Molecular Dynamics Simulations of Protein Fibrillization Carol K. Hall Department of Chemical

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Molecular Dynamics Simulations of Protein
Fibrillization Carol K. Hall Department of
Chemical Biomolecular Engineering North
Carolina State University http//turbo.che.ncsu.
edu
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Objective

• To develop a computational tool that allows
  investigation of spontaneous fibril formation.
• This tool should
• -capture the essential physical features (
  geometry and energetics) of real proteins
• -allow the simulation of many proteins within
  current computer capability
• -reveal the basic physical principles underlying
  fibril formation
• .

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Polyalanine A Model System for Studying
Fibrillization

• Speculation - fibril formation is natural
  consequence of peptide geometry, hydrogen-bonding
  capability and hydrophobic interactions under
  slightly-denatured, concentrated conditions.
• Polyalanine peptides form fibrils in vitro at
  high concentrations (C gt 1.5 mM) and high
  temperature (T gt 40oC) (Blondelle et al.,
  Biochem. 1997).
• Peptide Sequence KA14K

a-helix
b-sheets in a fibril
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Molecular Dynamics Simulations of Protein Folding

• Packages Amber, CHARMm, ENCAD, Discover, etc.
• Force fields describe interactions between all
  atoms on protein and in solvent at atomic
  resolution
• Desired Output folding trajectory of a
  protein
• Limitation very difficult (impossible?) to
  simulate folding of a single protein even with
  the fastest computers
• Implications for our work sacrifice the details
  if you want to learn anything about protein
  aggregation

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Discontinuous Molecular Dynamics

• Traditional MD
• Forces based on Lennard Jones (LJ) potential.
• Follow particle trajectories by numerically
  integrating Newtons 2nd law at regularly-spaced
  time steps.
• Simulations are slow
• Discontinuous MD
• Forces field based on square-well potential.
• Follow particle trajectories by analytically
  integrating Newtons 2nd law whenever collision,
  capture or bounce occur.

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Building a Protein Model to Use With DMD
Representation of Amino Acid Residue
CH3
CaH
CO
NH

• United atom NH, CaH, CO, R
• Excluded volume hard spheres with realistic
  diameters
• Virtual Atom Diameter, s (Ao)
  NH 3.3
• Ca 3.7
• CO 4.0 Smith Hall, Proteins
  (2001)
• RCH3 4.4 Smith Hall, JMB
  (2001)

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Building a Protein Model to Use With DMD
Maintaining Chain Connectivity

• Sliding links (repulsion at (1-d)l, attraction
  at (1d)l) allow bond
• length to fluctuate around ideal value, l, with
  tolerance d2.5.
• Bond lengths set to ideal experimental values.
• Bond Length l (Ao)
• Ni-Ca,i 1.46
• Ca,i-Ci 1.51
• Ci-Ni1 1.33
• Ca,i -R CH3,i 1.53

CH3,i
l
COi1
COi
CaHi1
CaHi
NHi1
NHi
CH3,i1
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Building a Protein Model Maintaining Proper
Bond Angles, Chirality, Peptide Bond

• Pseudo-bonds maintain
• ideal backbone bond angles
• residue L-isomerization
• trans-configuration
• Pseudo-bonds fluctuate around ideal lengths with
  tolerance d2.5.

CH3,i
COi1
COi
CaHi1
CaHi
NHi1
NHi
CH3,i1
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Model Forces Steric Interactions

• United atoms in the simulation are not allowed to
  overlap.

CH3,i
COi
CaHi
NHi
CH3,j
CaHj
NHj
COj
Hard-sphere repulsion
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Model Forces Hydrogen Bonding

• Hydrogen bonds between backbone amine and
  carbonyl groups are modeled with a directional
  square-well attraction of strength eH-bonding.

CH3,i
COi
CaHi
NHi
COj
CaHj
NHj
Square-well attraction
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Model Forces Hydrophobic Interactions

• The solvent is modeled implicitly by including
  the hydrophobic effect tendency of hydrophobic
  sidechains to cluster together through a
  hydrophobic interaction with a square-well
  attraction of strength ehydrophobicity

COi
NHi
CaHi
CH3,i
CH3,j
Square-well attraction
CaHj
NHj
COj

• ehydrophobicity R eH-bonding R 1/10

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Folding of Single KA14K Chain
t0
t50.99
t70.33
t86.16
t103.74
t130.11
Nguyen,Marchut Hall Biophys. J (2004)
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A Constant-Temperature Simulation 48 Peptides at
c10.0mM, T0.14
Nguyen Hall, PNAS (2005)
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a-Helix Formation at Various Concentrations and
Temperatures

• Formation of a-helices is highest at low
  temperatures and low concentrations.
• There is an optimal range of temperatures for
  forming a-helices.

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Fibril Formation at Various c T

• Fibril formation peaks at high temperatures and
  high concentrations.
• Critical temperature for fibril formation
  decreases with peptide concentration.

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Amorphous Aggregate Formation at Various c T
c2.5mm, T0.08

• Formation of amorphous aggregates at low
  temperatures and intermediate concentrations
• Amorphous aggregates contain a-helices
• The trends described thus far qualitatively agree
  with experimental data (Blondelle et al.,
  Biochem. 1997)

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Equilibrium Simulations 96 Peptides

• Use the replica-exchange methods to simulate
  96-peptide systems at different temperatures and
  peptide concentrations.
• These trends qualitatively agree with
  experimental data (Blondelle 1997)

Nguyen Hall Biophys. J. (2004)
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Fibril Structure Intra-sheet Distance

• Intra-sheet distance 5.05 0.07A, comparable to
  experimental values of 4.7 - 4.8A for a variety
  of peptides (Sunde et al., JMB 1997)

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Fibril Structure Inter-sheet Distance

• Inter-sheet distance 7.5 0.5A, comparable to
  experimental values of 8 10A for the
  transthyretin peptide (Jarvis et al., BBRC 1993)

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Fibril Structure Peptide Orientation

• 93.3 5.7 peptides in fibrils are parallel,
  same as experimental results for the Ab(1-40)
  peptide (Antzutkin et al., PNAS 2000)

-C
N-
-C
N-
N-
-C
C-
-N
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Fibril Structure Peptide Orientation

• Most peptides are in-register, same as
  experimental results for the Ab(10-35) peptide
  (Benzinger et al., PNAS 1998)

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Forming Various Structures versus t c5mM,
T0.14

• Amorphous aggregates form instantaneously,
  followed by b-sheets, and then fibrils after a
  delay, called the lag time.
• Appearance of a lag time indicates that this is a
  nucleated phenomenon.

all aggregates
Nguyen Hall, J. Biol. Chem (2005)
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Fibril Formation in Seeded and Unseeded Systems
at T0.14, c2mM

• Adding a seed eliminates the fibril formation lag
  time , as is found experimentally.

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Seeding Experiments to Find Nucleus
Sheets Peptides/Sheet Seeds
1 3 4.48
1 4 2.03
1 5 0.81
1 6 0.41
2 2 7.65
2 3 17.52
2 4 26.18
2 5 10.18
2 6 3.30
2 7 1.20
2 8 0.41
2 9 0.43
3 3 3.30
3 4 7.89
3 5 1.20
4 3 0.39
4 4 0.39
5 3 0.43

• 250 simulations conducted at T.150, each
  containing a seed with randomly-chosen size
  shape taken from simulations at T0.135
• What is minimum size seed that will lead to the
  formation of a fibril in a fixed time?

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Seeding Experiments to Find Nucleus
Sheets Peptides/Sheet Fibril Formed?
1 3 no
1 4 no
1 5 no
1 6 no
2 2 yes
2 3 yes
2 4 yes
2 5 yes
2 6 yes
2 7 yes
2 8 yes
2 9 yes
3 3 yes
3 4 yes
3 5 yes
4 3 yes
4 4 yes
5 3 yes

• Minimum size seed that can induce fibril
  formation at a high temperature (T0.150) is a
  fibril with two sheets, each containing two
  peptides

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Fibril Growth Mechanisms

• Two mechanisms of fibril growth
• Lateral addition adding already-formed b-sheets
  to the side of the fibril
• Elongation adding individual peptides to the end
  of each b-sheet of the fibril
• These mechanisms are similarly observed by Green
  et al. (J. Biol. Chem. 2004) on human amylin (hA)
  peptide (type 2 diabetes).

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Fibril Structure Size
12 peptides 2-3 b-sheets 24 peptides 3-4
b-sheets
48 peptides 3-6 b-sheets 96 peptides 4-6
b-sheets

• This fibril size is typical of experimental
  results (Serpell et al., JMB 2000)

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Effect of Chain Length Ac-KALK-NH2 on
Fibrillization at c2.5mM

• Increasing chain length shifts fibril formation
  to higher temperatures

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Fibril Formation at Various Hydrophobic
Interaction Strengths R for the 5mM System
Fibril formation

• Increasing the hydrophobic interaction strength
  further to R1/6 reduces b-sheet formation and
  totally prevents fibril formation. Amorphous
  aggregates are formed instead.

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Electrostatic Interaction

• The salt-bridge formed between residues D23 and
  K28 are modeled as
• a square-well attraction between the side
  chains with strength esalt-bridge
• where esalt-bridge is equal eH-bonding.

Square-well attraction

• Each side chain is represented by either one or
  two united atoms.

Wallqvist Ullner, 1994
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Simulation Snapshots ABeta 10-40
ABeta 10-40 (zoomed in)
Simulation Box with Periodic Boundary Conditions
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Simulation Snapshots ABeta 10-42
Simulation Box with Periodic Boundary Conditions
ABeta 10-42 (zoomed in)
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Comparison with Tycko Structure
Proposed Fibril Structure
Hydrophobic Positive Negative Polar
Cross-section of ABeta structure found By Petkova
et al.
ABeta 10-42 (zoomed in)
We see beta-hairpins form with intra-strand
hydrogen bonding and hydrophobic groups sticking
out of the plane of the strand while Tycko and
coworkers see a hydrophobic horseshoe which
leaves the peptide backbones free to hydrogen
bond with each other.
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Conclusions

• First simulations of spontaneous fibril formation
• Our results qualitatively agree with experimental
  data in general, and specifically with those
  obtained by Blondelle et al. (Biochemistry, 1997)
  on polyalanines.

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Acknowledgements

• Dr. Hung D. Nguyen
• Alexander J. Marchut
• Dr. Anne V. Smith
• Dr. Hyunbum Jang
• Dr. Andrew J. Schultz
• Victoria Wagoner
• Erin Phelps
• National Institutes of Health
• National Science Foundation

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Intermediate Resolution Model Representation of
Glutamine
CO
NH2
CH2
CH2
CaH
NH
CO
Blue spheres have square wells for hydrophobic
attraction. Green spheres have
directionally-dependent square wells for hydrogen
bond donors. Red spheres have
directionally-dependent square wells for hydrogen
bond acceptors.
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24 Polyglutamine 16mers Form Nanotube
R0.125 c5mM T0.155
Reminiscent of Perutzs prediction of nanotubes
(Perutz et al. 2002) Curved nature of
polyglutamine beta sheets leads them to roll into
a tube.
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Annular Structures Observed Experimentally
100nm
4nm
R0.125 c5mM T0.185
Wacker et al. 2004
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24 16-residue PolyQ Random Coils
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Model Test Steric Interactions
alanine
CH3
F
Y
CaH
CO
NH
Simulation results Voet
and Voet results
Voet Voet (1990)