Abstract
We introduce a set of ordinary differential equations (ODEs) that qualitatively reproduce delayed responses observed in immune checkpoint blockade therapy (e.g. anti-CTLA-4 ipilimumab). This type of immunotherapy has been at the forefront of novel and promising cancer treatments over the past decade and was recognised by the 2018 Nobel Prize in Medicine. Our model describes the competition between effector T cells and non-effector T cells in a tumour. By calibrating a small subset of parameters that control immune checkpoint expression along with the patient’s immune-system cancer readiness, our model is able to simulate either a complete absence of patient response to treatment, a quick anti-tumour T cell response (within days) or a delayed response (within months). Notably, the parameter space that generates a delayed response is thin and must be carefully calibrated, reflecting the observation that a small subset of patients experience such reactions to checkpoint blockade therapies. Finally, simulations predict that the anti-tumour T cell storm that breaks the delay is very short-lived compared to the length of time the cancer is able to stay suppressed. This suggests the tumour may subsist off an environment hostile to effector T cells; however, these cells are—at rare times—able to break through the tumour immunosuppressive defences to neutralise the tumour for a prolonged period. Our simulations aim to qualitatively describe the delayed response phenomenon without making precise fits to particular datasets, which are limited. It is our hope that our foundational model will stimulate further interest within the immunology modelling field.
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Data Availability
We reference one dataset belonging to a 2009 paper by J. D. Wolchok.
Code Availability
C. Y. Zheng used Python 3.6 from the Anaconda distribution for all simulations.
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Acknowledgements
This scientific work was supported by the Australian Postgraduate Award (CYZ) and the Australian Research Council Discovery Project DP180101512 (PSK). We thank Peter P. Lee (Beckman Research Institute, City of Hope, California, USA) for his guidance and insights on immune checkpoint blockades.
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This scientific work was supported by the Australian Postgraduate Award (CYZ) and the Australian Research Council Discovery Project DP180101512 (PSK).
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PSK is CYZ’s PhD supervisor. We also thank Peter P. Lee (Beckman Research Institute, City of Hope, California, USA) for his guidance and insights on immune checkpoint blockades.
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Zheng, C.Y., Kim, P.S. Mathematical Model for Delayed Responses in Immune Checkpoint Blockades. Bull Math Biol 83, 106 (2021). https://doi.org/10.1007/s11538-021-00933-0
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DOI: https://doi.org/10.1007/s11538-021-00933-0