Knowledge of the mechanisms of interaction between self-aggregating peptides and nucleic acids or other polyanions is key to the understanding of many aggregation processes underlying several human diseases (e.g. Alzheimer's and Parkinson's diseases). Determining the affinity and kinetic steps of such interactions is challenging due to the competition between hydrophobic self-aggregating forces and electrostatic binding forces. Kahalalide F (KF) is an anticancer hydrophobic peptide which contains a single positive charge that confers strong aggregative properties with polyanions. This makes KF an ideal model to elucidate the mechanisms by which self-aggregation competes with binding to a strongly charged polyelectrolyte such as DNA. We use optical tweezers to apply mechanical forces to single DNA molecules and show that KF and DNA interact in a two-step kinetic process promoted by the electrostatic binding of DNA to the aggregate surface followed by the stabilization of the complex due to hydrophobic interactions. From the measured pulling curves we determine the spectrum of binding affinities, kinetic barriers and lengths of DNA segments sequestered within the KF-DNA complex. We find there is a capture distance beyond which the complex collapses into compact aggregates stabilized by strong hydrophobic forces, and discuss how the bending rigidity of the nucleic acid affects such process. We hypothesize that within an in vivo context, the enhanced electrostatic interaction of KF due to its aggregation might mediate the binding to other polyanions. The proposed methodology should be useful to quantitatively characterize other compounds or proteins in which the formation of aggregates is relevant. ; Comment: 34 pages, 8 figures, Supplementary Information