  We propose and study a model of hypothetical magnetosensitive ionic channels
which are long thought to be a possible candidate to explain the influence of
weak magnetic fields on living organisms ranging from magnetotactic bacteria to
fishes, birds, rats, bats and other mammals including humans. The core of the
model is provided by a short chain of magnetosomes serving as a sensor which is
coupled by elastic linkers to the gating elements of ion channels forming a
small cluster in the cell membrane. The magnetic sensor is fixed by one end on
cytoskeleton elements attached to the membrane and is exposed to viscoelastic
cytosol. Its free end can reorient stochastically and subdiffusively in
viscoelastic cytosol responding to external magnetic field changes and open the
gates of coupled ion channels. The sensor dynamics is generally bistable due to
bistability of the gates which can be in two states with probabilities which
depend on the sensor orientation. For realistic parameters, it is shown that
this model channel can operate in the magnetic field of Earth for a small
number (5 to 7) of single-domain magnetosomes constituting the sensor rod each
of which has a typical size found in magnetotactic bacteria and other
organisms, or even just one sufficiently large nanoparticle of a characteristic
size also found in nature. It is shown that due to viscoelasticity of medium
the bistable gating dynamics generally exhibits power law and stretched
exponential distributions of the residence times of the channels in their open
and closed states. This provides a generic physical mechanism for explanation
of the origin of such anomalous kinetics for other ionic channels whose sensors
move in viscoelastic environment provided by either cytosol or biological
membrane, in a quite general context, beyond the fascinating hypothesis of
magnetosensitive ionic channels we explore.
