We present here a molecular dynamics study on a promising class of peptide nanotubes with a partially hydrophobic inner cavity and an easy chemical functionalization of the lumen of the cylindrical structure. The structural and dynamical behavior of the nanotube in water, methanol, and chloroform has been analyzed using state of the art theoretical methods. The nanotube structure is always well preserved, but solvent-dependent dynamic alterations are evident. Such dynamic effects are surprisingly more severe in the most viscous solvent (water), as a consequence of the competition in polar solvents between intra- and intermolecular hydrogen bonds. Stiffness analysis from the collected trajectories helped us to characterize the equilibrium deformability of the nanotube, while steered dynamics simulations were used to determine the magnitude of free energy associated with nanotube growth. Analysis of the carrier and permeation properties of the compounds reveals surprising properties: (i) permeability for the most polar solvent (water), (ii) carrier properties for the most apolar solvent (chloroform), and (iii) neither good permeation nor carrier properties for the intermediate solvent in polarity (methanol). Results reported here constitute the most extensive characterization of these nanotubes presented to date and open many intriguing questions on their stability, dynamics, and transport/carrier properties.