Identifying the driving forces and the mechanism of association of huntingtin-exon1, a close marker for the progress of Huntington's disease, is an important prerequisite to finding potential drug targets and, ultimately, a cure. We introduce here a modeling framework based on a key analogy of the physicochemical properties of the exon1 fragment to block copolymers. We use a systematic mesoscale methodology, based on dissipative particle dynamics, which is capable of overcoming kinetic barriers, thus capturing the dynamics of significantly larger systems over longer times than considered before. Our results reveal that the relative hydrophobicity of the poly(glutamine) block as compared with the rest of the (proline-based) exon1 fragment, ignored to date, constitutes a major factor in the initiation of the self-assembly process. We find that the assembly is governed by both the concentration of exon1 and the length of the poly(glutamine) stretch, with a low-length threshold for association, even at the lowest volume fractions we considered. Moreover, this self-association occurs irrespective of whether the glutamine stretch is in random-coil or hairpin configuration, leading to spherical or cylindrical assemblies, respectively. We discuss the implications of these results for reinterpretation of existing research within this context, including that the routes toward aggregation of exon1 may be distinct from those of the widely studied homopolymeric poly(glutamine) peptides.