RNA splicing and the renormalization group: why simple models can effectively describe complex and noisy gene networks

The regulatory networks governing gene expression are generally both complex (many chemical species interacting in nontrivial ways) and noisy (stochastic due to both intrinsic and extrinsic factors). A longstanding open question in the physics of living systems is: to what extent is this complexity irreducible? When can these apparently complex systems be described by simple models, and why might such reductions be possible? We introduce a framework for thinking about this question in the context of stochastic gene networks, and apply it to understanding RNA splicing and transcription. In that context, the operative question is: to what extent does the topology/time scale/complexity of the dynamics in between the production of nascent RNA and the appearance of fully processed RNA impact observable features (e.g. the probability distribution) of the processed RNA? More succinctly: when do the details of the intermediate dynamics matter? Our approach, which is inspired by renormalization group ideas, also makes use of other tools familiar from field theory, including path integrals and ladder operators. We comment on some conceptual links to other approaches, e.g. information-based approaches and time scale separation arguments.