Semi-synthetic bio-hybrid channels constructed by modifications of natural ion channels had been constructed.  Leveraging modern synthetic organic chemistry, these allows pinpoint modifications of existing structures to either elucidate their transport mechanisms or to graft on new functionalities.
Gramicidin and alamethicin had been popular starting points for selective modifications.  The above diagram illustrates one example, where a crown-ether was fixed across the mouth of the ion-passing portal.  This channel shows discrete conductance but different ion selectivity than wild type gramicidin in voltage-clamp experiments.
While modification of large protein channels using mutagenesis are generally considered out of the scope of synthetic channels, the demarcation is not sharp, as supramolecular or covalent bonding of cyclodextrins to alpha-hemolysin demonstrates.