1. Glycogen Phosphorylase Inhibitors: A Free Energy Perturbation Analysis of Glucopyranose Spirohydantoin Analogues G. Archontis, K. A. Watson, Q. Xie, G. Andreou, E. D. Chrysina, S. E. Zographos, N. G. Oikonomakos, and M. Karplus February 7, 2006

2. What is this paper all about ? Goal –Rationalize differences in binding of hydan analogs Method –MD Free energy simulations –Free energy decomposition analysis Results –Electrostatic and Van der Waals interaction –Role of water in ligand binding Questions

3. What are GP and hydan ? Glycogen Phosphorylase Molecular Weight (Da) : 97098 enzyme found in Endoplasmic Reticulum 1 Catalyzes phophosphorylation of glycogen to Glc-1-P Relevant to type II diabetes mellitus GP Hydan Spirohydantoin of glucopyranose Most potent catalytic-site inhibitor of GP N-HydanMethyl-Hydan 1. Human Protein Reference Database

4. Previous Work -80 well characterized glucose-analogue catalytic site inhibitors of GPb - Important features of these inhibitors -Strong selectivity of GPb -Stabilization of T-state enzyme upon binding -Competitive inhibition with respect to the substrate - Hydan is the most potent inhibitor with K i 550 times less than native ligand - X-ray structure of GP-hydan and analog complexes known - Kinetics and crystallographic studies of hydan analogs binding to GP - Better binding due to interaction with main-chain oxygen of His377 - Inhibitor binding stabilizes the water network in the protein active site

5. What are the numbers ? InhibitorBinding Constant K i Free Energy difference (exp/calc) Hydan3.1 µM0 kcal/mol M-Hydan1200 µM3.6 / 3.75 (1.4) kcal/mol N-Hydan146 µM2.3 / 1.0 (1.1) kcal/mol glucose1.7 mM Competitive inhibition equation Michaelis-Menton kinetics

6. How do they approach this ? MD Simulations for Free Energy Calculation –Thermodynamic cycle & mutation protocol –Gives the structures and interactions Free Energy decomposition analysis –Break down ΔH into components –Shows which interactions as important

7. Method and program CHARMM22 version c28b1 TIP3P model for Water Sugar portion with CHARMM22 parms Hydan portion with MMFF-derived Van der Waals from CHARMM22 parms for analogs Geometry constrained with SHAKE and WHAM method

8. Thermodynamic cycle Steps 3 & 4 Calculated to estimate steps 1 &2 -H -> M - “Dual Topology” -H -> N - “Dual Topology” - Modified two step pathway

9. Mutation protocol “Dual” Topology Modified method Used a “hybrid” ligand with one sugar moiety and two overlapping hydan parts – one with H on N1 and one with M/N on C1 Computed energy using expression 1 in going from H -> M/N i.e. computed H as a function of λ. Used a single ligand with one sugar moiety and a single hydan part but with charges on N turned off for step 1 and “hybrid” for step 2 Computed energy using expression 1 in going from charges turned off to charges turned on for step 1 and “dual” topology for step 2

10. Math of free energy Used data from multiple MD simulations, statistical mechanics and expression 2 to calculate the free energy Used a force field model to partition the energy into electrostatic and Van der Waals components Used expression 3 to do that for the mutation part

11. Summary of results Decreasing order of binding hydan > N-hydan > M-hydan Methyl or NH 2 group unfavorable in catalytic site more than in solvent Asp283 and X4 water affect Van der Waals term more for M-hydan than N-hydan N-hydan improves electrostatic interaction but not enough X4 water in better in position 1 for N-hydan and position 2 for M-hydan Van der Waals term is dominant in M-hydan while electronic term in N-hydan

12. Quality of results Calculated structures are in good agreement with X-ray structures Binding constants calculated are better for M-hydan than for N-hydan Simulations are allowed to equilibriate 20- 100 ps Many simulations are run Some shady constraints are imposed

13. GP:Hydan structures Structure and interaction around the sugar moiety

14. GP:Hydan structures Structure and interaction around the hydan moiety “Early” “Later”

15. GP:Hydan analog structures Methyl - hydan N - hydan

16. Summary of free energy

17. Summary of free energy decompostion Methyl - hydan N - hydan

18. Summary of free energy decompostion

19. Effect of water translocation

20. Questions Does having a potential to constrain the ligand affect this analysis? Is integral and MD approach really appropriate for the free energy calculations? Is the trend observed in free energy plot of X4 water just another view of the interaction with GP? Is turning off the N charge really a good way to describe the H ligand in modified method?