However, menaquinol (reduced menaquinone) does not have a sufficiently strong oxidation potential to reduce NAD into NADH, requiring an up-conversion of the menaquinone. We assume, given recent evidence by Rowe et al. \cite{Rowe:2017ei}, that the up-conversion process is powered by the transmembrane proton gradient across the inner membrane. Some incoming electrons from menaquinone are sent downhill in energy to a terminal electron acceptor, pumping protons against the gradient, and adding to a reservoir of stored energy that can be used to send some electrons uphill.  The number of protons that can be pumped up against the proton gradient by sending an electron downhill uses the floor function as following,