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Folding transition and „ foldability ”. The phase transition. Density of water: temperature and pressure dependence. The phase diagram of water. H [J/mol]. C v [J/( mol*K )]. Temperature [ o C]. Temperature [ o C]. Vapor. Liquid water. Ice. „Chemical” view. N. U. Two-state model.

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Folding transition and foldability
Foldingtransition and „foldability”


The phase transition
The phase transition

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

N

U

Two-state model

N

I

U

Three-state model



Wild (1995)type

Acid-denaturatedwildtype

L16A mutant

C-terminal peptide

Religa et al., J. Mol. Biol., 333, 977-991 (2003)


Millet et al.. (1995)Biochemistry 41, 321-325 (2002)



Chodankhar et al., (1995)PRAMANA Journal of Physics, 71,1021-1025 (2008)


Staphylococcal protein A, B-domain (46 residues) (1995)

  • 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)



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

C

N


Variation of C conformations (green) at T = 280 K a rmsd distribution with temperature

T = 280 K

T = 300 K

T = 320 K

T = 310 K

T = 315 K

Probability

T = 325 K

T = 350 K

Ca rmsd [Å]


Protein A @ the folding-transition temperature conformations (green) at T = 280 K

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


Ensemble-averaged contact-probability maps conformations (green) at T = 280 K

H-bonding contacts

Experimental (reference)

SC-SC contacts

T=300 K

T=325 K (Tf)

T=350 K


The folding funnel conformations (green) at T = 280 K


  • Criteria of foldability conformations (green) at T = 280 K

  • Gap criterion (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



Energy spectra of a lattice model conformations (green) at T = 280 K

level 0 level 1 level 2 native

tf – folding time (MFPT to the native structure)

ts – residence time

tfts

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


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