Proteindynamik i relation til funktion

1
Proteindynamik i relation til funktion

• Naturvidenskabelig kandidateksamen i
  biokemiSpecialeeksamen
• 12. marts 2007
• Intern Vejleder Karen Skriver
• Ekstern Vejleder Jens Erik Nielsen
• Censor Esben Peter Friis

2
Overview

• 12 months of computational work in Dublin
• Group of Jens Erik Nielsen
• Directionality of conformational changes in
  relation to enzymatic catalysis
• Preliminary results!
• 4 months of experimental NMR work in Lund
• With Kaare Teilum in group of Michael Akke
• Time scales of conformational changes in relation
  to protein folding
• Preliminary results!

3
Why study protein dynamics?

• Thermal equilibrium fluctuations
• X-ray Debye-Waller factors
• NMR S2 order parameters
• Functional dynamics
• Enzyme conformational variants
• Motor proteins (kinesin, myosin)

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Functions and time scales of protein dynamics

• Catalysis
• Folding
• Signal Transfer
• Thermodynamic Stability

Benkovic SJ, Hammes-Schiffer S, Science 301
(2003) 1196
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Normal modes, what are they?

• A set of 3N linearly independent vectors which
  describe the 3N degrees of freedom for a
  molecule of N atoms.
• 3N-6 vibrational normal modes if nonlinear
  molecule (e.g. water, a protein)
• Possible directions of initial movement from
  equilibrium upon addition of thermal energy.
  Different cost in energy associated with each
  vibrational mode.

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Normal modes are unlike MD trajectories linear
nAChR (2BG9) mode 7
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Why use normal modes instead of MD simulations?

• MD simulations in general dont sample
  biologically relevant time scales
• Normal modes
• do not describe the high-frequency side chain
  motions
• do describe the low frequency global motions
  (functional dynamics) of proteins

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Normal modes, how are they calculated?
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Connectivity of atoms an alpha carbon Gaussian
Phantom Network Model
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Connectivity of atoms sigmoidal cutoff and
structural variability
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Comparison of amplitudes of normal modes of
cytochrome C to x-ray temperature factors
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Overlap - comparing the directionality of two
eigenvectors

• overlap cos ?
• ranges between
• 1 (parallel vectors pointing in the same
  direction) and
• 0 (perpendicular vectors)

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Description of conformational changes using the
lowest non-zero modes
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Description of conformational changes using the
lowest non-zero modes
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Description of conformational changes using the
lowest non-zero modes

• Krebs, Gerstein 2002 Proteins 48 682 Normal
  Mode Analysis of Macromolecular Motions in a
  Database Framework Developing Mode Concentration
  as a Useful Classifying Statistic
• 3000 conformational changes from molmovdb.org

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Results for T4 lysozyme when removing
combinations of 2 residuesIdentification of T21,
E22, T142
?overlap
residue
overlap
residue
residue
overlap
residue
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Results for protein kinase A when removing
combinations of 2 residuesIdentification of K83,
Q84, T197, T201, N326, (S338)
?overlap
residue
overlap
residue
residue
overlap
residue
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polymerase.ucd.ie/goodvibes
1) PDB ID
2) upload PDB
3) paste PDB
Chain ID
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Additional standard results when using
polymerase.ucd.ie/goodvibes

• pdb trajectories for use in e.g. VMD
• relative residue fluctuations for individual or
  combined modes
• cross correlation maps
• correlation with x-ray Debye-Waller factors

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NMR methods

• 1012-109s-1 time scale
• S2 order parameters (R1, R2, NOE)
• Local dynamics

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NMR methods

• 103-106s-1
• CPMG relaxation dispersion experiments
• 100-3000s-1
• parameters
• thermodynamics (populations)
• kinetics (chemical exchange rate)
• experiments
• 15N amide nitrogens (backbone)
• 13C methyl carbons (side chains)

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NMR methods

• Residual Dipolar Couplings (RDCs)
• cylindrical coordinates, distances
• 1H/2H exchange (10-3-1s-1)
• buried, hydrogen bonded, partly exposed
• Line sharpening
• Independent mobility

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bovine acyl-coenzyme A binding protein (bACBP)

• 15N CPMG NMR relaxation experiments and
  stopped-flow kinetics
• not two-state
• kfold 72185 s-1
• 13C methyl CPMG NMR relaxation dispersion
• Teilum K, Poulsen FM, Akke M The inverted
  chevron plot measured by NMR relaxation reveals a
  native-like unfolding intermediate in acyl-CoA
  binding protein, PNAS 103 (2006) 6877

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Methyl groups

• Alaß, Ile?2, Iled, Leud, Mete, Thr?1, Val?
• Fully labelled 13C-glucose
• one-bond 13C-13C couplings
• 1-13C-glucose ?

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1-glucose VS fully labeled glucosezoom and point
out singlets VS dublets

• labelled fraction
• (Cs,i/Ns,average)/(Cu,i/Nu,average)

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1-glucose and Lorentzian line shapes
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1-glucose

• 50 labeling, 100 isolation
• Alaß, Ile?2,Leud, Mete, Val?

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Fits and parameters

• R2(?CPMG)
• Chemical exchange rate, kex
• Major population, pA
• Chemical shift difference, ??

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Future studies and applications

• Studies
• Ala mutate residues identified by GoodVibes
• Full force field molecular dynamics simulations
  to study changes in equilibrium fluctuations
• Study effects of binding ligands on amplitudes,
  directions and energies
• Determine time scales of conformational change in
  the presence of substrate and catalytic
  activities to investigate intrinsic dynamics
• Study changes in eigenvalues (energetics) and
  amplitude due to perturbations further
• Check correlation of amplitude with RDC
  experiments to validate method of residue
  identification
• Applications
• Structure ensemble for flexible protein-protein
  docking
• Guide mutational studies to avoid losing or
  increasing the energy of functionally important
  motions

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Acknowledgements

• Lund University
• Kaare Teilum, Michael Akke
• Department of Biophysical Chemistry
• University of Copenhagen
• Karen Skriver
• Protein Biology Group, Institute of Molecular
  Biology and Physiology
• University College Dublin
• Jens E. Nielsen
• School of Biomolecular and Biomedical Science

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Second order Taylor expansionand quadratic form
of the potential energy
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Harmonic potential and its second derivatives
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Orthogonal diagonalization of the symmetric
Hessian matrix

• Symmetric due to the rule of mixed partial
  derivatives
• Eigenvectors of a symmetric matrix are linearly
  independent

Taylor expansion of potential energy at an energy
minimum
Quadratic form of the multivariable second order
Taylor expansion
Symmetric Hessian matrix of second derivatives
Linearly independent eigenvectors (normal modes)
Second derivate of harmonic potential
Harmonic / Hookean potential
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What is the physical interpretation of the
eigenvalues associated with the eigenvectors?

• Eigenvectors are directions of initial movement
  from equilibrium upon addition of thermal energy.
• An eigenvalue is the cost of energy in following
  an eigenvector.
• Amplitude of eigenvectors inversely proportional
  to the eigenvalue.