  The mechanism of selectivity in ion channels is still an open question in
biology. According to recent proposals, it seems that the selectivity filter of
the ion channel, which plays a key role in the channel's function, may show
quantum coherence, which can play a role in explaining the selection mechanism
and conduction of ions. However, due to decoherence theory, the presence of
environmental noise causes decoherence and loss of quantum effects. Sometimes
we hope that the effect of calssical noise of the environment in ion channels
can be modeled through a picture whose the quantum decoherence theory presents.
In this paper, we simulated the behavior of the ion channel system in the
Spin-Boson model using the unitary evolution of a stochastic Hamiltonian
operator under the classical noise model. Also, in a different approach, we
modeled the system evolution as a two-level Spin-Boson model with tunneling
interacting with a bath of harmonic oscillators, using decoherence theory. The
results of this system were discussed in different classical and quantum
regimes. By examining the results it was found that the Spin-Boson model at a
high hopping rate of Potassium ions can simulate the behavior of the system in
the classical noise approach. This result is another proof for the fact that
ion channels need high speed for high selectivity.
