Model of gene transcription including the return of a RNA polymerase to the beginning of a transcriptional cycle Vladimir P. Zhdanov* PHYSICAL REVIEW E 80, (2009)

Outline  Preliminary  Introduction  Model of Gene Transcription  Experimental Results  Conclusion

Preliminary  Central dogma of molecular biology

Preliminary DNA->RNA  Gene Transcription: DNA->RNA Initiation Elongation Termination

Introduction  Regulation of Gene expression  DNA-binding Protein may facilitate or suppress the Transcription initiation

Introduction  What happens at end of transcriptional cycle?  RNAP diffuse along DNA  RNAP disassociate from DNA  RNAP start Transcription cycle again  A kinetic model of gene transcription  Include the return of RNAP to a transcription cycle  Show transcriptional burst

Model of Gene Transcription  Conventional Scheme:

Model of Gene Transcription  Conventional Scheme:  probability that the gene is in the P ⋆ 1 state:  Steady-state probability that the gene is in the P ⋆ 1 state:  Transcription Rate :

Model of Gene Transcription  Conventional Scheme + Diffusion:

Model of Gene Transcription  Conventional Scheme + Diffusion:  probabilities of P ⋆ 1, P * 1, P * 2, P ⋆ 2 state: Steady-state

Model of Gene Transcription  Conventional Scheme + Diffusion:  Transcription Rate :  With saturation Transcription rate:

Model of Gene Transcription  Conventional Scheme + Diffusion:  Transcription Rate : 

Model of Gene Transcription  Transcription Burst  The probability that RNAP produces n RNA after association is given by:

Model of Gene Transcription

Experimental Results burst Diffusion Without Diffusion

Experimental Results

diffusion jumps rate  = 100 s -1

Experimental Results diffusion jumps rate  = 200 s -1

Experimental Results diffusion jumps rate  = 500 s -1

Experimental Results?

Conclusion  Analyze the end of transcription cycle.  Transcriptional burst might occur without regulation of transcription by DNA-binding protein.