Noise is an important aspect of gene expression, and understanding the functional significance of the noise remains an important goal in systems biology. Theoretical models of gene expression are often based on the Master Equation (ME), but solving the ME is very challenging
and exact solutions exist for only a handful of systems. I will present the full analytical solution for the class MEs where the creation and degradation rates can be arbitrary functions, as long as they do not depend directly on the state of the ME. In particular, the solution applies to mixture models: MEs where the rates themselves are stochastic processes. I will derive the Poisson-Jacobi model, which is easy to interpret biologically and provides excellent fits to single-cell RT-qPCR
data, genome-wide single-cell RNA-Seq data and fluorescent protein time-series data. Finally, I will show some ways in which we can use the solution of the separable ME and the Poisson-Jacobi model to help deduce information about the system.
