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Gram-negative bacteria are a serious health concern due to the strong multidrug resistance that they display, partly due to the presence of a permeability barrier comprising two membranes with active efflux. New approaches are urgently needed to design antibiotics effective against these pathogens. In this work, we present a novel topological fragment-based approach ("Hunting Fragments Of X" or "Hunting FOX") to rationally "hunt for" chemical fragments that promote compound ability to permeate the outer membrane. Our approach generalizes to other drug design applications. We measure minimum inhibitory concentrations of compounds in two strains of Pseudomonas aeruginosa with variable permeability barriers and use them as an input to the Hunting FOX algorithm to identify molecular fragments responsible for enhanced outer membrane permeation properties and candidate molecules from an external library that demonstrate good permeation ability. Overall, we present proof of concept for a novel method that is expected to be valuable for rational design of hybrid drugs., Comment: 15 pages, 5 figures, 4 pages of supporting information, 3 supporting figures, 2 ancillary files