Heirene Luke A, Byrne Helen M, Yates James W T, Gaffney Eamonn A
Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, United Kingdom.
DMPK Modelling, DMPK, Preclinical Sciences, GSK, Gunnels Wood Road, Stevenage, SG1 2NY, UK.
Bull Math Biol. 2025 Aug 26;87(10):135. doi: 10.1007/s11538-025-01520-3.
Ligand-receptor interactions are fundamental to many biological processes. For example in antibody-based immunotherapies, the dynamics of an antibody binding with its target antigen directly influence the potency and efficacy of monoclonal antibody (mAb) therapies. In this paper, we present an asymptotic analysis of an ordinary differential equation (ODE) model of bivalent antibody-antigen binding in the context of mAb cancer therapies, highlighting the complexity associated with bivalency of the antibody. To understand what drives the complex temporal dynamics of bivalent antibody-antigen binding, we construct approximate solutions to the model equations at different timescales that are in good agreement with numerical simulations of the full model. We focus on two scenarios: one for which unbound antigens are abundant, and one for which they are scarce. We show how the dominant balance within the model equations changes between the two scenarios. Of particular importance to the potency and efficacy of mAb treatments are quantities such as antigen occupancy and bound antibody number. We use the results of our asymptotic analysis to estimate the long-time values of these quantities that could be combined with experimental data to facilitate parameter estimation.
配体-受体相互作用是许多生物过程的基础。例如，在基于抗体的免疫疗法中，抗体与其靶抗原结合的动力学直接影响单克隆抗体（mAb）疗法的效力和疗效。在本文中，我们对mAb癌症治疗背景下二价抗体-抗原结合的常微分方程（ODE）模型进行了渐近分析，突出了与抗体二价性相关的复杂性。为了理解驱动二价抗体-抗原结合复杂时间动态的因素，我们构建了模型方程在不同时间尺度下的近似解，这些解与完整模型的数值模拟结果高度吻合。我们关注两种情况：一种是未结合抗原丰富的情况，另一种是未结合抗原稀缺的情况。我们展示了模型方程中的主导平衡在这两种情况之间是如何变化的。对于mAb治疗的效力和疗效特别重要的是抗原占有率和结合抗体数量等数量。我们利用渐近分析的结果来估计这些数量的长期值，这些值可与实验数据相结合以促进参数估计。
