Statistical Mechanics of Copy-and-Paste Dynamics

Kenji Okubo, Special Postdoctoral Researcher, Division of Fundamental Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), Japan

Our genome contains many gene copies. Each copy accumulates mutations independently, so duplicated genes are expected to diverge over time. However, in many cases, gene copies remain highly similar. This similarity is maintained by a copy-and-paste-like molecular process called gene conversion, in which sequence information from one copy is copied to another. This process is a key mechanism of concerted evolution. An important feature of gene conversion is that it depends on sequence similarity: the more similar two DNA sequences are, the more likely gene conversion occurs between them. Based on this property, we hypothesized that if gene conversion becomes sharply stronger as sequence similarity increases, the diversity among gene copies may change abruptly, like a phase transition. To test this idea and to clarify the conditions for such a transition, we constructed a statistical-mechanical model of duplicated sequences. In this model, mutation acts as diffusion in sequence space, while gene conversion acts as an attractive interaction between similar sequences. We analyzed the instability of the uniform and clustered states, calculated the transition-like points of the model, and compared the theoretical predictions with numerical simulations. In this seminar, I will introduce the basic idea and formulation of this statistical-mechanical model. I will also discuss a broader possibility: the “copy-and-paste statistical mechanics” framework may be useful not only for molecular evolution, but also for understanding transition-like phenomena in language, culture, and social systems, where modification and similarity-dependent copying are common.