Using a metadynamics approach, we investigate the potential of mean force for Na+ permeation inside a cyclic peptide nanotube (CPN) with modified interior as a function of ion position, coordination number, and lumen chemistry. We show that functionalizing the lumen of a CPN with a methyl-benzoic acid group introduces non-periodic variations in the internal energy of the nanotube, which dictate the overall free energy roughness during the permeation of Na+. These non-periodic variations arise from the structural dynamics of the functional group, where changes in the dihedral angles induced by the proximity of the ion give rise to conformational changes that increase landscape roughness and thereby decrease transport rate. Our computational framework emphasizes the advantages of using the coordination number as a collective variable to investigate the available conformations during ion permeation through CPNs, and reveals new structure-function relations for chemically tunable CPNs, paving the way for rational design of nano-porous systems with tunable selectivity and flux.