Mori Ludovico, Ben Amar Martine
Laboratoire de Physique de l'Ecole Normale Supérieure, Ecole Normale Supérieure, Université PSL, CNRS, 75005 Paris, France.
Institut Universitaire de Cancérologie, Faculté de Médecine, Sorbonne Université, 91 Bd de l'Hôpital, 75013 Paris, France.
Cancers (Basel). 2023 Jan 21;15(3):677. doi: 10.3390/cancers15030677.
The Cancer Stem Model allows for a dynamical description of cancer colonies which accounts for the existence of different families of cells, namely stem cells, highly proliferating and quasi-immortal, and differentiated cells, both undergoing cellular processes under numerous activated pathways. In the present work, we investigate a dynamical model numerically, as a system of coupled differential equations, and include a plasticity mechanism, of differentiated cells turning into a stem state if the stem concentration drops low. We are particularly interested in the stability of the model once we introduce stochastically evolving parameters, associated with environmental and cellular intrinsic variabilities, as well as the response of the model after introducing a drug therapy. As long as we stay within the characteristic time scale of the system, defined on the base of the needed time for the trajectories to converge on stable states, we observe that the system remains stable for the main parameters evolving stochastically according to white noise. As for the drug treatments, we discuss a model both for the kinetics and the dynamics of the substance in the organism, and then consider the impact of different types of therapies in a few particular examples, outlining some interesting mechanisms, such as the tumor growth paradox, that possibly impact the outcome of therapy significantly.
癌症干细胞模型允许对癌集落进行动态描述，该描述考虑了不同细胞家族的存在，即高度增殖且近乎永生的干细胞以及分化细胞，这两类细胞都在众多激活途径下经历细胞过程。在本工作中，我们将一个动态模型作为耦合微分方程组进行数值研究，并纳入一种可塑性机制，即如果干细胞浓度降至很低，分化细胞会转变为干细胞状态。一旦我们引入与环境和细胞内在变异性相关的随机演化参数，以及引入药物治疗后模型的响应，我们就特别关注模型的稳定性。只要我们保持在系统的特征时间尺度内（该时间尺度基于轨迹收敛到稳定状态所需的时间来定义），我们就会观察到，对于根据白噪声随机演化的主要参数，系统保持稳定。至于药物治疗，我们讨论了一个关于药物在生物体中的动力学和动态的模型，然后在几个具体例子中考虑不同类型治疗的影响，概述了一些有趣的机制，如肿瘤生长悖论，这些机制可能会显著影响治疗结果。
