Self-aggregation of the microtubule-binding protein Tau reduces its functionality and is tightly associated with Tau-related diseases, termed tauopathies. Tau aggregation is also strongly associated with two nucleating six-residue segments, namely PHF6* (VQIVYK) and PHF6* (VQIINK). In this paper, using experiments and computational modeling, we study the self-assembly of individual and binary mixtures of Tau fragments containing PHF6* (R2/wt; (273)GKVQIINKKLDL(284)) and PHF6 (R3/wt; (306)VQIVYKPVDLSK(317)) and a mutant R2/Delta K280 associated with a neurodegenerative tauopathy. The initial stage of aggregation is probed by ion-mobility mass spectrometry, the kinetics of aggregation monitored with Thioflavin T assays, and the morphology of aggregates visualized by transmission electron microscopy. Insights into the structure of early aggregates and the factors stabilizing the aggregates are obtained from replica exchange molecular dynamics simulations. Our data suggest that R3/wt has a much stronger aggregation propensity than either R2/wt or R2/Delta K280. Heterodimers containing R3/wt are less stable than R3/wt homodimers but much more stable than homodimers of R2/wt and R2/Delta K280, suggesting a possible role of PHF6*-PHF6 interactions in initiating the aggregation of full-length Tau. Lastly, R2/Delta K280 binds more strongly to R3/wt than R2/wt, suggesting a possible mechanism for a pathological loss of normal Tau function.