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This article explores the folding transition and "foldability" in proteins, linking thermodynamics and phase behavior in water. It discusses water's density variations with temperature and pressure, highlighting phase diagrams and essential chemical interactions. Alongside theoretical models, experimental studies, including molecular dynamics simulations, are reviewed. Notable findings include the impact of temperature on protein structure, ensemble averages, and optimal conditions for folding, emphasizing the intricate balance between enthalpy and entropy in protein stability.
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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
Priovalov and Mathakhadze, Adv. Prot. Chem., 47, 307-425 (1995)
Wild type Acid-denaturatedwildtype L16A mutant C-terminal peptide Religa et al., J. Mol. Biol., 333, 977-991 (2003)
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)
Experimental structure of 1BDD (red) and most probable conformations (green) at T = 280 K C N
Variation of Ca 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 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 H-bonding contacts Experimental (reference) SC-SC contacts T=300 K T=325 K (Tf) T=350 K
Criteria of foldability • 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 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)