Peptide appended pillararene (PAP) is an artificial water channel resembling biological water channel proteins, which has shown a significant potential for designing bioinspired water purification systems. Given that PAP channels need to be incorporated at a high density in membrane matrices, it is critical to examine the role of channel-channel and channel-membrane interactions in governing the structural and functional characteristics of channels. To resolve the atomic-scale details of these interactions, we have carried out atomistic molecular dynamics (MD) simulations of multiple PAP channels inserted in a lipid or a block-copolymer (BCP) membrane matrix. Classical MD simulations on a sub-microsecond timescale showed clustering of channels only in the lipid membrane, but enhanced sampling MD simulations showed thermodynamically-favorable dimerized states of channels in both lipid and BCP membranes. The dimerized configurations of channels, with an extensive buried surface area, were stabilized via interactions between the aromatic groups in the peptide arms of neighboring channels. The conformational metrics characterizing the orientational and structural changes in channels revealed a higher flexibility in the lipid membrane as opposed to the BCP membrane although hydrogen bonds between the channel and the membrane molecules were not a major contributor to the stability of channels in the BCP membrane. We also found that the channels undergo wetting/dewetting transitions in both lipid and BCP membranes with a marginally higher probability of undergoing a dewetting transition in the BCP membrane. Collectively, these results highlight the role of channel dynamics in governing channel-channel and channel-membrane interfacial interactions, and provide atomic-scale insights needed to design stable and functional biomimetic membranes for efficient separations.