Dissecting the relationships of IgG subclasses and complements in membranous lupus nephritis and idiopathic membranous nephropathy

Abstract

Membranous lupus nephritis (MLN) and idiopathic membranous nephropathy (IMN) are kidney diseases with similar morphology, but distinct etiologies, both producing glomeruli with immune deposits. Immunoglobulins and complements, the main components of the deposits, can be detected by immunofluorescence (IF) microscopy. Previous researches characterized the immune deposits only individually, but not the interactions between them. To study these relationships we analyzed an IF profile of IgG subclasses and complements (IgG1, IgG2, IgG3, IgG4, C3, C1q, and C4) in 53 and 95 cases of biopsy-confirmed MLNs and IMNs, respectively, mainly using information theory and Bayesian networks. We identified significant entropy differences between MLN and IMN for all markers except C3 and IgG1, but mutual information (a measure of mutual dependence) were not significantly different for all the pairs of markers. The entropy differences between MLN and IMN, therefore, were not attributable to the mutual information. These findings suggest that disease type directly and/or indirectly influences the glomerular deposits of most of IgG subclasses and complements, and that the interactions between any pair of the markers were similar between the two diseases. A Markov chain of IgG subclasses was derived from the mutual information about each pair of IgG subclass. Finally we developed an integrated disease model, consistent with the previous findings, describing the glomerular immune deposits of the IgG subclasses and complements based on a Bayesian network using the Markov chain of IgG subclasses as seed. The relationships between the markers were effectively explored by information theory and Bayesian network. Although deposits of IgG subclasses and complements depended on both disease type and the other markers, the interaction between the markers appears conserved, independent from the disease type. The disease model provided an integrated and intuitive representation of the relationships of the IgG subclasses and complements in MLN and IMN.

Fig 1. Information diagrams for IgG subclasses, complements, and disease type.

Information diagram for IgG subclasses, complements, and disease type (a), for IgG subclasses (b), and for complements (c). Numbers in the diagram refer to bits.

Fig 2. Global trends of the IgG subclasses and complements in MLN and IMN estimated by Principal Component Analysis (PCA).

PCA of the IgG subclass and complements profile (a), profile of the IgG subclass only (b), and profile of complements only (c). Blue circles surrounding black, red, or cyan dots indicate that there is more than one case with the same profile. “Mixed” in (c) indicates that MLN and IMN cases have the same complement profile.

Fig 3. Comparison of entropy and Mutual Information (MI) in MLN and IMN.

The differences of entropy between LMN and IMN for seven IgG subclass markers and complements (a), and differences of mutual information for 21 pairs of seven markers (b) are illustrated. The purple, cyan, and blue lines in (a) indicates the difference of entropy for C3, IgG1, and IgG4, respectively.

Fig 4. Markov chain and Mutual Information (MI) of the IgG subclasses.

The structure of the Markov chain was inferred from the MIs, on the assumption that IgG1, IgG2, IgG3, and IgG4 form a single chain Markov chain, The MIs are represented in bits.

Fig 5. A model of IgG subclass and complement deposition in the glomeruli in MLN and IMN.

The deposits of the IgG subclasses and complements in MLN and IMN are illustrated as a Bayesian network. Nodes consist of disease type (MLN or IMN), IgG subclass, and complement, and edges with arrows represent cause and effect relationships. Conditional probabilities of the target variable given the source variable in each edge are represented as heatmaps over edges. In each heatmap, the x axis and y axis represent source and target variable, respectively, and each conditional probability is color coded. The values of glomerular deposits of IgG subclasses and complements are represented as ‘—‘,’-M’, ‘-G’, ‘GM’ each indicating no deposits (‘—‘), deposit only in the mesangium (‘-M’), deposit along the glomerular capillary wall (‘G-’), and deposit both in the mesangium and along the glomerular capillary wall (‘GM’), respectively. A column or row of the heatmap is omitted for simplicity if all the values in the corresponding line are 0.