Mathematical model of the chronic stage of SLE including the complement protein C1q

Systemic Lupus Erythematosus is a chronic autoimmune disease which exhibits complex pathogenesis and unpredictable course, making diagnosis and treatment particularly challenging. Understanding the dynamic interactions among the key components of the immune response is therefore of great importance. In this context, mathematical modeling is a powerful tool for investigating the disease progression and possibly the development of more effective therapy. We present a model for the chronic phase of SLE that incorporates interactions between T and B lymphocytes, dendritic cells in the role of antigen presenting cells, autoantigen, antibody, pro- and anti-inflammatory factors. What makes the model unique is the inclusion of the C1q complement protein and the immune complexes it forms. We examine whether and when periodic behaviour corresponding to the peaks and troughs typical of SLE (lupus flares) is observed. The results from the numerical experiments show that the presence of dendritic cells is essential for the existence of periodic dynamics. The model also suggests that that fluctuations in the C1q concentration that are characteristic for SLE patients may not be dependent on a reduced production of C1q in the organism.