1. FOLDING TRANSITION AND „FOLDABILITY”

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

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

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

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

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

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

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

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

12. 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 = 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)

13. Thermodynamics and ensemble averages

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

15. 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]

16. 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

17. 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

19. 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 = years
But proteins fold in SECONDS!!!
Nature does not have the protein-folding problem. We do.

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

21. 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

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

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

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

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

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

31. S0 = entropy of the „glassy” state