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Dynamical Simulation of Folding Equilibria under Different Thermodynamic and Kinetic Conditions

Until nine years ago, computer simulation could only be used to investigate the stability of the folds of proteins or peptides by submitting them in their folded form to strongly denaturing forces, e.g. at non-physiologically high temperatures [9, 10]. Folding into the native structure starting from an arbitrary structure under physiological conditions had not been observed at that time. In 1998 Daura et al. [11, 12] demonstrated the reversible folding of a peptide in solution and showed that the unfolded state was characterized by a limited number of peptide conformations. During the following years other studies of reversible peptide folding appeared [13-21]. It is now possible to investigate the folding equilibrium as function of temperature [12, 22], of pressure [23], of pH [24], of ionic strength [25, 26], and of solvent viscosity [27].

Figures 6.1 to 6.4 illustrate the effects of variation of the mentioned factors upon the folding equilibrium and kinetics for two 7-b-peptides and a 20-b-peptide in solution. The backbone atom-positional root-mean-square deviation (RMSD) from the 314-helical folded structure is shown as function of time. The 314-helical model structure (see Chapter 2) had been derived as most populated structure in methanol solution from NMR experiments [28, 29]. The upper panel of Fig. 6.1 shows that the helical fold of the 7-b-peptide is very stable at 298 K, only two major unfolding events are observed within 80 ns and the folded conformation is present for about 97% of the time. At 340 K (second panel) the 7-b-peptide is about 50% folded, in agreement with experimental data. The effect on the folding kinetics at 340 K by a change of the solvent viscosity by 3 or Jj is seen in the third and fourth panels. The folding equilibrium remains the same, but the folding kinetics is much faster [27]. Changing the pressure at 340 K from 1 atm to 1000 atm does shift the folding equilibrium towards the unfolded state, as is illustrated in Fig. 6.2 [23]. Figure 6.3 shows that the population of the helical fold decreases as the terminal groups change from (NH3+, COOH) in the upper panel, to (NH2, COO-) in the middle panel, to (NH2, COOH) in the lower panel. The 314-helical fold is more stable in the absence of protecting groups and is enhanced at acidic conditions [24]. Figure 6.4 shows that the presence of Cl- counterions stabilizes the 314-helical fold of the 20-b-peptide carrying all 20 proteinogenic side chains [26] by supporting side-chain salt-bridge formation.

Fig. 6.1 Backbone atom-positional root-mean-square deviation (residues 2-6) of MD trajectory structures with respect to the helical model structures derived from NMR data for b-heptapeptides of identical chain lengths in methanol at 1 atm (the structures are given in panel A and panel E) [57]. The

peptide with apolar side chains is simulated at 298 K (A) and at 340 K (B-D). The viscosity of the methanol solvent is reduced by a factor 3 (C) and by factor 10 (D) through mass scaling. The peptide with a few polar side chains is simulated at 340 K in normal methanol (E).

Fig. 6.2 Backbone atom-positional root-mean-square deviation (residues 2-6) of MD trajectory structures (340 K) with respect to the 314-helical model structure derived from NMR data for a b-heptapeptide (see panel A of Fig. 6.1) in methanol at 1 atm (upper panel) and at 1000 atm (lower panel) [23].
Fig. 6.3 (legend see p. 178)

Fig. 6.4 Time series of the backbone atom-positional root-mean-square distance (RMSD) (residues 2-19) of MD trajectory structures with respect to the ideal 314-helical structure for a 20-b3-peptide (sequence: Cys, Ala, Ser, His, Asn, Glu, Gly, Trp, Arg, Val, Asp, Gln, Ile, Lys, Thr, Leu, Tyr, Met, Phe, Pro). The top panel shows the results for the simulations in the methanol with the 53A6 force field. The lower left panel shows the

Fig. 6.4 Time series of the backbone atom-positional root-mean-square distance (RMSD) (residues 2-19) of MD trajectory structures with respect to the ideal 314-helical structure for a 20-b3-peptide (sequence: Cys, Ala, Ser, His, Asn, Glu, Gly, Trp, Arg, Val, Asp, Gln, Ile, Lys, Thr, Leu, Tyr, Met, Phe, Pro). The top panel shows the results for the simulations in the methanol with the 53A6 force field. The lower left panel shows the results for the simulations in water (53A6 force field) and the lower right panel the results for the simulations in methanol with the 45A3 force field. Colors represent different temperatures and ionic strengths. The magenta horizontal dashed line indicates the minimum RMSD value for which all NMR model structures would belong to the same conformational cluster (0.12 nm) [26].

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