J. Phys. Chem. 1996, 100, 4693-4696
4693
Inverted Regions in the Curve of Photodestruction Quantum Yield versus Photon Energy Kaiqin Lao Department of Molecular and Cell Biology, 229 Stanley Hall #3206, UniVersity of California, Berkeley, Berkeley, California 94720-3206 ReceiVed: NoVember 6, 1995; In Final Form: January 4, 1996X
The curve of photodestruction quantum yield versus photon energy for tryptophan and phycocyanin has an inverted region where the quantum yield decreases as the absorbed photon energy increases. A formula is proposed to predict the existence of inverted regions in photochemical reactions. This formula is used to describe the inverted behavior of the quantum yield of photodissociation for tryptophan and phycocyanin. The model also describes the quantum yields for the photodissociation of H2O and O3.
More than 30 years ago, Marcus predicted that the rate of an electron-transfer reaction would decrease when the free energy difference of a donor and an acceptor is greater than the reorganization energy of a molecule and its solvent.1 Marcus theory has inspired extensive research on long-distance electrontransfer reactions in biological systems, such as photosynthetic reaction centers.2,3 The existence of an inverted region in the curve of rate versus free energy was confirmed experimentally in 1984.4 Here we explore some experimental evidence for the existence of inverted regions in photochemical reactions. Photochemical reactions are among the most extensively studied reactions.5 Many successful quantum mechanical and semiclassical theories have been developed to describe the reaction mechanisms.6 The Landau-Zener formula predicts that the quantum yield for a photochemical reaction may decrease when the energy of photons absorbed is above a certain threshold.7 However, current theories do not adequately explain why the quantum yields of photochemical reactions, including important processes such as ozone depletion,8,9 decrease with increasing excitation energy in UV. Although there have been examples hinting at the existence of inverted regions,10-15 where the quantum yield decreases as the absorbed photon energy increases, we believe the data presented here to be the first unambiguous experimental evidence demonstrating the existence of inverted regions in photochemical reactions. Photodestruction quantum yield is a measure of the number of molecules that are damaged or dissociated after absorbing a photon. In our previous work, we have shown that the photodestruction quantum yield of phycobiliproteins in the UV-B region (280-320 nm) is about 4 orders of magnitude greater than that in the visible region.16 A logical question to ask is whether the photodestruction quantum yield decreases when the energy of absorbed photon is increased into the UV-C region (below 280 nm). Whether the photodestruction quantum yield of phycobiliprotein reaches its maximum in the UV-B region is also relevant to the issue of O3 depletion in the stratosphere. Experimental Section Illumination light from a 150 W xenon arc lamp was passed through a 1/4 m monochromator with 20 nm bandwidth. The wavelength dependence of photon flux was measured using rhodamine B as a quantum counter from 200 to 600 nm. The absolute photon flux at 568 ( 10 nm was measured with a power meter (Coherent model 212) and found to be 2.73 mW X
Abstract published in AdVance ACS Abstracts, March 1, 1996.
0022-3654/96/20100-4693$12.00/0
cm-2. The emitted photons were dispersed at 90˚ geometry by another 1/4 m monochromator and collected by a photomultiplier tube. Decays of fluorescence emission monitored at the emission peaks of tryptophan (360 ( 3 nm) and phycocyanin (640 ( 3 nm) for various illumination wavelengths (210-370 nm). The photodestruction quantum yield, Φ, was calculated as follows: n(t)/n(0) ) exp(-kdt), where n(0) is the total number of molecules at time 0 and n(t) is the number of undamaged molecules after time t of illumination; kd is the photodestructive rate. kd ) σIΦ, where σ is the absorption cross section (cm2) and is related to the molar absorption coefficient (M-1 cm-1): σ ) 3.8 × 10-21; I is the illuminating light intensity (photons -1 cm-2) and Φ is the photodestruction quantum yield s (molecule per absorbed photon). The curves of relative fluorescence intensities versus the number of photons absorbed (N ) 3.8 × 10-21It) per molecule after time t illumination were fitted with the equation n(t)/n(0) ) exp(-ΦN) to obtain Φ.17 L-Tryptophan was obtained from Mann Research Laboratories and used without further purification, and phycocyanin was purified from cyanobacterium Anabaena (strain PCC 7120) by standard methods.18 Samples were dissolved in 10 mM sodium phosphate buffer (pH ) 6.8). Extinction coefficients for tryptophan and phycocyanin18 are 280nm ) 5600 M-1 cm-1 and 614nm ) 279 000 M-1 cm-1, respectively. The photon flux of each illumination wavelength was corrected by a factor of 10(-lA), where l ) 0.4 cm is the pass length of the quartz cuvette contained sample. The illumination light was focused to 0.2 cm2 to match the cross section of 80 µL ()0.08 cm3) sample in a 0.4 cm pass length quartz cuvette. The temperature (4-25 °C) was controlled by a circulating water bath. The experimental error bars were the standard derivation of three independent measurements. Results and Discussion The photodestruction quantum yield of tryptophan (ΦTrp; Figure 1C), defined as the number of molecules damaged per photon absorbed, was calculated from the decay curve of fluorescence versus the number of absorbed photons (Figure 1A).17 The interesting feature of ΦTrp is the sharp decrease of ΦTrp after a maximum at about 240 nm. A similar feature was observed for the photodestruction quantum yield (ΦPC) of phycocyanin, a light-harvesting phycobiliprotein (Figure 2B). Such inverted behavior represents a dramatic deviation from all classical models, which predict a monatomic rise of the quantum yield as the absorbed photon energy increases.19 © 1996 American Chemical Society
4694 J. Phys. Chem., Vol. 100, No. 12, 1996
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Figure 2. (A) Absorption spectrum of phycocyanin in 10 mM sodium phosphate buffer, pH ) 6.8, T ) 25 °C (614nm ) 279 000 M-1 cm-1).18 The spectrum between 240 and 400 nm was expanded by a factor of 10 to show the small peaks at 280 and 355 nm. (B) Wavelength dependence of ΦPC (solid circles). The data of ΦPC was fit by eq 1 (solid line) as the sum of two initial excited states (n ) 2 in eq 1) (dotted lines, E1 ) 34 483 cm-1 (290 nm), ∆E1 ) 8606 cm-1, F1) 2.9 × 10-10 cm-2 s, E2 ) 42 194 cm-1 (237 nm), ∆E2 ) 27 674 cm-1, and F2 ) 1.2 × 10-9 cm-2 s).20 The experimental error bars are the standard derivation of three independent measurements. Figure 1. (A) Typical decay curves of relative fluorescence intensities versus the number of absorbed photons for tryptophan illuminated at 220 nm (top curve) and 235 nm (bottom curve). The curves were fitted with the equation n(t)/n(0) ) exp(-ΦN) to obtain Φ (dotted lines). The carves illuminated at other wavelengths and the data for phycocyanin did not show for the sake of simplicity. (B) Absorption spectrum of tryptophan in 10 mM sodium phosphate buffer, pH ) 6.8, T ) 25 °C (280nm ) 5600 M-1 cm-1). (C) Wavelength dependence of ΦTrp (diamonds). The data of ΦTrp were fit by eq 1 (solid line) with two initial excited states (n ) 2 in eq 1) (dotted lines, E1 ) 33 670 cm-1 (297 nm), ∆E1 ) 12 771 cm-1, F1 ) 3.3 × 10-9 cm-2 s, E2 ) 40 984 cm-1 (244 nm), ∆E2 ) 18 840 cm-1, and F2 ) 9.3 × 10-9 cm-2 s)20. The experimental error bars are the standard derivation of three independent measurements.
The following formula is proposed to describe inverted regions in photochemical reactions. The equation was inspired by Marcus’s electron-transfer theory:1
Figure 3. Schematic illustration of potential surfaces involved in photodissociation reaction. A photon (E ) hν) excites a molecule from its electronic ground state into the excited state which is coupled with a dissociated state. D0 is the dissociation energy of the ground state. Ei is the photon energy that gives maximum quantum yield for the ith electronic state and corresponds to the energy where the initial excited electronic state and dissociative state are crossing. ∆Ei is the energy difference of Ei and the origin of the ith electronic excited state, Ei0.
n
Φ(E) ) ∑ρi/h(4π∆EikBT)1/2exp[-(Ei - E)2/4∆EikBT] (1) i
Here Φ(E) is the total quantum yield; E is the energy of the absorbed photon (Figure 3); Ei is the photon energy that gives maximum quantum yield; Fi is a constant for the ith electronic state (Fi is related to the electronic coupling term, Vi, between the ith initial excited state and the dissociation state and is approximated by Fi ) |Vi|2/kitotal, where kitotal is the sum of the dissociation reaction rate and other competing rates); ∆Ei is the energy difference between Ei and the origin of the ith electronic state Ei0; n is the total number of initial excited electronic states involved in the photochemical reaction; kB is Boltzmann’s constant; T is the absolute temperature; and h is Planck’s constant. Ideally, Ei corresponds to the energy where the initial excited electronic state and the dissociated state intersect, and ∆Ei is related to the barrier height of the dissociation reaction20 (Figure 3). The electron-transfer rate (ket) in the Marcus formula reaches its maximum value when the free energy driving force (∆G) equals the reorganization energy (λ), whereas here the photodestruction quantum yield reaches its maximum value when the
absorbed photon energy E equals Ei in eq 1. The existence of an inverted region in the curve of quantum yield versus photon energy is predicted by eq 1. A two-level model (n ) 2 in eq 1) was used to fit the quantum yield data in Figure 1C (solid lines). The absorption spectrum of tryptophan near 280 nm corresponds to three low-lying, overlapping π f π* electronic transitions (Figure 1B): two correspond to the low-lying, closely overlapping π f π* electronic transitions (designated 1La and 1Lb )21 assigned to the absorption band of the indole ring for the region between 280 and 300 nm, and the other corresponds to the strong π f π* electronic transition assigned to the 220 nm absorption peak of the indole ring. ΦTrp is composed of two components with maxima around 297 and 244 nm, respectively (Figure 1C, dotted lines). Although the inverted region for the low-energy state of the tryptophan (below 297 nm) is not clear due to overlapping, the inverted region of the high-energy state (below 244 nm) is clearly seen. The invariance area of ΦTrp below 210 nm (which deviates from the model) is a consequence of overlap with electronic states from the carboxyl group of the amino acid. We have shown that the efficient energy-transfer processes within individual phycobiliproteins or phycobilisome light-
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J. Phys. Chem., Vol. 100, No. 12, 1996 4695
harvesting complexes do not affect the quantum yield of UV-B photodamage.16 Since such fast energy-transfer processes (
