Quantitative Interpretation of a Genetic Model of Carcinogenesis Using Computer Simulations

The genetic model of tumorigenesis by Vogelstein et al. (V theory) and the molecular definition of cancer hallmarks by Hanahan and Weinberg (W theory) represent two of the most comprehensive and systemic understandings of cancer. Here, we develop a mathematical model that quantitatively interprets these seminal cancer theories, starting from a set of equations describing the short life cycle of an individual cell in uterine epithelium during tissue regeneration. The process of malignant transformation of an individual cell is followed and the tissue (or tumor) is described as a composite of individual cells in order to quantitatively account for intra-tumor heterogeneity. Our model describes normal tissue regeneration, malignant transformation, cancer incidence including dormant/transient tumors, and tumor evolution. Further, a novel mechanism for the initiation of metastasis resulting from substantial cell death is proposed. Finally, model simulations suggest two different mechanisms of metastatic inefficiency for aggressive and less aggressive cancer cells. Our work suggests that cellular de-differentiation is one major oncogenic pathway, a hypothesis based on a numerical description of a cell's differentiation status that can effectively and mathematically interpret some major concepts in V/W theories such as progressive transformation of normal cells, tumor evolution, and cancer hallmarks. Our model is a mathematical interpretation of cancer phenotypes that complements the well developed V/W theories based upon description of causal biological and molecular events. It is possible that further developments incorporating patient- and tissue-specific variables may build an even more comprehensive model to explain clinical observations and provide some novel insights for understanding cancer.

Vogelstein等人提出的肿瘤发生遗传模型（V theory）与Hanahan和Weinberg提出的癌症标志（cancer hallmarks）分子定义（W theory），是当前对癌症最为全面且系统的两类认知成果。本研究构建了一款数学模型，可对上述两项开创性癌症理论进行定量阐释：模型以描述组织再生过程中子宫上皮单个细胞的短生命周期的方程组为起点，追踪单个细胞的恶性转化全过程，并将组织（或肿瘤）视为单个细胞的集合体，以此实现对肿瘤内异质性（intra-tumor heterogeneity）的定量表征。该模型可覆盖正常组织再生、细胞恶性转化、包括休眠/一过性肿瘤在内的癌症发生，以及肿瘤演化等过程。此外，本研究还提出了一种由大量细胞死亡引发的转移起始新机制。最后，模型模拟结果显示，侵袭性与低侵袭性癌细胞分别存在两种不同的转移低效机制。本研究表明，细胞去分化（cellular de-differentiation）是一条主要的致癌通路（oncogenic pathway）：该假说基于细胞分化状态的数值描述，可通过数学方法有效阐释V/W理论中的多项核心概念，例如正常细胞的渐进性转化、肿瘤演化以及癌症标志。本模型是对癌症表型（cancer phenotypes）的数学阐释，可对基于因果性生物学及分子事件描述所构建的成熟V/W理论形成补充。未来若在模型中纳入患者及组织特异性变量，有望构建出更为全面的模型，以阐释临床观测结果，并为癌症认知提供全新视角。