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Therapeutic modulation of immune states is central to the treatment of human disease. However, how drugs and drug combinations impact the diverse cell types in the human immune system remains poorly understood at the transcriptome scale. Here, we apply single-cell mRNA-seq to profile the response of human immune cells to 502 immunomodulatory drugs alone and in combination. We develop a unified mathematical model that quantitatively describes the transcriptome scale response of myeloid and lymphoid cell types to individual drugs and drug combinations through a single inferred regulatory network. The mathematical model reveals how drug combinations generate novel, macrophage and T-cell states by recruiting combinations of gene expression programs through both additive and non-additive drug interactions. A simplified drug response algebra allows us to predict the continuous modulation of immune cell populations between activated, resting and hyper-inhibited states through combinatorial drug dose titrations. Our results suggest that transcriptome-scale mathematical models could enable the design of therapeutic strategies for programming the human immune system using combinations of therapeutics.