FOLDING TRANSITION AND „FOLDABILITY”

The phase transition

The phase diagram of water

Density of water: temperature and pressure dependence

Vapor Liquid water Ice

Temperature [oC] Temperature [oC]

„Chemical” view

RT

TG

F

U UF ln

U N Two-state model

I N Three-state modelU

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

Wild typeAcid-denaturated wild typeL16A mutantC-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 @t = 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

N

C

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

C rmsd [Å]

Prob

abil

ity

T = 280 K T = 300 K

T = 310 K T = 315 K T = 320 K

T = 325 K T = 350 K

Variation of C rmsd distribution with temperature

Experimental (referemce)

Protein A @ the folding-transition temperature

rmsd=5.3 ÅNative topology

rmsd=9.5 ÅNative topology

rmsd=8.7 Å„mirror image”

topology

rmsd=9.8 Å„mirror image”

topology

Ensemble-averaged contact-probability maps

T=300 K T=325 K (Tf) T=350 K

Experimental (reference)

H-bonding contacts

SC-SC contacts

The folding funnel

Criteria of foldability

1. Gap criterion (Shakhnovich et al., 1994)

2. Large Tf/Tg, (folding to glass-transition temperature) ratio which is the principle of Z-score optimization (Wolynes et al., 1992)

3. Small (Tf-T)/T ratio (T being the hydrophobic collapse temperature; Thirumalai et al., 1996). Inverse proportionality found of the entropy of the excited states to Tf.

4. “Funnel sculpting” (Maritan and Seno, 2003 and Levitt et al., 2003)

5. Hierarchy

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

f s

level 0 level 1 level 2 native

f – folding time (MFPT to the native structure)

s – residence time

Energy spectra of a lattice model

Liwo et al., J. Phys. Chem. B, 108, 16934-16949 (2004)