Objective
description
Transcript of Objective
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Molecular Dynamics Molecular Dynamics Simulations of Protein Simulations of Protein
FibrillizationFibrillization
Carol K. Hall
Department of Chemical & Biomolecular Engineering
North Carolina State University
http://turbo.che.ncsu.edu
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ObjectiveObjective
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 Polyalanine– A Model System for Studying FibrillizationStudying 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 > 1.5 mM) and high temperature (T > 40oC) (Blondelle et al., Biochem. 1997).
• Peptide Sequence: KA14K
-helix -sheets in a fibril
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Molecular Dynamics Simulations of Molecular Dynamics Simulations of Protein FoldingProtein 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 DynamicsDiscontinuous Molecular Dynamics
Traditional MD:• Forces based on Lennard
Jones (LJ) potential.• Follow particle trajectories by
numerically integrating Newton’s 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 Newton’s 2nd law whenever collision, capture or bounce occur.
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Building a Protein Model to Use With Building a Protein Model to Use With DMD: Representation of Amino Acid DMD: Representation of Amino Acid
ResidueResidue
• United atom: NH, CaH, CO, R• Excluded volume: hard spheres with realistic diameters
Virtual Atom Diameter, s (Ao) NH 3.3
C 3.7CO 4.0 Smith & Hall, Proteins
(2001)RCH3 4.4 Smith & Hall, JMB
(2001)
CH3
CHCONH
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Building a Protein Model to Use With Building a Protein Model to Use With DMD: Maintaining Chain ConnectivityDMD: Maintaining Chain Connectivity
• Sliding links (repulsion at (1-)l, attraction at (1+)l) allow bond length to fluctuate around ideal value, l, with tolerance ~2.5%.
• Bond lengths set to ideal experimental values.Bond Length l (Ao)Ni-C,i 1.46C,i-Ci 1.51Ci-Ni+1 1.33C,i -R CH3,i 1.53
NHi
COi
CH3,i
CHi
COi+1
NHi+1
CHi+1
CH3,i+1
l
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• Pseudo-bonds maintain: ideal backbone bond angles residue L-isomerization trans-configuration
• Pseudo-bonds fluctuate around ideal lengths with tolerance ~2.5%.
NHi
COi
CH3,i
CHi
COi+1
CHi+1
CH3,i+1
Building a Protein Model: Maintaining Building a Protein Model: Maintaining Proper Bond Angles, Chirality, Peptide Proper Bond Angles, Chirality, Peptide
BondBond
NHi+1
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Model Forces: Steric InteractionsModel Forces: Steric Interactions
• United atoms in the simulation are not allowed to overlap.
NHi
CH3,iCHi
COjNHj
COi
CHj
CH3,j
Hard-sphere repulsion
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NHi
CH3,iCHi
COj
NHj
COi
CHj
Square-well attraction
• Hydrogen bonds between backbone amine and carbonyl groups are modeled with a directional square-well attraction of strength H-bonding.
Model Forces: Hydrogen BondingModel Forces: Hydrogen Bonding
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• 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 hydrophobicity
NHiCOi
CH3,i
CHi
COj
CHj
NHj
CH3,j
Square-well attraction
• hydrophobicity = R* H-bonding ; R = 1/10
Model Forces: Hydrophobic Model Forces: Hydrophobic InteractionsInteractions
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Folding of Single KA14K ChainFolding of Single KA14K Chain
t*=0 t*=50.99
t*=70.33
t*=86.16
t*=103.74
t*=130.11
Nguyen,Marchut & Hall Biophys. J
(2004)
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A Constant-Temperature A Constant-Temperature Simulation: 48 Peptides at Simulation: 48 Peptides at
c=10.0c=10.0mM, mM, T*=0.14T*=0.14Nguyen & Hall, PNAS (2005)
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-Helix Formation at Various -Helix Formation at Various Concentrations and TemperaturesConcentrations and Temperatures
• Formation of -helices is highest at low temperatures and low concentrations.
• There is an optimal range of temperatures for forming -helices.
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Fibril Formation at Various c & T*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 FormationAmorphous Aggregate Formation at Various c & T* at Various c & T*
• Formation of amorphous aggregates at low temperatures and intermediate concentrations
• Amorphous aggregates contain -helices• The trends described thus far qualitatively agree with
experimental data (Blondelle et al., Biochem. 1997)
c=2.5mm, T*=0.08
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Equilibrium Simulations: 96 PeptidesEquilibrium 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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• 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)
Fibril Structure: Intra-sheet DistanceFibril Structure: Intra-sheet Distance
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• Inter-sheet distance: 7.5 ± 0.5A, comparable to experimental values of 8 – 10A for the transthyretin peptide (Jarvis et al., BBRC 1993)
Fibril Structure: Inter-sheet DistanceFibril Structure: Inter-sheet Distance
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• 93.3 ± 5.7% peptides in fibrils are parallel, same as experimental results for the A1-40) peptide (Antzutkin et al., PNAS 2000)
Fibril Structure: Peptide OrientationFibril Structure: Peptide Orientation
N-
N-N-
C-
-C
-N
-C
-C
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Fibril Structure: Peptide OrientationFibril Structure: Peptide Orientation
• Most peptides are in-register, same as experimental results for the A10-35) peptide (Benzinger et al., PNAS 1998)
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Forming Various Structures versus t*: Forming Various Structures versus t*: c=5mM, T*=0.14c=5mM, T*=0.14
Amorphous aggregates form instantaneously, followed by -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 Fibril Formation in Seeded and Unseeded Systems at T*=0.14, Unseeded Systems at T*=0.14,
c=2mMc=2mM
• Adding a seed eliminates the fibril formation lag time , as is found experimentally.
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Seeding Experiments to Find NucleusSeeding 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 T*=0.135
• 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 NucleusSeeding Experiments to Find Nucleus
Minimum size seed that can induce fibril formation at a high temperature (T*=0.150) is a fibril with two sheets, each containing two peptides
# Sheets # Peptides/SheetFibril
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
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FibrilFibril Growth MechanismsGrowth Mechanisms Two mechanisms of fibril
growth:
Lateral addition: adding already-formed -sheets to the side of the fibril
Elongation: adding individual peptides to the end of each -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: SizeFibril Structure: Size
12 peptides: 2-3 -sheets 24 peptides: 3-4 -sheets
48 peptides: 3-6 -sheets 96 peptides: 4-6 -sheets• This fibril size is typical of experimental results (Serpell et al., JMB
2000)
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Effect of Chain Length Ac-KAEffect of Chain Length Ac-KALLK-NHK-NH22 on Fibrillization at c=2.5mMon Fibrillization at c=2.5mM
• Increasing chain length shifts fibril formation to higher temperatures
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Fibril Formation at Various Fibril Formation at Various Hydrophobic Interaction Strengths R Hydrophobic Interaction Strengths R
for the 5mM Systemfor the 5mM System
• Increasing the hydrophobic interaction strength further to R=1/6 reduces -sheet formation and totally prevents fibril formation. Amorphous aggregates are formed instead.
Fibril formation
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Electrostatic InteractionElectrostatic Interaction
U
0 r
σ λσ
εsalt-bridge
Square-well attraction
• The salt-bridge formed between residues D23 and K28 are modeled as a square-well attraction between the side chains with strength εsalt-bridge
where εsalt-bridge is equal εH-bonding.
D23
K281
K282
•Each side chain is represented by either one or two united atoms.**Wallqvist & Ullner, 1994
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Simulation Snapshots: ABeta 10-40Simulation Snapshots: ABeta 10-40
Simulation Box with Periodic Boundary Conditions
ABeta 10-40 (zoomed in)
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Simulation Snapshots: ABeta 10-42Simulation Snapshots: ABeta 10-42
Simulation Box with Periodic Boundary Conditions ABeta 10-42 (zoomed in)
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Comparison with Tycko Structure
ABeta 10-42 (zoomed in)
Cross-section of ABeta structure foundBy Petkova et al.
Proposed Fibril Structure
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 ahydrophobic horseshoe which leaves the peptide backbones free to hydrogen bondwith each other.
HydrophobicPositiveNegativePolar
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ConclusionsConclusions
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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AcknowledgementsAcknowledgements
• 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 Intermediate Resolution Model Representation of GlutamineRepresentation of Glutamine
NH2
CO
CH2
CH2
• 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.
NH2
CH2
CH2
CO
NHCO
CαHCαH
CONH
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24 Polyglutamine 16mers Form 24 Polyglutamine 16mers Form NanotubeNanotube
R=0.125; c=5mM; T*=0.155
• Reminiscent of Perutz’s 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 Annular Structures Observed ExperimentallyExperimentally
R=0.125 ; c=5mM ; T*=0.185 Wacker et al. 2004
4nm
100nm
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24 16-residue PolyQ Random Coils24 16-residue PolyQ Random Coils
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Simulation results: Voet and Voet* results:
Voet & Voet (1990)
Model Test: Steric InteractionsModel Test: Steric Interactions
alanine: CH3
CHCONH