This study aimed to identify copper-induced death genes in primary Sjögren’s syndrome (pSS) and explore immune infiltration, risk and drug prediction models for salivary glands (SGs) damage. The 3 datasets, including GSE40611, GSE23117, and GSE7451 from the Gene Expression Omnibus database were downloaded. The datasets were processed using the affy in R (version 4.0.3). In immune cells, copper-induced death genes were strongly expressed in “activated” dendritic cells (aDCs), macrophages and regulatory T cells (Treg). In immune functions, copper-induced death genes were strongly expressed in major histocompatibility complex (MHC) class I, human leukocyte antigen (HLA) and type I interferon (IFN) response. Correlation analysis showed that 5 genes including SLC31A1 , PDHA1 , DLD , ATP7B , and ATP7A were significantly correlated with immune infiltration. The nomogram suggested that the low expression of PDHA1 was significant for predicting the risk of pSS and the area under curve was 0.678. Drug model suggested that “Bathocuproine disulfonate CTD 00001350,” “Vitinoin CTD 00007069,” and “Resveratrol CTD 00002483” were the drugs most strongly associated with copper-induced death genes. In summary, copper-induced death genes are associated with SGs injury in pSS, which is worthy of clinicians’ attention.

In this article, primal-dual interior-point methods (IPMs) for second-order cone optimization (SOCO) based on the generalized trigonometric barrier function are studied. Furthermore, we derive the iteration bounds of large- and small-update IPMs for SOCO.

Background: Primary Sojgren's syndrome (pSS) is known as autoimmune disease of endocrine system. This study aimed to identify potential biomarkers for pSS using integrated bioinformatics analysis and explore the relationship between differentially expressed genes (DEGs) and immune infiltration. Methods: Three pSS datasets (GSE7451, GSE23117 and GSE40611) from the Gene Expression Omnibus (GEO) database were integrated. All the datasets were processed by affy in R (version 4.0.3).Results: A total of 16 immune cells and 13 immune functions infiltration scores were obtained. The top immune cell and immune function were "activated" dendritic cells (aDCs) and major histocompatibility complex (MHC) class I. Correlation analysis showed the top correlation among 16 immune cells were B cells and tumor infiltrating lymphocytes (TIL), check-point and T cell co-stimulation, respectively. In comparisons of immune score, aDCs (0.657 vs 0.594, P < 0.001), B cells (0.492 vs 0.434, P = 0.004), macrophages (0.631 vs 0.601, P = 0.010), inflammation-promoting (0.545 vs 0.478, P < 0.001), Type I interferon (IFN) Reponse (0.728 vs 0.625, P < 0.001) and so on were higher in pSS than control group. In correlation analysis, the up-regulation of IFIT1 gene was strongly correlated with Type I IFN Reponse with a correlation coefficient of 0.87. The ROC curve of 5 genes showed that the area under curve (AUC) was 0.891. In the verification model, the AUC was 0.881. In addition, DO analysis supported the association between DEGs and pSS. Conclusions: In summary, pSS has a variety of DEGs in immune infiltration, which is worthy of the attention from clinicians.