Forster energy transfer

The light energy that is absorbed in a particular antenna pigment molecule must be transported non-radiatively over relatively large distances of the order of hundreds Angstroms from the location of initial absorption to the RC. As we have already noted, this energy transfer must be very rapid in order to compete with intramolecular deactivation of excited states by processes such as internal conversion and intersystem crossing, which occur in the time range of a few ns. Several mechanisms that in principle allow energy migration through the antenna complexes on this timescale exist. The best known of these is the so-called very weak dipole interaction mechanism, better known as the Forster mechanism (Forster, 1965; Forster, 1959) (see Pearlstein, 1982a and 1982b for early reviews on photosynthetic energy transfer). The Forster mechanism is also known as the ‘hopping process’ of excitation energy transfer, since an excited state migrates through the system in a type of random walk process, albeit one which may be directionally biased depending on the amount of energetic funnelling built into the system architecture. The Forster mechanism is the most abundant mechanism of energy transfer in photosynthesis, being relevant in all photosynthetic systems, except at the shortest time scales where other mechanisms (see below) may apply.
 

The basis for the Forster mechanism is the coupling energy between the transition dipoles of the donor and acceptor molecules and an energetic restriction that is dealt with by the so-called overlap integral in the Forster equation. The advantage of the Forster formulation of energy-transfer rates is that it is directly based on easily accessible experimental quantities such as the absorption coefficient of the donor, the emission spectrum I F of the acceptor, the distance R between them, and the relative orientations of the donor and acceptor as reflected in the so-called orientation factor K* of the transition dipole moments of the donor and acceptor. The rate constant kET of a single energy-transfer step is given by

where n is the refractive index of the medium, 4~ the fluorescence yield, rF the lifetime of the donor molecule without energy transfer, and v the frequency. The part of the equation under the integral is the spectral overlap factor. Due to the inverse R6 dependence of the energy-transfer rate constant, the Forster mechanism allows energy transfer over relatively large distances, well up to 100 8, and beyond, depending on the molecular transition dipoles involved. However, for the fast transfer required in photosynthetic antenna, where single-step transfer times should typically be shorter than 1 ps, the typical maximum allowed distances R for Chl pairs are up to 15-20 A, depending somewhat on orientation.
 

The Forster mechanism assumes that both the donor and the acceptor molecules are in thermal equilibrium with the environment and that the interaction energy between the dipoles is very small compared with the energy of a typical molecular vibration. This means that the coupling does not influence the absorption spectra of the involved pigments in any appreciable fashion as compared with the uncoupled system. The mechanism allows electronic singlet-to-singlet, and also triplet-to-singlet, energy transfer. Transfer from a singlet to a triplet state is, however, not possible because the overlap integral is negligible (the ground-state-to-triplet absorption probability lying close to zero).
 

The kinetics of energy migration in the case of FiSrster transfer in the very weak coupling limit2 are described by the master equation

where pi is the probability of the excitation being located on pigment i, k"' is the rate of loss processes other than energy transfer, k, is the Forster rate of energy hopping from pigment i to pigment j , kRC is the rate of charge separation at the RC and PRC the probability of the RC being excited. Using this equation and the known Forster rate constants, the overall energy-transfer dynamics in a complex antenna system can in principle be fully calculated. However, the problem with using eq. 2.5 is the uncertainties in the Forster rate constants, which depend critically on the often-

 

unknown spectral properties of the individual pigments and on the distances and relative orientations of the pigments.
 

Due to the very large number of antenna chromophores comprising a particular antenna system, it is often not practical or possible to take into account all the individual chromophores. Rather, groups of pigments or chromophores with similar spectroscopic and kinetic properties are lumped together in a pseudo-pigment complex, called a 'compartment' when interpreting antenna energy-transfer spectra and kinetics. Such a 'compartment model', representing the general photosynthetic unit shown in Fig. 2.1, is given in Fig. 2.2. The 11 chromophores present in the antenna are lumped together into three different antenna compartments, which would differ in their spectra and kinetics. Very often such a compartment can be identified with a particular biochemical subunit of the antenna, although this is not necessarily always the case.