School of Mathematics and Statistics, University of Sydney, Sydney, Australia.
Bull Math Biol. 2021 Sep 3;83(10):106. doi: 10.1007/s11538-021-00933-0.
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.
我们提出了一组常微分方程（ODE），能够定性地再现免疫检查点阻断疗法（例如抗 CTLA-4 ipilimumab）中观察到的延迟反应。这种类型的免疫疗法在过去十年中一直是新型和有前途的癌症治疗的前沿，并获得了 2018 年诺贝尔医学奖的认可。我们的模型描述了肿瘤中效应 T 细胞和非效应 T 细胞之间的竞争。通过校准一小部分控制免疫检查点表达的参数以及患者的免疫系统对癌症的准备情况，我们的模型能够模拟患者对治疗完全没有反应、快速的抗肿瘤 T 细胞反应（在几天内）或延迟反应（在几个月内）。值得注意的是，产生延迟反应的参数空间很窄，必须仔细校准，这反映了一个观察结果，即一小部分患者对检查点阻断疗法会产生这种反应。最后，模拟预测，打破延迟的抗肿瘤 T 细胞风暴的持续时间非常短暂，与癌症能够被抑制的时间长度相比。这表明肿瘤可能在一个不利于效应 T 细胞的环境中生存；然而，这些细胞有时能够突破肿瘤的免疫抑制防御，使肿瘤得到长时间的中和。我们的模拟旨在定性描述延迟反应现象，而不针对特定数据集进行精确拟合，这些数据集是有限的。我们希望我们的基础模型将激发免疫建模领域的进一步兴趣。
