Quantifying the importance of pMHC valency, total pMHC dose and frequency on nanoparticle therapeutic efficacy

Nanoparticles (NPs) coated with β‐cell‐specific peptide major histocompatibility complex (pMHC) class I molecules can effectively restore normoglycemia in spontaneously diabetic nonobese diabetic mice. They do so by expanding pools of cognate memory autoreactive regulatory CD8+ T cells that arise from naive low‐avidity T‐cell precursors to therapeutic levels. Here we develop our previously constructed mathematical model to explore the effects of compound design parameters (NP dose and pMHC valency) on therapeutic efficacy with the underlying hypothesis that the functional correlates of the therapeutic response (expansion of autoregulatory T cells and deletion of autoantigen‐loaded antigen‐presenting cells by these T cells) are biphasic. We show, using bifurcation analysis, that the model exhibits a ‘resonance’‐like behavior for a given range of NP dose in which bistability between the healthy state (possessing zero level of effector T‐cell population) and autoimmune state (possessing elevated level of the same population) disappears. A heterogeneous population of model mice subjected to several treatment protocols under these new conditions is conducted to quantify both the average percentage of autoregulatory T cells in responsive and nonresponsive model mice, and the average valency‐dependent minimal optimal dose needed for effective therapy. Our results reveal that a moderate increase (⩾1.6‐fold) in the NP‐dependent expansion rate of autoregulatory T‐cell population leads to a significant increase in the efficacy and the area corresponding to the effective treatment regimen, provided that NP dose ⩾8 μg. We expect the model developed here to generalize to other autoimmune diseases and serve as a computational tool to understand and optimize pMHC–NP‐based therapies.