Glycogen%20Phosphorylase%20Inhibitors:%20A%20Free%20Energy%20Perturbation%20Analysis%20of%20Glucopyranose%20Spirohydantoin%20Analogues

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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
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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

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What are GP and hydan ?
GP
Glycogen Phosphorylase Molecular Weight (Da)
97098 enzyme found in Endoplasmic Reticulum1
Catalyzes phophosphorylation of glycogen to
Glc-1-P Relevant to type II diabetes mellitus
Hydan
Spirohydantoin of glucopyranose Most potent
catalytic-site inhibitor of GP
N-Hydan
Methyl-Hydan
1. Human Protein Reference Database
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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

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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
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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 ?H into components
• Shows which interactions as important

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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

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Thermodynamic cycle

• Steps 3 4 Calculated
• to estimate steps 1 2
• H -gt M
• Dual Topology
• H -gt N
• Dual Topology
• Modified two step
• pathway

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Mutation protocol
Dual Topology
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 -gt M/N i.e. computed
H as a function of ?.
Modified method
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
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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

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Summary of results

• Decreasing order of binding hydan gt N-hydan gt
  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

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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

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GPHydan structures
Structure and interaction around the sugar moiety
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GPHydan structures
Later
Early
Structure and interaction around the hydan moiety
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GPHydan analog structures
Methyl - hydan
N - hydan
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Summary of free energy
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Summary of free energy decompostion
Methyl - hydan
N - hydan
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Summary of free energy decompostion
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Effect of water translocation
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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?