1. Theoretical and computationalphysical chemistry group Theoretical characterization of  -helix and  -hairpin folding kinetics Theoretical characterization of  -helix and  -hairpin folding kinetics Isabella Daidone Cambridge, 26/07/2005

2. Theoretical and computationalphysical chemistry group Free energy Protein folding

3. Theoretical and computationalphysical chemistry group Folding kinetics [ms - minutes] [  s timescale] Proteins Peptides [10 ns – hundreds ns] [hundreds ns -  s] C-terminal  -hairpin of GB1 protein 6  s peptide I 760 ns alanine-rich peptides

4. Theoretical and computationalphysical chemistry group Folding kinetics folding kinetics is still computationally prohibitive !!! Peptides [10 ns – hundreds ns] [hundreds ns -  s] Molecular Dynamics (MD) simulations [hundreds of ns] Simplified protein models Massive parallel computing Transition path sampling Diffusive rate theory

5. Theoretical and computationalphysical chemistry group  (q,t), peptide probability density P k (t), time probability of secondary structure states, k equilibrium fraction of secondary structure states, k external potential given by the free energy  A (q) folding reaction coordinate, q

6. Theoretical and computationalphysical chemistry group MD simulation Starting structure Equations of motion (force field) Kinetic simulation Starting condition of the system Diffusion equations (free energy gradient)  A (kJ/mol) q

7. Theoretical and computationalphysical chemistry group Folding kinetic simulation Proper reaction coordinates, q Free energy profile,  A(q), and  k (q) Diffusion coefficient, D

8. Theoretical and computationalphysical chemistry group Folding kinetic simulation Proper reaction coordinates, q Free energy profile,  A(q), and  k (q) Diffusion coefficient, D

9. Theoretical and computationalphysical chemistry group “Reaction coordinates”: essential degrees of freedom A. Amadei et al., PROTEINS, 17:412-425, 1993. Essential dynamics of proteins

10. Theoretical and computationalphysical chemistry group “Reaction coordinates”: essential degrees of freedom A. Amadei et al., PROTEINS, 17:412-425, 1993. Essential dynamics of proteins Positional fluctuations covariance matrix Eigenvectors of fluctuations and corresponding eigenvalues q first essential eigenvector

11. Theoretical and computationalphysical chemistry group Folding kinetic simulation Proper reaction coordinates, q Free energy profile,  A(q), and  k (q) Diffusion coefficient, D

12. Theoretical and computationalphysical chemistry group Thermodynamic properties  A (q) q

13. Theoretical and computationalphysical chemistry group Folding kinetic simulation Proper reaction coordinates, q Free energy profile,  A(q), and  k (q) Diffusion coefficient, D

14. Theoretical and computationalphysical chemistry group Time (ns) Free diffusion over the essential eigenvector time (ns) q (nm) -3 -2 01

15. Theoretical and computationalphysical chemistry group D  and D 0 are the long and short-time diffusion constants, respectively  1,  2,  3 are the relaxation times of the two switching modes mean square displacement (nm 2 /ps) = 2 t + 2 (D 0 -A 1 )  1 (1-exp(-t/  1 )) + 2 (D 0 -A 2 )  2 (1-exp(-t/  2 )) + 2 (D 0 -A 3 )  3 (1-exp(-t/  3 )) D  Free diffusion over the essential eigenvector slope=2D 0 slope=2D 00

16. Theoretical and computationalphysical chemistry group Model systems Prion Protein H1 peptide (14 residues) Antimicrobial temporin L (13 residues) MKHMAGAAAAGAVVFVQWFSKFLGRIL Amyloidogenic (  -sheet rich firbrils)  -helical (circular dichroism)

17. Theoretical and computationalphysical chemistry group MD simulationsof the H1 peptide MD simulations * of the H1 peptide PME N,V,T (isokinetic) periodic truncated octahedron 1 nm explicit solvent on all sides * GROMACS software package Total simulation time of 1.1  s 850300 water (SPC)  -hairpin 240300water (SPC)  -helix Length (ns)Temp (K)SolventStarting structure

18. Theoretical and computationalphysical chemistry group MD simulationsof temporin L MD simulations * of temporin L 300 water (SPC)  -helix Length (ns)Temp (K)SolventStarting structure PME N,V,T (isokinetic) periodic truncated octahedron 1 nm explicit solvent on all sides * GROMACS software package

19. Theoretical and computationalphysical chemistry group 1 H1 peptide + +++++ = 30% = 70%

20. Theoretical and computationalphysical chemistry group 5 temporin L 280240 Time (ns) = 16% = 14%= 70%

21. Theoretical and computationalphysical chemistry group  A (kJ/mol) q (nm) 0 1234576 L=0L=1L=2 k qk q L=1 L=0 L=2

22. Theoretical and computationalphysical chemistry group Diffusion coefficients 2.4 10 -5 (0.5 10 -5 )  -hairpin 3.2 10 -5 (0.5 10 -5 )  -helix D nm 2 ps -1 system <1  1 ps 0.026 (0.001) 0.026 (0.001) D 0 nm 2 ps -1 7.8 (1) 4.3 (1)  2 ps 113.4 (2) 30.6 (2)  3 ps 

23. Theoretical and computationalphysical chemistry group Eigenvector I (nm)  (q,t) 0 50 150 100 Time (ns) 0 1 -2 200  A (kJ/mol) q (nm)

24. Theoretical and computationalphysical chemistry group  -hairpin mean folding time  fold  30 ns  -helix mean folding time  fold  8 ns P k (q,t) Time (ns) + +++++

25. Theoretical and computationalphysical chemistry group  s V. Munoz et al., Nature, Folding dynamics and mechanism of  -hairpin formation. 390:196-199, 1997. Terminal  -hairpin of Protein G  exp  s  A #  kJ/mol  A (kJ/mol) q (nm)

26. Theoretical and computationalphysical chemistry group q (nm)  A (kJ/mol)  -hairpin folding kinetics 1.22 Daidone et al., 2005. Theoretical characterization of  -helix and  -hairpin folding kinetics, Manuscript in preparation. q 1 (nm) q 2 (nm)

27. Theoretical and computationalphysical chemistry groupAcknowledgments Dr. Marco D’Abramo Prof. Jeremy Smith (University of Heidelberg) Prof. Alfredo Di Nola (University “La Sapienza” of Rome) Dr. Andrea Amadei (University of Rome “Tor Vergata” )