“…This assumption is consistent with viewing the periplasm as an effectively rigid body. We have previously suggested (Hussain et al, 2018 ) that a case in which the cytoplasm is isoosmotic with the periplasm (Sochacki et al, 2011 ; Erickson, 2017 , 2021 ), such that the OM is effectively rigid and the only load-bearing layer of the cellular envelope, is inconsistent with the mechanical stability of the periplasm because the bending energies of the membranes in Equation (1) are smaller for cylindrical shapes of larger radius: thus, in rod-like cells with sufficient IM surface area, the IM is predicted to press against the cell wall and OM and squeeze out any isoosmotic periplasmic space (see Hussain et al, 2018 for a detailed discussion). Nevertheless, this case can be accommodated in our model by (1) setting K = 0 and the elastic moduli of the cell wall, Y w , to be that of the rigid OM in the cylindrical bulk of the cell, and (2) viewing K as the area-stretch modulus of the cell wall-decoupled, fluid OM in the bulge.…”