Modeling magnetosensitive ion channels in the viscoelastic environment of living cells

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 can 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 (five to seven) 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 the viscoelasticity of the 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 the explanation of the origin of such anomalous kinetics for other ionic channels whose sensors move in a viscoelastic environment provided by either cytosol or biological membrane, in a quite general context, beyond the fascinating hypothesis of magnetosensitive ionic channels we explore.