1. Ligand configurational entropy and protein binding Chia-en A. Chang, Wei Chen, and Michael K. Gilson – PNAS(2007) Presented by Christopher Williams

2. Remember K*? Uses conformational entropy of side chains to better predict redesign mutations

3. What about ligands? Entropy is lost on binding How much? What kind? Do we care?

4. Configurational Entropy

5. Conformational EntropyVibrational Entropy

6. Configurational Entropy Conformational EntropyVibrational Entropy

7. Configurational Entropy Conformational EntropyVibrational Entropy Rotation/ Translation Torsion Angle Bending Bond Stretching

8. Energy Well More Wells Wider Well Higher Conformational Entropy Higher Vibrational Entropy

9. How to measure entropy S = k ln(W)  k = Boltzman constant  W = Multiplicity j

10. The test case Amprenavir, an HIV protease inhibitor

11. Results Configurational entropy loss on binding: 26.4 kcal/mol # of accessible conformations in solution: 960 # of accessible conformations bound: 1  ΔS = RT ln(960) Conformational entropy contribution: 4.1 kcal/mol

12. Results Configuational entropy loss on binding: 26.4 kcal/mol Entropy loss: torsion only: 12.2 kcal/mol Entropy loss: rotation/translation only: 15.7 kcal/mol 12.2 + 15.7 = 27.9 != 26.7 kcal/mol

14. Configurational Entropy Conformational EntropyVibrational Entropy Rotation/ Translation Torsion Angle Bending Bond Stretching There is correlation among the “separate” components of configurational entropy

15. Proof? Similar results were returned by a separate analysis  “Quasiharmonic analysis” – essentially an MD approach  Compare 11.6 kcal/ mol to 12.3 kcal/mol Cannot test in wetleb  Cannot yet measure separate components of entropy

16. Predictions and Observations Configurational entropy has a similar magnitude effect to electrostatics or hydrophobics ~25 kcal/mol  Does not include protein  Varies by ligand  Varies by tightness of binding

17. Predictions and Observations Vibrational entropy loss dominates  Not conformational/rotamer loss  This challenges conventional thinking Certain atom centers are more prone to vibrational entropy  sp3 versus ring structures

18. Applications to design Optimizing drugs  Entropy loss inhibits binding  Rigid ligands have less entropy to lose

19. Applications to design Improving Scoring Functions  Current functions overweight conformational entropy, underweight vibrational  Varies by ligand

20. Applications to design Computational savings  Vibrational entropy dominates  May not have to enumerate every minumum

21. Chia-en A. Chang, Wei Chen, & Michael K. Gilson. Ligand configurational entropy and protein binding. 2007 PNAS 104(5):1534-1539

22. Questions

23. Mining Minima Margin of Error: ± 0.8 kcal/mol

24. q.e.d