Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland.
Faculty of Electronics, Wrocław University of Science and Technology, Wrocław, Poland.
PLoS Comput Biol. 2020 Oct 2;16(10):e1008056. doi: 10.1371/journal.pcbi.1008056. eCollection 2020 Oct.
Metastases are the main reason for cancer-related deaths. Initiation of metastases, where newly seeded tumor cells expand into colonies, presents a tremendous bottleneck to metastasis formation. Despite its importance, a quantitative description of metastasis initiation and its clinical implications is lacking. Here, we set theoretical grounds for the metastatic bottleneck with a simple stochastic model. The model assumes that the proliferation-to-death rate ratio for the initiating metastatic cells increases when they are surrounded by more of their kind. For a total of 159,191 patients across 13 cancer types, we found that a single cell has an extremely low median probability of successful seeding of the order of 10-8. With increasing colony size, a sharp transition from very unlikely to very likely successful metastasis initiation occurs. The median metastatic bottleneck, defined as the critical colony size that marks this transition, was between 10 and 21 cells. We derived the probability of metastasis occurrence and patient outcome based on primary tumor size at diagnosis and tumor type. The model predicts that the efficacy of patient treatment depends on the primary tumor size but even more so on the severity of the metastatic bottleneck, which is estimated to largely vary between patients. We find that medical interventions aiming at tightening the bottleneck, such as immunotherapy, can be much more efficient than therapies that decrease overall tumor burden, such as chemotherapy.
转移是癌症相关死亡的主要原因。转移的启动，即新播种的肿瘤细胞扩展成 colonies，是转移形成的巨大瓶颈。尽管它很重要，但对转移启动的定量描述及其临床意义仍缺乏了解。在这里，我们用一个简单的随机模型为转移瓶颈提供了理论依据。该模型假设，当起始转移细胞周围有更多同种细胞时，其增殖-死亡比率会增加。对于 13 种癌症类型的总共 159191 名患者，我们发现单个细胞成功播种的中位数概率极低，约为 10-8。随着 colony 大小的增加，从极不可能到极有可能成功转移启动的 sharp transition 会发生。定义为标志这一转变的关键 colony 大小的中位数转移瓶颈在 10 到 21 个细胞之间。我们根据原发性肿瘤大小和肿瘤类型推导了转移发生和患者预后的概率。该模型预测，患者治疗的效果取决于原发性肿瘤的大小，但更取决于转移瓶颈的严重程度，这在患者之间估计差异很大。我们发现，旨在收紧瓶颈的医疗干预措施，如免疫疗法，可能比减少整体肿瘤负担的疗法（如化疗）更有效。
