Cancer is a set of genetic diseases that are driven by mutations. It was recently discovered that the temporal order of genetic mutations affects the cancer evolution and even the nature of the decease itself. The mechanistic origin of these observations, however, remain not well understood. Here we present a theoretical model for cancer initiation dynamics that allows us to quantify the impact of the temporal order of mutations. In our approach, the cancer initiation process is viewed as a set of stochastic transitions between discrete states defined by the different numbers of mutated cells. Using a first-passage analysis, probabilities and times before the cancer initiation are explicitly evaluated for two alternative sequences of two mutations. It is found that the probability of cancer initiation is determined only by the first mutation, while the dynamics depends on both mutations. In addition, it is shown that the acquisition of a mutation with higher fitness before mutation with lower fitness increases the probability of the tumor formation but delays the cancer initiation. Theoretical results are explained using effective free-energy landscapes.

癌症是一组由突变驱动的遗传疾病。最近发现，基因突变的时间顺序会影响癌症的进化甚至死亡本身的性质。然而，这些观察结果的机械起源仍然不是很清楚。在这里，我们提出了癌症起始动力学的理论模型，使我们能够量化突变时间顺序的影响。在我们的方法中，癌症起始过程被视为一组由不同数量的突变细胞定义的离散状态之间的随机转换。使用首代分析，明确评估癌症发生前的概率和时间，用于两个突变的两个替代序列。发现癌症发生的概率仅由第一个突变决定，而动态取决于两种突变。此外，研究表明，在适应度较低的突变之前获得适应度较高的突变会增加肿瘤形成的可能性，但会延迟癌症的发生。使用有效的自由能景观来解释理论结果。