Although the outward-directed proton transport across biological membranes is well studied and its importance for bioenergetics is clearly understood, inward-directed light-driven proton pumping by microbial rhodopsins has remained a mystery both physiologically and mechanistically. A new family of Antarctic rhodopsins, which is a subgroup within a novel class of schizorhodopsins reported recently, includes a member, denoted as AntR, which proved amenable to extensive characterization with experiments and computation. Phylogenetic analyses identify AntR as distinct from the well-studied microbial rhodopsins that function as outward-directed ion pumps, and bioinformatics sequence analyses reveal amino acid substitutions at conserved sites essential for outward proton pumping. Modeling and numerical simulations of AntR, combined with advanced analyses using the graph theory and centrality measures from social sciences, identify the dynamic three-dimensional network of hydrogen-bonded water molecules and amino acid residues that function as communication hubs in AntR. This network undergoes major rearrangement upon retinal isomerization, showing important changes in the connectivity of the active center, retinal Schiff base, to the opposing sides of the membrane, as required for proton transport. Numerical simulations and experimental studies of the photochemical cycle of AntR by spectroscopy and site-directed mutagenesis allowed us to identify pathways that could conduct protons in the direction opposite to that commonly known for outward-directed pumps.