Free Energy Change Calculation of Mutations on TetRTetO System

1
Free Energy Change Calculation of Mutations on
TetR/TetO System

• Yuhua Duan
• Chemical Engineering Department
• University of Minnesota

2
Outline

• Introduction
• TetR/TetO system
• Free energy calculation methodology
• Calculation procedure
• Results
• Conclusion

3
Introduction

• The biological function of many proteins is
  triggered and modulated by binding of effector
  molecules or cofactors
• Molecular recognition is a fundamental process in
  all living systems, regulating processes as
  diverse as transcription, cell signalling and
  immunity
• Binding energy is the key to understand the
  thermodynamic and kinetic principles of protein
  binding on DNA in more detail.

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Introduction TetR/TetO

• The Tet repressor protein(TetR) regulates
  transcription of a family of tetracycline(tc)
  resistance determinants in Gram-negative
  bacteria
• In the absence of inducer, TetR dimers bind to
  the operators TetO1 and TetO2, shutting down
  transcription of its own gene and the resistance
  gene.

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TetR/TetO
From Orth, p. et al, Nature Structural biology,
7, 215(2000)
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Binding Free energy explores mutation

• We are interested in exploring the binding free
  energy change due to the mutation on TetO.
• Explore how conformation change due to mutation
  results in the bind free energy change between
  TetR and TetO.
• Find the mechanism of binding change due to
  mutation to affect the regulation.

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Our Free energy change calculation scheme

• The free energy change for a biological system
  can be divided into several terms
• ?G ?Ges ?G cav ?Gvdw ?Gbinding
• ?Gcoulomb ?G pol ?Gnonpol ?Gbinding

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Free Energy Decomposition_?Gcoulumb

• Electrostatic potential F(r)coulomb
• Solve Poisson-Boltzmann equation
• ?.e(r).??(r)-?02?(r)4p?int(r) 0
• or non-linear eq.
• ?.e(r).??(r)-?02?(r)1 ?(r)2/6 ?(r)4/120
  4p?int(r) 0
• Generalized Born Theory(GB)

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Free Energy Decomposition_ ?Gpol

• Solute-solvent electrostatic polarization term
  ?Gpol can be calculated from GB model
• where fGB(rij2aij2e-D)0.5
• aij(aiaj)0.5
• Drij2/(2aij)2
• ai is the effective Born radius of atom i

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Free energy decomposition_ ?Gpol

• Salt concentration effects we can consider salt
  into GB model and get a modified ?Gpol
  form(Proteins, 55(2004)383)
• where ? is the Debye-Huckel screening
  parameter.

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Free Energy Decomposition_ ?Gbinding

• Binding Energy ?Gbinding for Protein and DNA can
  be obtained by using self-consistent
  Lennard-Jones 12-6 parameters(A,B) which have
  been used in AMBER and CHARMM software with the
  form
• For all different atom type, there are several
  different optimized parameter sets existed.

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Free Energy Decomposition_ ?Gnonpol

• We can calculate the solvent accessible surface
  area Ak for each residue and nucleotide(JMB,
  55(1971)379).
• Desolvation energy for non-polarized part
• For parameter sk of 20 amino acids, taking from
  Protein Sci. 4(1995)1402. ? for all case is
  7.2cal/mol(JACS, 112(1990)6127).

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The free energy change for TetR/TetO binding

• We are interested in the relative free energy
  change(??G) due to the mutation
• The wild-type as our reference state to estimated
  the free-energy change(??G).

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Wild-type TetR/TetO

• The initial atomic coordinates of TetR/TetO from
  PDB with code 1QPI
• Using Insight II to alignment the missed residues
  in 1QPI
• The missed residues 2,3, 207 and 208 built from
  2TRT
• For missed residues 156163, random generate a
  loop, then minimized them
• The missed residue 1(Met) was added in.

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Wild-type TetR/TetO

• The TetO sequence are palindromic symmetry. In
  1QPI there are only 15 base pairs.
• Using InsightII to append 2 more pairs on each
  DNA ends.

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1
2 3 4 5 6 7 8 9 5- A C T C T
A T C A T T G A T A G A G T
3 3- T G A G A T A G T A A C T
A T C T C A -5
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The wild type of TetR/TetO
Na
TetO
TetR
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Minimized Structure of TetR/TetO

• Using CHARMM to build in all missing atoms for
  TetR/TetO system.
• Add Na ions around the PO4- groups on DNA, the
  distance between P and Na is about 4.5Å
• Solvent the TetR/TetO system into water (boxsize
  90x90x100) and add NaCl into the water layer
  randomly(concentration 0.15M).

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The whole simulation system
Include TetR/TetO Salts Water
molecules Total number of atoms 80,000
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Minimization of TetR/TetO

• Fix all atoms of TetR/TetO except for the 4 added
  base pairs, minimization with Charmm to get TetO
  conformation right
• Fix all backbone atoms of TetR/TetO, minimize the
  side chain conformations
• Release all restrains and minimize the system to
  reach the equilibrium states.

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Mutations

• Take out the TetR/TetO from the whole system,
  using Insight II to mutate the base on TetO.
  Since the TetO is palindromic, mutation is done 2
  pairs at ?positions.
• Solvent mutated TetR/TetO into water, add salts,
  do the minimization without constrain to
  equilibrium structure.

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Free energy calculations

• Calculate the free energy change for the mutated
  systems and the wild-type TetR/TetO.
• Get the difference of each components of the ?G
  between the muated and wild-type TetR/TetO. Sum
  them togather to get the free energy change due
  to the mutation ??G.

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Our Scheme
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Results of TetR/TetO
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Results of TetR/TetO
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Results

• The experimental relative affinities are
  presented by
• derepression which is derived from
  ?-galactosidase activity.

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Results

• The relationship is not clear due to the
  experimential activity does not only depends on
  the binding.
• Further work is needed to explore this
  relationship.

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Conclusions

• Our free energy change calculations show all
  mutations are unfavourable due the positive ??G,
  which are in agreement of the experimental
  predictions
• The calculated ??G vs the experimental relative
  affinities are not coincidence. The reason could
  be the experimental activity are not only
  dependent on binding.

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Further Work

• Validation our method with other systems in which
  the experimental binding energy change due to
  mutation is known, such as ? repressor--DNA
  complexes
• Study the specificity of repressor by mutation
  amino acid on TetR and TetO.

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Acknowledgement

• Dr. Yuk Sham, Dr. B.V.B. Reddy.
• Supported by AHPCRC, DTC