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FOLDING TRANSITION AND „FOLDABILITY”
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The phase transition
The phase diagram of water
Density of water: temperature and pressure dependence
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Vapor Liquid water Ice
Temperature [oC] Temperature [oC]
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„Chemical” view
RT
TG
F
U UF ln
U N Two-state model
I N Three-state modelU
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Priovalov and Mathakhadze, Adv. Prot. Chem., 47, 307-425 (1995)
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Wild typeAcid-denaturated wild typeL16A mutantC-terminal peptide
Religa et al., J. Mol. Biol., 333, 977-991 (2003)
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Millet et al.. Biochemistry 41, 321-325 (2002)
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Meersham et al., Biophys. J. 99, 2255–2263 (2010)
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Chodankhar et al., PRAMANA Journal of Physics, 71, 1021-1025 (2008)
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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)
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Thermodynamics and ensemble averages
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N
C
Experimental structure of 1BDD (red) and most probable conformations (green) at T = 280 K
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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
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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
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Ensemble-averaged contact-probability maps
T=300 K T=325 K (Tf) T=350 K
Experimental (reference)
H-bonding contacts
SC-SC contacts
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The folding funnel
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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
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Klimov & Thirumalai, Phys. Rev. Lett., 76, 4070-4073 (1996)
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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)
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