Icosahedral pyruvate dehydrogenase (PDH) enzyme complexes are molecular machines consisting of a central E2 core decorated by a shell of peripheral enzymes (E1 and E3) found localized at a distance of approximately 75-90 A from the core. Using a combination of biochemical, biophysical, and cryo-electron microscopic techniques, we show here that the gap between the E2 core and the shell of peripheral enzymes is maintained by the flexible but extended conformation adopted by 60 linker polypeptides that radiate outwards from the inner E2 core, irrespective of the E1 or E3 occupancy. The constancy of the gap is thus not due to protein-protein interactions in the outer protein shell. The extended nature of the E2 inner-linker regions thereby creates the restricted annular space in which the lipoyl domains of E2 that carry catalytic intermediates shuttle between E1, E2, and E3 active sites, while their conformational flexibility facilitates productive encounters.