Exact solution of a two-type branching process: models of tumor progression
Exact solution of a two-type branching process: models of tumor progression
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DOI：
10.1088/1742-5468/2011/08/p08018
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发表时间：
2011-08-01
影响因子：
2.4
通讯作者：
Krapivsky, P. L.
中科院分区：
文献类型：
--
作者：
Antal, Tibor;Krapivsky, P. L.
给出了一类具有单向变异的一般两型生灭分枝过程的显式解。这种连续的时间过程模拟了对治疗的耐药性的演变，或肿瘤进展期间额外驱动突变的发生。我们得到了该过程在任意时刻的精确母函数，并导出了各种大时间标度极限。在同时发生小突变率和大时间尺度的限制下，突变细胞的分布出现了一些非典型的性质，包括幂律尾部和发散平均。
An explicit solution for a general two-type birth-death branching process with one-way mutation is presented. This continuous time process mimics the evolution of resistance to treatment, or the onset of an extra driver mutation during tumor progression. We obtain the exact generating function of the process at arbitrary times, and derive various large time scaling limits. In the limit of simultaneous small mutation rate and large time scaling, the distribution of the mutant cells develops some atypical properties, including a power law tail and diverging average.