  We study excitation energy transfer in a simple model of photosynthetic
complex. The model, described by Lindblad equation, consists of pigments
interacting via dipole-dipole interaction. Overlapping of pigments induces an
on-site energy disorder, providing a mechanism for blocking the excitation
transfer. Based on the average efficiency as well as robustness of random
configurations of pigments, we calculate the optimal number of pigments that
should be enclosed in a pigment-protein complex of a given size. The results
suggest that a large fraction of pigment configurations are efficient as well
as robust if the number of pigments is properly chosen. We compare optimal
results of the model to the structure of pigment-protein complexes as found in
nature, finding good agreement.
