In the name of GOD

1. In the name of GOD

2. Zeinab Mokhtari 06-Jan-2010

3. Macromolecules 06-Jan-2010

4. DNA a lattice-like macromolecule : such as a nucleic acid or a carbohydrate 06-Jan-2010

5. Binding number Macromolecules N : potential binding sites per macromolecule governers of the behavior of the system l : the length of the ligand Thermodynamic parameters(k , H, …) The number of ligand molecules bound per macromolecule 06-Jan-2010

6. Scatchard plot ν versus [L] : hyperbolic representation, requires nonlinear regression analysis Scatchard plot is a transformed representation. v /[L] as a function of ν N equivalent and independent binding sites and a ligand with size l = 1 a linear plot Several classes of binding sites, or interacting binding sites, or a ligand with size l > 1 a curved plot 06-Jan-2010

7. McGhee and von Hippel Valid for infinite homogeneous lattices with: any ligand size, l any ligand dissociation constant, k any level of cooperativity interaction between ligands bound contiguously,ω Extensions of this theory for : finite lattices heterogeneous systems ( the binding sites are not homogeneously distributed throughout the macromolecule) different classes of binding sites present in the macromolecule different ligand binding modes a mixture of different ligands 06-Jan-2010

8. Case I : non-cooperative (independent) ligand binding Case II : cooperative ligand binding 06-Jan-2010

9. ITC : Isothermal titration calorimetry An excellent tool for studying biomolecular reactions The heat associated with a binding process is measured. Injections of a ligand solution from a computer-controlled syringe into a macromolecule solution placed in a thermostatized cell. 06-Jan-2010

10. The syringe rotates in place during the ITC experiment. The end of the syringe has been adapted to provide continuous mixing in the ITC cell. The plunger is computer-controlled and injects precise volumes of ligand. The total concentration of each reactant in the cell after injection i : 06-Jan-2010

11. Case I Case I Lineal lattice-like macromolecule with noncooperative ligand binding: macromolecule with N equivalent and independent binding sites and ligand size l ≥ 1 06-Jan-2010

12. Case I linear in ν only if l = 1 As binding proceeds to saturation, it is more difficult to find l free consecutive binding sites when l is large. Then, the larger the ligand size l, the larger such effect. an (l + 1)-order polynomial equation A nonlinear regression : the optimal values of N, l, k, and H from the experimental data. 06-Jan-2010

13. Case I The larger the ligand size, the larger the difference between the apparent and the actual maximal binding numbers. N = 100 l = 3 l > 1 : entropic resistance to saturation Therefore, if the data analysis is performed with a model for a ligand with size l = 1, then, both the maximal binding number and the binding affinity will be estimated with a significant error. Fig. 1. Simulated calorimetric titration 06-Jan-2010

14. Case I N = 100 l = 1 N/l = 100 N = 200 l = 2 N = 1000 l = 10 The ratio N/l does not define univocally the geometric features of the system but also that the values of N and l by themselves are important. Therefore, fixing N to different values in the fitting procedure will give different sets of estimated thermodynamic parameters. Fig. 2. Effect of the ligand size on the calorimetric titration 06-Jan-2010

15. Case II Case II Lineal lattice-like macromolecule with cooperative ligand binding: macromolecule with N equivalent and dependent binding sites and ligand size l ≥ 1 06-Jan-2010

16. Case II an (l + 3)-order polynomial equation 06-Jan-2010

17. 1 ≤ω < ∞ Positive cooperativity ω = 1 No cooperation Negativecooperativity 0 ≤ω < 1 Case II It is obvious that at a given value of the ligand size l, there will be a value of the interaction parameter ω that almost compensates the negative entropic effect from l, resulting in a nearly linear plot. Difficult discriminating between different situations ITC allows discriminating between different cases. Interaction between bound ligands : an additional contribution to the overall enthalpy of binding (The interaction or cooperativity enthalpy h) 06-Jan-2010

18. Case II h : the enthalpy associated with the interaction of nearest neighbor bound ligands νisol : the partial number of ligand molecules bound isolated νsc : the partial number of ligand molecules bound with only one nearest neighbor (singly contiguous) νdc : the partial number of ligand molecules bound with two nearest neighbors (doubly contiguous) 06-Jan-2010

19. Case II 06-Jan-2010

20. Case II N = 100 l = 4 cooperativity parameter : ω = 0 (dashed-dotted line) ω = 0.1 (dotted line) ω = 1 (continuous line) ω = 10 (dashed line) Fig. 5. Effect of the cooperativity parameter on the evolution of the partial binding numbers along the titration 06-Jan-2010

21. Case II + 0 - h ω < 1 ω > 1 Fig. 6. Effect of the interaction enthalpy on the calorimetric titration 06-Jan-2010

22. Case II + 0 h direct reverse Fig. 7. Comparison between direct titrations (L into M) and reverse titrations (M into L). 06-Jan-2010

23. Thanks

24. A day without laughter is a day wasted. Charlie Chaplin