Spinocerebellar ataxia (SCA) 3, the most common form of SCA, is a neurodegenerative rare disease characterized by polyglutamine tract expansion and self-assembly of Ataxin3 (At3) misfolded proteins into highly organized fibrillar aggregates. The At3 N-terminal Josephin Domain (JD) has been suggested as being responsible for mediating the initial phase of the At3 double-step fibrillogenesis. Several issues concerning the residues involved in the JD's aggregation and, more generally, the JD clumping mechanism have not been clarified yet. In this paper we present an investigation focusing on the JD protein-protein interaction by means of molecular modeling. Our results suggest possible aminoacids involved in JD contact together with local and non-local effects following JD dimerization. Surprisingly, JD conformational changes following the binding may involve ubiquitin binding sites and hairpin region even though they do not pertain to the JD interaction surfaces. Moreover, the JD binding event has been found to alter the hairpin open-like conformation toward a closed-like arrangement over the simulated timescale. Finally, our results suggest that the JD aggregation might be a multi-step process, with an initial fast JD-JD binding mainly driven by Arg101, followed by slower structural global rearrangements involving the exposure to the solvent of Leu84-Trp87, which might play a role in a second step of JD aggregation.