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Mathematical Modeling of Networks

Mathematical Modeling of Networks. Regulatory Networks (continued). Dynamics of Reactions. Michaelis Menten Kinetics. Dynamics of Reactions. Michaelis Menten Kinetics. Dynamics of Reactions. Michaelis Menten Kinetics. Dynamics of Reactions. Michaelis Menten Kinetics.

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Mathematical Modeling of Networks

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  1. Mathematical Modeling of Networks

  2. Regulatory Networks (continued)

  3. Dynamics of Reactions • Michaelis Menten Kinetics

  4. Dynamics of Reactions • Michaelis Menten Kinetics

  5. Dynamics of Reactions • Michaelis Menten Kinetics

  6. Dynamics of Reactions • Michaelis Menten Kinetics

  7. Dynamics of Reactions • Michaelis Menten Kinetics

  8. Dynamics of Reactions • Beyond Michaelis Menten Kinetics

  9. Dynamics of Reactions

  10. Dynamics of Reactions

  11. Dynamics of Reactions

  12. What we can build with this machinery? • Genetic switches • Chemotaxis

  13. Genetic Switches • Life-cycle of a bacteriophage • A bacteriophage (from 'bacteria' and Greek φάγειν phagein "to eat") is any one of a number of viruses that infect bacteria. • Bacteriophages may have a lytic cycle or a lysogenic cycle, but a few viruses are capable of carrying out both. • With lytic phages such as the T4 phage, bacterial cells are broken open (lysed) and destroyed after immediate replication of the virion. As soon as the cell is destroyed, the new bacteriophages viruses can find new hosts. Lytic phages are the kind suitable for phage therapy.

  14. Genetic Switches • In Lysogenic cycle, the viral genome integrates with host DNA and replicates along with it fairly harmlessly. • The virus remains dormant until host conditions deteriorate, perhaps due to depletion of nutrients, then the endogenous phages (known as prophages) become active. • At this point they initiate the reproductive cycle resulting in lysis of the host cell. • As the lysogenic cycle allows the host cell to continue to survive and reproduce, the virus is reproduced in all of the cell’s offspring.

  15. Genetic Switches

  16. Genetic Switches

  17. Genetic Switches

  18. Genetic Switches

  19. Genetic Switches • The lambda repressor gene system consists of (from left to right on the chromosome): • cI gene • OR3 • OR2 • OR1 • cro gene • The lambda repressor is a dimer also known as the cI protein. It regulates the transcription of the cI protein and the Cro protein.

  20. Genetic Switches • The life cycle of lambda phages is controlled by cI and Cro proteins. The lambda phage will remain in the lysogenic state if cI proteins predominate, but will be transformed into the lytic cycle if cro proteins predominate. • The cI dimer may bind to any of three operators, OR1, OR2, and OR3, in the order OR1 = OR2 > OR3. • Binding of a cI dimer to OR1 enhances binding of a second cI dimer to OR2 • This does not increase the affinity between cI and OR3, which will be occupied only when the cI concentration is high. • In the absence of cI proteins, the cro gene may be transcribed. • In the presence of cI proteins, only the cI gene may be transcribed. • At high concentration of cI, transcriptions of both genes are repressed.

  21. Protein Structure Overview • cro; (Control of Repressor's Operator) Transcription inhibitor, binds OR3, OR2 and OR1 (affinity OR3 > OR2 = OR1) • cI; (Clear 1) Transcription inhibitor, binds OR1, OR2 and OR3 (affinity OR1 > OR2 = OR3, ie. preferentially binds OR1). Susceptible to cleavage by RecA* in cells undergoing the SOS response. • cII; (Clear 2) Transcription activator. Activates transcription from the pAQ, pRE and pI promoters. Low stability due to susceptibility to cellular HflB (FtsH) proteases (especially in healthy cells and cells undergoing the SOS response). • cIII;(Clear 3) HflB (FtsH) binding protein, protects cII from degradation by proteases. • xis; (eXcISion) excisionase and Int protein regulator, manages excision and insertion of phage genome into the host's genome. • int; (INTegration) Int protein, manages insertion of phage genome into the host's genome. In Conditions of low int concentration there is no effect. If xis is low in concentration and int high then this leads to the insertion of the phage genome. If xis and int have high (and approximately equal) concentrations this leads to the excision of phage genomes from the host's genome.

  22. Switch Control

  23. Switch Control

  24. Switch Control

  25. Switch Control

  26. Switch Control

  27. Switch Control

  28. Next Class • How do we build mathematical models?

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