Hydrogen-bond driven loop-closure kinetics in unfolded polypeptide chains

Abstract

Characterization of the length dependence of end-to-end loop-closure kinetics in unfolded polypeptide chains provides an understanding of early steps in protein folding. Here, loop-closure in poly-glycine-serine peptides is investigated by combining single-molecule fluorescence spectroscopy with molecular dynamics simulation. For chains containing more than 10 peptide bonds loop-closing rate constants on the 20-100 nanosecond time range exhibit a power-law length dependence. However, this scaling breaks down for shorter peptides, which exhibit slower kinetics arising from a perturbation induced by the dye reporter system used in the experimental setup. The loop-closure kinetics in the longer peptides is found to be determined by the formation of intra-peptide hydrogen bonds and transient beta-sheet structure, that accelerate the search for contacts among residues distant in sequence relative to the case of a polypeptide chain in which hydrogen bonds cannot form. Hydrogen-bond-driven polypeptide-chain collapse in unfolded peptides under physiological conditions found here is not only consistent with hierarchical models of protein folding, that highlights the importance of secondary structure formation early in the folding process, but is also shown to speed up the search for productive folding events.

Figure 1. Autocorrelation functions, G(), for the labelled peptides.

A) Molecular structure of the MR121- peptide. B) Autocorrelation functions, G() (Eq. 1), calculated from experiment and simulation for four different labelled peptides in the 6–300 ns time range. In black are shown the fits (Eq. 2) to the simulation-derived profiles.

Figure 2. Loop-closure rate constants, , for the labelled peptides.

Loop-closure rate constants evaluated from experimental- and simulation-derived autocorrelation functions in the 6–300 ns time range for labelled peptides as a function of the number of peptide bonds, . The dotted-dashed line shows the fit of a power-law function with exponent −1.4 to the experimental data for peptides with .

Figure 3. Autocorrelation functions and loop-closure rate constants for the unlabelled peptides.

A) Autocorrelation functions, G(), evaluated from simulation for unlabelled peptides with , 3, 5, 7 and 12. The curves were fitted as described in the caption of Table 2 (for clarity, the fit is shown only for the peptide - dashed black line). B) Corresponding loop-closure rate constants, and , are reported in the upper and lower half, respectively, as a function of the number of peptide bonds, . For comparison are shown in black the of the labelled peptides evaluated from the experiment (circles) and simulation (open squares). Note that fitting the G() of the unlabelled peptides as in the experiment, i.e., in the 6–300 ns time range, yields values within the error of the evaluated from the multiexponential fit described in Table 2. The dotted-dashed line shows the fit of a power-law function to the of unlabelled peptides with . C) Fraction of structures in the open state that possesses peptide hydrogen bonds (solid line) and -sheet structure (dashed line).

Figure 4. Time-dependent properties evaluated from MD simulation for the peptide.

A) End-to-end minimum distance. The horizontal line indicates the cut-off distance of 0.58 nm used to define if a conformation is closed or open. Loop-closure events on the different timescales can be observed: ps; –500 ps; ns; ns. Representative structures of the closed and open states are shown. B) Number of intra-backbone hydrogen bonds. C) Hydrogen bond existence autocorrelation function, , shown for two different kinds of hydrogen bonds present in open configurations: hydrogen bonds involved (i) and not involved (ii) in -sheet structure. Each of the two was fitted with a sum of a stretched exponential (in the picosecond time-range) and a single exponential (in the nanosecond time-range). Relaxation times in the nanosecond time-range are taken as the average hydrogen bond lifetimes and are shown in the figure. Errors are indicated in parentheses and correspond to one standard deviation obtained from 2 independent trajectories. Correlation coefficients were higher than 0.99.

Figure 5. Ramachandran plot of all nonglycine residues evaluated from simulation.

Frequency plot, analogous to the Ramachandran plot, showing the distribution of backbone conformations of all nonglycine residues evaluated from simulation for the unlabelled peptide. The plot is also representative for the other peptides. The most populated regions are the -sheet (at around −135°;135°) and polyproline II, PPII, (at around −75°; 140°) regions.

Figure 6. Effect of intra-backbone hydrogen bonds on the loop-closure kinetics.

Autocorrelation functions, G(), evaluated from simulation for the unlabelled peptide and for a -analog that was simulated in the same conditions as the peptide, but with all the charges of the backbone atoms set to zero (except for the two termini). The curves were fitted as described in the caption of Table 2.

Figure 7. Free energy profiles along the end-to-end distance.

Free energy profile along the end-to-end distance calculated from simulation for the unlabelled peptide (black) and for the uncharged -analog (red). The errors bars correspond to one standard deviation obtained from 2 independent trajectories.