  Selectivity filter is a gate in ion channels which are responsible for the
selection and fast conduction of particular ions across the membrane (with high
throughput rates of $10^8$ ions/sec and a high 1:$10^4$ discrimination rate
between ions). It is made of four strands as the backbone, and each strand is
composed of sequences of five amino acids connected by peptide units H-N-C=O in
which the main molecules in the backbone that interact with ions in the filter
are carbonyl (C=O) groups that mimic the transient interactions of ion with
binding sites during ion conduction. It has been suggested that quantum
coherence and possible emergence of resonances in the backbone carbonyl groups
may play a role in mediating ion conduction and selectivity in the filter.
Here, we investigate the influence of noise and disorder on the efficiency of
excitation energy transfer (EET) in a linear harmonic chain of $N=5$ sites with
dipole-dipole couplings as a simple model for one P-loop strand of the
selectivity filter backbone in biological ion channels. We include noise and
disorder inherent in real biological systems by including spatial disorder in
the chain, and random noise within a weak coupling quantum master equation
approach. Our results show that disorder in the backbone considerably reduces
EET, but the addition of noise helps to recover high EET for a wide range of
system parameters. Our analysis may help for better understanding of the
coordination of ions in the filter as well as the fast and efficient
functioning of the selectivity filters in ion channels.
