Patients were recruited at the Neurology Clinic of the Medical University, Sofia. Serum samples (0.5 ml) from patients with AD, FTD, DUE or no signs of dementia (n = 4 for each group) were collected after informed consent. The collection and the following studies were approved by the Human Studies Ethics Committee of the Medical University, Sofia. The anonymized samples were kept frozen at -15 °C until processing.

Each serum sample was thawed and incubated at 37 °C for 30 min for the dissolution of IgM complexes. Next, the sera were centrifuged and 30-fold diluted with PBS followed by ultrafiltration (Amicon-Ultra 100kDa membranes, Millipore) for initial fractionation of serum proteins above 100 kDa. The high-molecular fraction of serum proteins was applied in a series on columns (HiTrap Protein G High Performance and HiTrap IgM Purification, GE Healthcare) for affinity purification of IgM and IgG according to the manufacturer’s instructions.

Custom peptide microarray chips from containing 130 7 amino acid residues long linear or cyclic peptides produced by PEPperPRINT (Heidelberg, Germany) were used. The peptides were synthesized in situ in an oriented array, attached to the chip’s surface through their C-terminus (linear) or C- and N-terminus (cyclic) with a spacer sequence GSGSG. The microarray layout consisted of the peptide spots duplicated in random positions. The sequences of the peptides were selected from a larger IgOme library (Pashov et al. 2019) after preliminary analysis of the binding of IgM from patients with AD or FTD as well as IgM from healthy donors (IVIgM) (Pashov et al. 2019, manuscript in preparation). The present study uses sera from different patients than those used to determine the relevant mimotopes. The sequences of the peptides used is given in Table 1. The microarrays were blocked for 60 min using PBS, pH 7.4, and 0.05% Tween 20 with 1% BSA on a rocker; washed 3 × 1 min with PBS, pH 7.4, and 0.05% Tween 20; and incubated with sera in dilutions equivalent to 0.01 mg/mL IgM (∼1:100 serum dilution) on a rocker overnight at 4 °C. After 3 × 1 min washing, the chips were incubated with secondary antibodies at room temperature, washed, rinsed with distilled water, and dried by spinning in a vertical position in empty 50 mL test tubes at 100×g for 2 min. Two secondary antibodies with different fluorochromes and different wavelengths of detection were used to measure simultaneously the binding of IgG and IgM on the same array.

The microarray fluorescence images were acquired in a Innoscan 1100 (Innopsys, Carbonne, France). The densitometry was performed using MAPIX software. All further analysis was performed using publicly available packages of the R statistical environment (Bioconductor, Biostrings, limma, pepStat, sva, e1071, uwot, clvalid, etc.) as well as in-house developed R scripts. The data underpinning the analysis reported in this paper and the scripts of the analysis are deposited at https://github.com/ansts/cyclic. The details of the analysis procedures are described elsewhere (Pashov et al. 2019). The reactivity graph approach was largely following the previously described algorithms (Ferdinandov et al. 2023). Briefly, the densitometry data was cleaned based on the flags set during densitometry, the background was inferred based on the gradients of staining intensity between the randomly positioned duplicate peptide spots in the plane of the array. The background was subtracted by taking the residuals of the linear regression of the signal on the background followed by multiplying them by a factor compensating for the dependence of the standard deviation on the background (using a power law). This approach was adopted because the background was caused by insufficient mixing during the incubation.

Further, the logarithms of the data were normalized with respect to amino acid residue composition (Pashov et al. 2019) to compensate for changes in the binding due to overall charge and hydrophobicity rather than the dependence on the sequence which is the main interest. In addition, the data was normalized between arrays using the limma::normalizeCyclicLoess function with the “affy” method applied in 3 iterations separately for the 4 sets of data grouped by isotype and peptide topology. The 16 sets of data separated by isotype, peptide topology and diagnosis were used further to generate separate reactivity graphs. The criterion for cross-reactivity between two peptides used to define the edges of the graphs used a similarity measure based on a function of the correlation and the coefficient of variation of the two profiles compared. If the two vectors of reactivity values (logarithm of the staining intensity in arbitrary units) for two peptides across a set of n patients’ sera are v_i = x_i,1.. x_i,n and v_j = x_j,1.. x_j,n, ρ = corr (v_i, v_j) is their correlation and

$$cv=\frac{\sqrt{\Sigma \left(\left(v_i,v_j\right)-{\mu }_{\left(v_i,v_j\right)}\right)}}{2n-1}$$

is the coefficient of variation of their concatenation, then:

$$CCV=\rho +2-\frac{cv}{k+cv}$$

is a function which tends to ρ + 1 as cv → 1 and to ρ + 2 as cv → 0. The value for k = 0.3 was found to maximize the area under the ROC curve of the CCV criterion when classifying cross-reactive peptides. The CCV criterion remains relatively high even for low correlation if the coefficient of variation is also very low. In this way, reactivity profiles which are flat and very similar in mean values are estimated cross-reactive. The criterion was tested using the algorithm and the sequence set form (Ferdinandov et al. 2023). The ROC curve and the selected threshold for connecting vertices of the graphs are illustrated in Fig. 1. Vertices representing peptides reactivities with CCV lower than the threshold remain disconnected while those above the threshold are connected with the value of CCV used as a weight of the respective edge.

Figure 1. 

(A) ROC curve illustrating the capacity of the CCV criterion to classify 4150 pairs of peptides overlapping in 11/15 positions as a model of cross-reactive peptide pairs compared to a set of 10,000 pairs of dissimilar peptides (sharing a longest common subsequence of fewer than 3/15). The analysis is done on the basis of the dataset from [1]. The logarithms of the values of CCV are used. (B) Distributions of the log CCV values for dissimilar sequences (black) vs. cross-reactive sequences (red). The optimal tradeoff between sensitivity and specificity was found for CCV = 2 (specificity = 0.926, sensitivity = 0.69, AUC = 0.904)

In our previous reports we demonstrated the utility of antibody reactivity graphs as a tool for system level studies of the repertoires of antibody specificities. The reactivity graphs represent the antibody cross-reactivity relations between the peptide probes used. They are weighted and undirected. Also, they are usually highly connected due to antibody cross-reactivity especially when the IgM repertoire is probed with short peptides. Their capacity to encode diagnostically relevant information depends on the degree of cross-reactivity and specificity, the public nature of the repertoire features addressed (to ensure generalization), the diversity of the probe array, the use of targeted arrays with known relevance to the problem at hand, etc.

Here we address the question of the relative utility in binding assays of an array of peptide probes in linear (free) or cyclic (constrained) topology (conformation) in IgG or IgM reactivity graphs. Serum IgG and IgM from patients with AD, FTD, DUE or controls without dementia (n = 4 for each diagnosis) were tested using peptide arrays of 130 probes preselected for their significant over or under expression in AD and FTD. The binding of the antibodies was detected by a fluorochrome conjugated anti-IgG or anti-IgM secondary antibody and quantitated by scanning the fluorescence intensity. After acquisition, cleaning, background subtraction and normalization, the fluorescence data was used to construct 16 separate graphs using the binding profiles similarities (see Materials and methods).

The graphs represent data grouped by 3 factors: isotype (IgG and IgM), peptide topologies (cyclic or linear) and the diagnoses (n = 4) having also 4 different sera for each diagnosis. The graphs were studied either separately or by combining them in multigraphs, e.g. – grouped by isotype and/or topology, as well as after simplifying the multigraphs by summing up the weights of the parallel edges so that there is only one edge between two vertices. The overall graph produced as the union of all 16 graphs is shown on Fig. 2. For this graph the edge weight threshold of 17.4 was used (range – 2–36) which made the graph sparser and easier to visualize its core structure. The layout (embedding) of the graph is calculated using the eigenvectors of the graph Laplacian corresponding to the 16 lowest non-zero eigenvalues (the number of eigenvectors is determined by a dimensionality reduction algorithm). The 16-dimensional embedding was further transformed to 2 dimensions using the UMAP algorithm (R functions igraph::embed_laplacia_matrix and uwot::umap). The modularity of the graph partition according to peptide library equaled the 0.949 quantile of the simulated modularity distribution for equal sized random partitions.

Figure 2. 

Overview of the general reactivity graph constructed as the union of the reactivity graphs under different conditions (IgG or IgM binding; cyclic or linear peptides; AD, FTD, DUE and Control – altogether 16 different graphs based on the same vertices). The edge weights of the separate original graphs were summed. To outline only the strongest similarities, the edges were kept if their weight exceeded 17.4 (range 2–36). The vertices (peptide sequences) are color coded according to the source mimotope library (red – over expressed in AD, orange – under expressed in AD, dark blue – over expressed in FTD, light blue – under expressed in FTD). The color of the edges is a mixture of the colors of their incident vertices. The thickness of the edges is proportional to their weight interpreted as strength of cross-reactivity. The layout of the graph is an embedding based on the the 16 eigenvectors corresponding to the lowest non zero eigenvalues further projected to 2 dimensions using the UMAP algorithm. The modularity of the graph with respect to the partition by mimotope libraries equaled the 0.949 quantile of the bootstrapped modularity. When the modularity was bootstrapped dichotomously for each library against the rest, the quantiles were: 0.969 for AD high, 0.861 for FTD low, 0.647 for AD low and 0.626 for FTD high.

There was a weak but discernible separation between the peptide libraries with respect to their reactivities with the tested sera. When the modularity was calculated dichotomously for each library against the rest, the simulated distribution quantiles were respectively: 0.969 for AD high, 0.861 for FTD low, 0.647 for AD low, and 0.626 for FTD high. In all cases, the simulation was done by generating 1000 partitions of the same sizes as the tested.

When the graphs were grouped by topology/isotype, the four resultant multigraphs had significantly different mean intensities and graph densities (Fig. 3). The density of the reactivity graph can be interpreted as a correlate of the overall cross-reactivity of the antibodies tested with the peptide probes used. The graphs of linear peptide reactivities probed with IgM had a higher density compared to the IgG assay. For the cyclic peptides the difference between the IgG and IgM graphs was smaller than for the linear ones. These findings are interpretable in terms of difference in polyspecificities of IgG/IgM and in binding entropies as well as in the diversity of both the repertoire (Suppl. material 1: fig. S1) and the presented epitopes in constrained vs linear peptides.

Figure 3. 

A. Mean intensity of the binding data for the graphs grouped by the topology of the peptides (cyclic or linear) and by the isotype of the tested antibodies; B. Graph density of graphs grouped by the topology and isotype. The graph density is the ratio of the number of edges to the theoretical maximum for each graph. Among the graphs of the data based on linear peptides and tested with patients IgG showed lower density while those tested with IgM – higher than the cyclic peptide graphs. This is interpreted as lower, resp.: higher, cross-reactivity.

To study in more detail the commonality between the images of the IgG vs IgM repertoires probed with linear vs cyclic peptides, the sixteen original graphs were aggregated in 4 topology/isotype (T/I) graphs named linear_IgM, cyclic_IgM, linear_IgG and cyclic_IgG. These multigraphs were simplified by summing the parallel edges’ weights. The significance of the overlap of the individual T/I graphs was estimated calculating the sum of the weights of the parallel edges in all multigraphs generated by uniting the different combinations of the four T/I graphs. These were compared to weight sums of 1000 random graphs generated by scrambling the existing edges and their weights. The scrambling is done among all edges existing in the overall multigraph some of which are not found in individual graphs and thus are assigned weight 0 initially. Each of the graphs obtained by uniting a combination of T/I graphs was further stratified into 3 subgraphs based on edge weight using the ranges [2, 2.3), [2.3, 2.6) and >=2.6.

The magnitudes of the weight sums which are outside the 0.05–0.95 quantile range of the simulated values were considered significant. The significant weight sums are shown on Fig. 4. The distribution is drawn towards high cross-reactivity among multiple subgraphs which indicates a considerable consensus between the different conditions including between arrays of peptides in linear vs cyclic topology. Furthermore, the high overlap of high cross-reactivities between all four T/I graphs (∩(lIgM, lIgG, cIgM, cIgG)) in contrast to no over representation but some under representation for three of the four 3 T/I graph combinations (∩(lIgM, lIgG, cIgG)), ∩(lIgM, cIgM, lIgG), ∩(lIgM, cIgM, cIgG)) indicates also a non-random general agreement between the different assays for a substantial part of the peptide probes used. On the other hand, significant high cross-reactivity parts of the graphs remain which are not overlapping (the single graph edges of linear_IgM, linear_IgG and cyclic_IgM). Interestingly, there was a high agreement between profiles in the IgG assay irrespective of the topology of the peptides which is in contrast with no non-random overlap for the two IgM graphs while there is a better agreement between cyclic_IgM and the two IgG graphs (∩ (cIgM, lIgG, cIgG) as well as agreement between another subset of linear_IgM and linear_IgG.

Figure 4. 

Graph overlaps. The four T/I graphs and their various combinations had their edge weights categorized as low – [2, 2.3), medium – [2.3, 2.6) and, high – >2.6 indicating the respective levels of cross-reactivity (pattern similarity). The sums of the edge weights which were outside the 0.05–0.95 quantile range of the simulate distribution are illustrated. The thickness of the connecting strips corresponds to the sums of weights of the overlapping edges. For some of the graphs the number of overlapping edges is significantly increased (red) or decreased (green) relative to the simulated randomly connected graphs. The distribution is drawn towards high overlap among multiple subgraphs which indicates a considerable consensus between the different conditions including between arrays of peptides in linear vs cyclic topology.

Thus, despite the differences both in the repertoire of reactivities and in the binding mode, IgG and IgM repertoires are partially comparable in their cross-reactivity with the tested array of peptide probes with the distinction of repertoire compartments with high and low overlap of reactivities.

An efficient machine learning model based on repertoire patterns implies selecting a relevant subset among ~10³ peptide reactivities. Typically, less than a hundred peptides are selected which separate well the diagnostic groups of patients (Pashov et al. 2019; Ferdinandov et al. 2023). Previously, we have used a criterion which is a function of three clustering criteria: Dunn’s criterion, Baker-Hubert Gamma index and connectivity (Dunn 1974; Baker and Hubert 1975; Handl et al. 2005). When used on data labeled according to diagnosis, the combined criterion measures the degree of separation of the predefined clusters. Maximizing it over subsets of features helps select a (locally) optimal feature set which typically generalizes well the classification (Ferdinandov et al. 2023). This was done using recursive feature elimination (RFE).

In the present study, the size of the groups does not allow building a generalizing model. Nevertheless, RFE can still be used to measure the performance of the different data sets in a possible classifier. The effect of the tested factors can be compared using the maximal value of the clustering criterion achieved by the optimal feature set since the different assays are performed on the same set of peptide sequences. The distribution of the different subsets of peptides selected in RFE using the four T/I graphs is shown in Fig. 5A.

Figure 5. 

A. Venn diagram of the overlap of peptide sequences selected by recursive feature elimination as a minimal set of peptide reactivities which separates optimally the 4 diagnoses; B. Comparison of the quality of separation based on the different graphs. The separation of the cases of each pair of diagnosis was estimated using the clustering criterion and the six values from these comparisons were used to further compare the different feature sets. IgM based immunosignature patterns were more efficient. For IgG based patterns, the topology seemed to have a greater (and opposite to those in the IgM assays) effect but it did not reach statistical significance. (C) and (D) multidimensional scaling projections of the different patients’ sera profiles with the optimal feature sets (peptide sequences) for linear_IgM (C – best separation) and linear_IgG (D – worst separation).

The IgG and the cyclic peptide conditions led to selecting larger subsets of peptides (cyclic_IgG – 42, linear_IgG – 38, cyclic_IgM – 29, and linear_IgM – 28 sequences). This correlated inversely with the quality of the separation (Fig. 5B) with the linear peptides and IgM assay providing the best separation. Interestingly, measured by the Jaccard distance, the subsets selected in the IgG assays overlapped more than those in the IgM assays and the subsets selected both in the linear and cyclic IgM conditions overlapped better with the cyclic_IgG one than between themselves (not reaching statistical significance, though).

These findings indicate that IgM assays on linear peptides differentiate better the diagnoses especially with respect to the IgG conditions (Fig. 5C, D).