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.     

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.     

Kinetic analysis and modeling of the liquid-liquid conversion of emulsified di-rhamnolipids by Naringinase from Penicillium decumbens

The enzymatic conversion of an aggregate-forming substrate was kinetically analyzed and a model was applied for the prediction of reaction-time courses. An L-rhamnose molecule from a di-rhamnolipid is cleaved by Naringinase from Penicillium decumbens leading to a mono-rhamnolipid. Optimal reaction rates were found when both, substrate and product build large co-aggregates in a slightly acidic aqueous phase. On the other hand, reaction rates were independent of initial di-rhamnolipid concentration and this was interpreted by assuming that the reaction occurs in the aqueous phase according to Michaelis-Menten kinetics in combination with competitive L-rhamnose inhibition. Rhamnolipids were therefore assumed to be highly concentrated in aggregates, a second liquid phase, whereas diffusive rhamnolipid transport from and to the aqueous phase occurs due to the enzymatic reaction. Furthermore, ideal surfactant mixing between di- and mono-rhamnolipid was assumed for interpretation of the negative effect of the last on the reaction rate. A model was created that describes the system accordingly. The comparison of the experimental data, were in excellent agreement with the predicted values. The findings of this study may beneficially be adapted for any bioconversion involving aggregate-forming substrate and/or product being catalyzed by hydrophilic enzymes.     

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.     

Kinetic and thermodynamic investigation of enzymatic l-ascorbyl acetate synthesis

Kinetics and thermodynamics of lipase-catalyzed esterification of l-ascorbic acid in acetone were investigated by using vinyl acetate as acyl donor. The results showed that l-ascorbic acid could generate inhibition effect on lipase activity. A suitable model, Ping-Pong Bi-Bi mechanism having substrate inhibition, was thus introduced to describe the enzymatic kinetics. Furthermore, the kinetic and thermodynamic parameters were calculated from a series of experimental data according to the kinetic model. The inhibition constant of l-ascorbic acid was also obtained, which seemed to imply that enhancing reaction temperature could depress the substrate inhibition. Besides, the activation energy values of the first-step and the second-step reaction were estimated to be 37.31 and 4.94 kJ/mol, respectively, demonstrating that the first-step reaction was the rate-limiting reaction and could be easily improved by enhancing temperature.     

Theoretical analysis of intrinsic reaction kinetics and the behavior of immobilized enzymes system for steady-state conditions

Mathematical modeling of immobilized enzymes under different kinetics mechanism viz. simple Michaelis–Menten, uncompetitive substrate inhibition, total competitive product inhibition, total non-competitive product inhibition and reversible Michaelis–Menten reaction are discussed. These five kinetic models are based on reaction diffusion equations containing non-linear terms related to Michaelis–Menten kinetics of the enzymatic reaction. Modified Adomian decomposition method is employed to derive the general analytical expressions of substrate and product concentration for all these five mechanisms for all possible values of the parameters Φ_S (Thiele modulus for substrate), Φ_P (Thiele modulus for product) and α (dimensionless inhibition degree). Also we have presented the general analytical expressions for the mean integrated effectiveness factor for all values of parameters. Analytical results are compared with the numerical results and also with the limiting case results, which are found to be good in agreement.     

Kinetics and mathematical model of hydrolysis and transglycosylation catalysed by cellobiase

The kinetics of hydrolysis and transglycosylation reactions catalysed by cellobiase (β-d-glucoside glucohydrolase, EC 3.2.1.21) from Aspergillus foetidus in the cellobiose-d-glucose reaction system have been studied. The formation of transglycosylation products was observed at cellobiose concentrations $\text{>10}{}^{\mathrm{?2}}\text{m}$, whereas at lower substrate concentrations the only reaction product was d-glucose. In the cellobiase-catalysed transglycosylation a (1→6)-β-linkage was formed after the transfer of a d-glucose residue to acceptor molecule. The basic transglycosylation products were isocellotriose and gentiobiose. A small amount of oligosaccharides with a higher degree of polymerization was also formed. The maximum content of transglycosylation products amounted to 25–30% of the total saccharide content in the system at the initial cellobiose concentration (0.1–0.3 m). The processes in the reaction system were inhibited by the substrate and product (d-glucose). A general scheme for cellobiose hydrolysis has been proposed and validated, allowing for the inhibition and transglycosylation effects. Based on this scheme, a mathematical model for cellobiose hydrolysis has been suggested to describe the kinetics of substrate consumption and product (d-glucose) accumulation, as well as the kinetics of formation and consumption of transglycosylation products throughout the course of enzymatic reaction with various initial amounts of cellobiose, starting from low concentrations up to 0.2–0.3 m (7–11% bv weight).     

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%.     

高效液相色谱法在脱氧核糖核酸酶解动力学研究中的应用

为了更好地对脱氧核糖核酸酶解动力学过程进行研究,建立脱氧核糖核酸（DNA）酶解液中4种脱氧核苷酸（腺嘌呤脱氧核苷酸（dAMP）、鸟嘌呤脱氧核苷酸（dGMP）、胞嘧啶脱氧核苷酸（dCMP）、胸腺嘧啶脱氧核苷酸（dTMP））的高效液相测定方法,能将酶解液中4种脱氧核苷酸完全分离并准确定量。在此基础上,对DNA酶解的动力学进行初步研究,其反应机理为不存在底物和产物抑制的双底物顺序反应,动力学方程为x=1／bin（1＋abt）（其中a=0．3723p0—0．974;b=-0．0493p0^2＋1．1150p0-1．1103）,该方程可以很好地描述DNA酶解过程,误差仅为3．31％.     

Course of pH during the formation of amoxicillin by a suspension-to-suspension reaction

Amoxicillin can be produced in an enzymatic suspension-to-suspension reaction in which the substrate(s) and product(s) are mainly present as solid particles, while the reaction takes place in the liquid phase. During these suspension-to-suspension reactions different subprocesses take place, such as dissolution/crystallization of substrates and products, enzymatic synthesis of the product(s), and undesired enzymatic hydrolysis of substrates and/or products. All these subprocesses are influenced by pH and also influence the pH because the reactants are weak electrolytes. This paper describes a quantitative model for predicting pH and concentrations of reactants during suspension-to-suspension reactions. The model is based on mass and charge balances, pH-dependent solubilities of the reactants, and enzyme kinetics. For the validation of this model, the kinetically controlled synthesis of amoxicillin from 6-aminopenicillanic acid and D-(p)hydroxyphenylglycine methyl ester was studied. The pH and the dissolved concentrations took a very different course at different initial substrate amounts. This was described quite reasonably by the model. Therefore, the model can be used as a tool to optimize suspension-to-suspension reactions of weak electrolytes.     

Oscillatory enzyme reactions and Michaelis–Menten kinetics

Oscillations occur in a number of enzymatic systems as a result of feedback regulation. How Michaelis–Menten kinetics influences oscillatory behavior in enzyme systems is investigated in models for oscillations in the activity of phosphofructokinase (PFK) in glycolysis and of cyclin-dependent kinases in the cell cycle. The model for the PFK reaction is based on a product-activated allosteric enzyme reaction coupled to enzymatic degradation of the reaction product. The Michaelian nature of the product decay term markedly influences the period, amplitude and waveform of the oscillations. Likewise, a model for oscillations of Cdc2 kinase in embryonic cell cycles based on Michaelis–Menten phosphorylation–dephosphorylation kinetics shows that the occurrence and amplitude of the oscillations strongly depend on the ultrasensitivity of the enzymatic cascade that controls the activity of the cyclin-dependent kinase.     

A detailed biochemical characterization of phosphopantothenate synthetase, a novel enzyme involved in coenzyme A biosynthesis in the Archaea

We have previously reported that the majority of the archaea utilize a novel pathway for coenzyme A biosynthesis (CoA). Bacteria/eukaryotes commonly use pantothenate synthetase and pantothenate kinase to convert pantoate to 4′-phosphopantothenate. However, in the hyperthermophilic archaeon Thermococcus kodakarensis, two novel enzymes specific to the archaea, pantoate kinase and phosphopantothenate synthetase, are responsible for this conversion. Here, we examined the enzymatic properties of the archaeal phosphopantothenate synthetase, which catalyzes the ATP-dependent condensation of 4-phosphopantoate and β-alanine. The activation energy of the phosphopantothenate synthetase reaction was 82.3?kJ?mol^?1. In terms of substrate specificity toward nucleoside triphosphates, the enzyme displayed a strict preference for ATP. Among several amine substrates, activity was detected with β-alanine, but not with γ-aminobutyrate, glycine nor aspartate. The phosphopantothenate synthetase reaction followed Michaelis–Menten kinetics toward β-alanine, whereas substrate inhibition was observed with 4-phosphopantoate and ATP. Feedback inhibition by CoA/acetyl-CoA and product inhibition by 4′-phosphopantothenate were not observed. By contrast, the other archaeal enzyme pantoate kinase displayed product inhibition by 4-phosphopantoate in a non-competitive manner. Based on our results, we discuss the regulation of CoA biosynthesis in the archaea.     

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.     

Kinetic characteristics and enantioselective action of penicillinase in the hydrolysis reaction of N-phenylacetyl derivatives of 1-aminoethylphosphonic acid and its esters

Penicillin acylase from E. coli (EC 3.5.1.11) was found to hydrolyze N-phenylacetylated 1-aminoethylphosphonic acid and its esters. The enzyme preferentially converts the R-form of the substrates: the ratios of the bimolecular rate constants of penicillin acylasecatalyzed hydrolysis of R- and S-forms of 1-(N-phenylacetamino)-ethylphosphonic acid and its dimethyl- and diisopropyl-esters are 58000, 2300, 1800; these derivatives were shown to have the greatest values of the catalytic constants for enzymatic hydrolysis of all known substrates for penicillin acylase: 237, 148 and 134 s-1; the corresponding Km values are 3.7 10(-5), 6.8 10(-4) and 6.2 10(-4) M at pH 7.0. The kinetics of enzymatic hydrolysis of 1-(N-phenylacetamino)-ethylphosphonic acid was investigated up to high degrees of conversion. The inhibition of penicillin acylase by high concentrations of the R-form of the substrate (with substrate inhibition constant of 0.07 M) and competitive inhibition by the reaction product, phenylacetic acid (Ki = 3.5 10(-5) M), was observed.     

A kinetic study of lipase-catalyzed reversible kinetic resolution involving verification at miniplant-scale

Lipase-catalyzed kinetic resolution of racemates is a popular method for synthesis of chiral synthons. Most of these resolutions are reversible equilibrium limited reactions. For the first time, an extensive kinetic model is proposed for kinetic resolution reactions, which takes into account the full reversibility of the reaction, substrate inhibition by an acyl donor and an acyl acceptor as well as alternative substrate inhibition by each enantiomer. For this purpose, the reversible enantioselective transesterification of (R/S)-1-methoxy-2-propanol with ethyl acetate catalyzed by Candida antarctica lipase B (CAL-B) is investigated. The detailed model presented here is valid for a wide range of substrate and product concentrations. Following model discrimination and the application of Haldane equations to reduce the degree of freedom in parameter estimation, the 11 free parameters are successfully identified. All parameters are fitted to the complete data set simultaneously. Six types of independent initial rate studies provide a solid data basis for the model. The effect of changes in substrate and product concentration on reaction kinetics is discussed. The developed model is used for simulations to study the behavior of reaction kinetics in a fixed bed reactor. The typical plot of enantiomeric excess versus conversion of substrate and product is evaluated at various initial substrate mixtures. The model is validated by comparison with experimental results obtained with a fixed bed reactor, which is part of a fully automated state-of-the-art miniplant.     

Reaction mechanism of non-allosteric phosphofructokinase.

The reaction mechanism of the non-allosteric phosphofructokinase from Lactobacillus plantarum was investigated by initial-rate bisubstrate kinetics and product inhibition kinetics adn by the measurement of equilibrium isotope exchange in the presence of various substrate and product concentrations. The reaction mechanism is clearly sequential. The product inhibition and equilibrium isotope-exchange patterns are consistent with an ordered bi-bi reaction sequence with fructose 6-phosphate as the leading substrate and ADP as the first product released from the enzyme.     

Role of substrate inhibition kinetics in enzymatic chemical oscillations.

Two chemical kinetic models are investigated using standard nonlinear dynamics techniques to determine the conditions under which substrate inhibition kinetics can lead to oscillations. The first model is a classical substrate inhibition scheme based on Michaelis-Menten kinetics and involves a single substrate. Only when this reaction takes place in a flow reactor (i.e., both substrate and product are taken to follow reversible flow terms) are oscillations observed; however, the range of parameter values over which such oscillations occur is so narrow it is experimentally unobservable. A second model based on a general mechanism applied to the kinetics of many pH-dependent enzymes is also studied. This second model includes both substrate inhibition kinetics as well as autocatalysis through the activation of the enzyme by hydrogen ion. We find that it is the autocatalysis that is always responsible for oscillatory behavior in this scheme. The substrate inhibition terms affect the steady-state behavior but do not lead to oscillations unless product inhibition or multiple substrates are present; this is a general conclusion we can draw from our studies of both the classical substrate inhibition scheme and the pH-dependent enzyme mechanism. Finally, an analysis of the nullclines for these two models allows us to prove that the nullcline slopes must have a negative value for oscillatory behavior to exist; this proof can explain our results. From our analysis, we conclude with a brief discussion of other enzymes that might be expected to produce oscillatory behavior based on a pH-dependent substrate inhibition mechanism.     

Applying slow-release biocatalysis to the asymmetric reduction of ethyl 4-chloroacetoacetate

Amberlite XAD 2 resin enhanced the asymmetric reduction of ethyl 4-chloroacetoacetate (ECA) to S-4-chloro-3-hydroxybutyric acid ethyl ester as catalyzed by Saccharomyces cerevisiae. The absorbed ECA was released slowly to the solution during the reaction so that the substrate inhibition and the spontaneous chemical hydrolysis of ECA were considerably lessened. With 75 g resin l^–1 and ECA at 74 mM, the reaction yield and the product's optical purity increased from 75% to 84% and from 88% to 93%, respectively.     

Mathematical simulation of pseudo-crystallofermentation of hydrocortisone by Arthrobacter simplex

A mathematical model has been developed to simulate the pseudo-crystallofermentation process of hydrocortisone by Arthrobacter simplex. The model describing the process included considerations on the kinetics of microbial growth, the rate of enzyme formation, the rate of substrate dissolution, the rate of solute crystallization, and the kinetics of enzymatic reaction. The system of equations was solved numerically by the Runge-Kutta-Gill method. The good agreement between prediction and experiment indicated the reliability of the established model. The simulation was capable of predicting the time when the crystallization of product occurred, which could be further verified by microscopic observation on the culture medium, as well as cell growth, enzyme synthesis, product formation, and the composition of the final product crystals.     

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.