Background: A comprehensive intuition of the systemic lupus erythematosus (SLE), as a complex and multifactorial disease, is a biological challenge. Dealing with this challenge needs employing sophisticated bioinformatics algorithms to discover the unknown aspects. This study aimed to underscore key molecular characteristics of SLE pathogenesis, which may serve as effective targets for therapeutic intervention. Methods: In the present study, the human peripheral blood mononuclear cell (PBMC) microarray datasets (n = 6), generated by three platforms, which included SLE patients (n = 220) and healthy control samples (n = 135) were collected. Across each platform, we integrated the datasets by cross-platform normalization (CPN). Subsequently, through BNrich method, the structures of Bayesian networks (BNs) were extracted from KEGG-indexed SLE, TCR, and BCR signaling pathways; the values of the node (gene) and edge (intergenic relationships) parameters were estimated within each integrated datasets. Parameters with the FDR < 0.05 were considered significant. Finally, a mixture model was performed to decipher the signaling pathway alterations in the SLE patients compared to healthy controls. Results: In the SLE signaling pathway, we identified the dysregulation of several nodes involved in the (1) clearance mechanism (SSB, MACROH2A2, TRIM21, H2AX, and C1Q gene family), (2) autoantigen presentation by MHCII (HLA gene family, CD80, IL10, TNF, and CD86), and (3) end-organ damage (FCGR1A, ELANE, and FCGR2A). As a remarkable finding, we demonstrated significant perturbation in CD80 and CD86 to CD28, CD40LG to CD40, C1QA and C1R to C2, and C1S to C4A edges. Moreover, we not only replicated previous studies regarding alterations of subnetworks involved in TCR and BCR signaling pathways (PI3K/AKT, MAPK, VAV gene family, AP-1 transcription factor) but also distinguished several significant edges between genes (PPP3 to NFATC gene families). Our findings unprecedentedly showed that different parameter values assign to the same node based on the pathway topology (the PIK3CB parameter values were 1.7 in TCR vs − 0.5 in BCR signaling pathway). Conclusions: Applying the BNrich as a hybridized network construction method, we highlight under-appreciated systemic alterations of SLE, TCR, and BCR signaling pathways in SLE. Consequently, having such a systems biology approach opens new insights into the context of multifactorial disorders.

The dendritic spines play a crucial role in learning and memory processes, epileptogenesis, drug addiction, and postinjury recovery. The shape of the dendritic spine is a morphological key to understand learning and memory process. The classification of the dendritic spines is based on their shapes but the major questions are how the shapes changes in time, how the synaptic strength changes, and is there a correlation between shapes and synaptic strength? Because the changes of the classes by dendritic spines during activation are time dependent, the forward-directed autoregressive hidden Markov model (ARHMM) can be used to model these changes. It is also more appropriate to use an ARHMM directed backward in time. Thus, the mixture of forward-directed ARHMM and backward-directed ARHMM (MARHMM) is used to model time-dependent data related to the dendritic spines. In this article, we discuss (1) how to choose the initial probability vector and transition and dependence matrices in ARHMM and MARHMM for modeling the dendritic spines changes and (2) how to estimate these matrices. Many descriptors to classify dendritic spines in twodimensional or/and three-dimensional (3D) are available. Our results from sensitivity analysis show that the classification that comes from 3D descriptors is closer to the truth, and estimated transition and dependence probability matrices are connected with the molecular mechanism of the dendritic spines activation.