Gibbs Equation: G = H - TS Second Law: G = H - S T T Entropy of the Universe?? What contributes to H?

1. Gibbs Equation: G = H - TS Second Law: G = H - S T T Entropy of the Universe?? What contributes to H? What contributes to S? Binding opposes motion. Motion opposes binding. Thermodynamics!

2. S = k lnW S = qrev T Our Mischievous Friend, Entropy Stotal = Strans + Srot + Sconf + Svib + Selec + … Sx k kT << |TS|

3. Translational and Rotational Entropy y y z z 2 x x x Gt+r = -T(Strans + Srot)

4. Conformational Entropy Gc = -TSconf

5. What about the Solvent? Must consider IMF’s between: Receptor  Drug Receptor  Solvent Drug  Solvent Complex  Solvent Solvent  Solvent Total effects can be divided into two categories: Polar interactions Hydrophobic exclusion (effect)

6. The Hydrophobic Effect Gh

7. Average Parameter Values Parameter Physical Process Value (kcal/mol) Krel Gt+r cost of bimolecular +1.3 10 association Gc cost of restricting +0.3 2 an internal rotor Gh benefit of burying 33 Å2 -0.04 1 of hydrophobic surface Gp benefit of forming an -1.1 7 ideal, neutral H-bond Gionic benefit of forming an -2.0 28 ideal, ionic H-bond G = Gt+r+ nGc+ A Gh+ Gp Williams et al. Angew. Chem. Intl. Ed.2004, 43, 6596-6616

8. Boltzmann Strikes Back Remember: G = H - S T T Hopefully, you remember: Gº = -RT lnK which is also K = e which is a specialized version of n1 no (which is the Boltzmann distribution). • Gº • RT Ei unbound E1 • Eº • RT bound E0 = e ni

9. Drug + Receptor Complex (D) (R) (C) Chemical Equilibrium • Ka = Equilibrium Association Constant • (Binding Constant) • = [C]eq • [D]eq[R]eq • Kd = Equilibrium Dissociation Constant (Ka-1) • = [D]eq[R]eq • [C]eq Ka values are not usually reported in the drug literature. Kd values are usually reported in the drug literature. • approximate concentration at half-saturation • convenient measure of a drug’s activity

10. Drug + Receptor Complex (D) (R) (C) How do we measure K? 1:1 model Initial conditions: [D]total [R]total 0 Steady state: [D]total – x [R]total – x x • We know the initial concentrations of drug and receptor. • We need a way to measure the amount of complex formed. • What are some observables? • Labeling: Advantages and Disadvantages?

11. Ka = [C]eq [D]eq[R]eq Okay, so how do we measure K? • Simplest method • If you can measure [C]eqand either [R]eq or [D]eq • then you can just solve for K. • Most common method • Fractional Occupation () = fraction of drug bound to the receptor • = [C]eq • [D]total [D]total = [D]eq + [C]eq • (known) (unknown) (observable) • = [C]eq • [C]eq+ [D]eq • = Ka[R]eq • 1 + Ka[R]eq substitute from and rearrange

12. c = Ka[R]eq 1 + Ka[R]eq ( ) [C]eq = [D]total Ka[R]eq 1 + Ka[R]eq observable known unknown Binding Isotherm What about [R]eq? Choose conditions such that [R]eq ~ [R]total

13. Receptor  Substrate Receptor + Substrate Competitive Binding Kc Receptor  Substrate + Drug Receptor  Drug + Substrate Ks Ka Receptor + Drug Receptor  Drug Receptor  Substrate + Drug Receptor  Drug + Substrate Kc = KsKa