Computational Multiple Steady States of the Penicillin G Acylase‐Catalyzed Hydrolysis in an Isothermal CFSTR

A family of an enzymatically catalyzed reaction network was studied, which involves the hydrolysis of penicillin G by penicillin G acylase in an isothermal continuous flow stirred tank reactor (CFSTR). This system consisted of 10 coupled non‐linear equations and was found to be capable of exhibiting computational multiple steady states. A set of kinetic parameters determined from the existing experimental data were used to compute a set of rate constants and two corresponding steady states. This suggested that multiple steady states may occur in the system studied. The phenomena of bistability, hysteresis and bifurcation were discussed. Moreover, the capacity of steady state multiplicity was extended to its family of reaction networks.     

Multiple steady-state phenomena within enzyme reactors: The enzyme reaction with two substrates

The theoretical dynamic characteristics of an isothermal continuous flow stirred tank enzyme reactor (CFSTER) operating on two substrates are investigated. Under certain conditions multiple steady states are possible; namely, with an enzyme which binds with the two substrates sequentially. The occurrence of multiple steady states is found to be primarily dictated by three dimensionless parameters which incorporate rate law constants. The global stability of certain steady states is examined by numerically solving the transient material balance on the CFSTER. The effect of recycle on the dynamics of an isothermal plug flow enzyme reactor (PFER) is also studied. A general conclusion indicated by this work is that any open isothermal reaction system wherein the reaction rate law passes through a maximum with increasing substrate concentration and where back mixing occurs with exhibit multiple steady-state behavior in some operating range.     

Structures of steady states of an enzyme reaction in a CSTR

Structures at steady states have been investigated for an enzyme reaction in a continuous stirred tank reactor that has a random bi-uni reaction mechanism, using the imperfect bifurcation theory via singularities. The analysis has shown that two types of singular points exist. One of these points has the two types of transition states characterized by the hysteresis and double-limit points. It is obtained when the derivative of the steady-state equation with respect to the bifurcation parameter does not vanish. When the derivative vanishes, the other type of singular point is obtained. This point has the two transition states of hysteresis and bifurcation points.     

A comparative study of immobilized amyloglucosidase in a packed bed reactor and a continuous feed stirred tank reactor

The catalytic activity of amyloglucosidase covalently attached to DEAE-cellulose was studied in a packed bed reactor and a continuous feed stirred tank reactor (CSTR) for the reaction maltose → glucose. At low flow rates mass-transfer limitations in the bed reactor lead to lower conversions for this reactor compared to the CSTR. Simple theoretical expressions for these reactors were compared with the experimental results. There are significant differences between the kinetic parameters and pH profile of the immobilized and free enzyme. The immobilized enzyme also showed greater stability at 50°C than did free amyloglucosidase. The temperature dependence of the reaction rate was the same for immobilized and free enzyme.     

Computational multiple steady states for enzymatic esterification of ethanol and oleic acid in an isothermal CSTR

The capacity of complex biochemical reaction networks (consisting of 11 coupled non-linear ordinary differential equations) to show multiple steady states, was investigated. The system involved esterification of ethanol and oleic acid by lipase in an isothermal continuous stirred tank reactor (CSTR). The Deficiency One Algorithm and the Subnetwork Analysis were applied to determine the steady state multiplicity. A set of rate constants and two corresponding steady states are computed. The phenomena of bistability, hysteresis and bifurcation are discussed. Moreover, the capacity of steady state multiplicity is extended to the family of the studied reaction networks.     

Membrane reactor for enzymatic hydrolysis of cellobiose

A pressurized, stirred vessel attached with an ultrafiltration membrane was used as a membrane reactor, Cellobiose hydrolysis by cellobiase was carried out and theoretically analyzed in terms of steady-state conversion and flow rate through the membrane. When the flow rate exceeds a critical value, a significant fraction of the enzyme inside the reactor is localized in the concentration polarization layer where shear from stirring is high. Consequently, enzyme deactivation inside the concentration polarization layer is accelerated and the conversion decreases due to an exchange of active enzyme in bulk with deactivated enzyme in the polarization layer via convection and back diffusion. Successful operation can be obtained at flow rates lower than the critical point to avoid the polarization and thus the deactivation. It is shown that 6.5 L of 2 mg/mL of cellobiose solution is hydrolyzed to glucose with a conversion of 91% in 20 h with 1.617 mg of cellobiase enzyme, in a reactor attached with a PM 10 membrane of an effective surface area of 39.2 cm².     

In vitro demonstration of alternate stationary states in an open enzyme system containing phosphofructokinase

The kinetic properties of an open reconstituted enzyme system are investigated with the aim of demonstrating experimentally hysteretic transitions between alternate stationary states. The approach is based on a stirred flow-through reactor containing phosphofructokinase and pyruvate kinase entrapped in polyacrylamide gel. Through the reactor is pumped a solution containing fructose 6-phosphate, ATP, and phosphoenol pyruvate as well as adenylate kinase and glucose-6-phosphate isomerase. The latter two enzymes are in excess in respect to phosphofructokinase and pyruvate kinase. According to theoretical predictions the existence of multiple stationary states could be shown experimentally within precisely definable parameters. Switches between alternate stationary states have been caused by perturbations of flow rates and of reactant concentrations.     

Dynamic modeling of an enzymatic membrane reactor for the treatment of xenobiotic compounds

A membrane enzymatic reactor, consisting of a stirred tank coupled to an ultrafiltration membrane was set up for the enzymatic oxidation of xenobiotic compounds. The azo dye Orange II was selected for the model compound and manganese peroxidase for the oxidative enzyme. The ligninolytic cycle was initiated and maintained by the controlled addition of all factors (reactants, mediators, and stabilizers) at suitable rates. Considering the distinctiveness of this process, in which the substrate to be oxidized is not the primary substrate for the enzyme, a kinetic model was developed. The azo dye concentration and hydrogen peroxide addition rate were found to be the main factors affecting the process. The reaction kinetics was defined using a Michaelis-Menten model with respect to the Orange II concentration and a first-order linear dependence relative to the H(2)O(2) addition rate. The dynamic model, which takes into account both the kinetics and the hydraulics of the system, was validated by comparing the experimental results in continuous operation under steady and non-steady state to model predictions. In particular, the model predicted the behavior of the system when unexpected alterations in steady-state operation occurred. Furthermore, the model allowed us to obtain the most appropriate H(2)O(2)/Orange II ratio in the feed to maximize the process efficiency.     

A rapid-equilibrium model for the control of the Calvin photosynthesis cycle by cytosolic orthophosphate

1. A simple model based on rapid-equilibrium assumptions is derived which relates the steady-state activity of the Calvin cycle for photosynthetic carbohydrate formation in C3 plants to the kinetic properties of a single cycle enzyme (fructose bisphosphatase) and of the phosphate translocator which accounts for the export of photosynthate from the chloroplast. Depending on the kinetic interplay of these two catalysts, the model system may exhibit a single or two distinct modes of steady-state operation, or may be unable to reach a steady state. 2. The predictions of the model are analysed with regard to the effect of external orthophosphate on the steady-state rate of photosynthesis in isolated chloroplasts under conditions of saturating light and CO2. Due to the possible existence of two distinct steady states, the model may account for the stimulatory as well as the inhibitory effects of external phosphate observed in experiments with intact chloroplasts. Stability arguments indicate, however, that only the steady-state case corresponding to phosphate inhibition of the rate of photosynthesis could be of physiological interest. 3. It is concluded that chloroplasts under physiological conditions most likely operate in a high-velocity steady state characterized by a negative Calvin cycle flux control coefficient for the phosphate translocator. This means that any factor enhancing the export capacity of the phosphate translocator can be anticipated to decrease the actual steady-state rate of photosynthate export due to a decreased steady-state rate of cyclic photosynthate production.     

Effect of wall growth on the kinetic modeling of nitrite oxidation in a CSTR

A simple kinetic model was developed for describing nitrite oxidation by autotrophic aerobic nitrifiers in a continuous stirred tank reactor (CSTR), in which mixed (suspended and attached) growth conditions prevail. The CSTR system was operated under conditions of constant nitrite feed concentration and varying volumetric flow rates. Experimental data from steady-state conditions in the CSTR system and from batch experiments were used for the determination of the model's kinetic parameters. Model predictions were verified against experimental data obtained under transient operating conditions, when volumetric flow rate and nitrite feed concentration disturbances were imposed on the CSTR. The presented kinetic modeling procedure is quite simple and general and therefore can also be applied to other mixed growth biological systems.     

Application of the enzyme thermistor to the direct estimation of intrinsic kinetics using the saccharose-immobilized invertase system.

The possibility of using the enzyme thermistor (ET) for the direct determination of kinetic parameters (Km, Ki, Vm) of immobilized enzyme (IME) was evaluated using different preparations of invertase conjugated to bead celluloses. Two different ET columns packed with IME were operated in the mode of a differential enzyme reactor (short length, low substrate conversion). Kinetic parameters of the above IME reactor were computed by a nonlinear curve-fitting procedure. The obtained kinetic parameters were superverified by means of an independent differential reactor (DR) system. This system utilized an indirect postcolumn analytical method based on determination of glucose concentration in the stirred reservoir. Best agreement between the data acquired by direct (ET) and indirect (DR) methods was obtained if the ET column was operated at flow rates within the range of 1.0-1.5 ml min-1 using invertase-cellulose chlorotriazine conjugate. Influence of heat loss and flow nonideality is discussed. The proposed ET method offers a rapid, convenient, and general approach to determination of kinetic constants of IME preparations by omitting postcolumn analytical methods.     

Continuous cultivation of fission yeast: Classical and flow microfluorometry observations

The fission yeast Schizosaccharomyces pombe was grown in glucose-limited medium in a steady-state continuous flow reactor. Changes in mean cell protein and RNA contents with growth rate are consistent with earlier observations under different conditions. Flow microfluorometry measurements of the frequency functions of DNA at different dilution rates show changes in coordination of DNA synthesis and cell separation. Shifting from batch growth to small dilution rates results in unusual cell aggregation which leads to multiple steady states at identical operating conditions.     

Purification and properties of the deoxyribonucleic acid polymerase induced by vaccinia virus.

The vaccinia virus-induced DNA polymerase has been purified about 500-fold from a cytoplasmic extract of vaccinia-infected HeLa cells. Analysis of the purified fraction by sodium dodecyl sulfate-polyacrylamide gel electrophoresis reveals a single polypeptide of 110,000 daltons, which is greater than 95% pure. This polypeptide co-sediments with polymerase activity through a glycerol gradient. The sedimentation coefficient of the enzyme is 6.3 S, and its Stokes radius is 4.6 nm. The molecular weight of the native enzyme derived from these values is 115,000. Vaccinia polymerase is therefore a single large polypeptide of 110,000 to 115,000 daltons. The purified fraction has no significant endonuclease activity, but a strong exonuclease activity co-purifies with polymerase activity through every step in the isolation. The polymerase and exonuclease activities are inactivated at 45 degrees C at the same rate. It is likely, therefore, that both activities are catalyzed by the same polypeptide. The exonuclease hydrolyzes DNA predominantly in the 3' leads to 5' direction, to produce 5' mononucleotides. The exonuclease degrades single-stranded DNA more rapidly than duplex DNA, and the rate of digestion of both single-stranded and double-stranded DNA increases as the size of the substrate decreases. Single-stranded circular DNA is a potent inhibitor of the exonuclease activity, but duplex circular DNA has no significant effect on its activity.     

Continuous alpha-amylase production using Bacillus amyloliquefaciens adsorbed on an ion exchange resin

Summary A method for the continuous production of extracellular alpha amylase by surface immobilized cells of Bacillus amyloliquefaciens NRC 2147 has been developed. A large-pore, macroreticular anionic exchange resin was capable of initially immobilizing an effective cell concentration of 17.5 g DW/1 (based on a total reactor volume of 160 ml). The reactor was operated continuously with a nutrient medium containing 15 g/l soluble starch, as well as yeast extract and salts. Aeration was achieved by sparging oxygen enriched air into the column inlet. Fermentor plugging by cells was avoided by periodically substituting the nutrient medium with medium lacking in both soluble starch and yeast extract. This fermentor was operated for over 200 h and obtained a steady state enzyme concentration of 18700 amylase activity units per litre (18.7 kU/l), and an enzyme volumetric productivity of 9700 amylase activity units per litre per hour (9.7 kU/l-h). Parallel fermentations were performed using a 2 l stirred vessel fermentor capable of operation in batch and continuous mode. All fermentation conditions employed were identical to those of the immobilized cell experiments in order to assess the performance of the immobilized cell reactor. Batch stirred tank operation yielded a maximum amylase activity of 150 kU/l and a volumetric productivity of 2.45 kU/l-h. The maximum cell concentration obtained was 5.85 g DW/l. Continuous stirred tank fermentation obtained a maximum effluent amylase activity of 6.9 kU/l and a maximum enzyme volumetric productivity of 2.73 kU/l-h. Both of these maximum values were observed at a dilution rate of 0.345 l/h. The immobilized cell reactor was observed to achieve larger volumetric productivities than either mode of stirred tank fermentation, but achieved an enzyme activity concentration lower than that of the batch stirred tank fermentor.     

Regulation of the NAD Malic Enzyme from Crassula

Using size exclusion chromatography, the nicotinamide adenine dinucleotide malic enzyme purified to near homogeneity from leaves of Crassula argentea was found to exist in at least three aggregational states (dimer, tetramer, and octamer). These forms differ in their apparent kinetic characteristics in initial rate assays, but all display similar characteristics at the steady state. The presence of 50 millimolar malate during chromatography causes a shift in favor of the smaller forms with the tetramer predominating. The native enzyme, when diluted 1/1000 and incubated 18 hours in buffer of high ionic strength, changes its steady state kinetic parameters to ones which indicate a low activity and low affinity for malate. When 50 millimolar malate or 50 micromolar coenzyme A are present the loss of activity and increase in K_m is reduced. When both malate and coenzyme A are present the effects in minimizing the change in kinetic characteristics are additive.     

Cellulase production by Trichoderma reesei

Summary A model is proposed for the enzyme production by Trichoderma reesei (QM 9414), which assumes control of the active enzyme transport through the cell membrane as a key parameter for the enzyme activity change in the culture filtrate. In a stirred tank reactor, continuous cultivation of the fungus was carried out in the dilution rate range of D=0.01–0.032 h^–1. After changing the dilution rate it took 3–4 weeks to attain a steady state in enzyme activity. Reducing sugars, dissolved protein, enzyme activity (filter-paper and glucosidase activities), cellulose and nitrogen content of the sediment, the elementary analysis of the cell and the composition of the outlet gas were all determined during cultivation. At a dilution rate of D=0.025 h^–1 all of these properties change due to derepression (for D<0.025 h^–1) or repression (for D>0.025 h^–1) of the enzymes which are responsible for the active transport of cellulases from the cell into the medium. The cellulase excretion causes a decrease of the yield coefficient of growth and a reduction of the nitrogen content of the cells.In a two-stage system the time to attain a steady state increases to 4–6 weeks. At low dilution rates the enzyme activity is only slightly higher in the second stage than in the first. At high dilution rates, at which the enzyme is not excreted into the medium in the first stage, enzyme activity can be increased considerably in the second stage.     

Rapid-quench and isotope-trapping studies on fructose-1,6-bisphosphatase

Rapid-quench kinetic measurements yielded presteady-state rate data for rabbit liver fructose-1,6-bisphosphatase (FBPase) (a tetramer of four identical subunits) that are triphasic: the rapid release of Pi (complete within 5 ms), followed by a second reaction phase liberating additional Pi that completes the initial turnover of two or four subunits of the enzyme (requiring 100-150 ms), and a steady-state rate whose magnitude depends on the [alpha-Fru-1,6-P2]/[FBPase] ratio. With Mg2+ in the presence of excess alpha-fructose 1,6-bisphosphate (alpha-Fru-1,6-P2) all four subunits turn over in the pre steady state; with Mn2+ only two of the four are active. Thus the expression of half-site reactivity is a consequence of the nature of the metal ion and not a subunit asymmetry. In the presence of limiting alpha-anomer concentrations only two of the four subunits now remain active with Mg2+ as well as with Mn2+ in the pre steady state. However, so that the amount of Pi released can be accounted for, a beta leads to alpha anomerization or direct beta utilization is required at the active site of one subunit. Such behavior is consistent with the two-state conformational hysteresis displayed by the enzyme and altered affinities manifested within these states for alpha and beta substrate analogues. Under these limiting conditions the subsequent steady-state rate is limited by the beta leads to alpha solution anomerization. These data in combination with pulse--chase experiments permit evaluation of the internal equilibrium, which in the case of Mg2+ is unequivocally higher in favor of product complexes and represents a departure from balanced internal substrate-product complexes.     

Processivity and kinetics of the reaction of exonuclease I from Escherichia coli with polydeoxyribonucleotides

The enzyme exonuclease I from Escherichia coli hydrolyzes successive nucleotides from the 3'-termini of single-stranded deoxyribonucleotide homopolymers. When the reaction is stopped after partial hydrolysis, only intact starting material and small oligomers can be isolated. The distribution of oligomeric products varies with the base composition of the polymer but the largest oligomer that can be isolated from the reaction of exonuclease I with homopolymers of deoxyadenylate, deoxythymidylate, or deoxycytidylate is a decamer. These results suggest a model in which exonuclease I possesses at least two nucleotide binding sites. When both sites are filled, with 11-mers and longer polymers, the enzyme does not dissociate from the polymer during hydrolysis. When, with smaller oligomers, only a single site is filled, the reaction partitions at each oligomer between hydrolysis and dissociation. The kinetics of the reactions of exonuclease I with purified polydeoxyriboadenylates of defined size distributions have been investigated. The maximum rates of hydrolysis are nearly independent of polymer size while the apparent Michaelis constants are inversely proportional to the polymer size. A simple steady state model yields a kinetic equation that is consistent with our results. Competition experiments indicate that the rate at which exonuclease I associates with the 3'-terminus of a polydeoxyribonucleotide is independent of the polymer's chain length.     

Enzymes as biosensors. 1. Enzyme memory and sensing chemical signals

When a free enzyme exists under different conformations that 'slowly' isomerize during the conversion of a substrate into a product, the corresponding 'slow' relaxation component may interfere with the steady-state component. The apparent steady-state rate that may be measured under these conditions is called the meta-steady-state rate for it refers to the existence of metastable states of the enzyme during the reaction. By contrast to the real steady-state rate, the meta-steady-state rate is dependent upon the initial state of the enzyme, that is on the respective concentrations of the free enzyme forms. The simplest model that may display this type of behaviour is the mnemonical model. For a fixed concentration of the last product of the reaction sequence the meta-steady state is different depending on that concentration being reached by an increase or a decrease of a previous concentration. This means that the meta-steady-state rate describes a hysteresis loop as the product concentration is increased and decreased. Owing to the existence of metastable states, the enzyme system behaves as a biosensor that is able to detect both a concentration and the direction of a concentration change. The existence of the hysteresis loop of the meta-steady-state rate implies that the two free enzyme forms display hysteresis as well. A chemical potential, called the sensing potential, is specifically associated with the 'perception' of the direction of the thermodynamic force generated by the decrease or the increase of the concentration of the ligand that binds to one of the enzyme conformations. The sensing potential of the enzyme conformer that does not bind the product increases and reaches a plateau as the chemical potential of that product is raised. Alternatively the sensing potential of the other conformer vanishes at low and high chemical potentials of the product and is significant for intermediate chemical potentials. Enzymes that display very slow conformation changes may thus be viewed as elementary sensor devices.     

Effect of mixing on the washout and steady-state performance of continuous cultures

The effects of mixing on the critical mean holding time for washout and the steady state performance of growth processes in continuous flow reactors are investigated. Macromixing, micromixing, and cell recycle arc considered. The tanks-in-series model composed of N completely mixed flow reactors, the dispersion model, the plug flow model, and a combined model composed of a plug flow reactor and a continuous stirred tank flow reactor connected in series arc used to represent the macro-mixing or residence time distribution. The extreme cases of micromixing, namely, complete segregation and maximum mixedness, as well as intermediate states of micromixing are investigated to determine their effects on washout and the occurence of multiple steady states. A technique for predicting the maximum mixedness washout condition from a knowledge of the residence time distribution is presented and used to determine the washout condition for the dispersion model under maximum mixedness conditions.