1. Dynamics of the trp Operon Refs: Sántilan & Mackey, PNAS 98 (4), 1364-69 [2001] I. Rahmim doctoral thesis, Columbia Univ., 1990 Alberts, MBOTC III, pp. 417-419, Lewin, Genes V, 435-7 AKH9

2. O v e r v i e w (Santillan)

3. Organization of the trp Operon* 5 genes code for enzymes: * Cluster of genes controlled by a single (?) feedback regulatory mechanism.

4. The five genes are transcribed as a single mRNA molecule, allowing their expression to be controlled coordinately. There is one promoter. Within the promoter is an operator. Tryptophan repressor can bind to operator and deny access to RNA polymerase. Because repressor binding stops transcription the regulation mode is called negative control.

5. Repressor Terminology

6. Activation (binding) of repressor requires binding of two tryptophan molecules:

7. Multiple RNA polymerases act together on an operon; multiple ribosomes act together on even partially formed mRNAs:

8. Attenuators… act to terminate transcription prematurely. They act before or within the coding region When they are non-functional, transcription continues past attenuation region When they are functional, termination occurs

9. Tryptophan synthesis: chorismate  l-tryptophan (the 5 enzymes that make tryptophan) trp EAnthranilate synthase Phosphoribosyl anthranilae transferase trp D trp CPhosphoribosyl isomerase/indoleglycerol phosphate synthase trp B Tryptophan synthetase  Tryptophan synthase  trp A

10. Tryptophan Operon Promoters: p1 (strong): Active repressor binds to trp operator and overlaps p1 with physical exclusion of RNA polymerase p2 (low efficiency): Within distal part of trpD, results in production of mRNAs C, B, and A. Thus, production of trp E and D is differentiated from production of trp C, B, and A. Additionally, deactivation and degradation of mRNA CBA is much slower than for mRNA ED. Just before trpE transcription is regulated through attenuation. At low tryptophan levels, reduces by 8 

11. Enzymatic Control of Tryptophan Levels: Production: Anthranilate synthase inhibited up to 100% by tryptophan. Interconversion: Tryptophanase (tna) catalyzes tryptophan- indole interconversion. Transport Control of Tryptophan levels: aro P product facilitates transport of aromatic amino acids. mtr product facilitates tryptophan transport. (mtr is activated with phenylalanine present, tryptophan absent.) Product of tyrR modulates expression of aroP and mtr. Transport dynamics have not been studied – we don’t know the transporter kinetic coefficients.

12. Goodwin’s compartmental triad in bacterial gene expression:

13. Hill Functions : F, F +, F -

14. Overall Model for trp Operon

15. About concentrations: Molecules per cell (with a 'standard' cell size). Intuitive but not usually measured. Standard chemical concentrations, e.g.  moles/ml, etc. Normal measurement. Stochasticity issues. 50 molecules per cell of volume 1  m 3 ~ 0.1  M.

16. The Effect of Cell Expansion on Concentration Expanding (dividing) cultures lose concentration even without degradation – amount in one cell is unaffected until division, and is then suddenly halved. concentration decreases steadily up to, during, and after division. Intracellular heterogeneous kinetics are affected by concentration, not amount.

17. Allowing for Volume Expansion

18. Cell Volume

19. mRNA Equations

20. Repression:

21. Intracellular Concentration* of Bound trp Repressors: __________________________________ * = molecules per cell/ (cell volume  N A )

22. Finally, for repression:

23. Attenuation

24. trp leader region: Transcription is stalled on the pause site until a ribosome arrives at base 27

25. How long does RNA polymerase take to move from the pause site to the potential termination site, i.e. what is T? How far does the ribosome travel during time T?

26. Simulation: RNA polymerase transcribes at an average rate of 42 nt/sec, but follows Poisson distribution. Ribosome adds residues at a corresponding average rate of 14/sec, but dependent on amino acid availability. Rate is maximum at high, and zero at zero, concentration. Assume tryptophan concentration controlling.

27. Monte Carlo Simulation Results:

28. Other Coefficients Needed mRNA Degradation Rates (t 1/2 values) Transcription Initiation Rates

29. Enzyme Balances

30. Biosynthesis Pathway

31. Redux: Overall Model for trp Operon