Kinetics of complexing activation by the magnesium ion on green crab (Scylla serrata) alkaline phosphatase.

As with mammalian enzymes, green crab (Scylla serrata) alkaline phosphatase can be activated by Mg2+ through a time-dependent course. The activation is mainly a Vmax effect. Tsou's method was used to study the kinetic course of activation. The results show that the enzyme was activated by a complexing scheme that had not been previously identified: the enzyme first reversibly and quickly binds Mg2+ and then undergoes a slow reversible course to activation, with a relatively high activation energy (78 +/- 4 kJ/mol) and a slow conformational change. The activation reaction is a single molecule reaction, and the apparent activation rate constant is independent of Mg2+ concentration if the concentration is sufficiently high. The microscopic rate constants of activation and the association constant were determined from the measurements. The proposed scheme may also be applied to the Mg2+ activation mechanism for mammalian enzyme, to explain why the activation rate is time-dependent and not diffusion controlled. Substrate binding was also shown to affect the activation rate constant.     

Shape and dynamics of thermoregulating honey bee clusters

Bacterial transport systems are traditionally treated as enzymes exhibiting a saturable binding site giving rise to an apparent K(m)of transport, whereas the maximal rate of transport is regarded equivalent to the V(max)of enzymatic reactions. Thus, the Michaelis-Menten theory is usually applied in the analysis of transport data and K(m)and V(max)are derived from the treatment of data obtained from the rate of transport at varying substrate concentrations. Such an analysis tacitly assumes that the substrate recognition site of the transport system is freely accessible to substrate. However, this is not always the case. In systems endowed with high affinity in the micro M range or those recognizing large substrates or those exhibiting high V(max), the diffusion through the outer membrane may become rate determining, particularly at low external substrate concentrations. In such a situation the dependence of the overall rate of transport (from the medium into the cytoplasm) on the substrate concentration in the medium will no longer follow Michaelis-Menten kinetics. By analysing the deviation of transport data from the corresponding ideal Michaelis-Menten plot we developed a method that allows us to determine diffusion limitation through the outer membrane. The method allows us to find the correct K(m)of the transport system functioning at the inner membrane even under conditions of strong diffusion limitation through the outer membrane. The model was tested and validified with the Escherichia coli binding protein-dependent ABC transporter for maltose. The corresponding systems for sn -glycerol-3-phospate of Escherichia coli and the alpha -cyclodextrin transport of Klebsiella oxitoca were used as test systems.     

External and internal diffusion in heterogeneous enzymes systems

The intrusion of diffusion in heterogeneous enzyme reactions, which follow. Michaelis-Menten kinetics, is quantitatively characterized by dimensionless parameters that are independent of the substrate concentration. The effects of these parameters on the overall rate of reaction is illustrated on plots commonly employed in enzyme kinetics. The departure from Michaelis-Menten kinetics due to diffusion limitations can be best assessed by using Hofstee plots which are also suitable to distinguish between internal and external transport effects. A graphical method is described for the evaluation of the reaction rate as a function of the surface concentration of the substrate from measured data.     

A comparison of the in vitro activity of DNA-armed and all-RNA hammerhead ribozymes.

Hammerhead ribozymes targeted against two unrelated RNA substrates have been prepared. For each substrate, four ribozymes, differing in their hybridising arm length and composition (DNA or RNA), have been synthesised and kinetically characterised. The presence of DNA in the hybridising arms had little effect on the overall cleavage rate when the cleavage step was rate determining. Shortening each of the hybridising arms of ribozymes from 10 to 6 nucleotides generally resulted in modest changes in rate constants for cleavage of the same 13mer substrate. In one case the presence of long RNA hybridising arms significantly impeded the cleavage reaction. Cleavage rates displayed first order dependence on hydroxide ion concentration at low pHs. At higher pH, some ribozymes deviated from this first order dependence because of a change in the rate-determining step, possibly due to a requirement for a conformation change in the ribozyme-substrate complex prior to cleavage. Ribozyme cleavage was strongly dependent on temperature in the range 5-45 degrees C, with an activation energy for the reaction of approximately 60 kJ mol-1. The ribozymes displayed biphasic dependence on magnesium ion concentration; evidence of strong apparent binding (Kd approximately 10 mM) as well as a looser interaction was observed for all ribozymes.     

An enzyme rate equation for the overall rate of reaction of gel-immobilized glucose oxidase particles under buffered conditions. I. Pseudo-one substrate conditions

The overall rate of reaction of buffered gel-immobilized glucose oxidase particles is described by means of an enzyme rate equation which relates the overall reaction rate of a particle to the free solution characteristics of the enzyme, the effective diffusivity of the limiting substrate in the gel, the characteristic particle size, and the limiting substrate concentration adjacent to the gel surface. This equation accounts quantitatively for the limitation of the overall rate of reaction by substrate diffusion, and it is used to illustrate the influence of the system parameters, i. e., particle size, enzyme concentration, and pH, on the extent of the diffusional resistance associated with gel-immobilized glucose oxidase particles. The enzyme rate equation is generally applicable to those enzymes whose kinetics approximately follow Michaelis-Menten form when in free solution.     

Gelatin-entrapped whole-cell invertase

Summary The investigated biocatalyst consists of gelatin-entrapped cells of Saccharomyces cerevisiae retaining invertase activity. Comparative examination of pH profile, apparent K_m, saturation velocity and activation energy indicates that the entrapment procedure did not influence invertase affinity with sucrose but lead to some loss of activity probably due to either enzyme inactivation or cell-wall impairment as well as to substrate diffusion limitation in the gel matrix.     

Effects of diffusion limitation on immobilized nitrifying microorganisms at low temperatures

Activation energies of suspended and immobilized nitrifying bacteria were determined and compared to determine if diffusion limitation results in decreased sensitivity for temperature. The activation energy for the respiration activity of suspended Nitrosomonas europaea and Nitrobacter agilis was found to be 86.4 and 58.4 kJ mol(-1), respectively. The activation energy for oxygen diffusion in the support material, kappa-carrageenan, determined from the effect of temperature on the effective diffusion coefficient (D), was 17.2 kJ mol(-1). Consequently, the apparent actvation energy of diffusion limited cells should be lower. It was indeed shown that due to the effect of diffusion limitation and to temperature effects on the Monod constant K(s), the immobilized-cell activity was less sensitive to temperature. The apparent activation energy for immobilized Ns. europaea was between 28.6 and 94.2 kJ mol(-1) and for immobilized Nb. agilis between 1.4 and 72.9 kJ mol(-1), depending on the oxygen concentration and temperature. (c) 1995 John Wiley & Sons, Inc.     

Acetylcholinesterase: diffusional encounter rate constants for dumbbell models of ligand.

For some enzymes, virtually every substrate molecule that encounters the entrance to the active site proceeds to reaction, at low substrate concentrations. Such diffusion-limited enzymes display high apparent bimolecular rate constants ((kcat/KM)), which depend strongly upon solvent viscosity. Some experimental studies provide evidence that acetylcholinesterase falls into this category. Interestingly, the asymmetric charge distribution of acetylcholinesterase, apparent from the crystallographic structure, suggests that its electrostatic field accelerates the encounter of its cationic substrate, acetylcholine, with the entrance to the active site. Here we report simulations of the diffusion of substrate in the electrostatic field of acetylcholinesterase. We find that the field indeed guides the substrate to the mouth of the active site. The computed encounter rate constants depend upon the particular relative geometries of substrate and enzyme that are considered to represent successful encounters. With loose reaction criteria, the computed rates exceed those measured experimentally, but the rate constants vary appropriately with ionic strength. Although more restrictive reaction criteria lower the computed rates, they also lead to unrealistic variation of the rate constants with ionic strength. That these simulations do not agree well with experiment suggests that the simple diffusion model is incomplete. Structural fluctuations in the enzyme or events after the encounter may well contribute to rate limitation.     

Bovine adrenocortical microsomal hydroxylase and thermotropic transitions substrate-cytochrome P-450 binding reaction versus substrate hydroxylation

The effect of temperture on steroid C-21 hydroxylation and substrate-cytochrome P-450 binding reaction under turnover conditions (NADPH + O₂ are investigated. The Arrhenius activity plot exhibited a single break, while the van 't Hoff plot of the substrate dissociation constant (K_s) exhibited four breaks between 10 and 40°C which corresponded to the characteristic temperatures of the lipids' phase transitions. Unlike the case of the K_s value, the detergent Triton X-114 was without effect on the Arrhenius activity plot. This indicates that the single break in the case of the enzyme activity is distinct from but not necessarily independent of the multiple breaks in the case of the K_s. At physiologic temperature and concentration of the substrate, the free energy (?9.5 kcal/mol) of the substrate-cytochrome binding reaction is more than sufficient to account for the apparent activation energy (6.6 kcal/mol) of the overall hydroxylation. This suggests that the substrate-cytochrome P-450 binding reaction has the potential of being a source of energy for the overall reaction.     

Lipase-catalyzed synthesis of sorbitol-fatty acid esters at extremely high substrate concentrations

Lipase-catalyzed synthesis of sorbitol-fatty acid esters was performed in eutectic media with extremely high substrate concentrations. Homogeneous eutectic melts of sorbitol and fatty acids of C6-C16 were prepared using an adjuvant mixture. Enhanced homogeneity of mixtures was confirmed by X-ray diffraction analysis. The substrate concentration was 3.63-6.67 M in the eutectic media, whereas in organic media the concentration was below 0.10 M. Esters were synthesized with an immobilized Candida antarctica lipase, and optimum conditions were analyzed. Compared to reactions in organic media, the initial reaction rate of ester synthesis and the overall productivity were significantly enhanced in eutectic media while the conversion yields were similar. Based on the kinetic analysis, highly viscous eutectic media were shown to influence the initial reaction rate and the apparent activation energy resulting in diffusion limitations.     

Effect of pore diffusion limitation on dextrin hydrolysis by immobilized glucoamylase

Data reported here and previously indicate that when dextrin is hydrolyzed in the presence of immobilized glucoamylase, use of a larger average molecular weight substrate leads to lower overall rates of hydrolysis, while the maltose concentration during the bulk of the reaction and the maximum glucose concentration are lower than when the soluble form of the enzyme is employed under the same conditions. Computer simulation of the system demonstrated that all three observations were caused by pore diffusion limitation: the first by slow diffusion of substrate, the second by slow diffusion of intermediates, and the third by slow diffusion of glucose. Follow-up experiments with glucoamylase immobilized to particles of different sizes confirmed this finding, as results with the smallest beads were identical to those with soluble glucoamylase.     

Kinetic studies of alpha-galactosidase-containing mold pellets on PNPG hydrolysis.

Little is known about techniques for applying untreated microbial cells containing enzymes directly to industrial processes as a biocatalyst. The kinetic behavior of alpha-galactosidase-containing spherical pellets which are formed naturally under given conditions in a submerged culture of Mortierella vinacea was studied on the hydrolysis of PNPG (p-nitrophenyl-alpha-D-galactopyranoside). The effect on intraparticle diffusion on the overall reaction rate was assessed by the use of an effectiveness factor, which was calculated by the approximate solution to the equation derived from the mass balance within a pellet. The experimental effectiveness factors were found to be represented as a single function of the modified Thiele modulus, including such parameters as pellet size, enzyme concentration in the pellet, and substrate concentration. As the diffusional effect became more significant, the marked substrate inhibition as seen for a free enzyme disappeared gradually. The effect of product inhibition on the pellets was much weaker than that for a free enzyme at a given substrate concentration. In the region of diffusion controlled reaction, it was found that the rate is proportional to the square root of the enzyme concentration in the pellet. In addition, similarly to what was reported previously for a free enzyme,the reaction in a batch system was found to be approximately representable as simple first-order kinetics in which the rate constant was dependent on the initial substrate concentration.     

Urokinase bound to fibrocollagenous tubes: an in vitro kinetic study

Urokinase (UK) has been immobilized to the inner surfaces of fibrocollagenous tubes (FCT) in an attempt to develop a fibrinolytic biomaterial which may be suitable for use as a small diameter vascular prosthesis. The enzyme was bound by adsorption followed by glutaraldehyde crosslinking. An in virto kinetic study of immobilized urokinase was conducted by employing the tubular material as a flow through reactor operated in a batch recycle mode in which the esterolysis of the model substrate, N-alpha-acetyl-L-lysine methyl ester (ALME), was monitored as a function of substrate concentration, recycle flow rate, and temperature. Results were compared with data from the soluble enzyme reaction, which was conducted in the presence and absence of 10% swine skin gelatin, in order to identify the specific effects of a collagenous microenvironment. Observed rates for the UK-FCT catalyzed reaction were observed to be dependent on recycle flow rates below 12 mL/min (Re = 107). Apparent Michaelis-Menten rate parameters were determined by a nonlinear search technique for two flow rates: one above the critical point for external diffusion effects (Re = 282) and one within the mass-transfer-limited region (Re = 71). When the latter data were corrected for external diffusion by applying the Graetz correlation for laminar flow in tubes to estimate themass transfer coefficient, the corrected K(m) of 6.45 +/- 0.38 mM agreed very closely with the diffusion free parameter (i.e. 6.13 +/- 0.63). Furthermore, this value was observed to be an order of magnitude higher than that of the soluble enzyme but approximately equal to the K(m) of the soluble enzyme in a 10% gelatin environment (8.13 +/- 1.53 mM). It is postulated that the difference in kinetic parameters between soluble and collagen immobilized UK is due to an inherent interaction between collagen and enzyme rather than to mass transfer effects. Such aninteraction is supported by the effects of collagen on thermal stability and energy of activation.     

Enzyme reactions at the surface of living cells. I. Electric repulsion of charged ligands and recognition of signals from the external milieu

The dynamic behaviour of a polyelectrolyte-bound enzyme is studied when diffusion of substrate or diffusion of product is coupled to electric repulsion and to Michaelis-Menten enzyme reaction. The definition of the classical concepts of electric partition coefficients and Donnan potential of a polyelectrolyte membrane has been extended under global non-equilibrium conditions. This extension is permissible when a strong repulsion exists of substrate and product by the fixed negative charges of the membrane. Coupling between product diffusion, electric repulsion and enzyme reaction at constant advancement may result in a hysteresis loop of the partition coefficient as the product concentration is increased in the reservoir. This hysteresis loop vanishes as the rate of product diffusion increases. No hysteresis loop may occur when electric repulsion effects are coupled to substrate diffusion and reaction. The existence of multiple values of the partition coefficient for a fixed concentration of product implies that the membrane may store short-term memory of the former product concentration present in the external milieu. The occurrence of hysteresis generated by coupling enzyme reaction, product diffusion, electric partition effects at constant advancement of the reaction may be viewed as a sensing device of product concentration in the external milieu. Surprisingly, non-linearities required to generate this sensing device come from electrostatic effects and not from enzyme kinetics.     

Erythrocytes possess an intrinsic barrier to nitric oxide consumption

It has been reported that free hemoglobin (Hb) reacts with NO at an extremely high rate (K(Hb) approximately 10(7) M(-1) s(-1)) and that the red blood cell (RBC) membrane is highly permeable to NO. RBCs, however, react with NO 500-1000 times slower. This reduction of NO reaction rate by RBCs has been attributed to the extracellular diffusion limitation. To test whether additional limitations are also important, we designed a competition test, which allows the extracellular diffusion limitation to be distinguished from transmembrane or intracellular resistance. This test exploited the competition between free Hb and RBCs for NO generated in a homogenous phase by an NO donor. If the extracellular diffusion resistance is negligible, then the results would follow a kinetic model that assumes homogenous reaction without extracellular diffusion limitation. In this case, the measured effective reaction rate constant, K(RBC), would remain invariant of the hematocrit, extracellular-free Hb concentration, and NO donor concentration. Results show that the K(RBC) approaches a constant only when the hematocrit is greater than 10%, suggesting that at higher hematocrit, the extracellular diffusion resistance is negligible. Under such a condition, the NO consumption by RBCs is still 500-1000 times slower than that by free Hb. This result suggests that intrinsic RBC factors, such as transmembrane diffusion limitation or intracellular mechanisms, exist to reduce the NO consumption by RBCs.     

Prediction of continuous reactors performance based on batch reactor deactivation kinetics data of immobilized lipase

Experiments on deactivation kinetics of immobilized lipase enzyme fromCandida cylindracea were performed in stirred batch reactor using rice bran oil as the substrate and temperature as the deactivation parameter. The data were fitted in first order deactivation model. The effect of temperature on deactivation rate was represented by Arrhenius equation. Theoretical equations were developed based on pseudo-steady state approximation and Michaelis-Menten rate expression to predict the time course of conversion due to enzyme deactivation and apparent half-life of the immobilized enzyme activity in PFR and CSTR under constant feed rate policy for no diffusion limitation and diffusion limitation of first order. Stability of enzyme in these continuous reactors was predicted and factors affecting the stability were analyzed.     

Diffusion control in blood coagulation. Activation of factor X by factors IXa/VIIIa assembled on human monocyte membranes.

This study examines mechanisms that regulate the activation of blood coagulation proteases on intact cell membranes. The activation of factor X by factors IXa and VIIIa assembled on viable monocytes is presented as a biologically relevant model for membrane-dependent proteolysis of coagulation zymogens. The hypothesis that this reaction is limited by diffusion was tested by comparing predicted with observed concentration dependence, temperature dependence, and effective rate coefficient. Rates of factor X catalysis were measured using a chromogenic substrate specific for the product, factor Xa. The value of KR and of K1/2, i.e. concentrations giving half-maximal rates in reciprocal functional titrations with substrate and enzyme, respectively, were directly correlated with the concentration of the titrated component. Arrhenius plots constructed over temperatures encompassing 10-35 degrees C were biphasic with downward concavity. Apparent activation energies were 6.01 +/- 0.93 and 35.84 +/- 8.9 kcal/mol for the interval above and below the inflection point, respectively. The effective rate coefficient calculated from apparent kinetic parameters was 3.58 +/- 0.1 x 10(12) M-1 s-1. This rate is similar to the maximal rate of collision between factor X molecules and the monocyte, i.e. 2.9 x 10(12) M-1 s-1 estimated from the steady-state von Smoluchowski equation for uniformly reacting spherical particles. The observed agreement between predicted and experimental results indicates that under biologically relevant conditions, the rate of factor X activation by the intrinsic protease is controlled by diffusion of factor X toward the catalytic site.     

Estimation of intrinsic kinetic constants for pore diffusion-limited immobilized enzyme reactions

A simple method is presented that establishes intrinsic rate parameters when slow pore diffusion of substrate limits immobilized enzyme reactions that obey Michaelis-Menten kinetics. The Aris-Bischoff modulus is employed. Data at high substrate concentrations, where the enzyme would be saturated in the absence of diffusion limitation, and at low substrate concentrations, where effectiveness factors are inversely proportional to reaction modulus, are used to determine maximum rate and Michaelis constant, respectively. Because Michaelis-Menten and Langmuir-Hinshelwood kinetics are formally identical, this method may be used to estimate intrinsic rate parameters of many heterogeneous catalysts. The technique is demonstrated using experimental data from the hydrolysis of maize dextrin with diffusion-limited immobilized glucoamylase. This system yields a Michaelis constant of 0.14%, compared to 0.11% for soluble glucoamylase and 0.24% for immobilized glucoamylase free of diffusional effects.     

Transient response of encapsulated enzymes in hollow-fiber reactor

A mathematical model for the transient response of encapsulated enzymes is developed showing the effects of the outer boundary layer, the encapsulating membrane, the partition coefficient, and diffusion with reaction within the encapsulating medium. The model incorporates both first-order kinetics and Michaelis-Menten kinetics for the reaction rate. Using typical hollow-fiber or microcapsule parameters, the model shows that (a) the partition coefficient affects the overall rate only when the rate-limiting step is diffusion through the membrane, (b) the transient overall effectiveness factor rises sharply with time and approaches an asymptotic value for most situations, and (c) the first-order approximation to Michaelis-Menten kinetics is not valid when the initial outside bulk concentration is higher than the Michaelis constant and the overall rate is reaction limited. The model is compared with experimental data using uricase in a hollow-fiber enzyme reactor configuration. Batch assay and CSTUER (continuous-stirred ultrafiltration enzyme reactor) studies were conducted on the free enzyme to provide some of the parameters used in the model. The CSTUER data fit the case of substrate inhibition kinetics with the apparent Michaelis constant approaching zero. The hollow-fiber reactor was conducted with uricase dissolved in both a buffer solution and a concentrated hemoglobin solution. Diffusivities of the solute were measured in both solutions as was the osmotic pressure of the hemoglobin solution. While experimental data for uricase in buffer solution could easily be matched by the model, that in the concentrated hemoglobin solution could not.     

Purification, properties and temperature dependence of the adenosine deaminase from a poikilotherm (bay scallop)

The adenosine deaminase of the digestive diverticulum of the bay scallop was purified and electrophoresis of the purified enzyme yielded a single enzymatically active band at several different pH values. A molecular weight of 130,000 was estimated using gel filtration and sucrose density gradient centrifugation. The enzyme had spectral properties typical of simple proteins and its isoelectric point proved to be 4.8. The scallop enzyme was stable at room temperature from pH 5.0 to 7.0, and in this range it was exceptionally resistant to heat inactivation.The effect of the substrate, adenosine, on the reaction velocity was followed over a 10,000-fold concentration range, and no deviation from Michaelis-Menten kinetics was observed. The following rate equation applies to the enzyme: $\text{1}\text{^v}\text{= (}\text{1}\text{α[}\text{S}\text{]}\text{) + (}\text{1}\text{β}\text{)}$.The effect of pH on the reaction, using adenosine as the substrate, was studied; and it was found that pH had a much greater effect on the α parameter of the rate equation than on the β parameter and that pH had little effect on the apparent activation energy of either parameter. The apparent activation energy of the β parameter was 12.2 kcal with adenosine as the substrate, while the apparent activation energy of the α parameter was zero. The α parameter of the rate equation, using other substrates, was also insensitive to temperature.