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The development of membranes that separate molecules based on chemical factors, rather than physical factors, is one promising approach to meeting the demand for highly-permeable membranes that are more selective. In this study, the design of multifunctional, pH-responsive membranes that selectively pump a target solute is detailed. The membranes consist of a gate layer made from an amine-functionalized copolymer and a reactive matrix lined by iminodiacetic acid groups, which bind divalent cations reversibly. These chemistries exhibit concurrent changes in the cation binding affinity and gate permeability in response to the pH value of the surrounding solution such that when they are exposed to an oscillating pH, the combination drives a facilitated transport mechanism that mimics ion pumps. In mixed solute systems, calcium permeated through the membrane four times faster than sucrose in the presence of an oscillating pH even though the solutes possess similar hydrodynamic sizes and permeated through the membrane at the same rate when the pH value was constant. The development of the polymeric ion pumps was guided by a model that provided several critical insights. First, the solute binding capacity and thickness of the membrane define the asymptotic limit for enhanced selectivity. Second, the maximum enhancement in selectivity is realized in the limit of infinitely rapid oscillations. The multifunctional membranes discussed here provide a platform for the development of processes that can fractionate molecules of similar size but varying chemistry.