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.     

A mechanistic model for enzymatic saccharification of cellulose using continuous distribution kinetics II: cooperative enzyme action, solution kinetics, and product inhibition

The projected cost for the enzymatic hydrolysis of cellulosic biomass continues to be a barrier for the commercial production of liquid transportation fuels from renewable feedstocks. Predictive models for the kinetics of the enzymatic reactions will enable an improved understanding of current limitations, such as the slow-down of the overall conversion rate, and may point the way for more efficient utilization of the enzymes in order to achieve higher conversion yields. A mechanistically based kinetic model for the enzymatic hydrolysis of cellulose was recently reported in Griggs et al. (2011) (Part I). In this article (Part II), the enzyme system is expanded to include solution-phase kinetics, particularly cellobiose-to-glucose conversion by β-glucosidase (βG), and novel adsorption and product inhibition schemes have been incorporated, based on current structural knowledge of the component enzymes. Model results show cases of cooperative and non-cooperative hydrolysis for an enzyme system consisting of EG(I) and CBH(I). The model is used to explore various potential rate-limiting phenomena, such as substrate accessibility, product inhibition, sterically hindered enzyme adsorption, and the molecular weight of the cellulose substrate.     

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.     

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.     

Lipase-mediated hydrolysis of corn DDGS oil: Kinetics of linoleic acid production

In this study, we investigated the kinetics of linoleic acid production via lipase-mediated hydrolysis of corn DDGS oil in a batch reactor with continuous mechanical agitation and developed a kinetic model that incorporated the product inhibition to study the complete hydrolysis. The model agreed very well with observed data; though situations with low enzyme dosage or low stirring rates were modeled successfully without product inhibition, actual product concentration in such situations was too low to exert any inhibitory effects. Increasing the enzyme concentration increased hydrolysis, and beyond certain enzyme concentrations, effects tended to fade away because of excessive enzyme desorption from the interface. An enzyme dosage within the range of 40–60 KLU/L of oil dispersion could be successfully applied for a substrate concentration of 25–50 g/L of DDGS oil. Increasing the agitation rates improved enzymatic hydrolysis, but a higher stirring rate of 1000 rpm moderately improved production of linoleic acid compared with a stirring rate of 750 rpm. Within the range of substrate concentrations studied, enzymatic inhibition was moderate but still evident. The high degree of hydrolysis (i.e., ∼96% of theoretical linoleic acid yield) from DDGS oil suggests this method has potential for commercial production of linoleic acid.     

Kinetic modeling of rapid enzymatic hydrolysis of crystalline cellulose after pretreatment by NMMO

Pretreatment of cellulose with an industrial cellulosic solvent, N-methylmorpholine-N-oxide, showed promising results in increasing the rate of subsequent enzymatic hydrolysis. Cotton linter was used as high crystalline cellulose. After the pretreatment, the cellulose was almost completely hydrolyzed in less than 12 h, using low enzyme loading (15 FPU/g cellulose). The pretreatment significantly decreased the total crystallinity of cellulose from 7.1 to 3.3, and drastically increased the enzyme adsorption capacity of cellulose by approximately 42 times. A semi-mechanistic model was used to describe the relationship between the cellulose concentration and the enzyme loading. In this model, two reactions for heterogeneous reaction of cellulose to glucose and cellobiose, and a homogenous reaction for cellobiose conversion to glucose was incorporated. The Langmuir model was applied to model the adsorption of cellulase onto the treated cellulose. The competitive inhibition was also considered for the effects of sugar inhibition on the rate of enzymatic hydrolysis. The kinetic parameters of the model were estimated by experimental results and evaluated.     

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.     

Soluble and insoluble solids contributions to high-solids enzymatic hydrolysis of lignocellulose

The rates and extents of enzymatic cellulose hydrolysis of dilute acid pretreated corn stover (PCS) decline with increasing slurry concentration. However, mass transfer limitations are not apparent until insoluble solids concentrations approach 20% w/w, indicating that inhibition of enzyme hydrolysis at lower solids concentrations is primarily due to soluble components. Consequently, the inhibitory effects of pH-adjusted pretreatment liquor on the enzymatic hydrolysis of PCS were investigated. A response surface methodology (RSM) was applied to empirically model how hydrolysis performance varied as a function of enzyme loading (12-40mg protein/g cellulose) and insoluble solids concentration (5-13%) in full-slurry hydrolyzates. Factorial design and analysis of variance (ANOVA) were also used to assess the contribution of the major classes of soluble components (acetic acid, phenolics, furans, sugars) to total inhibition. High sugar concentrations (130g/L total initial background sugars) were shown to be the primary cause of performance inhibition, with acetic acid (15g/L) only slightly inhibiting enzymatic hydrolysis and phenolic compounds (9g/L total including vanillin, syringaldehyde, and 4-hydroxycinnamic acid) and furans (8g/L total of furfural and hydroxymethylfurfural, HMF) with only a minor effect on reaction kinetics. It was also demonstrated that this enzyme inhibition in high-solids PCS slurries can be approximated using a synthetic hydrolyzate composed of pure sugars supplemented with a mixture of acetic acid, furans, and phenolic compounds, which indicates that generally all of the reaction rate-determining soluble compounds for this system can be approximated synthetically.     

Kinetics of the hydrolysis of lean meat protein by alcalase: Derivation of two alternative rate equations and their fit to experimental data

Two rate equations have been developed to model the hydrolysis of ground lean meat protein by Alcalase. The first equation was based on classical Michaelis-Menten kinetics and the second on the adsorption of enzyme to the protein prior to reaction. It was assumed that this adsorption could be modelled by a Langmuir-type adsorption isotherm. Each equation considered the enzyme to be competitively inhibited by reaction product, and considered enzyme inactivation to be first order. Both rate equations have been fitted to experimental data obtained from the hydrolysis of meat protein by Alcalase. Initial rate data indicated that the adsorption model was more appropriate. However, both equations gave satisfactory fits to 11 reaction progress curves determined over a wide range of enzyme and substrate concentrations.     

Kinetic modeling for enzymatic hydrolysis of pretreated creeping wild ryegrass

A semimechanistic multi‐reaction kinetic model was developed to describe the enzymatic hydrolysis of a lignocellulosic biomass, creeping wild ryegrass (CWR; Leymus triticoides). This model incorporated one homogeneous reaction of cellobiose‐to‐glucose and two heterogeneous reactions of cellulose‐to‐cellobiose and cellulose‐to‐glucose. Adsorption of cellulase onto pretreated CWR during enzymatic hydrolysis was modeled via a Langmuir adsorption isotherm. This is the first kinetic model which incorporated the negative role of lignin (nonproductive adsorption) using a Langmuir‐type isotherm adsorption of cellulase onto lignin. The model also reflected the competitive inhibitions of cellulase by glucose and cellobiose. The Matlab optimization function of “lsqnonlin” was used to fit the model and estimate kinetic parameters based on experimental data generated under typical conditions (8% solid loading and 15 FPU/g‐cellulose enzyme concentration without the addition of background sugars). The model showed high fidelity for predicting cellulose hydrolysis behavior over a broad range of solid loading (4–12%, w/w, dry basis), enzyme concentration (15–150 FPU/ g‐cellulose), sugar inhibition (glucose of 30 and 60 mg/mL and cellobiose of 10 mg/mL). In addition, sensitivity analysis showed that the incorporation of the nonproductive adsorption of cellulase onto lignin significantly improved the predictability of the kinetic model. Our model can serve as a robust tool for developing kinetic models for system optimization of enzymatic hydrolysis, hydrolysis reactor design, and/or other hydrolysis systems with different type of enzymes and substrates. Biotechnol. Bioeng. 2009;102: 1558–1569. © 2008 Wiley Periodicals, Inc.     

Enzymatic hydrolysis of molasses

Kinetic studies of the enzymatic hydrolysis of molasses were conducted using glucoamylase. Central Sugar Refinery SDN BHD contains 13-20% glucose. The molasses was diluted and the kinetic experiments were conducted at 67 degrees C with 100-1000 mg/l of glucoamylase. The glucose contents of the molasses were enhanced after hydrolysis of molasses solution with 1000 mg/l glucoamylase. A Lineweaver-Burk plot was obtained based on enzyme kinetic data. The rate constant, Km and maximum reaction rate, Vmax for 500 mg/l of glucoamylase were 100 mmol/l (18 g/l) and 5 mmol/l min (0.9 g/l min), respectively. The maximum reaction rate, Vmax for 1000 mg/l of glucoamylase was doubled, to 100 mmol/l (18 g/l) and the rate constant, Km was the same for 500 mg/l of glucoamylase. The substrate inhibition model was noncompetitive based on the resulting Lineweaver-Burk plot for enzyme concentration of 500 and 1000 mg/l.     

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.     

Three-stage enzymatic hydrolysis of steam-exploded corn stover at high substrate concentration

The feasibility of three-stage hydrolysis of steam-exploded corn stover at high-substrate concentration was investigated. When substrate concentration was 30% and enzyme loading was 15-30 FPU/g cellulose, three-stage (9+9+12 h) hydrolysis could reach a hydrolysis yield of 59.9-81.4% in 30 h. Compared with one-stage hydrolysis for 72 h, an increase of 34-37% in hydrolysis yield could be achieved. When steam-exploded corn stover was used as the substrate for enzyme synthesis and hydrolysis was conducted at a substrate concentration of 25% with an enzyme loading of 20 FPU/g cellulose, a hydrolysis yield of 85.1% was obtained, 19% higher than that the commercial cellulase could reach under the same conditions. The removal of end products was suggested to improve the adsorption of cellulase on the substrate and enhance the productivity of enzymatic hydrolysis.     

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.     

Enzymatic hydrolysis of sodium-hydroxide-pretreated sallow in an ultrafiltration membrane reactor

An ultrafiltration membrane reactor was used to investigate the recovery of biocatalysts during enzymatic hydrolysis of pretreated sallow. Product inhibition could be eliminated by continuous removal of products through the ultrafiltration membrane, thus retaining the macromolecular substrate and enzymes. In this way, the degree of conversion was improved from 40% in a batch hydrolysis to 95% (within 20 h), and the initial hydrolysis rate was increased up to seven times. The recovery studies were focused on mechanical deactivation and irreversible adsorption on to the nonconvertible fraction of the substrate. Cellulase deactivation during mechanical agitation was not significant, and the loss of activity was attributed mainly to strong adsorption of the enzymes onto undigested material. This process was studied in semicontinuous hydrolyses, where fresh substrate was added intermittently. The amount of reducing sugars produced in this experiment was 25.7 g/g enzyme, compared to 4.7 g/g enzyme in a batch hydrolysis.     

Relation between filter paper activity and saccharifying ability of a Trichoderma cellulase system

Summary Tests made to study the relation between filter paper activity and actual saccharifying ability of Trichoderma cellulases show that 30 IU/g of cellulose were sufficient to achieve over 80% hydrolysis of a 25 g/L cellulose suspension in 24 h. With the same enzyme/substrate ratio, but double the concentration of substrate, about 60% hydrolysis was achieved. End- product inhibition is one factor which seriously limits the degree of hydrolysis and therefore the concentration of sugars achievable by enzymatic hydrolysis at high levels of substrate concentration or enzyme/substrate ratio.     

Kinetic studies on insoluble cellulose-cellulase system.

Enzymatic hydrolysis of insoluble amorphous cellulose by Trichoderma viride cellulase was investigated in a batch reactor at several substrate concentrations and three enzyme levels. The reactions were carried out at 50 degrees C and pH 4.8. Enzyme was rapidly adsorbed onto solids on contact, then gradually returned to the liquid phase as the reaction proceeded. A kinetic model that considered the fast adsorption which was followed by the slow reaction, and subsequent product inhibition was developed to interpret the experimental observations. The resulting equation successfully correlated the data for up to 70% conversion. The methods for determining the kinetic parameters are discussed.     

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).     

Modelling of the enzymatic hydrolysis of cellobiose and cellulose by a complex enzyme mixture of Trichoderma reesei QM 9414

Summary The enzymatic hydrolysis of cellobiose and cellulose by the cell-free culture filtrate of Trichoderma reesei QM 9414 was investigated. The concentrations of cellobiose and glucose were measured as a function of time for different initial concentrations of cellobiose. It was not possible to describe these concentration variations by a model which considers only the cellobiase hydrolysis with competitive and noncompetitive substrate and product inhibition; it is necessary that the endo--1.4-glucanase with competitive product inhibition is also taken into account.The enzymatic hydrolysis of cellulose (Avicel) was described with a mathematical model by using the results of the decomposition of cellobiose by the same enzyme mixture.the identified model parameters are presented. A sensitivity analysis of the parameter was carried out also.     

Modeling of product removal during enzymatic conversions by using affinity molecules

The feasibility of using magnetic particles for in-line product isolation during enzymatic conversion was studied. A comparison was made between a process based on magnetic particles and a conventional adsorption column. The enzymatic reaction was described by two consecutive first-order reactions (synthesis and subsequent hydrolysis), while the adsorption of substrate and product was described by multicomponent Langmuir isotherms. The yield as well as synthesis/hydrolysis ratio were calculated for various system characteristics. The results show that magnetic particles are very effective when the affinity with the particles is specific and for enzymatic conversions involving low ratios of the rate of synthesis versus the rate of hydrolysis. For slow conversions and for low specific affinity molecules column separations are more appropriate.