the binding affinity of the commercially available polyclonal antibodies. Due to their probabilistic binding kinetics, they cannot mark all successfully retrieved serotonin receptors.

We used the fluorescently labeled glia cells for orientation within the tissue slice by keeping the density of the glia cells in the imaged areas constant. Those receptor signals which did not colocalize with the glial skeleton are neural receptors and, interestingly, they also form clusters. However, only the anti-$5{\mathrm{HT}}_{1\mathrm{A}}$ antibodies were characterized via localization microscopy. To apply dSTORM imaging, the photoswitching rate of Atto655 fluorophores needed to be adjusted to ensure sufficient long fluorophore off times. A 40 mM of cysteamin (MEA) were added to the measurement buffer. The Atto655-conjugated antibody was continuously illuminated at $4\mathrm{mW}/{\mathrm{cm}}^2$ power with a frame rate of $20\text{frames}/\mathrm{s}$ ($\sim 800\text{photons}/\text{fluorophore}$). Fast illumination times and rather sparse serotonin clusters required 1200 frames for a fully reconstructed image. It was acquired within 1 min with localization accuracy down to 22.5 nm (Fig. 5). The described system adjustments are necessary to arrange two-color imaging and localization microscopy of fixed brain tissues (Fig. 6).

Fig. 5

(a) Single-molecule imaging setup. (b) Image of a single molecule with localized centers of all detected events from this molecule. (c) Zoom of the center pixel from (b).

Fig. 6

(a) Image of the cryofixed brain tissue; green-labeled glia tissue with white-marked localized serotonin receptors (circle radius $27\pm 4.3\mathrm{nm}$, pixel size 160 nm). The areas A and B represent zoomed out clusters of reconstructed images. In the reconstructed image, the localized single-molecule positions were fitted with a normalized Gauss, multiplied with maximal intensity of the dyes, and detected within ${\mathrm{PA}}_g$ (Gaussian $\mathrm{FWHM}={\mathrm{PA}}_g$, pixel size 15 nm). (b) Image of the paraffin-fixed brain tissue (conserved in 2010; epitope retrieval 2012); green-labeled glia tissue with white-marked localized serotonin receptors (circle radius $28\pm 3.6\mathrm{nm}$, pixel size 160 nm). The areas C and D represent zoomed out clusters of reconstructed images. All detected fluorophores were Gaussian fitted at their original positions ($\mathrm{FWHM}={\mathrm{PA}}_l$, pixel size 15 nm).

3.2.

Sample Comparison

The presented image analysis was tested using samples from different patients (see Table 1), which were prepared following different fixation protocols. Generally, the test samples can be classified in the following groups: cryopreserved brain tissue of healthy individuals (Group A—13 samples), paraffin-fixed samples of healthy individuals (Group B—6 samples), samples taken from MDD patient with Alzheimer (Group C—2 samples), samples of a depressive (MDD) alcoholic patient (Group D—4 samples), and long-time preserved paraffin-fixed samples (Group E—3 samples).

We computed the aggregated $p{v}_{\mathrm{agg}}(d)$ functions for cluster size $d\in [d_{\min },d_{\max }]$ and similarity coefficient for each pair of images within the same sample group and between different groups.

Figure 7 presents the pairwise comparison matrix of images from all samples [Fig. 7(a)] and sample groups [Fig. 7(b)]. The grayscale (black—similarity $\text{coefficient}=1$, white—similarity $\text{coefficient}=0$) matrix elements represent the mean of the aggregated $p$-values, i.e., the pairwise similarity coefficient between the samples.

Fig. 7

(a) The similarity coefficient values between compared pairs of images from all sample groups (test of null hypothesis I). The submatrix A represents data from cryopreserved samples, submatrix B—paraffin-fixed samples prepared in 2010, submatrix C—a major depressive disorder (MDD) patient with Alzheimer as well as Parkinson, submatrix D—a depressive (MDD) alcoholic patient, and submatrix E—paraffin-fixed samples prepared 2007. A strong similarity between images from cryopreserved and paraffin-fixed samples (year 2010) is observed. Long-time preserved paraffin-fixed samples (year 2007) show much lower comparability to the earlier fixed and cryopreserved samples. Moreover, a strong dissimilarity between the cryopreserved and fixed samples versus patient group was observed. (b) Average of similarity coefficient values calculated between all samples groups—global similarity coefficient for null hypothesis I.

Based on this pairwise comparison, we constructed the global statistical similarity coefficient between the different sample groups. The global similarity coefficient between two groups of samples can be calculated as the mean value of similarity coefficients between all sample pairs from both groups.

3.3.

Spatial Cluster Analysis of Cryopreserved Samples (Group A)

The first measurements were performed on cryopreserved samples. The cryogenic tissue preservation method was used for two reasons: first, to test the consistency of the brain slices, and second, to find a reference system for optimizing the fixation protocols for two-color imaging and for comparison with fixed healthy/pathologic tissue samples. Furthermore, the cryo-preservation method is also used to determine the antibody concentration required to saturate the serotonin H1 receptors in the brain tissue and to quantify the unspecific binding (incubation with unspecific Alexa647-labeled anti-GFP antibody). The concentration used was estimated to be 0.8 μg of antibodies per sample with almost 2 orders of magnitude higher specificity. The samples are derived from patients with no mental disability and died of cardiac decompensation and pulmonary edema with previous records of atrial fibrillation (see Table 1). The data were obtained from two patients with five and eight technical replicas, respectively [Fig. 7(a), submatrix A]. To ensure comparison between the same regions, only samples of the prefrontal cortex have been used. Moreover, we chose images with a similar density of the glia cells ($21\pm 1.5\%$ average density), which was determined via intensity thresholding of the images’ sectors, the same as used for cluster analysis. The threshold level was kept manually constant in all images. The comparison shows a 0.33 global similarity coefficient agreement between the cryopreserved samples. This result implies a good similarity between the samples regarding their cluster size, elliptic elongation, and density distribution in relation to the structure of the fluorescent bulk signal (glial tissue). Moreover, the results show that the proposed spatial analysis method is able to characterize serotonin H1 receptor clusters within human brain tissue at single-molecule level.

3.4.

Characterization of Fixation Artifacts (Groups B and E)

The main objective of this study was to develop a method to quantify receptor distributions in thin sections of brain tissue on a nanoscopic level. Such a method should also be applicable to fixed samples stored for long periods. In a second step, we used the presented spatial analysis method to study the impact of the fixation method on sample quality. Therefore, we compared cryopreserved with paraffin-embedded tissues. The data of the paraffin-embedded tissue were collected from two patients [fixation year 2010 and three technical replicas for each patient—Fig. 7(a), submatrix B]. The analyzed images have a $20\pm 3\%$ glia cell density. The comparison indicates a global similarity coefficient agreement of 0.2 inside the sample groups. Moreover, we also observed a high similarity between the cryo- and paraffin-preserved tissues with global similarity coefficient of $\sim 0.2$ between the samples. This confirms a good capability of our method for the comparison of tissue samples.

Furthermore, we wanted to test whether differences in the fixation protocols and extended storing times will have an impact on sample comparison. The comparability between differently treated and stored samples would significantly extend the applicability of the method [Fig. 7(a), submatrix E]. Paraffin samples had been prepared before 2007 by using a different fixation method and were compared with cryopreserved and freshly prepared paraffin samples. The comparison shows a global similarity of $\sim 0.1$ to the cryopreserved tissue and a negligible similarity (global similarity of 0.018) to the paraffin-embedded slice. The data suggest that both the longer alcohol treatment in the older fixation procedure and the longer storage may have a negative impact on sample quality by causing a stronger epitope damage of the target protein. Consequently, for a precise comparison, our method requires consistency in sample conservation and fixation date as well.

3.5.

Spatial Cluster Analysis of Brain Tissue of Patients Suffering from a Mental Disorder (Groups C and D)

To test the applicability of the localization microscopy and the cluster analysis in neuropathology, we concentrated on a very challenging field—the neuropathology of psychiatric disease. We compared healthy brain samples with samples of MDD patients (two patients with two and four technical replicas, respectively, each prepared in two individual batches). The first patient suffered from MDD and additionally from other diseases like Alzheimer’s and Parkinson’s (two technical replicas). The glia tissue density was shown to be around $19\pm 0.5\%$ [Fig. 7(a), submatrix C]. This tissue displays a high 0.48 global similarity value for sample comparison inside the group. The second patient analyzed suffered from alcoholism; the four samples of this patient display a global similarity value of 0.24 at a glia tissue density of $20\pm 3\%$ [Fig. 7(a), submatrix D]. We observed a dissimilarity between the brain tissues of the MDD patients and the healthy patient. We denote global similarity of 0.07 and 0.05 compared with healthy cryopreserved and paraffin-fixed tissues, respectively. The comparison between the two MDD patients displays a similarity coefficient value of $\sim 0.14$, which shows a moderate agreement between the samples. These first results are promising for the future use of localization microscopy and the proposed special analysis technique for characterization and classification of human brain tissue. Although our study is limited to a small number of patients and to a single cortical region, the analysis reveals differences between pathological and healthy brain tissues which render the method applicable in the complex field of biological psychiatry.

3.6.

Relative Comparison of Cluster Features Between the Samples

The presented method allows the classification of the samples based on their similarity; however, it does not provide statistical information about the relative cluster fluorophore number or density. Therefore, in a second comparison we determined the $p_{\text{larger}}$-value to test the null hypothesis II (for a definition see Sec. 2), which assumes that the first-sample empirical distribution CDF is larger than (or equal to) the second-sample empirical distribution CDF. A larger distribution corresponds to a larger cluster size and density by comparing one sample with the other. The comparison is restricted to individual features, for example, the relative number of fluorophores per cluster—$\mathrm{fluor}(d)$ or relative cluster density—$\mathrm{dens}(d)$. The test is performed within a cluster size interval of $d\in [1,35]\text{pixels}$. The result for relative cluster density distribution is presented in Fig. 8. The test of the null hypothesis II of cluster relative density was prepared on pairs of samples from groups A and B and samples from groups C and D.

Fig. 8

(a) Mean $p$-value obtained from comparison between pairs of samples (over the complete distance interval) for testing of null hypothesis II [for dens($c[d]$)]: Group A—cryopreserved samples, group B—healthy paraffin-fixed samples, group C—first MDD patient, group D—second MDD patient. The distribution CDF of ${\mathrm{dens}}_1(d)$ of sample 1 (rows) is larger than the distribution CDF of ${\mathrm{dens}}_2(d)$ of sample 2 (columns). (b) Average $p{v}_{\text{large}}$-values between samples groups.

The mean cluster density derived from C and D samples is smaller than from samples of healthy individuals (A and B samples). Cryopreserved as well as paraffin-fixed samples of healthy individuals [Fig. 8(a), rows of submatrices A and B] show a high similarity between empirical CDFs of cluster density and fluorophore ratio with aggregated $p_{\text{larger}}$-values between 0.4 and 0.7 for cluster density and between 0.7 and 0.9 for cluster fluorophore ratio. In contrast, the samples from C and D groups [Fig. 8(a), rows of submatrices C and D] manifest a significantly lower similarity between CDFs of density and fluorophore ratio (aggregated $p_{\text{larger}}$-values between 0.04 and 0.09) compared with healthy brains samples from groups A and B.