FOLDING TRANSITION AND „FOLDABILITY”

The phase transition The phase diagram of water Density of water: temperature and pressure dependence The phase diagram of water

H [J/mol] Cv [J/(mol*K)] Temperature [oC] Temperature [oC] Vapor Liquid water Ice

„Chemical” view U N Two-state model U I N Three-state model

Priovalov and Mathakhadze, Adv. Prot. Chem., 47, 307-425 (1995)

Acid-denaturated wild type L16A mutant C-terminal peptide Religa et al., J. Mol. Biol., 333, 977-991 (2003)

Millet et al.. Biochemistry 41, 321-325 (2002)

Meersham et al., Biophys. J. 99, 2255–2263 (2010)

Chodankhar et al., PRAMANA Journal of Physics, 71, 1021-1025 (2008)

Staphylococcal protein A, B-domain (46 residues) UNRES/MREMD simulations Berendsen thermostat 32 temperatures (250 K £T £500 K) 4 trajectories/temperature (a total of 128 trajectories) 28 million MD steps @Dt = 4.9 fs Last 4 million steps for analysis WHAM to compute ensemble averages Maisuradze et al., J. Am. Chem. Soc. 132, 9444–9452 (2010)

Thermodynamics and ensemble averages

Experimental structure of 1BDD (red) and most probable conformations (green) at T = 280 K

Variation of Ca rmsd distribution with temperature T = 280 K T = 300 K T = 310 K T = 315 K T = 320 K Probability T = 325 K T = 350 K Ca rmsd [Å]

Protein A @ the folding-transition temperature Experimental (referemce) rmsd=8.7 Å „mirror image” topology rmsd=9.8 Å „mirror image” topology rmsd=5.3 Å Native topology rmsd=9.5 Å Native topology

Experimental (reference) Ensemble-averaged contact-probability maps H-bonding contacts Experimental (reference) SC-SC contacts T=300 K T=325 K (Tf) T=350 K

The Levinthal paradox C The Levinthal paradox C. Levinthal, in Mossbauer Spectroscopy in Biological Systems, edited by P. Debrunner, J. C. M. Tsibris, and E. Münck (University of Illinois Press, Urbana, 1968). Suppose the protein has 100 residues Suppose that there are 2 conformational states/residue (e.g., helix and extended), each can be visited every femtosecond. On random-search basis tf=2100*10-15 = 1015 s = 3 000 000 years But proteins fold in SECONDS!!! Nature does not have the protein-folding problem. We do.

The folding funnel (Wolynes, 1987) Entropy Energy The folding funnel (Wolynes, 1987)

Criteria of foldability Energy-gap criterion (Crippen, 1990; Shakhnovich et al., 1994) Large Tf/Tg, (folding to glass-transition temperature) ratio which is the principle of Z-score optimization (Wolynes et al., 1992) Small (Tf-Tq)/Tq ratio (Tq being the hydrophobic collapse temperature; Thirumalai et al., 1996). Inverse proportionality found of the entropy of the excited states to Tf. “Funnel sculpting” (Maritan and Seno, 2003 and Levitt et al., 2003) Hierarchy

The s criterion (Klimov, Camacho and Thirumalai, 1996) Tq – collapse transition temperature Tf – folding transition temperature

Klimov & Thirumalai, Phys. Rev. Lett., 76, 4070-4073 (1996)

Plaxco and coworkers, Biochemistry, 2002, 41, 321-325 CD data SAXS data Plaxco and coworkers, Biochemistry, 2002, 41, 321-325

Plaxco and coworkers, Biochemistry, 2002, 41, 321-325

tf ts Energy spectra of a lattice model level 0 level 1 level 2 native tf – folding time (MFPT to the native structure) ts – residence time tf ts Liwo et al., J. Phys. Chem. B, 108, 16934-16949 (2004)

S0 = entropy of the „glassy” state