发表机构
The Chinese University of Hong Kong, Shenzhen; University of Minnesota, Twin Cities（香港中文大学（深圳）; 明尼苏达大学双城分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过多类型分支过程模型，揭示突变顺序和选择如何共同决定肿瘤演化中的瘤内异质性，并推导出辛普森指数的闭式表达式，阐明驱动因子获得时间对克隆集中度的关键影响。
AI 中文摘要
癌症进展通常需要多个驱动突变，但相同的驱动因子可能以不同的顺序被获得。这些通路如何共同塑造肿瘤克隆结构仍不清楚。我们开发了一个多类型分支过程模型，其中恶性转化需要两个驱动突变，通过突变顺序和建立其克隆的独立转化事件来区分恶性细胞。在连续指数近似下，我们建立了通路特异性克隆大小的点过程极限，并推导了联合恶性群体限制性期望辛普森指数的闭式表达式。当两种突变顺序产生的恶性细胞具有相同的净增长率时，该指数分解为有效通路权重（由突变率和前阶段的出生-死亡动态决定）和通路内集中度项（由中间态到恶性生长率比率决定）。因此，驱动因子对异质性的影响关键取决于其获得时间。早期获得的强驱动因子扩增中间谱系并增加独立恶性创始细胞的供应，而相同的驱动因子最后获得则增强早期建立的恶性克隆的生长和年龄优势。在加性适应度效应下，这些相反机制可产生选择优势与克隆集中度之间的非单调关系。阈值样非加性适应度效应可生成高度集中的恶性群体，而顺序依赖的终端适应度导致生长更快的通路在渐近上占主导。这些结果展示了突变顺序、突变可及性、选择和上位性如何共同决定谱系水平的瘤内异质性。
英文摘要
Cancer progression often requires multiple driver mutations, but the same drivers may be acquired in different orders. How these pathways jointly shape tumor clonal structure remains unclear. We develop a multitype branching-process model in which malignant transformation requires two driver mutations, distinguishing malignant cells by mutation order and the independent transformation event that founded their clone. Under a successive exponential approximation, we establish point-process limits for pathway-specific clone sizes and derive a closed-form expression for the limiting expected Simpson's index of the combined malignant population. When both mutation orders yield malignant cells with the same net growth rate, the index decomposes into effective pathway weights, determined by mutation rates and birth-death dynamics at preceding stages, and within-pathway concentration terms, determined by intermediate-to-malignant growth-rate ratios. A driver's effect on heterogeneity thus depends critically on when it is acquired. A strong driver acquired early expands the intermediate lineage and increases the supply of independent malignant founders, whereas the same driver acquired last strengthens the growth and age advantage of early-founded malignant clones. Under additive fitness effects, these opposing mechanisms can produce a non-monotone relationship between selective advantage and clonal concentration. Threshold-like non-additive fitness effects can generate highly concentrated malignant populations, while order-dependent terminal fitness causes the faster-growing pathway to dominate asymptotically. These results show how mutation order, mutational accessibility, selection, and epistasis jointly determine lineage-level intratumor heterogeneity.
