Empirical amide I vibrational frequency map: application to 2D-IR line shapes for isotope-edited membrane peptide bundles

Abstract

The amide I vibrational mode, primarily associated with peptide-bond carbonyl stretches, has long been used to probe the structures and dynamics of peptides and proteins by infrared (IR) spectroscopy. A number of ab initio-based amide I vibrational frequency maps have been developed for calculating IR line shapes. In this paper, a new empirical amide I vibrational frequency map is developed. To evaluate its performance, we applied this map to a system of isotope-edited CD3-zeta membrane peptide bundles in aqueous solution. The calculated 2D-IR diagonal line widths vary from residue to residue and show an asymmetric pattern as a function of position in the membrane. The theoretical results are in fair agreement with experiments on the same system. Through analysis of the computed frequency time-correlation functions, it is found that the 2D-IR diagonal widths are dominated by contributions from the inhomogeneous frequency distributions, from which it follows that these widths are a good probe of the extent of local structural fluctuations. Thus, the asymmetric pattern of line widths follows from the asymmetric structure of the bundle in the membrane.

FIG. 1

Schematic representation of the CD3-ζ peptide in the lipid bilayer.

FIG. 2

Snapshot of the system from the MD simulation of CD3-ζ. The tetrameric CD3-ζ peptide bundle is represented by green ribbons. The tails of the lipid molecules are shown as light green lines while the yellow and blue spheres represent the N and P atoms in the head groups, respectively. Oxygen and hydrogen of water are in red and light gray, respectively.

FIG. 3

Frequency shifts from gas-phase values, Δω, versus residue number. Calculations using Methods I and II are described in the text. The numbers reported are the averages of the four helices in the CD3-ζ bundle; the (one-sigma) error bars indicate the standard deviations of the mean.

FIG. 4

Contributions to frequency shifts for Methods I and II from atoms on the residues of interest, and those on its two nearest-neighbor residues, versus residue number. Δωⁿⁿ denotes contributions from backbone atoms on nearest-neighbor residues, and Δω^sc denotes contributions from side-chain atoms on all three residues.

FIG. 5

Contributions to frequency shifts for Method I versus residue number, from: all (including side-chain) atoms not subject to the 1-4 exclusion on the residue of interest and its two nearest-neighbor residues (Δω^loc), all other peptide atoms (Δω^nloc), all lipid atoms (Δω^lipid), all water atoms (Δω^water), and the four counterions (Δω^ion).

FIG. 6

2D-IR spectrum for Leu-49 calculated using Method I. The line shape shown is averaged over the four helices in the CD3-ζ bundle. The frequencies in the figure have been shifted by 59.6 cm^-1 for a direct comparison with the experimental ¹³C=¹⁸O spectrum. The diagonal width (the dashed line is the FWHM) is calculated from a diagonal slice through the maximum; the anti-diagonal width (the dotted line is the FWHM) is calculated from an anti-diagonal slice through the maximum.

FIG. 7

Diagonal widths in 2D-IR spectra; the error bars indicate the standard deviations of the mean.

FIG. 8

Anti-diagonal widths in 2D-IR spectra; the error bars indicate the standard deviations of the mean.

FIG. 9

FTCFs for four residues in the CD3-ζ bundle calculated using Method I. The long-time exponential decays obtained from fitting data for t ≥ 500 fs are plotted as dashed lines.

FIG. 10

Time constants for the slow decay, τ_s, obtained for each residue by fitting its FTCF for t ≥ 500 fs. The numbers reported are the averages of the four helices in the CD3-ζ bundle; the error bars indicate the standard deviations of the mean.

FIG. 11

Diagonal 2D-IR widths using exact and approximate line-shape functions (see text).

FIG. 12

Homogeneous and inhomogeneous IR linewidths (see text).