Protein Folding

1
Protein Folding
Experiments Temperature jump spectroscopy Time-res
olved infrared Time-resolved fluorescent energy
transfer Time scales for formation of secondary
structure b-sheet a-helix
2
Protein folding exampleTwo state model
kf

• U F
• Unfolded Folded
• K F/U
• K ff/(1-ff)
• Fraction folded ff Fraction unfolded 1-ff

ku
3
Thermodynamic model fortwo-state equilibria

• Kff/(1-ff)
• ff K/(K1)
• K e-DGo/RT
• ff 1/(1 eDGo/RT)
• ff 1/(1 eDHo/RTe-DSo/R)
• The temperature at which the protein is 50
  folded or DNA is 50 hybridized can be defined as
  Tm the melt temperature.
• At Tm , DGo 0 or Tm DHo/DSo.

4
Equilibrium melt curves
Proteins or DNA
o
o
Mostly folded Mostly hybridized
Mostly unfolded Mostly ssDNA
Tm

• In this case Tm 300 K DHo/DSo

5
Vant Hoff plots
Slope -DHo/R

• The standard method for obtaining the reaction
  enthalpy is a plot of ln K vs. 1/T

6
Non-covalent forces in proteinsWhat holds them
together?

• Hydrogen bonds
• Salt-bridges
• Dipole-dipole interactions
• Hydrophobic effect
• Van der Waals forces

What pulls them apart?

• Conformational Entropy

7
Dipole-Dipole Interactions
Dipoles often line up in this manner. Example
a-helix
8
Electrostatic Interactions
Coulombs Law V q1q2/er
Example of a hydrogen bond
-N-H..OC-
Example of a Salt Bridge
Main Chain
Main Chain
Lysine
Glutamate
9
Hydrogen bonding in water
10
Hydrophobic interactions
11
Contributions to DG
- 0
-TDS
Conformational Entropy
DH
Internal Interactions
-TDS
Hydrophobic Effect
Net
DG
Folding
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Mechanism of ?-Hairpin Formation

• Key Issues
• What is the characteristic rate of ?-hairpin
  formation?
• Folding mechanism
• Transition state barrier entropic or enthalpic?
• First step turn formation or nonspecific
  hydrophobic collapse

13
Two ?-Sheet Folding Models

• Formation of the turn region followed by hydrogen
  bond propagation

• Hydrophobic collapse then propagation

14
Experimental

• Two Types of Measurements
• Static, temperature dependent Fourier Transform
  Infrared (FTIR)
• calibrate temperature jumps
• determine wavenumber to probe components of
  secondary structure
• Infrared Temperature Jump (T-jump)
• meausure observed relaxation times of unfolding
  and/or folding

15
Infrared Spectroscopy of Protein Amide Backbone
IR Amide I Frequencies Structure
Frequency (cm-1) ?-helix
1648-1655 Random coil 1655-1675 ?-sheet
1620-1635,1675-1690
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Temperature Jump Setup
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Sample Cell
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GB1 Peptide
GB1 GEWTYDDATKTFTVTE
Muñoz et al (1997) Nature 390, 196-199.
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b-sheet folding followed by T-jump
GB1
3.5 ms
Tryptophan fluorescence Dansyl fluorescence
GB1
3.5 ms
Eaton et al. Acc. Chem. Res. 1998, 31, 745
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The time scale for b-sheet folding is ms
Tryptophan fluorescence is higher in the
hydrophobic folded state and decreases when
exposed to water.
Eaton et al. Acc. Chem. Res. 1998, 31, 745
21
The time scale for a-helix folding by T-jump
fluorescence experiment
Tryptophan fluorescence
Helix melting
Heating
Eaton et al. Acc. Chem. Res. 1998, 31, 745
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The time scale for a-helix folding is hundreds of
ns
Tryptophan Histidine
Tryptophan is quenched by proximity to histidine.
Eaton et al. Acc. Chem. Res. 1998, 31, 745
23
Folding properties of cyclic b-sheet forming
peptides

• NMR and UV dichroism shows that the b-sheet
  structure depends on the number of residues.
  This structural periodicity has been called a
  2(2n1) rule.

Gibbs, Wishart et al. Nature Struct Biol. 1998,
5, 284
24
Simulated Annealing Studies
6-mer
Folded
Unfolded
Top View
25
Simulated Annealing Studies
6-mer
Folded
Unfolded
Side View
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6-mer FTIR Data
?-sheet at 1621 cm-1 Disordered structure at 1653
cm-1
Disordered structure appears as ?-sheet melts.
27
10-mer FTIR Data
VKLYPVKLYP
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14-mer FTIR Data
VKLKVYPLKVKLYP
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Melt Curve Analysis
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Analysis two state model
The observed rate constant kobs is the sum of the
unfolding and the folding rate constants. kobs
kfolding kunfolding In order to separate the
two contributions the equilbrium melt curves are
used. According to the principle of microscopic
reversibility the equilibrium constant is, K
kfolding / kunfolding
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Approach to equilibrium

• A B and B A
• Rate equations are
• dA/dt -k1A k-1B
• dB/dt k1A - k-1B
• Simultaneous solutions of these equations leads
  to a rate constant of
• k1 k-1.
• Equilibrium is approached
• as the sum of the forward
• and reverse rate constants.

32
Approach to equilibrium

• Let x be the deviation from equilibrium
• x A Aeq Beq B
• then A Aeq x and B Beq x
• Rate equations are
• -dA/dt k1A - k-1B k1(Aeq x) -
  k-1(Beq x)
• and
• -dAeq/dt k1Aeq - k-1Beq 0
• Therefore,
• -dx/dt (k1 k-1)x
• x/x exp - (k1 k-1)t

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Principle of microscopic reversibility

• A B and B A
• The equilibrium constant for such a process can
  be related for the forward and reverse rate
  constants.
• From before

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Infrared T-Jump Investigation of the Folding
Kinetics of the Villin
Headpiece Subdomain Scott H. Brewer, Dung M.
Vu, Yuefeng Tang, Daniel P.
Raleigh, R. Brian Dyer and Stefan Franzen
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Protein Folding Problem Sequence Structure Fu
nction
Folding Dynamics
36

• Diseases Related to Protein Folding/Misfolding
• Alzheimers Disease
• Plaques of ?-amyloid
• Prion Diseases (PrP prion protein)
• Mad Cow disease
• Sheep Scrapie
• Creutzfeldt-Jakob disease in humans
• Possible Mechanism
• Nucleation followed by polymerization

37

• Folding Times and Proposed Mechanisms of
  Secondary Structure Formation
• b Sheet
• 6 ms (b hairpins) (GB1) (Eaton and co-workers)
• Eaton and co-workers nucleation at the b
  hairpin turn followed by H-bond
  propagation
• Karplus and co-workers hydrophobic collapse
  followed by H-bond zipping
• lt 100 ns cyclic b sheet peptides (Dyer and
  co-workers)
• a Helix
• 100 200 ns (Dyer and co-workers, Asher and
  co-workers)
• Zimm-Bragg nucleation barrier given by
  -kTln(s) where s is the
  nucleation parameter
• Eaton and co-workers kinetic-zipper model

38
HP36 Villin Headpiece Subdomain
F58
F51
F47
N
MLSDEDFKAVFGMTRSAFANLPLWKQQNLKKEKGLF
39
Literature Experimental Studies of HP36
1H NMR Temperature Dependent Spectra of HP36
Raleigh and co-workers
Protein folds on 10 ms time scale
40
Literature Experimental Studies of HP35 N27H
T-Jump Fluorescence Folding Kinetics of HP35 N27H
Eaton and Co-workers
N27H
Relaxation Times of 70 ns, 4.3 ms at 300 K
N
H
41

• Theoretical Investigations of the Folding of the
  Villin Headpiece
• Zagrovic et. al.
• Molecular dynamic (MD) simulations with implicit
  solvent using worldwide distributed computing
• Folding rate 5 ms
• Hydrophobic collapse happens first in folding
• Duan and Kollman
• MD simulation using explicit solvent with
  parallel computing
• Simulation time of 1 ms
• Predicts intermediate in folding pathway

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• Infrared Spectroscopy
• IR structural probe Amide I (predominately
  CO stretch)
• Sensitive to secondary (b sheet, a helix, random
  coil)
• and tertiary structure
• Sensitive to H-bonding and dielectric
  environment
• (solvent exposed or buried)
• Sensitive to isotopic labels (13CO)
• Internal temperature probe (D2O)

• Amide I Positions
• b sheet 1620 1635 cm-1
• a helix 1648 1655 cm-1
• random coil 1655 1675 cm-1

43
HP36 Static T-Dependent FTIR Spectra
HP36 Villin Headpiece (pH 5.3 in D2O) Temperature
Range of 3 93oC
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HP36 Difference Static T-Dependent FTIR Spectra
Temperature Range of 3 93oC Mode assignment
1632 cm-1 solvated helix, 1646 cm-1 buried helix,
1674 cm-1 turn region or TFA
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HP36 Static FTIR T-Melt Curves
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HP36 Fraction Folded (1646 cm-1)
Three State
Two State
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HP36 vant Hoff Plot (1646 cm-1)
DHu 75.7 kJ/mol DSu 225 J/mol
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Time-Resolved Infrared Temperature Jump Apparatus
H2 Raman shifter 1.91 mm, 20 mJ/pulse
NdYAG 1.06 mM, 10 ns pulse
sample
Tunable IR diode laser 1620 1680 cm-1
Fast IR detector PV MCT, 20 ns rise time
T-Jump
Ti
Relaxation
D2O protein
D2O
split sample cell
DT
Tf
49
Kinetic Data Processing
Transient Absorption Spectra
minus
Difference Spectrum
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HP36 Kinetic T-Jump Data
1632 cm-1 9.63x106 s-1, 3.96x105 s-1 (104 ns,
2.53 ms) 1650 cm-1 8.19x106 s-1, 3.87x105 s-1
(122 ns, 2.58 ms)
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HP36 Arrhenius Plot Two State Model (1646 cm-1)

• DH 5 kJ/mol
• DS -126 J/mol
• DH 77 kJ/mol
• DS 90 J/mol

k1 k-1
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HP36 Gibbs Free Energy Plot Two State Model
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HP36 F4751L Villin Headpiece Subdomain
F58
F51
F47
F
L
N
MLSDEDFKAVFGMTRSAFANLPLWKQQNLKKEKGLF
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HP36 F4751L Static T-Dependent FTIR Spectra
HP36 F4751L (pH 5.3 in D2O) Temperature Range of
5 83oC
55
HP36 F4751L Difference Static T-Dependent FTIR
Spectra
Temperature Range of 5 83oC Mode assignment
1632 cm-1 solvated helix 1646
cm-1 buried helix
56
HP36 F4751L Static FTIR T-Melt Curves
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HP36 F4751L vant Hoff Plot (1646 cm-1)
DHu 24.3 kJ/mol DSu 76 J/mol
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HP36 F4751L Kinetic T-Jump Data
1632 cm-1 1.76x107 s-1, 8.81x105 s-1 (57 ns,
1.13 ms) 1650 cm-1 1.03x107 s-1, 6.63x105 s-1
(97 ns, 1.51 ms)
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HP36 F4751L Arrhenius Plot Two State Model (1646
cm-1)

• DH 23 kJ/mol
• DS -66 J/mol
• DH 47 kJ/mol
• DS 8 J/mol

k1 k-1
60
HP36 F4751L Gibbs Free Energy Plot Two State
Model
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HP36 vant Hoff Plot Three State Model
HP36 1646 cm-1
DHi 59.6 kJ/mol DSi 176 J/mol
KT/Keq2
HP36F4751L 1632 cm-1
DHu 16.0 kJ/mol DSu 49.9 J/mol
62
HP36 Arrhenius Plot Three State Model

• DH -8 kJ/mol
• DS -140 J/mol
• DH 7 kJ/mol
• DS -95 J/mol

• DH 6 kJ/mol
• DS -117 J/mol
• DH 63 kJ/mol
• DS 51 J/mol

k1 k-1
k2 k-2
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HP36 Gibbs Free Energy Plot Three State Model
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• Conclusions
• Amide I of HP36 comprised of solvated (1632
  cm-1) and buried (1646 cm-1) helix components
• Relaxation kinetics of HP36 are biphasic
  ( 100 ns, 2.5 ms)
• Helix-coil transition ( 100 ns) followed by
  formation of tertiary contacts ( 2.5 ms)
• HP36 is thermodynamically more stable than HP36
  F4751L
• HP36 unfolds slower than HP36 F4751L
• Helix-coil transition has an entropic barrier
  while formation of tertiary contacts have both an
  enthalpic and entropic barrier to folding for HP36