1. 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, 051925 (2009)

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

3. Preliminary  Central dogma of molecular biology

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

5. Introduction  Regulation of Gene expression  DNA-binding Protein may increase or suppress the Transcription initiation rate

6. 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

7. Model of Gene Transcription  Conventional Scheme:

8. 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 :

9. 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 :

10. Model of Gene Transcription  Definition  k a : associate rate (P o ->P ⋆ 1 )  k d : disassociate rate (P o <-P ⋆ 1 )  c : RNAP concentration  k 0 : disassociate rate (P ⋆ ->P * )  k 1 : transition rate (P * 1 ->P * 2 )  k 2 : transition rate (P * 2 -> P ⋆ 1 )   : diffusion jumps rate (P ⋆ 1 P ⋆ 2 )  P : states for RNAP, p :probability … ⋆ : associated o : unbound * : elongated

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

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

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

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

15. Model of Gene Transcription

16. Experimental Results burst Diffusion Without Diffusion

17. Experimental Results

18. diffusion jumps rate  = 100 s -1

19. Experimental Results diffusion jumps rate  = 200 s -1

20. Experimental Results diffusion jumps rate  = 500 s -1

21. Experimental Results?

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