On several occasions, the People’s Republic of China refused to share influenza viruses isolated on their territory with the World Health Organization pandemic flu surveillance system. Scholars in STS and allied disciplines have described these disputes as examples of growing conflict between global health norms of free exchange and Asian state claims of viral sovereignty. However, the discussion has largely overlooked the fact that laboratories in China freely shared genetic sequence data from isolated viruses, even when they refused to ship physical samples, a fact that complicates the opposition of open data and viral sovereignty with the different material forms of the physical sample and the nucleotide sequence. This article provides a comprehensive comparison of the heterogeneous circulations of influenza virus samples and virus gene sequences in global health influenza surveillance and argues this difference is rooted in the different knowledge-control regimes designed for exchanging samples and sequences. Engaging with debates on the position of Asian science within global scientific circulations, the article suggests that Asian scientists confront a multiplicity of global scientific infrastructures and do not necessarily rely on the authority of nation-state sovereignty to reshape global exchanges.