Despite decades of effort, it remains challenging, if not impossible, to achieve similar transport performance similar to natural channels. Inspired by the known crystal structures of transmembrane channel proteins, protein sequence-structure-transport relationships have been applied to guide material design. However, producing both molecularly defined channel sizes and channel lumen surfaces that are chemically diverse and spatially heterogeneous have been out of reach. We show that a 4-monomer-based random heteropolymer (RHP) exhibits selective proton transport at a rate similar to those of natural proton channels. Statistical control over the monomer distribution in the RHP leads to well-modulated segmental heterogeneity in hydrophobicity, which facilitates the single RHP chains to insert into lipid bilayers. This in turn produces rapid and selective proton transport, despite the sequence variability among RHP chains. We have demonstrated the importance of:the adaptability enabled by the statistical similaritythe modularity afforded by monomer chemical diversity to achieve uniform behavior in heterogeneous systems.