A THEORY OF ENERGY TRANSFER IN THE PHOTOSYNTHETIC UNIT

Abstract

A mathematical model of energy transfer in the photosynthetic unit, based on weak interactions, is developed. Predictions of mean trapping time are derived from the estimated (dipole-dipole) interaction strength. A diffusion equation, derived directly from the delocalized picture, is used in the calculations. The trapping times calculated are surprisingly short compared to previous estimates based on a random-walk description. It appears that 2 points were overlooked in the latter. First, the number of "jumps" depends sensitively on the number of dimensions. Second, a simple pairwise interaction is inadequate because the transfer rate is proportional to the number of nearest neighbors. These points are accounted for automatically by the diffusion treatment. Estimates of transfer times, based on the dimensions of the quanta-some, are given. Using these, explicit results for fluorescence lifetime and yield are calculated for the long-wavelength absorbing pigment system. The fluorescence lifetime of the short-wavelength system may be somewhat (~ 4 times) longer. The compatibility of the short calculated lifetimes (~ 10 sec) with known experimental results is demonstrated. Both 2 and 3-dimensional arrays of chlorophyll-a molecules are considered. Experimental evidence favors the latter.