One may well ask why photosynthetic antenna systems are necessary for the functioning of photosynthesis. After all, the reaction centres themselves contain several chromophores that absorb visible light, and they are in principle fully capable of performing the processes of light absorption and charge separation by themselves. However, all photosynthetic organisms have developed photosynthetic antennae, thereby dramatically increasing the effective absorption cross-section of their RCs. The reason is that the complex machinery of an RC would not be able to work at an optimal rate and yield under typical sunlight conditions (we are thinking here of higher plants located at Earth’s surface: conditions for most photosynthetic bacteria would be even worse). A bare RC would have a light-limited turnover rate of 1- 10 min-I, but it is capable of operating at turnover rates of up to a few hundreds per second. Thus an RC without its antenna would use only a small fraction of its photosynthetic capacity. Moreover, the limitation of the absorption cross-section would further reduce turnover rates by additional quantum losses in the intermediate charge-separated states, which have a finite lifetime before recombining to the ground state. This can only be prevented if a second photon, leading to another turnover, is absorbed within a short time. Thus an increase in the light-limited turnover rate by a factor of at least several hundred as compared with the bare RCs would be optimal. This has been achieved by the development of light-harvesting antennae that increase the effective absorption cross-section of the RC by factors of up to several hundred. Moreover, antennae systems coupled to RCs can harvest a larger bandwidth of the solar spectrum by combining pigments that absorb at different energies.
One might conclude that very large antenna sizes would be the most desirable. However, there are several limitations on maximal antenna size, because it is essentially limited by the relative rates of energy migration through the antenna to the RC and the rate of charge separation in the RC. The larger the antenna system, the longer the average time for the arrival of excitation energy at the RC (this is often called the ‘first passage time’ of the antenna), a:id thus the larger the energy lost through competing processes in the antenna such as fluorescence and radiationless decays. Furthermore, larger antennae (other than the so-called diffusion-limited PSUs) are typically associated with longer average times for charge separation, which also increases the probability that loss processes will occur.
Let us consider some basics in order to gain insight into the principles. We can distinguish two extreme cases of antenna kinetics: ( I ) The so-called eriergy-trurzsferlimited case, where the overall rate-limiting step is energy transfer through the antenna to the RC. In this case, the intrinsic electron-transfer step in the RC is very fast (faster than the first passage time); and (2) the so-called trap-limited case, where energy transfer through the antenna is faster than charge separation in the RC. This leads to quasi-equilibrium between excited antenna and excited RC chromophores, such that energy migrates back and forth between antenna and RC several times For case (l), the average time zET for energy transfer from a regular lattice of identical chromophores to the RC can be estimated asbefore charge separation occurs.
where N is the number of antenna chromophores (the antenna size), and z,, the time of a single pairwise energy-transfer step. For a typical z,, of -100 fs, the overall transfer time is -50-100 ps for antenna sizes N of 200-300 and antenna pigments with excited-state lifetimes of -1-3 ns. Under these conditions the yield of the photosynthetic process is limited to a maximum of about 90%; the rest of the excitation energy would be dissipated in the antenna as heat and would be lost. However, the yield is well above 90% in most photosynthetic systems. Thus for the transfer-limited case the maximal antenna size is expected to be -200 chromophores per RC, or somewhat higher in the case of energetically heterogeneous antennae.
A similar limitation on antenna size arises, albeit for different reasons, in the other extreme case, case (2), that of trap-limited kinetics. In this case, energy transfer is assumed to be very fast (although there are limits on the maximal rates), but the excitation migrates through the system from pigment to pigment in a random, hopping process. If we assume that the excited-state energy of the RC is identical to that of the antenna pigments, the probability of the excitation being located on the RC becomes smaller as the antenna size increases for statistical reasons. This reduces the effective rate k,, of charge separation in the system, according to
Again using typical values for the deactivation processes in the antenna, it becomes clear that k,, must be at least 2 ns-', corresponding to an overall charge separation lifetime of about 500 ps, in order to achieve a quantum yield of more than 90%. This again limits the maximal antenna size to about 200 chromophores if severe losses in overall quantum yield are to be avoided. For heterogeneous antenna systems with chromophore energies higher than the RC energy, the maximal antenna sizes are somewhat higher.
The numbers resulting from these simple considerations agree very well with actual antenna sizes of higher plants, which range from about 100 up to a maximum of 250-300 chromophores per RC. However, in organisms which contain highly heterogeneous antenna systems, such as green photosynthetic bacteria, the number of chromophores per RC can increase to several thousands, because excitation is funnelled to the RC rather than encountering it by random hops.
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