Insight into peptide folding role of solvent and hydrophobicity dynamics of conformational transitions

Hydration thermodynamics of purely hydrophobic solutes Chandler, D. et al. (2005). “Interfaces and the driving force of hydrophobic assembly", Nature 437: Small molecules Bulk-like water (~4 hydrogen bonds) “WET” hydration Clusters Fewer hydrogen bonds DEWETTING - “DRY” regime

Hydration thermodynamics of purely hydrophobic solutes Chandler, D. et al. (2005). “Interfaces and the driving force of hydrophobic assembly", Nature 437: Rr

Hydration thermodynamics of purely hydrophobic solutes Chandler, D. et al. (2005). “Interfaces and the driving force of hydrophobic assembly", Nature 437: ~4/3  R 3 ~4  R 2  4  R 2

Isabella Daidone Total free energy of solvation: Non-polar term Polar term Chothia, C. (1974). “Hydrophobic bonding and accessible surface area in proteins”. Nature 248: Solvent accessible surface area Effective surface tension Implicit solvent model: GB/SA  in  ex – Linear isotropic dielectric – Solute: Solvent:

Poisson-Boltzmann equation  in  ex – Linear isotropic dielectric – Solute: Solvent: Implicit solvent model: GB/SA Generalized Born formula for an arbitrary charge distribution Still, W. C., A. Tempczyk, et al. (1990). "Semianalytical Treatment of Solvation for Molecular Mechanics and Dynamics." JACS 112(16):

Met109 Lys 110 His111 Met 112 Ala 113 Gly 114 Ala 115 Ala 116 Ala 117 Ala 118 Gly 119 Ala 120 Val 121 Val 122 Inouye, H and Kirschner, DA. (1998). “Polypeptide chain folding in the hydrophobic core of hamster scrapie prion: analysis by X-ray diffraction”. J. Struct. Biol. 122: Prion Protein H1 peptide

H1 peptide molecular dynamics simulations Total simulation time of 1.1  s water (SPC)  -helix Length (ns)Temp (K)SolventStarting structure PME N,V,T periodic truncated octahedron 1 nm explicit solvent on all sides * * Gromos96 force field, GROMACS software package

0 1 MDpme Time (  s) 0.24 V121 G114 A115 A116 A113 H111 A118 G119 M109 M112 A117 V122 A120 K110 A115 A116 A117 A118 A120 V121 A113 M112 M109 V122 Daidone I. et al. (2005). “Theoretical characterization of  -helix and  -hairpin folding kinetics”. J. Am. Chem. Soc. 127:

Time (  s) Implicit GB/SA Explicit 0.24 Both simulations are performed with Gromos96 force field MD simulations of the H1 peptide

Thermodynamic properties  A coil k = -RT ln pkpk p coil p k, p coil probability of the system of being in state k,coil Helmholtz free energy  coil helix

~1 kJ/mol ~ 10 kJ/mol ~ 8 kJ/mol AA Explicit Implicit Explicit Implicit coilhelix  coil AA  A coil k = -RT ln pkpk p coil p k, p coil probability of the system of being in state k,coil Helmholtz free energy statistical error < 0.5 kJ/mol

1 kJ/mol 10 kJ/mol 8 kJ/mol AA Explicit Implicit Explicit Implicit coilhelix  coil AA

V121 G114 A115 A116 A113 H111 A118 G119 M109 M112 A117 V122 A120 K110 Characterization of the  -hairpin state  A coil k = -RT ln pkpk p coil 2 HB 1 HB coil......

Characterization of the  -hairpin state

V121 M109

Solvent density at the hydrophobic surface R= nm “DRY”

Solvent density at the hydrophobic surface Hydrophobic Solvent Exposed Surface Area (nm 2 ) First Hydration Shell Density (nm -2 ) around hydrophilic around hydrophobic hydrophobic analog “DRY” “WET”

Influence of hydration density on peptide thermodynamics Met 109 (H) –Val 121 (O) (nm)

Influence of hydration density on peptide thermodynamics

Dynamic characterization of the conformational transitions

“Reaction coordinates”: principal components Positional fluctuations covariance matrix Eigenvectors of fluctuations and corresponding eigenvalues q first essential eigenvector A. Amadei et al., PROTEINS, 17: , “Essential dynamics of proteins”

Time (ns) Mean square displacement along q time (  s) q (nm) projection of the trajectory on q 01

D  and D 0 are the long and short-time diffusion constants, respectively  1,  2,  3 are the relaxation times of the switching modes mean square displacement (nm 2 /ps) Free diffusion along q slope=2D 0 slope=2D 

Isabella Daidone implicit explicit   Conformational dynamics of the H1 peptide D nm 2 ps -1 D 0 nm 2 ps ( ) 0.09 (0.001) Implicit ( ) 0.02 (0.001) Explicit  3 ps  2 ps  1 ps 43 (4) - <1 102 (5) 7 (1) <1 8

water-peptide Hydrogen bond life times   Conformational dynamics of the H1 peptide D nm 2 ps -1 D 0 nm 2 ps ( ) 0.09 (0.001) Implicit ( ) Explicit  3 ps  2 ps  1 ps 43 (4) - <1 102 (5) 7 (1) < (0.001) ImplicitExplicit 49 (10) (21) 8 (3)  pp ps  wp ps intra-peptide

Acknowledgments Jeremy Alfredo Di Nola (University “La Sapienza” of Rome) Andrea Amadei (University of Rome “Tor Vergata” )