Objective

1. Molecular Dynamics Simulations of Protein FibrillizationCarol K. HallDepartment of Chemical & Biomolecular Engineering North Carolina State University http://turbo.che.ncsu.edu

2. 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 .

3. 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 > 1.5 mM) and high temperature (T > 40oC) (Blondelle et al., Biochem. 1997). Peptide Sequence: KA14K a-helix b-sheets in a fibril

4. 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

5. Discontinuous 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.

6. 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)

7. Building a Protein Model to Use With DMD: Maintaining Chain Connectivity CH3,i l COi+1 COi CaHi+1 CaHi NHi+1 Sliding links (repulsion at (1-d)l, attraction at (1+d)l) allow bond length to fluctuate around ideal value, l, with tolerance d~2.5%. Bond lengths set to ideal experimental values. BondLength l (Ao) Ni-Ca,i 1.46 Ca,i-Ci 1.51 Ci-Ni+1 1.33 Ca,i -R CH3,i 1.53 NHi CH3,i+1

8. Building a Protein Model: Maintaining Proper Bond Angles, Chirality, Peptide Bond CH3,i COi+1 Pseudo-bonds maintain: ideal backbone bond angles residue L-isomerization trans-configuration Pseudo-bonds fluctuate around ideal lengths with tolerance d~2.5%. COi CaHi+1 CaHi NHi+1 NHi CH3,i+1

9. 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

10. 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

11. Model Forces: Hydrophobic Interactions COi NHi • 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 CaHi CH3,i CH3,j Square-well attraction CaHj NHj COj • ehydrophobicity= R* eH-bonding ; R = 1/10

12. Folding 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)

13. A Constant-Temperature Simulation: 48 Peptides at c=10.0mM, T*=0.14 Nguyen & Hall, PNAS (2005)

14. 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.

15. Fibril Formation at Various c & T* Fibril formation peaks at high temperatures and high concentrations. Critical temperature for fibril formation decreases with peptide concentration.

16. Amorphous Aggregate Formation at Various c & T* c=2.5mm, T*=0.08 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)

17. 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)

18. 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)

19. 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)

20. 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

21. Fibril Structure: Peptide Orientation Most peptides are in-register, same as experimental results for the Ab(10-35) peptide (Benzinger et al., PNAS 1998)

22. Forming Various Structures versus t*: c=5mM, T*=0.14 • Amorphous aggregatesform 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)

23. Fibril Formation in Seeded and Unseeded Systems at T*=0.14, c=2mM Adding a seed eliminates the fibril formation lag time , as is found experimentally.

24. Seeding Experiments to Find Nucleus 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?

25. Seeding 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

26. FibrilGrowth 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).

27. 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)

28. Effect of Chain Length Ac-KALK-NH2 on Fibrillization at c=2.5mM Increasing chain length shifts fibril formation to higher temperatures

29. Fibril Formation at Various Hydrophobic Interaction Strengths R for the 5mM System Fibril formation Increasing the hydrophobic interaction strength further to R=1/6 reduces b-sheet formation and totally prevents fibril formation. Amorphous aggregates are formed instead.

30. U D23 K282 r 0 εsalt-bridge K281 σλσ Electrostatic Interaction • 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. Square-well attraction Each side chain is represented by either one or two united atoms.* *Wallqvist & Ullner, 1994

31. Simulation Snapshots: ABeta 10-40 ABeta 10-40 (zoomed in) Simulation Box with Periodic Boundary Conditions

32. Simulation Snapshots: ABeta 10-42 Simulation Box with Periodic Boundary Conditions ABeta 10-42 (zoomed in)

33. 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.

34. 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.

35. 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

36. NH2 CO CH2 CH2 CαH NH CO Intermediate Resolution Model Representation of Glutamine CO NH2 CH2 CH2 CαH NH CO • Blue spheres have square wells for hydrophobic attraction. • Greenspheres have directionally-dependent square wells for hydrogen bond donors. • Red spheres have directionally-dependent square wells for hydrogen bond acceptors.

37. 24 Polyglutamine 16mers Form Nanotube 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.

38. Annular Structures Observed Experimentally 100nm 4nm R=0.125 ; c=5mM ; T*=0.185 Wacker et al. 2004

39. 24 16-residue PolyQ Random Coils

40. Model Test: Steric Interactions alanine: CH3 F Y CaH CO NH Simulation results: Voet and Voet* results: Voet & Voet (1990)