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

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

.

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

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

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.

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

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

• 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

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

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

• 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

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)

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)

-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.

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.

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

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)

• 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

• 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

• 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

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)

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)

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.

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?

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

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).

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)

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

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

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

Simulation Snapshots: ABeta 10-40Simulation Snapshots: ABeta 10-40

Simulation Box with Periodic Boundary Conditions

ABeta 10-40 (zoomed in)

Simulation Snapshots: ABeta 10-42Simulation Snapshots: ABeta 10-42

Simulation Box with Periodic Boundary Conditions ABeta 10-42 (zoomed in)

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

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.

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

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

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.

Annular Structures Observed Annular Structures Observed ExperimentallyExperimentally

R=0.125 ; c=5mM ; T*=0.185 Wacker et al. 2004

4nm

100nm

24 16-residue PolyQ Random Coils24 16-residue PolyQ Random Coils

Simulation results: Voet and Voet* results:

Voet & Voet (1990)

Model Test: Steric InteractionsModel Test: Steric Interactions

alanine: CH3

CHCONH