SUPA, School of Physics and Astronomy, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom.
Program for Evolutionary Dynamics, Harvard University, One Brattle Square, Cambridge, Massachusetts, USA.
Sci Rep. 2016 Dec 22;6:39511. doi: 10.1038/srep39511.
One of the hallmarks of cancer is the accumulation of driver mutations which increase the net reproductive rate of cancer cells and allow them to spread. This process has been studied in mathematical models of well mixed populations, and in computer simulations of three-dimensional spatial models. But the computational complexity of these more realistic, spatial models makes it difficult to simulate realistically large and clinically detectable solid tumours. Here we describe an exactly solvable mathematical model of a tumour featuring replication, mutation and local migration of cancer cells. The model predicts a quasi-exponential growth of large tumours, even if different fragments of the tumour grow sub-exponentially due to nutrient and space limitations. The model reproduces clinically observed tumour growth times using biologically plausible rates for cell birth, death, and migration rates. We also show that the expected number of accumulated driver mutations increases exponentially in time if the average fitness gain per driver is constant, and that it reaches a plateau if the gains decrease over time. We discuss the realism of the underlying assumptions and possible extensions of the model.
癌症的一个标志是积累了驱动突变，这些突变增加了癌细胞的净繁殖率，并使它们能够扩散。这个过程已经在充分混合种群的数学模型和三维空间模型的计算机模拟中进行了研究。但是，这些更现实的空间模型的计算复杂性使得很难对实际的大型和临床可检测的实体瘤进行真实模拟。在这里，我们描述了一个具有复制、突变和癌细胞局部迁移特征的肿瘤的精确可解数学模型。该模型预测了大型肿瘤的准指数增长，即使由于营养和空间限制，肿瘤的不同片段呈亚指数增长。该模型使用细胞出生、死亡和迁移率的生物学上合理的速率来重现临床上观察到的肿瘤生长时间。我们还表明，如果每个驱动突变的平均适应度增益是常数，那么积累的驱动突变的预期数量会随时间呈指数增长，如果增益随时间减少，则会达到一个平台。我们讨论了基本假设的现实性和模型的可能扩展。
