Energy migration and trapping in a spectrally and spatially inhomogeneous light-harvesting antenna

In this paper, we analyze the process of excitation energy migration and trapping by reaction centres in photosynthesis and discuss the mechanisms that may provide an overall description of this process in the photosynthetic bacterium Rhodospirillum (Rs.) rubrum and related organisms. A wide range of values have been published for the pigment to pigment transfer rate varying from less than 1 ps up to 10 ps. These differences occur because the interpretation of trapping measurements depend on the assumptions made regarding the organization of the photosynthetic system. As we show, they can be reconciled by assuming a spatially inhomogeneous model where the distance of the reaction center to its surrounding pigments is larger than the pigment-pigment distances within the antenna. We estimate their ratio to be 1.7-1.8. The observed spectral inhomogeneity (at low temperature) of the photosynthetic antenna has resulted in various models. We demonstrate that the excitation kinetics can be modelled at all temperatures by assuming an inhomogeneous distribution of spectral shifts for each pigment. A transition temperature can be distinguished where the effects of spectral inhomogeneity become apparent and we discuss the ranges above (e.g., room temperature), around (e.g., 77K) and below (e.g., 4K) this temperature. Although the basic model is the same in all cases, the dominant mechanism differs in each range. We present explicit expressions for the exciton lifetime in the first two cases and demonstrate that at both temperatures the transfer rate from the light-harvesting antenna to the special pair of the reaction center is the rate-limiting step. Furthermore we demonstrate that at all temperatures a finite number of functional "levels" can be distinguished in the spectral distribution. At high temperature all pigments can be considered spectrally identical and only one level is needed. In the intermediate range a blue-shifted fraction is necessary. At low temperature a third redshifted fraction must be introduced.