Detailed-nRNA-Model

Here I detail the SSA for a detailed model of nascent RNA (nRNA), that incorporates:

• nRNA production rate rho,
• delayed nRNA degradation at time tau ,
• on/off gene switching at rates sigma_on and sigma_off,
• hopping rate between the cell cycle stages k,
• number of cell cycle stages N_0,
• the fraction denoting the gene dosage compensation after gene replication kappa.

The output of the SSA here is the number of nRNA at some time t. Note that the gene is assumed to replicate at stage int(N/2), after which the transcription rate of each gene becomes kappa x rho. The different stages of the cell cycle pass with exponentially distributed waiting times at rate k. After cell cycle stage N (need a diagram for this) cell division occurs and the only one (random) copy of the gene remains, keeping only the nRNA that gene produced.

@Prashant: to run the simulation code see the example in Cell-cycle-example.ipynb.

Could later on incorporate an RNAp description, being produced at some rate and only removed via dilution at the binomial partitioning that occurs at cell division.