Abstract
This chapter introduces the theory of optical spectra and excitation energy transfer of light harvesting complexes in photosynthesis. The light energy absorbed by protein bound pigments in these complexes is transferred via an exciton mechanism to the photosynthetic reaction center where it drives the photochemical reactions. The protein holds the pigments in optimal orientation for excitation energy transfer and creates an energy sink by shifting the local transition energies of the pigments. In this way, the excitation energy is directed with high efficiency (close to 100 %) to the reaction center. In the present chapter, this energy transfer is studied theoretically. Based on crystal structure data, the excitonic couplings are calculated taking into account also the polarizability of the protein. The local transition energies are obtained by two independent methods and are used to predict the orientation of the FMO protein relative to the reaction center.
TopIntroduction
In photosynthesis energy from the sunlight is converted to chemical energy (Figure 1). The photons of the sunlight are absorbed by so-called antenna pigments (chlorophylls, bacteriochlorophylls and carotenoids) and the excitation energy is transferred to the photosynthetic reaction centre (RC), where transmembrane charge transfer reactions are driven.
Figure 1. Cartoon of the photosynthesis
In the oxygenic photosynthesis water is used as an electron source and the electron transfer is accompanied by proton gradients, which drive the production of ATP (Adenosine triphosphate), the universal energy currency, from ADP (Adenosine diphosphate). In this way light energy is converted to chemical energy. As a by-product of the water-fission, oxygen is released, which forms a basis of our life.
The oxygenic photosynthesis is performed by higher plants, algae and cyanobacteria. The water splitting of oxygenic photosynthesis requires a relatively high redox potential, which can only be achieved with two RCs connected in series. These two RCs are called photosystem (PS) I and II. Both PSs receive energy from antenna pigments or in principal from direct optical excitation. PS II is the first one in the serial connection and it is the water splitting part while PS I is the second part and the one where the proton gradient drives the ADP to ATP synthesis. The well known overall equation for the oxygenic photosynthesis reads:
where
hν is the energy of a photon with frequency
ν and
h is Planck’s constant and
C6H12O6 is the chemical formula for glucose. Another, in the sense of evolution older process
1, is the anoxygenic photosynthesis, performed by anaerobic bacteria, such as green sulfur bacteria. In contrast to the organisms performing oxygenic photosynthesis, they have only one RC. It is called bacterial reaction centre (bRC) and is structurally similar to PS I. It is able to oxidize H
2S and similar compounds. Its reaction is described in simplified form by:
where
CH2O is the chemical formula of formaldehyde. Although the scheme of the primary photosynthetic reaction is in the main well understood, the molecular mechanisms are still unclear in many cases. A combined approach by high-resolution structure determination, optical spectroscopy and theory is necessary to understand the building principles of photosynthetic systems und how function and structure of these nano-machines are related. This progress was initiated by the first high-resolution x-ray structure (2.8 Angstrom) determination of a photosynthetic pigment-protein complex (PPC) by Fenna and Matthews in 1975 (Fenna & Matthews, 1975) and 1988 the Nobel Prize in chemistry was awarded to Deisenhofer, Huber and Michel (Deisenhofer et al., 1985) for the determination of the first three-dimensional structure of a photosynthetic reaction centre, namely the RC of the purpur bacteria
Rhodopseudomonas viridis, which proceeds anoxygenic photosynthesis.
Key Terms in this Chapter
CHARMM: Chemistry at HARvard Molecular Mechanics www.charmm.org
Wavenumber: Reciprocal wavelength. Unit: cm-1, 8065.54 cm-1 = 1 eV, energy unit used typically in spectroscopy.
Monte Carlo Methods: A common type of computational algorithms used in many fields, such as simulation of the behaviour of physical systems. In contrast to other simulation methods, they are stochastic, i.e. based on (pseudo-) random numbers. In our case we vary the site energies with the help of a gaussian random distribution of a suitable width (100 cm-1) and calculate N (= 5000-10000) slightly different spectra. The resulting spectrum ist the sum over these random varied spectra. This procedure is done to simulate the natural line broadening, caused by disordered pigment motions.
Exciton State: Delocalized excited state of pigments.
Formaldehyde: CH2O. The simplest aldehyde: one hydrogen atom bonded to an aldehyde group.
Debye: 1 Debye = 1 D, CGS-unit for the electric dipole moment. Definition: Two charges +e and –e, separated by 1 Angstrom, have a dipole moment of 4.8 D; i.e. 1 D = 3.33564.10-30 Cm.
Chl: Chlorophyll
Glucose: C6H12O6. A monosaccharide (also known as sugar) and an important carbohydrate in biology.
MEAD: Macroscopic Electrostatics with Atomic Detail www.scripps.edu/mb/bashford/
FMO: Fenna-Matthews-Olson (Complex)
Vibrational Sidebands: Due to the Franck-Condon principle, the electronic excitation takes place from the electronic ground state (which is vibrationally equilibrated, i.e. is also in the vibrational ground state) to vibrational ground and higher states of the excited electronic state. The transition from the vibrational groundstate of the electronic groundstate to the vibrational groundstate of the excited electronic state is called 0-0 transition. The energy gap between the electronic groundstate and vibrational excited states of the excited electronic state is larger than that of the 0-0 transition, therefor the 0-0 spectral line is accompanied by spectral lines with higher energy due to 0-1, 0-2, … transitions. In case of the FMO protein, the 0-0 transition is dominating and the sidebands just broaden the spectral lines on the high energy side.
Gaussian Distribution (bell curve): of width (fwhm) ?.
Site Energy: Local transition energy (of a pigment) due to its environment. The so-called vacuum transition energy is the same for identical pigments. It can be estimated from the pigment transition energy in solution (Knox & Spring, 2003). We are interested in the local transition energies, which deviate from each other due to different electrostatic surroundings (protein, water, the other pigments). There is no way to directly measure the site energy!
Tetrapyrroles: Compounds containing four pyrrole rings.
Lifetime Broadening: The linewidth of the Lorentzian shaped spectral lines of the 0-0 transition is determined by the dephasing time of exciton relaxation tM . A longer dephasing time causes narrower spectral lines.
Genetic Algorithm (evolutionary algorithm): Optimization algorithm that imitates the biological evolution to find the global minimum of a non-linear multi-dimensional optimization problem. Genetic algorithms are used in multitudinous optimization problems in mathematics, physics, for technical applications and so on, so it is a very usefull concept.
Chlorosomes: Large photosynthetic antenna complex found in green sulfur bacteria. They are ellipsoidal bodies, their length is around 100 to 200 nm, width of 50 to 100 nm and height of 15 - 30 nm. They are mostly composed of BChl (c, d or e) with small amounts of carotenoids and quinones surrounded by a galactolipid monolayer.
PS: Photosystem
ATP: Adenosine triphosphate
bRC: Bacterial reaction centre
Electron Volt (eV): 1 eV = 1.60217 · 10-19 J, energy unit.
Hydrogen Sulfide: H2S. A colorless, toxic and flammable gas and responsible for the foul odor of rotten eggs. It often results from the bacterial break down of organic matter in the absence of oxygen, such as in swamps and sewers. It also occurs in volcanic gases and natural gas.
Pyrrole: C4H5N. An aromatic organic compound, arranged in a pentagon.
Chromosomes (in the context of genetic algorithms): A set of values for the quantities that have to be fitted are called a chromosome. In our case a chromosome is a set of seven values for the seven site energies we are fitting.
ADP: Adenosine diphosphate
Angstrom: 1 Angstom = 1 = 10-10 m, distance unit.
Phytol: C20H40O. A natural linear diterpene alcohol. It is an oily liquid that is nearly insoluble in water, but soluble in most organic solvents.
?G: Difference in Gibbs (free) energy.
Aldehyde Group: A functional group, which consists of a carbon atom which is bonded to a hydrogen atom and double-bonded to an oxygen atom.
fwhm: Full width at half maximum
RC: Reaction centre
BChl: Bacteriochlorophyll
Poisson Equation: . electrostatic potential, charge density, dielectric constant, nabla operator.