the intermembrane space by the energy of the electrons going through the electron transport chain. Four electrons are finally accepted by oxygen in the matrix to complete the electron transport chain. The protons return to the mitochondrial matrix through the protein ATP synthase. The energy is used in order to rotate ATP synthase which facilitates the passage of a proton, producing ATP. A pH difference between the matrix and intermembrane space creates an electrochemical gradient by which ATP synthase can pass a proton into the matrix favorably. Urea cycle The first two steps of the urea cycle take place within the mitochondrial matrix of liver and kidney cells. In the first step ammonia is converted into carbamoyl phosphate through the investment of two ATP molecules. This step is facilitated by carbamoyl phosphate synthetase I. The second step facilitated by ornithine transcarbamylase converts carbamoyl phosphate and ornithine into citrulline. After these initial steps the urea cycle continues in the inner membrane space until ornithine once again enters the matrix through a transport channel to continue the first to steps within matrix. Transamination α-Ketoglutarate and oxaloacetate can be converted into amino acids within the matrix through the process of transamination. These reactions are facilitated by transaminases in order to produce aspartate and asparagine from oxaloacetate. Transamination of α-ketoglutarate produces glutamate, proline, and arginine. These amino acids are then used either within the matrix or transported into the cytosol to produce proteins. Regulation Regulation within the matrix is primarily controlled by ion concentration, metabolite concentration and energy charge. Availability of ions such as Ca2+ control various functions of the citric acid cycle. in the matrix activates pyruvate dehydrogenase, isocitrate dehydrogenase, and α-ketoglutarate dehydrogenase which increases the reaction rate in the cycle. Concentration of intermediates and coenzymes in the matrix also increase or decrease the rate of ATP production due to anaplerotic and cataplerotic effects. NADH can act as an inhibitor for α-ketoglutarate, isocitrate dehydrogenase, citrate synthase, and pyruvate dehydrogenase. The concentration of oxaloacetate in particular is kept low, so any fluctuations in this concentrations serve to drive the citric acid cycle forward. The production of ATP also serves as a means of regulation by acting as an inhibitor for isocitrate dehydrogenase, pyruvate dehydrogenase, the electron transport chain protein complexes, and ATP synthase. ADP acts as an activator. Protein synthesis The mitochondria contains its own set of DNA used to produce proteins found in