群体适应性进化、化疗耐药与多种抗癌疗法
Populational adaptive evolution, chemotherapeutic resistance and multiple anti-cancer therapies
摘要：
对化疗，特别是抗癌治疗的抗性是日益增加的医学问题。在癌症中起作用的许多机制中，最重要的机制之一是选择表达抗性基因或表型的肿瘤细胞。受适应性进化中突变选择理论的启发，我们提出了一个基于连续变量的模型，该变量代表影响健康和肿瘤细胞出生/死亡率的抗性基因（或基因，产生表型）的表达水平，化疗（细胞毒性和细胞抑制）和突变的影响。我们扩展了以前的工作，展示了如何定性不同的化疗和细胞生长抑制治疗的行动可能会引起不同程度的阻力。我们研究的数学兴趣是在黏性解框架下的约束Hamilton-Jacobi方程的形式。我们得出的长期时间动态的最适合的性状在政权的小突变。在适应性癌症管理的背景下，我们还分析了最佳药物水平是否优于最大耐受剂量。
英文摘要：
Resistance to chemotherapies, particularly to anticancer treatments, is an increasing medical concern. Among the many mechanisms at work in cancers, one of the most important is the selection of tumor cells expressing resistance genes or phenotypes. Motivated by the theory of mutation-selection in adaptive evolution, we propose a model based on a continuous variable that represents the expression level of a resistance gene (or genes, yielding a phenotype) influencing in healthy and tumor cells birth/death rates, effects of chemotherapies (both cytotoxic and cytostatic) and mutations. We extend previous work by demonstrating how qualitatively different actions of chemotherapeutic and cytostatic treatments may induce different levels of resistance. The mathematical interest of our study is in the formalism of constrained Hamilton-Jacobi equations in the framework of viscosity solutions. We derive the long-term temporal dynamics of the fittest traits in the regime of small mutations. In the context of adaptive cancer management, we also analyse whether an optimal drug level is better than the maximal tolerated dose.
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