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Models for Molecular Events

Models for Molecular Events. Receptor Ligand Binding. Definitions. Dimer: a molecule which consists of two similar (but not necessarily identical) subunits Homodimer: A dimeric protein made of paired identical subunits Heterodimer: a dimer in which the two subunits are different

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Models for Molecular Events

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  1. Models for Molecular Events Receptor Ligand Binding

  2. Definitions • Dimer: a molecule which consists of two similar (but not necessarily identical) subunits • Homodimer: A dimeric protein made of paired identical subunits • Heterodimer: a dimer in which the two subunits are different • Both receptors and ligands can be homodimers or heterodimers • Dimeric ligands can dimerize (bring together) monomeric receptors

  3. Homodimeric Receptor-Ligand Binding • Consider the following schematic diagram • Draw a reaction diagram that corresponds to this situation • Write down a system of equations that models this situation

  4. Full Reaction Diagram For a Homodimeric Receptor k1 k1 k2 k2 + + k-1 k-2 + +

  5. Simplified Reaction Diagram For a Homodimeric Receptor 2N + R C R + 2P k1 k1 k2 k2 + + k-1 k-1

  6. Model Equations

  7. Reduced Model Equations • p-equation is decoupled and r = r0 – c

  8. QSSA Equation

  9. Sigmoidal Kinetics kmax n

  10. Full Reaction Diagram For a Homodimeric Receptor • Under what conditions does this reduce to the simplified, sigmoid kinetics? • Note: if the receptor sites act independently and identically, then k1 = 2k2 and k-1 = 2k-2 + + k1 k1 k2 k2 k-1 k-2 + +

  11. Model Equations

  12. Model Reduction • p-equation is decoupled and r = r0 – c1 – c2

  13. QSSA

  14. Comparison ? Require:

  15. Comparison ? Require:

  16. Comparison ? Require: Interpretation: The simple sigmoid kinetics are valid if (1) there are no products produced in intermediate steps of the reaction and (2) the tendency of the second binding step to proceed forward is greater than for the first binding step.

  17. Cooperative Reactions • In other words, once a single ligand has bound, a second binds more readily. This is called a cooperative reaction. • Intermediate stages are short-lived and can almost be neglected • Example hemoglobin can bind up to four oxygen molecules

  18. Generalization • In general, for highly cooperative reactions, if “a” ligand molecules can bind to a receptor; the following holds as a good approximation for the rate of change of the ligand:

  19. Competitive Binding • Consider the following reaction diagram that corresponds to the competitive binding of two ligands to the same receptor • Write down a system of equations that models this situation k2 k1 k3 + + k-1 k-3 +

  20. Model Equations

  21. Model Reduction • p-equation is decoupled and r = r0 – c1 – c2

  22. QSSA • Define the velocity of the reaction, V = dp/dt

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