  Using a classical master equation that describes energy transfer over a given
lattice, we explore how energy transfer efficiency along with the photon
capturing ability depends on network connectivity, on transfer rates, and on
volume fractions - the numbers and relative ratio of fluorescence chromophore
components, e.g., donor (D), acceptor (A), and bridge (B) chromophores. For a
one-dimensional AD array, the exact analytical expression for efficiency shows
a steep increase with a D-to-A transfer rate when a spontaneous decay is
sufficiently slow. This result implies that the introduction of B chromophores
can be a useful method for improving efficiency for a two-component AD system
with inefficient D-to-A transfer and slow spontaneous decay. Analysis of this
one-dimensional system can be extended to higher-dimensional systems with
chromophores arranged in structures such as a helical or stacked-disk rod,
which models the self-assembling monomers of the tobacco mosaic virus coat
protein. For the stacked-disk rod, we observe the following: (1) With spacings
between sites fixed, a staggered conformation is more efficient than an
eclipsed conformation. (2) For a given ratio of A and D chromophores, the
uniform distribution of acceptors that minimizes the mean first passage time to
acceptors is a key point to designing the optimal network for a donor-acceptor
system with a relatively small D-to-A transfer rate. (3) For a three-component
ABD system with a large B-to-A transfer rate, a key design strategy is to
increase the number of the pathways in accordance with the directional energy
flow from D to B to A chromophores.
