Quantification of transition dipole strengths using 1D and 2D spectroscopy for the identification of molecular structures via exciton delocalization: application to α-helices

Abstract

Vibrational and electronic transition dipole strengths are often good probes of molecular structures, especially in excitonically coupled systems of chromophores. One cannot determine transition dipole strengths using linear spectroscopy unless the concentration is known, which in many cases it is not. In this paper, we report a simple method for measuring transition dipole moments from linear absorption and 2D IR spectra that does not require knowledge of concentrations. Our method is tested on several model compounds and applied to the amide I(') band of a polypeptide in its random coil and α-helical conformation as modulated by the solution temperature. It is often difficult to confidently assign polypeptide and protein secondary structures to random coil or α-helix by linear spectroscopy alone, because they absorb in the same frequency range. We find that the transition dipole strength of the random coil state is 0.12 ± 0.013 D(2), which is similar to a single peptide unit, indicating that the vibrational mode of random coil is localized on a single peptide unit. In an α-helix, the lower bound of transition dipole strength is 0.26 ± 0.03 D(2). When taking into account the angle of the amide I(') transition dipole vector with respect to the helix axis, our measurements indicate that the amide I(') vibrational mode is delocalized across a minimum of 3.5 residues in an α-helix. Thus, one can confidently assign secondary structure based on exciton delocalization through its effect on the transition dipole strength. Our method will be especially useful for kinetically evolving systems, systems with overlapping molecular conformations, and other situations in which concentrations are difficult to determine.

Figure 1

Illustration of the effects of coupling on transition dipole strengths, frequencies and intensities in 1D and 2D IR spectra. (a) Two carbonyl groups at angle 25° separated by distance d. (b) Simulated absorbance spectrum of the carbonyls shown in (a) in the uncoupled (solid line) and coupled (dashed line) regime. (c) Simulated absorbance spectrum and (d) diagonal slice of simulated 2D IR spectrum of two near degenerate parallel (θ = 0) oscillators. In (c) and (d) uncoupled and coupled regimes are shown by solid and dashed lines, respectively.

Figure 2

Spectra of 1,3-cyclohexanedione. (a) Absorptive 2D IR spectrum. (b) Diagonal slice of the absorptive 2D IR spectrum measured at 107 mM (black lines) and 27 mM (red lines), full (solid lines) and 22% (dashed lines) intensity of the pump beam. Blue line presents the result of the measurement at 107 mM and full intensity but with intentionally misaligned pump beam. (c) Absorbance spectrum at 107 mM (black line) and 27 mM (red line). (d) Calculated d(ω) (line assignment is the same as in (b)).

Figure 3

Spectra of NMA. (a) Absorptive 2D IR spectrum. (b) Diagonal slice of the absorptive 2D IR spectrum. (c) Absorbance spectrum. (d) Calculated d(ω).

Figure 4

Absorptive 2D IR spectra of AKA peptide measured at (a) 60 °C, (b) 23 °C, and (c) 6 °C.

Figure 5

Spectra of AKA peptide at different temperatures. (a) Diagonal slice of the absorptive 2D IR spectrum at 60 °C (red line), 23 °C (blue line), and 6 °C (black line). (b) Absorbance spectrum. (c) Calculated d(ω). Line assignment in (b) and (c) is the same as in (a).

Figure 6

Derived spectra for AKA α-helix. (a) Diagonal slice of the absorptive 2D IR spectrum at 23 °C (blue line) and 6 °C (black line). (b) Absorbance spectrum. (c) Calculated d(ω). Line assignment in (b) and (c) is the same as in (a).