Kinetics of milk coagulation: II. Kinetics of the secondary phase: micelle flocculation

A kinetic model for the agglomeration of milk micelles following kappa-casein hydrolysis is described. The key features of the model are: (1) the surface potential of casein micelles is sufficient to explain the colloidal stability of the milk system; (2) the reduction in surface potential following kappa-casein hydrolysis explains the loss of stability; (3) partial hydrolysis leads to limited agglomeration; and (4) the kinetics of agglomeration are compatible with the theory that completely hydrolyzed micelles have only a limited number of interaction sites. The model accurately predicts solution turbidity increase assuming that micelles have only circa 1.2 interaction sites on the average under the experimental conditions of this study.     

Kinetics of milk coagulation: III. Mathematical modeling of the kinetics of curd formation following enzymatic hydrolysis of kappa-casein--parameter estimation

A step function model of milk micelle agglomeration is proposed to explain the observed kinetics of milk clotting following rennet addition. The model ties together the primary and secondary phases of coagulation. The basis of the model is that no micelle flocculation takes place until ca. 75% of the kappa-casein in the milk is hydrolyzed, at which time flocculation occurs rapidly and the rate limiting step for the clotting process shifts to the kappa-casein hydrolysis reaction. Using such a model, it is possible to explain the clotting kinetics for both rapidly denaturing enzymes and stable enzyme systems. The average rate of the flocculation reaction can be obtained from clotting time-versus-reciprocal-enzyme-concentration data by extrapolating the data to infinite enzyme concentration. The critical conversion required for imminent flocculation can be found by extrapolating the enzyme concentration to zero. This approach indicates that the critical conversion necessary for gelation is temperature dependent changing from a limiting value of essentially 100% hydrolysis at temperatures below 15 degrees C to only 60% conversion at temperatures above 30 degrees C.     

The kinetics of milk coagulation: IV. The kinetics of the gel-firming process

A mechanistic kinetic model of gel firmness development during milk gel formation is presented. The model correctly accounts for the influence of enzymatic kappa-casein hydrolysis on the rate of firmness development in renneted milk gels. The model used is based on two first-order reactions occurring in series. The first reaction is enzymatically controlled and corresponds to the formation of gel crosslink sites by kappa-casein hydrolysis. The second reaction is nonenzymatic and corresponds to the process of crosslink formation and depletion of active sites. The model successfully predicts gel firmness development in the temperature range 31-45 degrees C for a variety of initial enzyme concentrations.     

Kinetics of lipase-catalyzed hydrolysis of olive oil in AOT/isooctane reversed micelles

The kinetics of lipase-catalyzed hydrolysis of olive oil in AOT/isooctane reversed micellar media was studied. It was shown that the deactivation of lipase had a great influence on the reaction kinetics. Based on whether the enzyme deactivation and influences of both product and substrate on enzyme stability were included or not, four different kinetic models were established. The simulating results demonstrated that the kinetic model, which including product inhibition, enzyme deactivation and the improvements of lipase stability by both product and substrate, fit the experimental data best with an overall relative error of 4.68%.     

Optimization of enzyme loading and hydrolytic time in the hydrolysis of mixtures of cotton gin waste and recycled paper sludge for the maximum profit rate

The hydrolytic kinetics of mixtures of cotton gin waste (CGW) and recycled paper sludge (RPS) at various initial enzyme concentrations of Spezyme™ AO3117 was investigated. The experiments showed that the concentrations of reducing sugars and the conversions of the mixtures increased with increasing initial enzyme concentration. The reducing sugar concentration and conversion of the mixture of 75% CGW and 25% RPS were higher than those of the mixture of 80% CGW and 20% RPS. The conversion of the former can reach 73.8% after a 72-h hydrolysis at the initial enzyme loading of 17.4 Filter Paper Unit (FPU)/g substrate. A three-parameter kinetic model based on enzyme deactivation and its analytical expression were derived. Using nonlinear regression, the parameters of the model were determined for the experimental data of hydrolytic kinetics of the mixtures. Based on this kinetic model of hydrolysis, two profit rate models, representing two kinds of operating modes with and without feedstock recycling, were developed. Using the profit rate models, the optimal enzyme loading and hydrolytic time can be predicted for the maximum profit rate in ethanol production according to the costs of enzyme and operation, enzyme loading, and ethanol market price. Simulated results from the models based on the experimental data of hydrolysis of the mixture of 75% CGW and 25% RPS showed that use of a high substrate concentration and an operating mode with feedstock recycle can greatly increase the profit rate in ethanol production. The results also demonstrated that the hydrolysis at a low enzyme loading is economically required for systematic optimization of ethanol production.     

Reactor Performance in the Presence of Catalyst Deactivation

The main variable of enzymatic processes is often found to be the operating temperature. An increase in temperature leads to higher rates for the catalytic transformation. However, beyond a certain temperature catalyst deactivation is winning the game. Therefore, processes should be optimized in order to determine the temperature which leads to a minimal demand of enzyme preparation. For the prediction of such optimal reactor operation, modeling of the temperature dependence of the process has to be performed. Examples of such modeling are given for the hydrolysis of lactose in UHT milk by means of three different β‐galactosidases – those from Aspergillus oryzae, Kluyveromyces lactis, and Escherichia coli. The reaction kinetics for a constant initial lactose concentration can be described by a model of two parameters, of which only one depends on temperature. For the lactase of E. coli the reaction can be described as a simple reaction with first order kinetics. The deactivation mechanism includes a reversible as well as an irreversible path of denaturation. The temperature dependent parameters follow Arrhenius' and van't Hoff's law, respectively. On the basis of their particular reaction models all three enzymes can be compared with respect to their optimum use. The models have been verified under laboratory conditions and have shown their usefulness for the prediction of optimum operating variables. Quite remarkable features have been found for the lactase of E. coli.     

Hydrolysis of cellobiose using β-glucosidase from Penicillium funiculosum. Kinetic analysis

The kinetics of cellobiose hydrolysis was studied using β-glucosidase from Penicillium funiculosum, both free and immobilized on nylon powder, at different temperatures, pH values, enzymatic activities and initial cellobiose and glucose concentrations. The experimental results were fitted to a kinetic model by considering the substrate and product inhibitions as well as the thermal deactivation of β-glucosidase with a mean deviation of less than 10%. The immobilization of β-glucosidase led to an increase in the stability of the enzyme against changes in the pH value.     

Application of extended Kalman filter to identification of enzymatic deactivation

A recursive estimation scheme, the Extended Kalman Filter (EKF) technique, was applied to study enzymatic deactivation in the enzymatic hydrolysis of pretreated cellulose using a model previously developed by the authors. When no deactivation model was assumed, the results showed no variation with time for all the model parameters except for the maximum rate of cellobiose-to-glucose conversion (r'(m)).The r'(m) variation occurred in two zones with a grace period. A new model of enzymatic hydrolysis of pretreated cellulose deactivation was proposed and validated showing better behavior than the old deactivation model. This approach allows one to study enzyme deactivation without additional experiments and within operational conditions.     

Enzyme deactivation

Enzyme deactivation kinetics is often first-order. Different examples of first-order deactivation kinetics exhibited by different enzymes under a wide variety of conditions are presented. Examples of both soluble and immobilized enzymes are presented. The influence of different parameters, chemical modification of specific residues, inhibitors, inactivators, protecting agents, induced conformational changes by external agents, enzyme concentration, and different substrates on the first-order inactivation kinetics of different enzymes is analyzed. The different examples presented from a variety of different areas provides a judicious framework and collection demonstrating the wide applicability of first-order deactivation kinetics. Examples of reversible first-order deactivation kinetics and deactivation-disguise kinetics are also presented.Different mechanisms are also presented to model complex enzyme deactivations. The non-series type mechanisms are emphasized and these involve the substrate and chemical modifiers. Substrate-dependent deactivation rate expressions that are of "separable" and "non-separable" type are presented. Rate expressions involving time-dependent rate constants along with their corresponding mechanisms are presented. Examples of enzymes that exhibit a deactivation-free grace period are also given. An interesting case of enzyme inactivation is the loss of activity in the presence of an auto-decaying reagent. The method is presented by which the intrinsic inactivation rate constants may be obtained. Examples of pH-dependent enzyme inactivation are presented that may be modelled by a five-step (or a simplified two-step) mechanism, and also by a single-step mechanism involving residual activity for the final state. Appropriate examples of enzyme inactivation are presented in each case to highlight the different mechanisms involved.     

Transient model of thermal deactivation of enzymes

The kinetics of enzyme deactivation provide useful insights on processes that determine the level of biological function of any enzyme. Photinus pyralis (firefly) luciferase is a convenient enzyme system for studying mechanisms and kinetics of enzyme deactivation, refolding, and denaturation caused by various external factors, physical or chemical by nature. In this report we present a study of luciferase deactivation caused by increased temperature (i.e., thermal deactivation). We found that deactivation occurs through a reversible intermediate state and can be described by a Transient model that includes active and reversibly inactive states. The model can be used as a general framework for analysis of complex, multiexponential transient kinetics that can be observed for some enzymes by reaction progression assays. In this study the Transient model has been used to develop an analytical model for studying a time course of luciferase deactivation. The model might be applicable toward enzymes in general and can be used to determine if the enzyme exposed to external factors, physical or chemical by nature, undergoes structural transformation consistent with thermal mechanisms of deactivation.     

Kinetic modeling of the enzymatic hydrolysis of pretreated cellulose

The production of sugars by the enzymatic hydrolysis of cellulose is a two-step process that includes conversion of the intermediate cellobiose to glucose by beta-glucosidase. The hydrolysis was followed by analyzing the two sugar products (cellobiose and glucose). The enzyme showed maximum activity at pH 4.8. Thermal deactivation was significant at temperatures above 45 degrees C. At 50 degrees C (optimum temperature) thermal deactivation was found to follow first-order kinetics. Several models were tested by modeling the kinetics of the reaction. Their parameter values were determined by numerical optimization, including temperature dependence. The best fitting model was a competitive product inhibition for the two reactions in the operational range.     

Acid phosphatase deactivation by a series mechanism

Acid phosphatase (E.C.3.1.3.2.) thermal deactivation at pH 3.77 has been investigated by monitoring the enzyme activity as a function of time in the hydrolysis of p-nitrophenyl phosphate. The experimental curves obtained show a two-slope behavior in a log (activity)versus-time plot, which indicates that deactivation occurs via a complex mechanism. From the dependence of the kinetic parameters on both deactivation and hydrolysis temperatures, it is inferred that the deactivation mechanism involves intermediate, temperature-dependent, less-active forms of the enzyme. This interpretation is confirmed by the results of additional tests in which the temperature was suddenly changed during the deactivation process.     

Evaluation of the factors affecting avicel reactivity using multi-stage enzymatic hydrolysis

Multi-stage and single-stage enzymatic hydrolysis of cellulose (Avicel PH-101) were conducted to investigate individual factors that affect the rate-reducing kinetics of enzymatic hydrolysis. Understanding factors affecting enzymatic hydrolysis of Avicel will help improve hydrolysis of various biomasses. Product inhibition, enzyme deactivation, and the changes of substrate are potential factors that can affect the hydrolysis efficiency of Avicel. Multi-stage enzymatic hydrolysis resulted in 36.9% and 25.4% higher carbohydrate conversion as compared to a single-stage enzymatic hydrolysis with an enzyme loading of 5 and 20 FPU/g in a 96 h reaction. However, a decline in carbohydrate conversion of 1.6% and 2.6% was observed through each stage with 5 and 20 FPU/g, respectively. This indicated that the substrate became more recalcitrant as hydrolysis progressed. The decreased reactivity was not due to crystallinity because no significant change in crystallinity was detected by X-ray diffraction. Product inhibition was significant at low enzyme loading, while it was marginal at high enzyme loading. Therefore, product inhibition can only partially explain this decreased conversion. Another important factor, enzyme deactivation, contributed to 20.3% and 25.4% decrease in the total carbohydrate conversion of 96 h hydrolysis with 5 and 20 FPU/g, respectively. This work shows that an important reason for the decreased Avicel digestibility is the effect of enzyme blockage, which refers to the enzymes that irreversibly adsorb on accessible sites of substrate. About 45.3% and 63.2% of the total decreased conversion at the end of the 8th stage with 5 and 20 FPU/g, respectively, was due to the presence of irreversibly adsorbed enzymes. This blockage of active sites by enzymes has been speculated by other researchers, but this article shows further evidence of this effect.     

Effects of temperature on the hydrolysis of lactose by immobilized beta-galactosidase in a capillary bed reactor

The effects of temperature on the hydrolysis of lactose by immobilized beta-galactosidase were studied in a continuous flow capillary bed reactor. Temperature affects the rates of enzymatic reactions in two ways. Higher temperatures increase the rate of the hydrolysis reaction, but also increase the rate of thermal deactivation of the enzyme. The effect of temperature on the kinetic parameters was studied by performing lactose hydrolysis experiments at 15, 20, 25, 30, and 40 degrees C. The kinetic parameters were observed to follow an Arrhenius-type temperature dependence. Galactose mutarotation has a significant impact on the overall rate of lactose hydrolysis. The temperature dependence of the mutarotation of galactose was effectively modelled by first-order reversible kinetics. The thermal deactivation characteristics of the immobilized enzyme reactor were investigated by performing lactose hydrolysis experiments at 52, 56, 60, and 64 degrees C. The thermal deactivation was modelled effectively as a first order decay process. Based on the estimated thermal deactivation rate constants, at an operating temperature of 40 degrees C, 10% of the enzyme activity would be lost in one year.     

Series mechanism of enzyme deactivation. Characterization of intermediate forms

Acid phosphatase (E.C. 3.1.3.2) undergoes complex thermal deactivation phenomena, as revealed by the two-slope pattern of the enzyme logarithmic-specific-activity versus time curves. The native enzyme first decays toward an equilibrium distribution of less, but still active, intermediate structures and these, in turn, undergo a final degradation to a completely inactive form. The effect of the experimental conditions at which the enzyme is kept during the deactivation process on the characteristics of these intermediate enzymatic structures has been investigated. The kinetic parameters of p-nitro-phenyl phosphate hydrolysis, as catalyzed by some of these intermediate forms, have been determined and the results compared to those obtained with the native enzyme.     

Detection of the cholera toxin-binding activity of kappa-casein macropeptide and optimization of its production by the response surface methodology

The cholera toxin (CT)-binding activity of purified kappa-casein macropeptide (CMP) from bovine kappa-casein was detected. In addition, a statistical model was developed to optimize the production of CMP. CMP was prepared by chymosin hydrolysis of kappa-casein and a subsequent 3% trichloroacetic acid treatment. CMP was further fractionated in an ion-exchange column by FPLC. CT binding activity was eluted at 0.18 M NaCl and was a single 8.9 kDa peptide without tyrosine and arginine residues. The CT binding activity was rapidly lost by a carbohydrase treatment. The conditions for CMP production with chymosin were optimized by using the response surface methodology (RSM). The estimated optimum levels of the factors were as follows: reaction temperature, 38.5 degrees C; pH, 6.44; and time, 35.9 min. A validation experiment was performed in which CMP was prepared under the predicted parameters, and it was ascertained that the estimated optimum conditions gave better production of CMP than any other conditions.     

Fractal kinetic analysis of the enzymatic saccharification of CO2 laser pretreated corn stover

The enzymatic hydrolyses of laser pretreated corn stover as a novel pretreatment method were examined to establish a simplified kinetic model for the complicated hydrolysis process. The time dependence of the total reducing sugars amount was closely related to the amounts of cellulosic materials and amounts of cellulase. The evaluated model fitted very well with the experimental data of enzymatic hydrolysis of laser pretreated corn stover under different conditions, including cellulase loading, nature of substrate, substrate loading in the reaction medium. The results indicated that the complex kinetics of cellulase enzymatic saccharification could be assessed with the fractal kinetic model. The cellulase enzymatic reaction process was effectively predicted and controlled with the kinetic model. The result showed that the model could effectively reflect dynamic process of enzyme hydrolysis.     

Purification and characterization of milk clotting enzyme from goat (Capra hircus)

Chymosin, the major component of rennet (milk clotting enzyme), is an acid protease produced in the fourth stomach of milk-fed ruminants including goat and sheep in the form of an inactive precursor prochymosin. It is responsible for hydrolysis of kappa-casein chain in casein micelles of milk and therefore, used as milk coagulant in cheese preparation. The present investigation was undertaken to purify and characterize goat (Capra hircus) chymosin for its suitability as milk coagulant. The enzyme was extracted from abomasal tissue of kid and purified nearly 30-fold using anion exchanger and gel filtration chromatography. Goat chymosin resolved into three major active peaks, indicating possible heterogeneity when passed through DEAE-cellulose ion exchange column. The purified enzyme had a molecular mass of 36 kDa on SDS-PAGE, which was further confirmed by Western blot analysis. The purified enzyme preparation was stable up to 55 degrees C with maximum activity at 30 degrees C. The milk clotting activity was decreased steadily as pH is increased and indicated maximum activity at pH 5.5. Proteolytic activity of goat chymosin increased with incubation time at 37 degrees C. Goat chymosin was found to be more thermostable than cattle chymosin and equally stable to buffalo chymosin.     

Effects of ionic surfactants used in reversed micelles on cutinase activity and stability

The effects of aqueous surfactant solutions on the kinetics and stability of cutinase from Fusarium solani pisi were studied. The surfactant sodium bis[2-ethylhexyl]ester sulfosuccinic acid (AOT) acts as a pseudo-competitive inhibitor within a limited concentration range relative to the hydrolysis of short-chain p-nitrophenyl esters. For higher concentrations a hyperbolic mixed inhibition takes place. A pseudo-activation of hydrolysis in presence of AOT and hexadecyltrimethyl-ammonium bromide (CTAB) was observed. CTAB has similar effects on kinetics of cutinase. Cutinase revealed to be stable in CTAB solutions, with activity retention as high as 80%. AOT has a deleterious effect on the enzyme in the time course, resulting in acute loss of activity possibly related with unfolding of the protein structure. A relation between deactivation rate constants and AOT/cutinase concentration ratios is suggested. The presence of the linear alcohol, 1-hexanol, was included in these solutions, in the attempt to interpret the deactivation of cutinase when encapsulated in reversed micelle systems in the absence of this co-surfactant.     

Kinetic studies of enzymatic hydrolysis of insoluble cellulose: analysis of the initial rates

A study was conducted on the kinetics of enzymatic hydrolysis of pure insoluble cellulose using unpurified culture filtrate Trichoderma reesei, with the emphasis on the initial reaction period. The initial hydrolysis rate and extent of enzyme (soluble protein)adsorption, either apparent or initial, were evaluated under various experimental conditions. It has been found that the various mass-transfer steps do not control the overall hydrolysis rate and that the hydrolysis rate is mainly controlled by the surface reaction step promoted by the adsorbed enzyme. It has also been found that the initial hydrolysis rate strongly depends on the initial extent of soluble protein adsorption and the effectiveness of the adsorbed soluble protein to promote the hydrolysis. The initial extent of soluble protein adsorption, in turn, is related to the initial cellulose concentration, enzyme concentration, and specific surface area of cellulose, whereas the effectiveness of the initially adsorbed soluble protein to promote the derived to interrelate these parameters without resorting to the Michaelis-Menten kinetics. The present result appear to imply that the role of enzyme-substrate complex formation should not be ignored in deriving a mechanistic kinetic model for enzymatic hydrolysis of cellulose.