Hole-Burning Spectroscopy on Excitonically Coupled Pigments in Proteins: Theory Meets Experiment

Abstract

A theory for the calculation of resonant and nonresonant hole-burning (HB) spectra of pigment-protein complexes is presented and applied to the water-soluble chlorophyll-binding protein (WSCP) from cauliflower. The theory is based on a non-Markovian line shape theory ( Renger and Marcus J. Chem. Phys. 2002 , 116 , 9997 ) and includes exciton delocalization, vibrational sidebands, and lifetime broadening. An earlier approach by Reppert ( J. Phys. Chem. Lett. 2011 , 2 , 2716 ) is found to describe nonresonant HB spectra only. Here we present a theory that can be used for a quantitative description of HB data for both nonresonant and resonant burning conditions. We find that it is important to take into account the excess energy of the excitation in the HB process. Whereas excitation of the zero-phonon transition of the lowest exciton state, that is, resonant burning allows the protein to access only its conformational substates in the neighborhood of the preburn state, any higher excitation gives the protein full access to all conformations present in the original inhomogeneous ensemble. Application of the theory to recombinant WSCP from cauliflower, reconstituted with chlorophyll a or chlorophyll b, gives excellent agreement with experimental data by Pieper et al. ( J. Phys. Chem. B 2011 , 115 , 4053 ) and allows us to obtain an upper bound of the lifetime of the upper exciton state directly from the HB experiments in agreement with lifetimes measured recently in time domain 2D experiments by Alster et al. ( J. Phys. Chem. B 2014 , 118 , 3524 ).

Figure 1

(left) Illustration of free energy surfaces of ground state |g⟩ and exciton states |M⟩ and of conformational transitions induced by multiple excitation/de-excitation processes. The optical transitions to the vibrational ground state of the lowest exciton state (resonant excitation) are shown in red; the transitions to higher excited states (nonresonant excitation) are shown in blue. (right) Probability distributions for the postburn site energy of pigment m corresponding to the different excitation conditions in the left part (same color code). Note that the distributions are not normalized due to illustrative purposes.

Figure 2

Low temperature linear absorption (T = 4 K) of Chla–WSCP (upper part) and Chlb–WSCP (lower part). The dots show the experimental data from Pieper et al.; lines show the calculations using the parameters given in Table 1. In the lower part, in addition, a calculation is shown in which the opening angle β = 30° between transition dipole moments from the crystal structure of class IIb WSCP (containing Chla) was applied, assuming that the latter are oriented along the N_B−N_D axis of Chls.

Figure 3

Low temperature (T = 4 K) linear absorption (OD) and hole-burning (HB) spectra of Chlb–WSCP. Black dashed and solid lines show experimental absorption and HB data, respectively, from Pieper et al., red solid lines show the calculations using eq 14, and blue dashed lines show the calculation using eq 13, which corresponds to the approach by Reppert. In the lower part, the blue dashed line coincides with the red line. The Δω in the lower part denotes the fwhm of the high-energy bleaching, which is used in the main text to obtain an upper bound to the lifetime of the upper exciton state. The parameters used for the calculations are given in Table 1. The arrows indicate the burn wavelength.

Figure 4

Low temperature (T = 4 K) linear absorption (OD) and hole-burning (HB) spectra of Chla–WSCP. Black dashed and solid lines show experimental absorption and HB data, respectively, from Pieper et al.; red line shows the calculation using the parameters given in Table 1.

Figure 5

Calculated absorption spectrum (black dotted curve), as well as the calculated positive (α₊(ω), red curve) and negative (α_–(ω), green curve) contributions to the hole burning spectrum α_HB(ω) = α₊(ω) – α_–(ω) (blue curve) are shown, assuming resonant burning conditions in the upper and middle parts and nonresonant burning conditions in the lower part. The HB spectra in the upper part were calculated with eq 14, in the middle part eq 13 (corresponding to Reppert’s theory) was used, and in the lower part eqs 13 and 14 yield identical results.