Novel synthetic mimics of antimicrobial peptides have been developed to exhibit structural properties and antimicrobial activity similar to those of natural antimicrobial peptides (AMPs) of the innate immune system. These molecules have a number of potential advantages over conventional antibiotics, including reduced bacterial resistance, cost-effective preparation, and customizable designs. In this study, we investigate a family of nylon-3 polymer-based antimicrobials. By combining vesicle dye leakage, bacterial permeation, and bactericidal assays with small-angle X-ray scattering (SAXS), we find that these polymers are capable of two interdependent mechanisms of action: permeation of bacterial membranes and binding to intracellular targets such as DNA, with the latter necessarily dependent on the former. We systemically examine polymer-induced membrane deformation modes across a range of lipid compositions that mimic both bacteria and mammalian cell membranes. The results show that the polymers' ability to generate negative Gaussian curvature (NGC), a topological requirement for membrane permeation and cellular entry, in model Escherichia coli membranes correlates with their ability to permeate membranes without complete membrane disruption and kill E. coli cells. Our findings suggest that these polymers operate with a concentration-dependent mechanism of action: at low concentrations permeation and DNA binding occur without membrane disruption, while at high concentrations complete disruption of the membrane occurs. This article is part of a Special Issue entitled: Interfacially Active Peptides and Proteins. Guest Editors: William C. Wimley and Kalina Hristova.