Soluble huntingtin exon 1 (Httex1) with expanded polyglutamine (polyQ) engenders neurotoxicity in Huntington's disease. To uncover the physical basis of this toxicity, we performed structural studies of soluble Httex1 for wild-type and mutant polyQ lengths. Nuclear magnetic resonance experiments show evidence for conformational rigidity across the polyQ region. In contrast, hydrogen-deuterium exchange shows absence of backbone amide protection, suggesting negligible persistence of hydrogen bonds. The seemingly conflicting results are explained by all-atom simulations, which show that Httex1 adopts tadpole-like structures with a globular head encompassing the N-terminal amphipathic and polyQ regions and the tail encompassing the C-terminal proline-rich region. The surface area of the globular domain increases monotonically with polyQ length. This stimulates sharp increases in gain-of-function interactions in cells for expanded polyQ, and one of these interactions is with the stress-granule protein Fus. Our results highlight plausible connections between Httex1 structure and routes to neurotoxicity.