肿瘤内异质性时空演变的统计力学理论：多区域测序数据分析
Statistical Mechanical theory for spatio-temporal evolution of Intra-tumor heterogeneity in cancers: Analysis of Multiregion sequencing data
摘要：
从一个区域（亚群）到另一个区域（亚群）的异质性特征，通常在复杂系统中观察到，例如玻璃和细胞集合，很难在理论上描述。在癌症的背景下，肿瘤内异质性（ITH），其特征在于具有遗传和表型变异性的细胞共存于单个肿瘤内，通常是无效治疗和癌症复发的原因。通过对单个肿瘤的多个区域进行采样而获得的多区域测序（M-Seq）已经生动地证明了ITH的普遍性质，从而提出了对解释肿瘤异质性演变的理论的需要。在这里，我们开发了一种统计力学理论来量化ITH，使用汉明距离，在单个肿瘤内不同区域的基因突变之间。ITH的解析表达式，表示在细胞分裂概率（$α$）和突变概率（$p$），验证使用细胞自动机类型的模拟。该理论的应用成功地捕获了从外源性癌症（黑色素瘤和肺癌）患者的M-seq数据中提取的ITH。该理论基于肿瘤早期阶段的间断进化，随后是中性进化，只要肿瘤突变负荷的空间变化不大，该理论是准确的。我们发现，在单个实体瘤的不同区域中，ITH存在实质性变化，这支持了不同亚克隆可以共存的观点。模拟结果表明，有很大的变化，在子种群，与ITH增加的区域之间的距离增加。这里开发的分析和模拟框架可用于实验（M-Seq）数据的定量分析。更广泛地说，我们的理论可能是有用的，在分析动态异质性复杂系统，如过冷液体。
英文摘要：
Heterogeneity in characteristics from one region (sub-population) to another, commonly observed in complex systems, such as glasses and a collection of cells, is hard to describe theoretically. In the context of cancer, intra-tumor heterogeneity (ITH), characterized by cells with genetic and phenotypic variability that co-exist within a single tumor, is often the cause of ineffective therapy and recurrence of cancer. Multi-region sequencing (M-Seq), obtained by sampling multiple regions of a single tumor, has vividly demonstrated the pervasive nature of ITH, raising the need for a theory that accounts for evolution of tumor heterogeneity. Here, we develop a statistical mechanical theory to quantify ITH, using the Hamming distance, between genetic mutations in distinct regions within a single tumor. An analytic expression for ITH, expressed in terms of cell division probability ($α$) and mutation probability ($p$), is validated using cellular-automaton type simulations. Application of the theory successfully captures ITH extracted from M-seq data in patients with exogenous cancers (melanoma and lung). The theory, based on punctuated evolution at the early stages of the tumor followed by neutral evolution, is accurate provided the spatial variation in the tumor mutation burden is not large. We show that there are substantial variations in ITH in distinct regions of a single solid tumor, which supports the notion that distinct subclones could co-exist. The simulations show that there are substantial variations in the sub-populations, with the ITH increasing as the distance between the regions increases. The analytical and simulation framework developed here could be used in the quantitative analyses of the experimental (M-Seq) data. More broadly, our theory is likely to be useful in analyzing dynamic heterogeneity in complex systems such as super-cooled liquids.
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