AN EVOLUTIONARY MODEL OF TUMOR CELL KINETICS AND THE EMERGENCE OF MOLECULAR HETEROGENEITY DRIVING GOMPERTZIAN GROWTH.
AN EVOLUTIONARY MODEL OF TUMOR CELL KINETICS AND THE EMERGENCE OF MOLECULAR HETEROGENEITY DRIVING GOMPERTZIAN GROWTH.
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肿瘤细胞动力学的进化模型和驱动 Gompertzian 生长的分子异质性的出现。
DOI：
10.1137/15m1044825
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Newton,PaulK
中科院分区：
文献类型：
--
作者：
West,Jeffrey;Hasnain,Zaki;Macklin,Paul;Newton,PaulK
我们描述了一个基于细胞分子的肿瘤发展的进化数学模型，该模型由随机Moran出生-死亡过程驱动。肿瘤中的细胞以数字基因组的形式携带分子信息，我们将其表示为四位数二进制字符串，用于将细胞区分为16种分子类型。二进制字符串能够经历随机点突变，在每次出生事件后传递给子细胞。二进制字符串的值决定细胞适应度，低适应度细胞（例如，0000）定义为健康表型，高适应度细胞（例如，1111）定义为恶性表型。在生-死过程的每一步，两个表型亚群在囚徒困境进化博弈中竞争，健康细胞扮演合作者的角色，而癌细胞扮演叛逃者的角色。适应度、细胞群的出生死亡率和总体肿瘤适应度通过囚徒困境收益矩阵定义。突变参数包括乘客突变（没有适应度优势的突变）和驱动突变（增加细胞适应度的突变）。该模型用于探索与肿瘤发展相关的关键突现特征，包括肿瘤生长速度，因为它与肿瘤内分子异质性有关。肿瘤生长方程表明，生长速率与细胞多样性/异质性的对数成正比。基于细胞群产生的四位数二进制序列的分布，信息论中的香农熵被用作异质性和肿瘤复杂性的定量度量。为了追踪健康细胞（0000）的初始群体异质性的发展，我们使用动态系统发育树来显示初始恶性细胞的癌细胞亚群的克隆和亚克隆扩增。我们发现肿瘤生长速率在整个肿瘤发展过程中并不是恒定的，通常在亚临床范围内比在发展后期要高得多，这导致了Gompertzian生长曲线。我们利用与细胞状态功能耦合程度相关的简单统计力学原理，解释了肿瘤的早期指数增长和后期饱和与贡柏兹曲线相关的进化模拟结果。然后，我们比较了肿瘤早期发展、中期（临床阶段）和晚期发展的剂量策略。如果在肿瘤发展的亚临床阶段早期使用，在癌细胞群被选择生长之前，治疗在破坏肿瘤发展的关键新特征方面是最有效的。
We describe a cell-molecular-based evolutionary mathematical model of tumor development driven by a stochastic Moran birth-death process. The cells in the tumor carry molecular information in the form of a numerical genome which we represent as a four-digit binary string used to differentiate cells into 16 molecular types. The binary string is able to undergo stochastic point mutations that are passed to a daughter cell after each birth event. The value of the binary string determines the cell fitness, with lower fit cells (e.g., 0000) defined as healthy phenotypes, and higher fit cells (e.g., 1111) defined as malignant phenotypes. At each step of the birth-death process, the two phenotypic subpopulations compete in a prisoner's dilemma evolutionary game with the healthy cells playing the role of cooperators, and the cancer cells playing the role of defectors. Fitness, birth-death rates of the cell populations, and overall tumor fitness are defined via the prisoner's dilemma payoff matrix. Mutation parameters include passenger mutations (mutations conferring no fitness advantage) and driver mutations (mutations which increase cell fitness). The model is used to explore key emergent features associated with tumor development, including tumor growth rates as it relates to intratumor molecular heterogeneity. The tumor growth equation states that the growth rate is proportional to the logarithm of cellular diversity/heterogeneity. The Shannon entropy from information theory is used as a quantitative measure of heterogeneity and tumor complexity based on the distribution of the four-digit binary sequences produced by the cell population. To track the development of heterogeneity from an initial population of healthy cells (0000), we use dynamic phylogenetic trees which show clonal and subclonal expansions of cancer cell subpopulations from an initial malignant cell. We show that tumor growth rates are not constant throughout tumor development and are generally much higher in the subclinical range than in later stages of development, which leads to a Gompertzian growth curve. We explain the early exponential growth of the tumor and the later saturation associated with the Gompertzian curve which results from our evolutionary simulations using simple statistical mechanics principles related to the degree of functional coupling of the cell states. We then compare dosing strategies at early stage development, midstage (clinical stage), and late-stage development of the tumor. If used early during tumor development in the subclinical stage, well before the cancer cell population is selected for growth, therapy is most effective at disrupting key emergent features of tumor development.