Peptide self-assembly has been used to design an array of nanostructures that possess functional biomedical applications. Experimental studies have reported nanofilament and nanotube formation from peptide-based drug amphiphiles (DAs). These DAs have shown to possess an inherently high drug loading with a tunable release mechanism. Herein, we report rational coarse-grained molecular dynamics simulations of the self-assembly process and the structure and stability of preassembled nanotubes at longer timescales (mu s). We find that aggregation between these DAs at the submicrosecond timescale is driven by directional aromatic interactions between the drugs. The drugs form a large and high-density nucleus that is stable throughout microsecond timescales. Simulations of nanotubes characterize the drug-drug stacking and find correlations at nanometer length scales. These simulations can inform the rational molecular design of drug amphiphiles.