Ancliff Mark, Park Jeong-Man
Department of Physics, The Catholic University of Korea, Bucheon 420-743, Korea.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jun;89(6):062702. doi: 10.1103/PhysRevE.89.062702. Epub 2014 Jun 3.
We present and solve the dynamics of a model for gene duplication showing escape from adaptive conflict. We use a Crow-Kimura quasispecies model of evolution where the fitness landscape is a function of Hamming distances from two reference sequences, which are assumed to optimize two different gene functions, to describe the dynamics of a mixed population of individuals with single and double copies of a pleiotropic gene. The evolution equations are solved through a spin coherent state path integral, and we find two phases: one is an escape from an adaptive conflict phase, where each copy of a duplicated gene evolves toward subfunctionalization, and the other is a duplication loss of function phase, where one copy maintains its pleiotropic form and the other copy undergoes neutral mutation. The phase is determined by a competition between the fitness benefits of subfunctionalization and the greater mutational load associated with maintaining two gene copies. In the escape phase, we find a dynamics of an initial population of single gene sequences only which escape adaptive conflict through gene duplication and find that there are two time regimes: until a time t single gene sequences dominate, and after t double gene sequences outgrow single gene sequences. The time t is identified as the time necessary for subfunctionalization to evolve and spread throughout the double gene sequences, and we show that there is an optimum mutation rate which minimizes this time scale.
我们提出并求解了一个显示摆脱适应性冲突的基因复制模型的动力学。我们使用一种Crow-Kimura准物种进化模型，其中适应度景观是与两个参考序列的汉明距离的函数，这两个参考序列被假定优化两种不同的基因功能，以描述具有多效性基因单拷贝和双拷贝的个体混合群体的动力学。通过自旋相干态路径积分求解进化方程，我们发现两个阶段：一个是摆脱适应性冲突阶段，其中复制基因的每个拷贝朝着亚功能化进化，另一个是复制功能丧失阶段，其中一个拷贝保持其多效性形式，另一个拷贝经历中性突变。该阶段由亚功能化的适应度益处与维持两个基因拷贝相关的更大突变负荷之间的竞争决定。在逃逸阶段，我们发现仅由单基因序列组成的初始群体的动力学，其通过基因复制摆脱适应性冲突，并发现存在两个时间阶段：直到时间t单基因序列占主导，以及在t之后双基因序列超过单基因序列。时间t被确定为亚功能化进化并在双基因序列中传播所需的时间，并且我们表明存在一个最优突变率，该突变率使这个时间尺度最小化。
