Kinetics of the enzymatic hydrolysis of cellulose: 2. A mathematical model for the process in a plug-flow column reactor

The kinetics of enzymatic cellulose hydrolysis in a plug-flow column reactor catalysed by cellulases [see 1,4-(1,3;1,4)-β-d-glucan 4-glucanohydrolase, EC 3.2.1.4] from Trichoderma longibrachiatum adsorbed on cellulose surface have been studied. The maximum substrate conversion achieved was 90–94%. The possibility of enzyme recovery for a reactor of this type is discussed. A mathematical model for enzymatic cellulose hydrolysis in a plug-flow column reactor has been developed. The model allows for the component composition of the cellulase complex, adsorption of cellulases on the substrate surface, inhibition by reaction products, changes in cellulose reactivity and the inactivation of enzymes in the course of hydrolysis. The model affords a reliable prediction of the kinetics of d-glucose and cellobiose formation from cellulose in a column reactor as well as the degree of substrate conversion and reactor productivity with various amounts of adsorbed enzymes and at various flow rates.     

Kinetics of the enzymatic hydrolysis of cellulose: 1. A mathematical model for a batch reactor process

A mathematical model for enzymatic cellulose hydrolysis, based on experimental kinetics of the process catalysed by a cellulase [see 1,4-(1,3;1,4)-β-d-glucan 4-glucanohydrolase, EC 3.2.1.4] preparation from Trichoderma longibrachiatum has been developed. The model takes into account the composition of the cellulase complex, the structural complexity of cellulose, the inhibition by reaction products, the inactivation of enzymes in the course of the enzymatic hydrolysis and describes the kinetics of d-glucose and cellobiose formation from cellulose. The rate of d-glucose formation decelerated through the hydrolysis due to a change in cellulose reactivity and inhibition by the reaction product, d-glucose. The rate of cellobiose formation decelerated due to inhibition by the product, cellobiose, and inactivation of enzymes adsorbed on the cellulose surface. Inactivation of the cellobiose-producing enzymes as a result of their adsorption was found to be reversible. The model satisfactorily predicts the kinetics of d-glucose and cellobiose accumulation in a batch reactor up to 70–80% substrate conversion on changing substrate concentration from 5 to 100 g l^?1and the concentration of the enzymic preparation from 5 to 60 g l^?1.     

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.     

Substrate heterogeneity causes the nonlinear kinetics of insoluble cellulose hydrolysis

Nonlinear kinetics are commonly observed in the enzymatic hydrolysis of cellulose. This nonlinearity could be explained by any or all of the following three factors: enzyme inactivation, product inhibition, or substrate heterogeneity. In this study, four different approaches were applied to test the above hypotheses using two Thermomonospora fusca endocellulases, E2 and E5. The lack of stimulation of cellulase activity by beta-glucosidase rules out the possibility of product inhibition as a cause of the observed nonlinearity. The results from the other three approaches all provide strong evidence against enzyme inactivation and strong evidence for substrate heterogeneity as the cause of the nonlinear kinetics. The most direct evidence for substrate heterogeneity is that pretreatment of swollen cellulose with either E2cd or E5cd gave a product that was hydrolyzed at a much (3- to 4-fold) slower rate than untreated swollen cellulose even though the initial treatment degraded only 15-18% of the substrate. Furthermore, the activation energy of E2 catalyzed hydrolysis of swollen cellulose increased from 10 kcal/mol for the initial rate to 29 kcal/mol for hydrolysis after 24% digestion.     

Acetic acid formation in Escherichia coli fermentation

Theoretical analysis of cellulase product inhibition (by cellobiose and glucose) has been performed in terms of the mathematical model for enzymatic cellulose hydrolysis. The analysis showed that even in those cases when consideration of multienzyme cellulase system as one enzyme (cellulase) or two enzymes (cellulase and beta-glucosidase) is valid, double-reciprocal plots, usually used in a product inhibition study, may be nonlinear, and different inhibition patterns (noncompetitive, competitive, or mixed type) may be observed. Inhibition pattern depends on the cellulase binding constant, enzyme concentration, maximum adsorption of the enzyme (cellulose surface area accessible to the enzyme), the range in which substrate concentration is varied, and beta-glucosidase activity. A limitation of cellulase adsorption by cellulose surface area that may occur at high enzyme/substrate ratio is the main reason for nonlinearity of double-reciprocal plots. Also, the results of calculations showed that material balance by substrate, which is usually neglected by researchers studying cellulase product inhibition, must be taken into account in kinetic analysis even in those cases when the enzyme concentration is rather low. (c) 1992 John Wiley & Sons, Inc.     

Modeling intrinsic kinetics of enzymatic cellulose hydrolysis

A multistep approach was taken to investigate the intrinsic kinetics of the cellulase enzyme complex as observed with hydrolysis of noncrystalline cellulose (NCC). In the first stage, published initial rate mechanistic models were built and critically evaluated for their performance in predicting time-course kinetics, using the data obtained from enzymatic hydrolysis experiments performed on two substrates: NCC and alpha-cellulose. In the second stage, assessment of the effect of reaction intermediates and products on intrinsic kinetics of enzymatic hydrolysis was performed using NCC hydrolysis experiments, isolating external factors such as mass transfer effects, physical properties of substrate, etc. In the final stage, a comprehensive intrinsic kinetics mechanism was proposed. From batch experiments using NCC, the time-course data on cellulose, cello-oligosaccharides (COS), cellobiose, and glucose were taken and used to estimate the parameters in the kinetic model. The model predictions of NCC, COS, cellobiose, and glucose profiles show a good agreement with experimental data generated from hydrolysis of different initial compositions of substrate (NCC supplemented with COS, cellobiose, and glucose). Finally, sensitivity analysis was performed on each model parameter; this analysis provides some insights into the yield of glucose in the enzymatic hydrolysis. The proposed intrinsic kinetic model parametrized for dilute cellulose systems forms a basis for modeling the complex enzymatic kinetics of cellulose hydrolysis in the presence of limiting factors offered by substrate and enzyme characteristics.     

Reactor design for minimizing product inhibition during enzymatic lignocellulose hydrolysis: I. Significance and mechanism of cellobiose and glucose inhibition on cellulolytic enzymes

Achievement of efficient enzymatic degradation of cellulose to glucose is one of the main prerequisites and one of the main challenges in the biological conversion of lignocellulosic biomass to liquid fuels and other valuable products. The specific inhibitory interferences by cellobiose and glucose on enzyme-catalyzed cellulose hydrolysis reactions impose significant limitations on the efficiency of lignocellulose conversion — especially at high-biomass dry matter conditions. To provide the base for selecting the optimal reactor conditions, this paper reviews the reaction kinetics, mechanisms, and significance of this product inhibition, notably the cellobiose and glucose inhibition, on enzymatic cellulose hydrolysis. Particular emphasis is put on the distinct complexity of cellulose as a substrate, the multi-enzymatic nature of the cellulolytic degradation, and the particular features of cellulase inhibition mechanisms and kinetics. The data show that new strategies that place the bioreactor design at the center stage are required to alleviate the product inhibition and in turn to enhance the efficiency of enzymatic cellulose hydrolysis. Accomplishment of the enzymatic hydrolysis at medium substrate concentration in separate hydrolysis reactors that allow continuous glucose removal is proposed to be the way forward for obtaining feasible enzymatic degradation in lignocellulose processing.     

Modeling cellulase kinetics on lignocellulosic substrates

The enzymatic hydrolysis of cellulose to glucose by cellulases is one of the major steps involved in the conversion of lignocellulosic biomass to yield biofuel. This hydrolysis by cellulases, a heterogeneous reaction, currently suffers from some major limitations, most importantly a dramatic rate slowdown at high degrees of conversion. To render the process economically viable, increases in hydrolysis rates and yields are necessary and require improvement both in enzymes (via protein engineering) and processing, i.e. optimization of reaction conditions, reactor design, enzyme and substrate cocktail compositions, enzyme recycling and recovery strategies. Advances in both areas in turn strongly depend on the progress in the accurate quantification of substrate–enzyme interactions and causes for the rate slowdown. The past five years have seen a significant increase in the number of studies on the kinetics of the enzymatic hydrolysis of cellulose. This review provides an overview of the models published thus far, classifies and tabulates these models, and presents an analysis of their basic assumptions. While the exact mechanism of cellulases on lignocellulosic biomass is not completely understood yet, models in the literature have elucidated various factors affecting the enzymatic rates and activities. Different assumptions regarding rate-limiting factors and basic substrate–enzyme interactions were employed to develop and validate these models. However, the models need to be further tested against additional experimental data to validate or disprove any underlying hypothesis. It should also provide better insight on additional parameters required in the case that more substrate and enzyme properties are to be included in a model.     

Kinetic modeling of enzymatic hydrolysis of cellulose in differently pretreated fibers from dairy manure

A kinetic model incorporating dynamic adsorption, enzymatic hydrolysis, and product inhibition was developed for enzymatic hydrolysis of differently pretreated fibers from a nitrogen-rich lignocellulosic material-dairy manure. The effects of manure proteins on the enzyme adsorption profile during hydrolysis have been discussed. Enzyme activity, instead of protein concentration, was used to describe the enzymatic hydrolysis in order to avoid the effect of manure protein on enzyme protein analysis. Dynamic enzyme adsorption was modeled based on a Langmiur-type isotherm. A first-order reaction was applied to model the hydrolysis with consideration being given for the product inhibition. The model satisfactorily predicted the behaviors of enzyme adsorption, hydrolysis, and product inhibition for all five sample manure fibers. The reaction conditions were the substrate concentrations of 10-50 g/L, enzyme loadings of 7-150 FPU/g total substrate, and the reaction temperature of 50 degrees C.     

Preparation of cellulase concoction using differential adsorption phenomenon

Controlled depolymerization of cellulose is essential for the production of valuable cellooligosaccharides and cellobiose from lignocellulosic biomass. However, enzymatic cellulose hydrolysis involves multiple synergistically acting enzymes, making difficult to control the depolymerization process and generate desired product. This work exploits the varying adsorption properties of the cellulase components to the cellulosic substrate and aims to control the enzyme activity. Cellulase adsorption was favored on pretreated cellulosic biomass as compared to synthetic cellulose. Preferential adsorption of exocellulases was observed over endocellulase, while β-glucosidases remained unadsorbed. Adsorbed enzyme fraction with bound exocellulases when used for hydrolysis generated cellobiose predominantly, while the unadsorbed enzymes in the liquid fraction produced cellooligosaccharides majorly, owing to its high endocellulases activity. Thus, the differential adsorption phenomenon of the cellulase components can be used for the controlling cellulose hydrolysis for the production of an array of sugars.     

Reactor design for minimizing product inhibition during enzymatic lignocellulose hydrolysis: II. Quantification of inhibition and suitability of membrane reactors

Product inhibition of cellulolytic enzymes affects the efficiency of the biocatalytic conversion of lignocellulosic biomass to ethanol and other valuable products. New strategies that focus on reactor designs encompassing product removal, notably glucose removal, during enzymatic cellulose conversion are required for alleviation of glucose product inhibition. Supported by numerous calculations this review assesses the quantitative aspects of glucose product inhibition on enzyme-catalyzed cellulose degradation rates. The significance of glucose product inhibition on dimensioning of different ideal reactor types, i.e. batch, continuous stirred, and plug-flow, is illustrated quantitatively by modeling different extents of cellulose conversion at different reaction conditions. The main operational challenges of membrane reactors for lignocellulose conversion are highlighted. Key membrane reactor features, including system set-up, dilution rate, glucose output profile, and the problem of cellobiose are examined to illustrate the quantitative significance of the glucose product inhibition and the total glucose concentration on the cellulolytic conversion rate. Comprehensive overviews of the available literature data for glucose removal by membranes and for cellulose enzyme stability in membrane reactors are given. The treatise clearly shows that membrane reactors allowing continuous, complete, glucose removal during enzymatic cellulose hydrolysis, can provide for both higher cellulose hydrolysis rates and higher enzyme usage efficiency (kg_product/kg_enzyme). Current membrane reactor designs are however not feasible for large scale operations. The report emphasizes that the industrial realization of cellulosic ethanol requires more focus on the operational feasibility within the different hydrolysis reactor designs, notably for membrane reactors, to achieve efficient enzyme-catalyzed cellulose degradation.     

Kinetics of the enzymatic hydrolysis of cellulose

Enzymatic hydrolysis of cellulose for sugar production offers advantages of higher conversion, minimal by-product formation, low energy requirements, and mild operating conditions over other chemical conversions. The development of a kinetic model, based on observable, macroscopic properties of the overall system, is helpful in design and economic evaluation of processes for sugar conversion and ethanol production. A kinetic model is presented, incorporating enzyme adsorption, product inhibition, and considers a multiple enzyme and substrate system. This model was capable of simulating saccharification of a lignocellulosic material, rice straw, at high substrate (up to 333 g/L) and enzyme concentrations (up to 9.2 FPU/mL) that are common to proposed process designs.     

Changes in the enzymatic hydrolysis rate of Avicel cellulose with conversion

The slow down in enzymatic hydrolysis of cellulose with conversion has often been attributed to declining reactivity of the substrate as the more easily reacted material is thought to be consumed preferentially. To better understand the cause of this phenomenon, the enzymatic reaction of the nearly pure cellulose in Avicel was interrupted over the course of nearly complete hydrolysis. Then, the solids were treated with proteinase to degrade the cellulase enzymes remaining on the solid surface, followed by proteinase inhibitors to inactive the proteinase and successive washing with water, 1.0 M NaCl solution, and water. Next, fresh cellulase and buffer were added to the solids to restart hydrolysis. The rate of cellulose hydrolysis, expressed as a percent of substrate remaining at that time, was approximately constant over a wide range of conversions for restart experiments but declined continually with conversion for uninterrupted hydrolysis. Furthermore, the cellulose hydrolysis rate per adsorbed enzyme was approximately constant for the restart procedure but declined with conversion when enzymes were left to react. Thus, the drop off in reaction rate for uninterrupted cellulose digestion by enzymes could not be attributed to changes in substrate reactivity, suggesting that other effects such as enzymes getting "stuck" or otherwise slowing down may be responsible.     

A new approach for modeling cellulase-cellulose adsorption and the kinetics of the enzymatic hydrolysis of microcrystalline cellulose

Two fractions of substrate in microcrystalline cellulose which differ in their adsorption capacities for the cellulases and their susceptibility to enzymatic attack have been identified. On the basis of a two-substrate hypothesis, mathematical models to describe enzyme adsorption and the kinetics of hydrolysis have been derived. A new nonequilibrium approach was chosen to predict cellulase-cellulose adsorption. A maximum binding capacity of 76 mg protein per gram substrate and a half-maximum saturation constant of 26 filter paper units (FPU) per gram substrate have been calculated, and a linear relationship of hydrolysis rate vs. adsorbed protein has been found. The fraction of substrate more easily hydrolyzed, as calculated from hydrolysis data, represents 19% of the total effective substrate concentration. This fraction is only slightly different from that of other celluloses and has been estimated to be 27% and 30% for NaOH- and H(3)PO(4)-swollen cellulose, respectively. The effective substrate concentration is equal to the maximum amount of the substrate which can be converted during exhaustive hydrolysis. This in turn is determined by the overall degradability of the substrate by the cellulases (85-90% for microcrystalline cellulose) and by the cellobiose concentration during hydrolysis. The kinetic model is based on a summation of two integrated first-order reactions with respect to the effective substrate concentration. Furthermore, it includes the principal factors influencing the reaction rates: the ratio of filter paper and beta-glucosidase units per gram substrate and the initial substrate concentration. (c) 1993 John Wiley & Sons, Inc.     

Kinetic studies of enzymatic hydrolysis of insoluble cellulose: (II). Analysis of extended hydrolysis times

The kinetics of enzymatic hydrolysis of pure insoluble cellulose by means of unpurified culture filtrate of Trichoderma reesei was studied, emphasizing the kinetic characteristics associated with the extended hydrolysis times. The changes in the hydrolysis rate and extent of soluble protein adsorption during the progress of reaction, either apparent or intrinsic, were investigated. The hydrolysis rate declined drastically during the initial hours of hydrolysis. The factors causing the reduction in the hydrolysis rate were examined; these include the transformation of cellulose into a less digestible form and product inhibition. The structural transformation can be partially explained by changes in the crystallinity index and surface area. The product inhibition was caused by the deactivation of the adsorbed soluble protein by the products, which essentially represents the so-called "un-competitive" inhibition. The kinetics of beta-glucosidase were also studied. The result has shown that the action of beta-glucosidase is competitively inhibited by glucose. It has been found that the integrated form of the initial rate expression cannot be used in predicting the progress of reaction because the digestibility of cellulose changes drastically as the hydrolysis proceeds, and that the rate expression for enzymatic hydrolysis of cellulose cannot be simplified or approximated by resorting to the pseudo-steady-state assumption. A mechanistic kinetic model of cellulose hydrolysis should include the following major influencing factors: (1)mode of action of enzyme, (2) structure of cellulose, and (3) mode of interaction between the enzyme and cellulose molecules.     

Cellobiase from Trichoderma viride: purification, properties, kinetics, and mechanism

Three distinct cellobiase components were isolated from a commercial Trichoderma viride cellulase preparation by repeated chromatography on DEAE cellulose eluting by a salt gradient. The purified cellobiase preparations were evaluated for physical properties, kinetics, and mechanism. Results from this work include: 1) development of one step enzyme purification procedure using DEAE-cellulose; 2) isolation of three chromatographically distinct, yet kinetically similar, cellobiase fractions of molecular weight of approximately 76,000; 3) determination of kinetics which shows that cellobiase hydrolyzes cellobiose by a noncompetitive mechanism and that the product, glucose, inhibits the enzyme, and 4) development of an equation, based on the mechanism of cellobiase action, which accurately predicts the time course of cellobiose hydrolysis over an eightfold range of substrate concentration and conversions of up to 90%. Based on the data presented in the paper, it is shown that product inhibition of cellobiase significantly retards the rate of cellobiose hydrolysis.     

Kinetic analysis of enzymatic hydrolysis of crystalline cellulose by cellobiohydrolase using an amperometric biosensor

An amperometric biosensor for the detection of cellobiose has been introduced to study the kinetics of enzymatic hydrolysis of crystalline cellulose by cellobiohydrolase. By use of a sensor in which pyrroloquinoline quinone-dependent glucose dehydrogenase was immobilized on the surface of electrode, direct and continuous observation of the hydrolysis can be achieved even in a thick cellulose suspension. The steady-state rate of the hydrolysis increased with increasing concentrations of the enzyme to approach a saturation value and was proportional to the amount of the substrate. The experimental results can be explained well by the rate equations derived from a three-step mechanism consisting of the adsorption of the free enzyme onto the surface of the substrate, the reaction of the adsorbed enzyme with the substrate, and the liberation of the product. The catalytic constant of the adsorbed enzyme was determined to be 0.044+/-0.011s(-1).     

Enzyme adsorption on SO2 catalyzed steam-pretreated wheat and spruce material

Lignocellulose is widely recognized as a sustainable substrate for biofuels production, and the enzymatic hydrolysis is regarded as a critical step for the development of an effective process for the conversion of cellulose into ethanol. One key factor affecting the overall conversion rate is the adsorption capacity of the cellulase enzymes to the surface of the insoluble substrate. Pretreatment has a strong impact on hydrolysis, which could be related to both chemical changes and morphological changes of the material. In the current work, the accessibility of four differently pretreated wheat straw substrates, two differently pretreated spruce materials, and Avicel cellulose was investigated. Adsorption isotherms (at 4 °C and 30 °C) for a cellulase preparation were obtained, and the rates of hydrolysis were determined for the different materials. Furthermore, the surface area and pore size distribution of the various materials were measured and compared to adsorption and hydrolysis properties, and the structures of the pretreated materials were examined using scanning electron microscopy (SEM).The results demonstrated a positive correlation between enzyme adsorption and the substrate specific surface area within each feedstock. Overall, the amount of enzyme adsorbed was higher for pretreated spruce than for the pretreated wheat straw, but this was not accompanied by a higher initial rate of hydrolysis for spruce. Also, the difference in the measured endoglucanase adsorption and overall FPU adsorption suggests that a larger fraction of the enzyme adsorbed on spruce was unproductive binding. The SEM analysis of the material illustrated the structural effects of pretreatment harshness on the materials, and suggested that increased porosity explains the higher rate of hydrolysis of more severely pretreated biomass.