Mechanical Engineering, University College London, London, United Kingdom.
Department for Applied Mathematics, University of Strathclyde, Glasgow, United Kingdom.
PLoS One. 2021 Jul 22;16(7):e0254208. doi: 10.1371/journal.pone.0254208. eCollection 2021.
Nanoparticles have the potential to increase the efficacy of anticancer drugs whilst reducing off-target side effects. However, there remain uncertainties regarding the cellular uptake kinetics of nanoparticles which could have implications for nanoparticle design and delivery. Polymersomes are nanoparticle candidates for cancer therapy which encapsulate chemotherapy drugs. Here we develop a mathematical model to simulate the uptake of polymersomes via endocytosis, a process by which polymersomes bind to the cell surface before becoming internalised by the cell where they then break down, releasing their contents which could include chemotherapy drugs. We focus on two in vitro configurations relevant to the testing and development of cancer therapies: a well-mixed culture model and a tumour spheroid setup. Our mathematical model of the well-mixed culture model comprises a set of coupled ordinary differential equations for the unbound and bound polymersomes and associated binding dynamics. Using a singular perturbation analysis we identify an optimal number of ligands on the polymersome surface which maximises internalised polymersomes and thus intracellular chemotherapy drug concentration. In our mathematical model of the spheroid, a multiphase system of partial differential equations is developed to describe the spatial and temporal distribution of bound and unbound polymersomes via advection and diffusion, alongside oxygen, tumour growth, cell proliferation and viability. Consistent with experimental observations, the model predicts the evolution of oxygen gradients leading to a necrotic core. We investigate the impact of two different internalisation functions on spheroid growth, a constant and a bond dependent function. It was found that the constant function yields faster uptake and therefore chemotherapy delivery. We also show how various parameters, such as spheroid permeability, lead to travelling wave or steady-state solutions.
纳米粒子有提高抗癌药物疗效的潜力，同时减少非靶向副作用。然而，关于纳米粒子的细胞摄取动力学仍存在不确定性，这可能对纳米粒子的设计和输送有影响。聚合物囊泡是一种用于癌症治疗的纳米粒子候选物，它可以包裹化疗药物。在这里，我们开发了一个数学模型来模拟聚合物囊泡通过内吞作用的摄取，内吞作用是指聚合物囊泡在被细胞内化之前与细胞表面结合的过程，然后它们会分解，释放出其内容物，其中可能包括化疗药物。我们专注于两种与癌症治疗的测试和开发相关的体外配置：混合培养模型和肿瘤球体设置。我们的混合培养模型的数学模型由一组未结合和结合的聚合物囊泡以及相关的结合动力学的耦合常微分方程组成。通过奇异摄动分析，我们确定了聚合物囊泡表面上的最佳配体数量，该数量最大化了内化的聚合物囊泡，从而使细胞内化疗药物浓度最大化。在我们的球体模型中，开发了一个多相偏微分方程组来描述通过对流和扩散以及氧气、肿瘤生长、细胞增殖和活力来描述结合和未结合的聚合物囊泡的空间和时间分布。与实验观察一致，该模型预测了氧气梯度的演变，导致坏死核心。我们研究了两种不同的内化函数（常数和依赖键的函数）对球体生长的影响。结果发现，常数函数会导致更快的内化和因此更快的化疗药物输送。我们还展示了各种参数，如球体渗透性，如何导致行波或稳态解。
