Glycogen Phosphorylase Inhibitors: A Free EnergyPerturbation Analysis of Glucopyranose

SpirohydantoinAnalogues

G. Archontis, K. A. Watson, Q. Xie, G. Andreou, E. D. Chrysina, S. E. Zographos, N. G. Oikonomakos, and

M. Karplus

February 7, 2006

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

What are GP and hydan ?Glycogen Phosphorylase Molecular Weight (Da) : 97098 enzyme found in Endoplasmic Reticulum1 Catalyzes phophosphorylation of glycogen to Glc-1-PRelevant to type II diabetes mellitus

GP

HydanSpirohydantoin of glucopyranoseMost potent catalytic-site inhibitor of GP

N-Hydan Methyl-Hydan

1. Human Protein Reference Database

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 Ki 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

What are the numbers ?

Inhibitor Binding Constant Ki Free Energy difference (exp/calc)

Hydan 3.1 µM 0 kcal/mol

M-Hydan 1200 µM 3.6 / 3.75 (1.4) kcal/mol

N-Hydan 146 µM 2.3 / 1.0 (1.1) kcal/mol

glucose 1.7 mM

Competitive inhibition equation Michaelis-Menton kinetics

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

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

Thermodynamic cycle

Steps 3 & 4 Calculatedto estimate steps 1 &2

-H -> M- “Dual Topology”

-H -> N- “Dual Topology”- Modified two step pathway

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

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

Summary of results• Decreasing order of binding hydan > N-hydan > M-hydan• Methyl or NH2 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

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

GP:Hydan structures

Structure and interaction around the sugar moiety

GP:Hydan structures

Structure and interaction around the hydan moiety

“Early”“Later”

GP:Hydan analog structures

Methyl - hydanN - hydan

Summary of free energy

Summary of free energy decompostion

Methyl - hydanN - hydan

Summary of free energy decompostion

Effect of water translocation

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?