Increased blood ammonium concentrations cause neurological complications. Existing drugs are not always sufficiently effective. Alternatively, erythrocytes-bioreactors (EBRs) loaded with enzymes utilizing ammonium, were suggested for ammonium removal from blood. However all they worked only for a short period of time. The reasons for this were not investigated. In this study, EBR mathematical models were developed and analysed based on the reactions of glycolysis and different enzymes utilizing ammonium, which showed that the efficiency and duration of EBRs' functioning could be limited due to low permeability of the cell membrane for some key substrates and products. A new enzyme system including glutamate dehydrogenase and alanine aminotransferase was proposed and realised experimentally, which was not limited by cell membrane permeability for glutamate and α-ketoglutarate due to creating metabolic pathway where these metabolites were produced and consumed cyclically. New bioreactors removed ammonium in vitro at the rate of 1.5 mmol/h × lRBCs (for human bioreactors) and in vivo in a model of hyperammoniemia in mice at the rate of 2.0 mmol/h × lRBCs (for mouse bioreactors), which correlated with model calculations. Experimental studies proved the proposed mathematical models are correct. Mathematical simulation of erythrocyte-bioreactors opens new opportunities for analysing the efficiency of any enzyme included in erythrocytes.