Cryogenic Single-Molecule Fluorescence Detection of the Mid-Infrared Response of an Intrinsic Pigment in a Light-Harvesting Complex

We observed the mid-infrared (MIR) response of a single pigment of bacteriochlorophyll a at the B800 binding site of a light-harvesting 2 complex. At a temperature of 1.5 K, a single complex in a spatially isolated spot in a near-infrared (NIR) fluorescence image was selected and was simultaneously irradiated with MIR and NIR light. We found that the temporal behavior of the NIR fluorescence excitation spectrum of individual pigments in a single complex was modulated by the MIR irradiation at 1650 cm–1. The MIR modulation of a single pigment was linearly proportional to the MIR intensity. The MIR linear response was detected in the range from 1580 to 1670 cm–1.


S2
MIR light was detected through the temporal behaviour of the fluorescence-excitation spectrum of the probe molecule. If we could directly observe the absorption of MIR photons by a single LH2 complex, we would obtain a spectrum of the absorption cross-section of LH2, s(LH2). Because nuclear vibrational motion can be treated as an ensemble of independent harmonic oscillators along normal coordinates, the absorption cross-section of the whole LH2 complex is a summation of the cross-section of all of the individual vibrational modes. The vibrational modes are labelled by number, and the absorption cross-section of the i-th vibrational mode is denoted by s i , In practice, the number of the vibrational modes to be summed depends on the wavenumber region of interest. In the MIR region of 1600-1700 cm -1 , the LH2 complex has one thousand C=O stretching vibrations as well as other types of vibrations.
In order to extract the MIR response from the NIR excitation spectrum (Fig. 3a), we chose spectral jumps between a wavenumber region above 12,620 cm -1 (state A) and another region below 12,565 cm -1 (state B).
The MIR effect was quantified by the ratio of the residence time in state B (tB) to that in state A (tA), i.e., the residence-time ratio, tB/tA. From measurements of the fluorescence-excitation spectrum, the slope of tB/tA against the MIR intensity (IMIR) was determined ( Figure 4) and plotted as the MIR response spectrum of a single BChl a molecule ( Figure 5). The response spectrum is different from the FTIR spectrum of LH2, which represents s(LH2) of eq. (S1). In order to relate this slope to the absorption cross-section, a kinetics model describing the MIR-induced spectral jumps is necessary. On this note, a simple model will be introduced, and the relation between the response spectrum and the absorption spectrum will be discussed.
The tB/tA is equivalent to the ratio of the probability of finding the molecule in state B (PB) to that in state A (PA), i.e., PB/PA. The time evolution of PB can be described by the following rate equation.
The equation consists of four terms; the first two terms represent MIR-independent jumps, and the third and the fourth represent MIR-dependent jumps. The MIR-independent jumps are characterized by the rate constants kA and kB, where kA is a probability of making a jump in unit time from state A to B and kB is the probability of a jump from B to A. The MIR-dependent jump occurs as one of the results of the absorption of a MIR photon by LH2. Strictly speaking, the absorption cross-section may differ from state A to state B. In eq. (S2) the cross-section of the i-th vibrational mode of state A is represented by # ! and that of the j-th mode of B is represented by " ' . Because the photon absorption takes place in the individual vibrational modes, the quantum efficiency with which a spectral jump occurs when a vibrational mode is excited with a MIR photon is defined for each individual vibrational mode, and designated as # ! for the i-th mode of state A and " ' for the j-th mode of state B.
The steady-state solution of the residence-time ratio is (S3) As the spectral jumps between states A and B represent isomerization between two conformational isomers of LH2, the steady-state residence-time ratio can be regarded as an equilibrium constant of the isomerization reaction between states A and B, "⇌# = [B] *+ /[A] *+ . Because this is the exact solution to eq. (S2), the equation is valid at any intensity of MIR irradiation, from the weak-irradiation limit where the MIR effect can be expanded as a power series of the MIR intensity, to the strong MIR-irradiation limit where the effect saturates at (S4b) The MIR intensity used in our experiments turned out to be within the linear range. A plot of tB / tA against IMIR showed a linear relationship (Figure 4d). This means that the MIR-independent rate of kB dominates the numerator in eq. (S3), kB >> FMIR∑ " ' " ' ' , which leads to Note that the MIR irradiation is now expressed by photon energy intensity IMIR = hnMIR FMIR. The result of the fitting to eq. (S4) is tB / tA = 0.21 + 0.0047 ´ (IMIR / W cm -2 ). Two parameters, the intercept and the slope, are determined. The intercept kA /kB = 0.21, corresponds to the residence-time ratio measured without MIR irradiation. The slope, = 0.0047 W -1 cm 2 , is variation of tB / tA per a unit IMIR increment by 1 W cm -2 . Equation (S5) indicates experimentally that the nMIR dependence can be extracted only for a quantity . When the difference of the normal modes between states A and B is ignored and the value of the intercept is substituted for kA /kB, the expression for the MIR-response becomes a little simpler: The FTIR spectrum measures the absorption cross-section of the whole LH2 The MIR-response spectrum is different from the FTIR spectrum in that, for each vibrational mode, the MIR absorption cross-section is weighted by the net effect of the MIR-induced spectral jump to change the equilibrium between states A and B.
The MIR response ∑ ! K # ! − 0.21 " ! M ! at the MIR frequency nMIR is determined from the measurement of tB / tA under MIR irradiation at frequency nMIR and intensity IMIR by The MIR-response spectrum consisting of nine different MIR frequencies is shown in Figure 5.