Methotrexate’s effect on cells and adalimumab immunogenicity in axial spondyloarthritis: A mathematical study

Axial spondyloarthritis is a chronic inflammatory disease impacting the spine and joints. Tumour necrosis factor inhibitors, like adalimumab, are used to treat severe cases, but up to 25% of patients discontinue due to reduced effectiveness, often from emergence of anti-drug antibodies. Methotrexate, while ineffective alone in treatment, has shown potential in reducing the formation of anti-drug antibodies to the therapeutic compound, but its mechanism of action on the immune response remains unclear. The objective of the study is to develop a mathematical model that describes the impact of methotrexate in reducing the immunogenicity of adalimumab in axial spondyloarthritis. Based on mathematical models established in the literature, we formulate a system of ordinary differential equations to describe the temporal dynamics of the immune cells (T and B lymphocytes), the therapeutic compounds in the study (adalimumab and methotrexate), and TNF α . The data used to calibrate the model are sourced from previously published in vitro experiments and a clinical trial which involved 110 patients who received adalimumab alone or adalimumab in combination with methotrexate, from whom adalimumab concentration, lymphocyte counts, and antibody titres collected along five visits during the course of treatment. A computational model is used to generate virtual patient cohorts reflecting the original data and to simulate immunogenic responses to adalimumab. Simulations across 31 scenarios for the mechanism whereby methotrexate acts on the immune cell subsets, predict that methotrexate likely reduces immunogenicity by increasing apoptosis of activated T cells.