Department of Physics & Astronomy, University of Southern California, Los Angeles, California 90089-1191, USA.
Department of Aerospace & Mechanical Engineering, Mathematics, and The Ellison Institute, University of Southern California, Los Angeles, California 90089-1191, USA.
Phys Rev E. 2021 Mar;103(3-1):032408. doi: 10.1103/PhysRevE.103.032408.
Chemotherapeutic resistance via the mechanism of competitive release of resistant tumor cell subpopulations is a major problem associated with cancer treatments and one of the main causes of tumor recurrence. Often, chemoresistance is mitigated by using multidrug schedules (two or more combination therapies) that can act synergistically, additively, or antagonistically on the heterogeneous population of cells as they evolve. In this paper, we develop a three-component evolutionary game theory model to design two-drug adaptive schedules that mitigate chemoresistance and delay tumor recurrence in an evolving collection of tumor cells with two resistant subpopulations and one chemosensitive population that has a higher baseline fitness but is not resistant to either drug. Using the nonlinear replicator dynamical system with a payoff matrix of Prisoner's Dilemma (PD) type (enforcing a cost to resistance), we investigate the nonlinear dynamics of this three-component system along with an additional tumor growth model whose growth rate is a function of the fitness landscape of the tumor cell populations. A key parameter determines whether the two drugs interact synergistically, additively, or antagonistically. We show that antagonistic drug interactions generally result in slower rates of adaptation of the resistant cells than synergistic ones, making them more effective in combating the evolution of resistance. We then design evolutionary cycles (closed loops) in the three-component phase space by shaping the fitness landscape of the cell populations (i.e., altering the evolutionary stable states of the game) using appropriately designed time-dependent schedules (adaptive therapy), altering the dosages and timing of the two drugs. We describe two key bifurcations associated with our drug interaction parameter which help explain why antagonistic interactions are more effective at controlling competitive release of the resistant population than synergistic interactions in the context of an evolving tumor.
通过竞争释放耐药肿瘤细胞亚群的机制产生的化疗耐药性是与癌症治疗相关的主要问题之一，也是肿瘤复发的主要原因之一。通常，通过使用多药方案（两种或多种联合疗法）来减轻化疗耐药性，这些方案可以协同作用、相加作用或拮抗作用于细胞异质性群体，因为它们在进化。在本文中，我们开发了一个三组分进化博弈论模型，设计了两种药物适应性方案，以减轻耐药性并延迟具有两个耐药亚群和一个对两种药物均不耐药但基础适应性更高的化疗敏感群体的肿瘤细胞不断进化的肿瘤的复发。使用具有囚徒困境（PD）类型收益矩阵（对耐药性施加成本）的非线性复制者动力系统，我们研究了这个三组分系统的非线性动力学，以及一个额外的肿瘤生长模型，其增长率是肿瘤细胞群体的适应性景观的函数。一个关键参数决定了两种药物是协同作用、相加作用还是拮抗作用。我们表明，拮抗药物相互作用通常导致耐药细胞的适应速度比协同作用慢，从而使它们在对抗耐药性进化方面更有效。然后，我们通过塑造细胞群体的适应性景观（即改变博弈的进化稳定状态）来设计三组分相空间中的进化循环（封闭循环），使用适当设计的时变方案（适应性治疗）改变两种药物的剂量和时间。我们描述了与我们的药物相互作用参数相关的两个关键分岔，这有助于解释为什么在不断进化的肿瘤中，拮抗相互作用比协同相互作用更有效地控制耐药群体的竞争释放。
