Khatri Bhavin S, Goldstein Richard A
The Francis Crick Institute, Mill Hill Laboratory, The Ridgeway, London NW7 1AA, UK; Division of Infection & Immunity, University College London, London WC1E 6BT, UK.
Division of Infection & Immunity, University College London, London WC1E 6BT, UK.
J Theor Biol. 2015 Aug 7;378:56-64. doi: 10.1016/j.jtbi.2015.04.027. Epub 2015 Apr 30.
Speciation is fundamental to understanding the huge diversity of life on Earth. Although still controversial, empirical evidence suggests that the rate of speciation is larger for smaller populations. Here, we explore a biophysical model of speciation by developing a simple coarse-grained theory of transcription factor-DNA binding and how their co-evolution in two geographically isolated lineages leads to incompatibilities. To develop a tractable analytical theory, we derive a Smoluchowski equation for the dynamics of binding energy evolution that accounts for the fact that natural selection acts on phenotypes, but variation arises from mutations in sequences; the Smoluchowski equation includes selection due to both gradients in fitness and gradients in sequence entropy, which is the logarithm of the number of sequences that correspond to a particular binding energy. This simple consideration predicts that smaller populations develop incompatibilities more quickly in the weak mutation regime; this trend arises as sequence entropy poises smaller populations closer to incompatible regions of phenotype space. These results suggest a generic coarse-grained approach to evolutionary stochastic dynamics, allowing realistic modelling at the phenotypic level.
物种形成是理解地球上生命巨大多样性的基础。尽管仍存在争议，但经验证据表明，较小种群的物种形成速率更高。在此，我们通过建立一个简单的转录因子 - DNA 结合粗粒化理论，探讨物种形成的生物物理模型，以及它们在两个地理隔离谱系中的共同进化如何导致不相容性。为了建立一个易于处理的分析理论，我们推导了一个用于结合能进化动力学的斯莫卢霍夫斯基方程，该方程考虑到自然选择作用于表型，但变异源于序列中的突变这一事实；斯莫卢霍夫斯基方程包括因适应度梯度和序列熵梯度引起的选择，序列熵是对应于特定结合能的序列数量的对数。这一简单考量预测，在弱突变 regime 中，较小种群更快地产生不相容性；这种趋势的出现是因为序列熵使较小种群更接近表型空间的不相容区域。这些结果表明了一种用于进化随机动力学的通用粗粒化方法，允许在表型水平进行现实的建模。
