A large variety of animals has the ability to sense the geomagnetic field a
nd utilize it as a source of directional (compass) information. It is not k
nown by which biophysical mechanism this magnetoreception is achieved. We i
nvestigate the possibility that magnetoreception involves radical-pair proc
esses that are governed by anisotropic hyperfine coupling between (unpaired
) electron and nuclear spins. We will show theoretically that fields of geo
magnetic field strength and weaker can produce significantly different reac
tion yields for different alignments of the radical pairs with the magnetic
field. As a model for a magnetic sensory organ we propose a system of radi
cal pairs being 1) orientationally ordered in a molecular substrate and 2)
exhibiting changes in the reaction yields that affect the visual transducti
on pathway. We evaluate three-dimensional visual modulation patterns that c
an arise from the influence of the geomagnetic field on radical-pair system
s. The variations of these patterns with orientation and field strength can
furnish the magnetic compass ability of birds with the same characteristic
s as observed in behavioral experiments. We propose that the recently disco
vered photoreceptor cryptochrome is part of the magnetoreception system and
suggest further studies to prove or disprove this hypothesis.