The algae Chlamydomonas reinhardtii and Polytomella sp., a green and a colorless member of the chlorophycean lineage respectively, exhibit a highly-stable dimeric mitochondrial F1Fo-ATP synthase (complex V), with a molecular mass of 1600 kDa. Polytomella, lacking both chloroplasts and a cell wall, has greatly facilitated the purification of the algal ATP-synthase. Each monomer of the enzyme has 17 polypeptides, eight of which are the conserved, main functional components, and nine polypeptides (Asa1 to Asa9) unique to chlorophycean algae. These atypical subunits form the two robust peripheral stalks observed in the highly-stable dimer of the algal ATP synthase in several electron-microscopy studies. The topological disposition of the components of the enzyme has been addressed with cross-linking experiments in the isolated complex; generation of subcomplexes by limited dissociation of complex V; detection of subunit-subunit interactions using recombinant subunits; in vitro reconstitution of subcomplexes; silencing of the expression of Asa subunits; and modeling of the overall structural features of the complex by EM image reconstruction. Here, we report that the amphipathic polymer Amphipol A8-35 partially dissociates the enzyme, giving rise to two discrete dimeric subcomplexes, whose compositions were characterized. An updated model for the topological disposition of the 17 polypeptides that constitute the algal enzyme is suggested. This article is part of a Special Issue entitled 'EBEC 2016: 19th European Bioenergetics Conference, Riva del Garda, Italy, July 2-6, 2016', edited by Prof. Paolo Bernardi.