Erythrocytes as bioreactors to decrease excess ammonium concentration in blood

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.

The study developed several mathematical models for various included into red blood cells (erythrocytes, RBCs) enzymatic systems, which were supposed could be able to remove ammonium from the blood. The systems of differential equations for all these models had a common part that included equations for glycolysis metabolites, which did not change because of the encapsulation of additional enzymes into erythrocytes. These equations are presented in Table S1. Further, in Tables S2-S6 the residual parts of the differential equation systems are presented describing the glycolysis metabolites (for each of the models separately), which were changed as a result of the investigated enzymes encapsulation into RBCs. Tables S7 and S8 present equations for enzymes of glycolysis, pentose phosphate pathway and energy-consuming processes in RBCs, as well as equations for enzymes included into RBCs, respectively. Each Vi symbol presents the rate of the reaction catalysed by the enzyme i. Table S1. Differential equations for the glycolysis metabolites, common for all models a) .

Variable
Differential equation V NADP-GDH is a rate of NADP-dependent GDH. V transpRYP , V transpAKG , and V transpALA represent rates of PYR, AKG and ALA transport across the RBC membrane. V ox is the oxidation rate for NADPH. 3   Table S3. Differential equations for the glycolysis metabolites in the presence of AAT and NAD-dependent GDH, co-encapsulated in erythrocytes a) .

Variable
Differential equation The equations for metabolites that are absent in Table 3 coincide with the corresponding equations in Table S2. V NAD-GDH is the rate for NAD-dependent GDH. Table S4. Differential equations for the glycolysis metabolites in the presence of coencapsulated in erythrocytes universal GDH and AAT a) .

Variable
Differential equation Universal GDH (GDH-UNI) is simultaneously NAD-and NADP-dependent.   Table S6. Differential equations for the glycolysis metabolites in erythrocytes with encapsulated glutamine synthetase (GS).

Variable
Differential equation All other ATP-ases are presented by the following equation Data on glycolysis and processes with energy consumption was taken from 1 .
8 Table S8. Equations for the description of enzymes encapsulated in erythrocytes a) NADP-dependent glutamate dehydrogenase 2-5 10 NAD/NADP-dependent glutamate dehydrogenase (item for NADP) a) Alanine aminotransferase 6 9 a) The rate for universal NAD-and NADP-dependent glutamate dehydrogenase (V GDH-UNI ) may be presented by the equation:

Determination of the steady-state rate of ammonium processing
The stationary rate of ammonium processing (V AMM ) can be achieved only under conditions of a quasi-stationary state in vivo, if the ammonium concentration is constant (in other words, if the system constantly has an ammonium inflow). This rate is determined, as shown in Fig. S1.

Dependence of the stationary V AMM on the relative AKG-permeability of the RBC membrane
The stationary V AMM for erythrocyte bioreactors (EBRs), loaded with GDH and AAT, is limited by the permeability of the RBC membrane for AKG. The entire calculated curve is 11 shown in Fig. S2. The inset shows a part of this curve with the linear dependence of the V AMM on AKG-permeability.  The permeability of the erythrocyte membrane for AKG in normal physiological conditions was accepted as the unit permeability.
In practice, we can not significantly change the membrane permeability, however, if this could be done, this could not correct the situation, because even the 100-fold increase in membrane permeability leads to a very low rate of ammonium removal. For maximum increasing in V AMM (to ~2.25 mmol/h×l RBCs ), the membrane permeability for AKG should be increased by 10 4 times, that is hardly achievable (Fig. S2).

Accumulation of glutamate into EBRs with GDH
With an increase in the permeability of the erythrocyte membrane for AKG, the rate of GLU accumulation within the erythrocyte containing GDH will increase (Fig. S3). Accumulation of this metabolite inside the cell will lead to a shift in the equilibrium of the reaction toward ammonium formation. In physiological conditions the erythrocyte has an excess of surface area relative to its volume (in 1.8-2 times). Thus, RBC may be osmotically destroyed if relative cell   Fig. S3. The accumulation of GLU inside ammocytes containing GDH at different relative RBC membrane permeability for AKG. The GDH activity is 10 IU/ml RBCs . The relative RBC membrane permeability for AKG (P AKG ) was equal: 1to the normal physiological permeability (P AKG =1 arb. un.); 2 -P AKG =10 arb. un.; 3 -P AKG =100 arb. un.; 4 -P AKG =1000 arb. un.

GLU, mmol/l RBCs
volume increases more than 1.8-2 times. Model calculations of increasing RBC volume with an increase in the concentration of non-penetrating molecules of different charge inside the cell are presented in Fig. S4. They show, that theoretically, the accumulation of GLU inside erythrocytes in concentrations above 40-50 mmol/l RBCs can cause accelerated cell destruction due to impaired osmotic balance between cells and the external environment 1 (Fig. S4). 13 However, this is hardly possible in real conditions. With the physiological permeability of the membrane for AKG, accumulating such concentration of GLU within the erythrocyte will take a very long time (about several months). Theoretically, the time to reach this concentration decreases with increasing permeability of the membrane for AKG by 100 or more times. The intracellular concentration of GLU 40 mmol/l RBCs can be achieved for ~270 or 50 h at a 100-and 1000-fold increase in this permeability, respectively (Fig. S3).

Erythrocytes and bioreactors quality evaluation
Quality was studied for the initial erythrocytes, bioreactors loaded with GDH and AAT, as well as control erythrocytes, which underwent a complete protein encapsulation procedure, but

Preservation of GDH and AAT activity inside bioreactors at storage
The activity of each enzyme in EBRs was measured spectrophotometrically as described in the main text (Methods), on the day of preparation and during the weekly storage (see above).
The results obtained showed that intracellular activity decreased relatively quickly in the first two days of storage. Then this decrease almost ceased. After 6 days of storage (i.e., on the seventh day after EBRs preparation), the activity of AAT and GDH decreased on average by about 24 and 50%, respectively (Fig. S5a).

Haematological indices
Haematological indices of the initial and control RBCs, as well as EBRs, were measured using the automatic haematological analyser Micros OT (АВХ-France, Montpellier, France).
The mean cell volume (МСV in fl) and the mean cell haemoglobin concentration (МСНС, in g/dl) in EBRs and control erythrocytes were about 30% lower than those in native RBCs.
Especially strong (~ by 45% compared to native RBCs) was a decrease in the mean cellular haemoglobin (МСН, in pg) for cells treated with hypoosmotic dialysis (Figs S5b, S5d, and S5c, respectively). Included enzymes did not affect haematological indices, since the values of these indices in EBRs were very close to those in control RBCs that did not contain GDH and AAT.
The decrease in indices of the EBRs was slightly higher than previously reported when GDH was included in mouse erythrocytes 10 . This may indicate that the dialysis procedure in our case was slightly more stringent, because was performed at a lower osmolality of the dialysis solution (65 mOsm/kg compared to ~100 mOsm/kg in the study 10 ). Despite the fact that during the enzyme encapsulation the RBCs indices were changed sufficiently, further decrease of these indices virtually did not occur during the storage of EBRs and control RBCs at 4 o C (Figs S5b-d).

Osmotic fragility curves of the initial RBCs and EBRs with GDH and AAT
The osmotic fragility curves of the original (native) erythrocytes and EBRs obtained were measured as dependence of the value of lysed cells fraction on the osmolality of the solution.
These fractions were measured after the addition of the cell suspension to a series of saline solutions with different osmolality. The measurements were performed on an Biochrom® Anthos Zenyth 340rt microplate reader (Biochrom, Ltd., Cambridge, UK). To a number of NaCl solutions of different osmolality (from 0 to 300 mOsm/kg) (980 μl each), a cell suspension with a haematocrit of 5% was added (on 20 μl). The resulting suspensions were incubated for 30 min at room temperature. Then the samples were centrifuged (8 min at 1000 g) and absorbance was measured in supernatants at λ=540 nm (D 540 ). The percentage of lysed cells was determined as the ratio (in %) of D 540 measured in the supernatant of a specific sample to D 540 of the same sample at 100% lysis (in a solution with zero osmolality). The value of osmotic resistance was characterised by the osmolality of the solution, at which 50% of the original cells were lysed (Hc 50 ). The osmolality of solutions was determined using a Vapor Pressure Osmometer (Vapro 5600) (Wescor Inc., Logan, UT, USA).
The osmotic fragility curves (Fig. S6a) were measured on different days of storage. In order not to overload the figure, only the averaged curves for day 0 (day of the EBRs preparation) and the curves obtained after 6 days of storage are given. The shape of the osmotic resistance curve for the EBRs on the day of their production differs significantly from the curve for the initial native RBCs. However, during storage, the curve for EBRs changes its shape and shifts to the left (Fig. S6a). After 6 days of storage, these curves hardly differ at the 50% level of haemolysis, but the EBRs have a slightly higher resistance to low osmolality than the suspension of the initial RBCs. The osmolality values, at which 50% haemolysis occurs, were somewhat decreased for both curves at storage, but this decrease was not very significant (Fig. S6b). The activity of some glycolytic enzymes and the concentrations of metabolites used in the mouse erythrocyte-bioreactor model * ) All parameter values are presented in Table 1 and Table 2 in the main text.