Kinetic modeling of a bi-enzymatic system for efficient conversion of lactose to lactobionic acid

A model has been developed to describe the interaction between two enzymes and an intermediary redox mediator. In this bi-enzymatic process, the enzyme cellobiose dehydrogenase oxidizes lactose at the C-1 position of the reducing sugar moiety to lactobionolactone, which spontaneously hydrolyzes to lactobionic acid. 2,2'-Azino-bis(3-ethylbenzothiazoline-6-sulfonic acid) diammonium salt is used as electron acceptor and is continuously regenerated by laccase. Oxygen is the terminal electron acceptor and is fully reduced to water by laccase, a copper-containing oxidase. Oxygen is added to the system by means of bubble-free oxygenation. Using the model, the productivity of the process is investigated by simultaneous solution of the rate equations for varying enzyme quantities and redox mediator concentrations, solved with the aid of a numerical solution. The isocharts developed in this work provide an easy-to-use graphical tool to determine optimal process conditions. The model allows the optimization of the employed activities of the two enzymes and the redox mediator concentration for a given overall oxygen mass transfer coefficient by using the isocharts. Model predictions are well in agreement with the experimental data.     

Continuous enzymatic regeneration of redox mediators used in biotransformation reactions employing flavoproteins

Oxidoreductases are a group of enzymes that have been regarded uneconomical for industrial processes due to their dependence on cofactors or prosthetic groups for activity and the difficulties of regenerating these. Especially, flavoproteins have long been neglected for biocatalytical applications. The prosthetic group of some of these enzymes, but not all, can be regenerated by oxygen, resulting in hydrogen peroxide formation, which is detrimental to enzyme stability. As a contribution to alleviating this problem, a novel concept for the regeneration of electron acceptors (redox mediators) for flavoenzymes is described. Flavin-containing enzymes such as cellobiose dehydrogenase (CDH) or pyranose oxidase (P2O) are used in conjunction with laccases and a redox mediator. The flavin of the synthetic enzyme is reduced while the oxidized product of interest is formed, in turn, the flavin is reoxidized with the help of an electron acceptor, which then is regenerated using a laccase. Laccases are copper containing phenol oxidases that can transfer four electrons to oxygen, producing two molecules of water. Preliminary screening experiments with different redox mediators, and a coupled enzyme system of CDH and laccase, showed that a wide variety of different substances can efficiently shuttle electrons between these two enzymes. Among them are substituted and unsubstituted ortho- and para-quinones, benzoquinone imines, cation radicals such as 2,2′-azinobis(3-ethylbenzthiazoline-6-sulfonic acid) (ABTS), redox dyes such as phenothiazines or phenoxazines, as well as iron complexes.

Experiments in which CDH completely oxidizes lactose to lactobionic acid and P2O entirely converts glucose to 2-keto-glucose are presented. Catalytic amounts of redox mediators are used and continuously regenerated by a laccase. Specific productivities of up to 19.3 g·(h·kU)⁻¹ and 72 g·(h·kU)⁻¹ for CDH and P2O, respectively, were found. The total turnover numbers (TTNs) for the two enzymes used were in the range of 10⁵–10⁶. Oxygen supply for the laccase is a crucial factor in avoiding rate limitation. Undeniably, this system facilitates the efficient use of a hitherto underexploited group of enzymes for preparative purposes.     

Continuous Enzymatic Regeneration of Electron Acceptors Used by Flavoenzymes: Cellobiose Dehydrogenase-Catalyzed Production of Lactobionic Acid as an Example

An efficient enzymatic bioprocess is described in which lactose, an abundant renewable resource produced by the dairy industry, is completely and efficiently converted with a specific productivity of up to 32 g (kU h)^-1 into lactobionic acid, without the formation of any by-products. The key biocatalyst of this new process is the fungal enzyme cellobiose dehydrogenase which oxidizes several β-1,4-linked disaccharides including lactose specifically at position C-1 of the reducing sugar moiety to the corresponding lactones. The electron acceptor employed in this reaction is continuously regenerated with the help of laccase, a H₂O-producing, copper-containing oxidase, and therefore has to be added in low, catalytic amounts only. Redox mediators that were successfully employed in this novel process and hence are compatible with the laccase regeneration system include benzoquinone, ABTS, ferricyanide, or ferrocene, amongst others. Factors affecting operational stability of the biocatalysts employed in this process include the redox mediator used, the temperature, and importantly the volumetric gas flow necessary for maintaining the dissolved oxygen tension. Lactobionic acid is a mild and sweet tasting acid with excellent chelating properties. These useful characteristics have lead to a growing number of patents for diverse applications in the food, pharmaceutical and detergent industries.     

Continuous Enzymatic Regeneration of Electron Acceptors Used by Flavoenzymes: Cellobiose Dehydrogenase-Catalyzed Production of Lactobionic Acid as an Example

An efficient enzymatic bioprocess is described in which lactose, an abundant renewable resource produced by the dairy industry, is completely and efficiently converted with a specific productivity of up to 32 g (kU h)^?1 into lactobionic acid, without the formation of any by-products. The key biocatalyst of this new process is the fungal enzyme cellobiose dehydrogenase which oxidizes several β-1,4-linked disaccharides including lactose specifically at position C-1 of the reducing sugar moiety to the corresponding lactones. The electron acceptor employed in this reaction is continuously regenerated with the help of laccase, a H₂O-producing, copper-containing oxidase, and therefore has to be added in low, catalytic amounts only. Redox mediators that were successfully employed in this novel process and hence are compatible with the laccase regeneration system include benzoquinone, ABTS, ferricyanide, or ferrocene, amongst others. Factors affecting operational stability of the biocatalysts employed in this process include the redox mediator used, the temperature, and importantly the volumetric gas flow necessary for maintaining the dissolved oxygen tension. Lactobionic acid is a mild and sweet tasting acid with excellent chelating properties. These useful characteristics have lead to a growing number of patents for diverse applications in the food, pharmaceutical and detergent industries.     

Assay for cellobiose dehydrogenase in the presence of laccase

The currently used assay for cellobiose dehydrogenase (CDH), an enzyme produced by many wood degrading fungi, lacks specificity and can give false results. The presence of laccase interferes with the standard assay. We have developed an assay for CDH that is insensitive to the presence of both laccase and other phenoloxidases. The method is based on the decrease of reducing end groups in lactose determined by the DNS method. Ferricyanide is present as electron acceptor. Advantages and drawbacks of CDH assay methods are discussed     

Production of Cellobionate from Cellulose Using an Engineered Neurospora crassa Strain with Laccase and Redox Mediator Addition

We report a novel production process for cellobionic acid from cellulose using an engineered fungal strain with the exogenous addition of laccase and a redox mediator. A previously engineered strain of Neurospora crassa (F5∆ace-1∆cre-1∆ndvB) was shown to produce cellobionate directly from cellulose without the addition of exogenous cellulases. Specifically, N. crassa produces cellulases, which hydrolyze cellulose to cellobiose, and cellobiose dehydrogenase (CDH), which oxidizes cellobiose to cellobionate. However, the conversion of cellobiose to cellobionate is limited by the slow re-oxidation of CDH by molecular oxygen. By adding low concentrations of laccase and a redox mediator to the fermentation, CDH can be efficiently oxidized by the redox mediator, with in-situ re-oxidation of the redox mediator by laccase. The conversion of cellulose to cellobionate was optimized by evaluating pH, buffer, and laccase and redox mediator addition time on the yield of cellobionate. Mass and material balances were performed, and the use of the native N. crassa laccase in such a conversion system was evaluated against the exogenous Pleurotus ostreatus laccase. This paper describes a working concept of cellobionate production from cellulose using the CDH-ATBS-laccase system in a fermentation system.     

A novel combined thermometric and amperometric biosensor for lactose determination based on immobilised cellobiose dehydrogenase

A novel method for lactose determination in milk is proposed. It is based on oxidation of lactose by cellobiose dehydrogenase (CDH) from the basidiomycete Phanerochaete chrysosporium, immobilised in an enzyme reactor. The reactor was prepared by cross-linking CDH onto aminopropyl-silanised controlled pore glass (CPG) beads using glutaraldehyde. The combined biosensor worked in flow injection analysis (FIA) mode and was developed for simultaneous monitoring of the thermometric signal associated with the enzymatic oxidation of lactose using p-benzoquinone as electron acceptor and the electrochemically generated current associated with the oxidation of the hydroquinone formed. A highly reproducible linear response for lactose was obtained between 0.05 mM and 30 mM. For a set of more than 500 samples an R.S.D. of less than 10% was achieved. The assay time was ca. 2 min per sample. The sensor was applied for the determination of lactose in dairy milk samples (milk with a fat content of 1.5% or 3% and also "lactose free" milk). No sample preparation except dilution with buffer was needed. The proposed method is rapid, suitable for repeated use and allows the possibility to compare results from two different detection methods, thus providing a built-in quality assurance. Some differences in the response observed between the methods indicate that the dual approach can be useful in mechanistic studies of redox enzymes. In addition, a dual system opens up interesting possibilities for studies of enzyme properties and mechanisms.     

Use of laccase together with redox mediators to decolourize Remazol Brilliant Blue R

A pure fungal laccase, obtained from a commercial formulation used in the textile industry, did not decolourize Remazol Brilliant Blue R (RBBR). Decolourization was only observed when a small molecular weight redox mediator was added together with the laccase. Under the conditions specified, violuric acid (5.7 mM) was the most effective mediator studied and almost complete decolourization was observed within 20 min. In contrast, 1-hydroxybenzotriazole (HOBT, 11 mM) decolourized RBBR at about a two-fold slower rate and to a lesser extent. Also, higher concentrations of HOBT were inhibitory which could be due to inactivation of laccase by the toxic HOBT radical. The commercial laccase formulation that contained phenothiazine-10-propionic acid as the mediator was least effective, giving 30% decolourization under equivalent conditions. We suggest that similar laccase plus mediator systems could be used for the detoxification of related anthraquinone textile dyes.     

Biocatalytic cascade oxidation using laccase for pyranose 2-oxidase regeneration

The interactions between two oxidoreductases coupled by an artificial redox mediator have been described quantitatively to increase both stability and productivity. In this cascade oxidation, pyranose 2-oxidase oxidizes several aldoses at the C-2 position to 2-ketoaldoses. A redox mediator is used as electron acceptor for pyranose 2-oxidase because it shows more favourable kinetics in comparison to oxygen. The reduced redox mediator is in turn re-oxidized by laccase, which uses oxygen as the terminal electron acceptor, reducing it fully to water. However, pyranose 2-oxidase is capable of using oxygen as an electron acceptor in a competing side reaction, leading to the formation of hydrogen peroxide, which is detrimental for both enzymes and seriously limits the operational stability of both enzymes.The experimental results showed full conversion of the aldose to the 2-ketoaldose and a good agreement with the simulations of the process.     

Decolorization of reactive dyes by a thermostable laccase produced by Ganoderma lucidum in solid state culture

Dye decolorizing potential of the white rot fungus Ganoderma lucidum KMK2 was demonstrated for recalcitrant textile dyes. G. lucidum produced laccase as the dominant lignolytic enzyme during solid state fermentation (SSF) of wheat bran (WB), a natural lignocellulosic substrate. Crude enzyme shows excellent decolorization activity to anthraquinone dye Remazol Brilliant Blue R (RBBR) without redox mediator whereas diazo dye Remazol Black-5 (RB-5) requires a redox mediator. Polyacrylamide gel electrophoresis (PAGE) of crude enzyme confirms that the laccase enzyme was the major enzyme involved in decolorization of either dyes. Native and SDS-PAGE indicates that the presence of single laccase with molecular weight of 43 kDa. N-Hydroxybenzotriazole (HBT) at a concentration of 1 mM was found as the best redox mediator. RB-5 (50 mg l^−l) was decolorized by 62% and 77.4% within 1 and 2 h, respectively by the crude laccase (25 U ml⁻¹). RBBR (50 mg l^−l) was decolorized by 90% within 20 h, however, it was more efficient in presence of HBT showing 92% decolorization within 2 h. Crude laccase showed high thermostability and maximum decolorization activity at 60 °C and pH 4.0. The decolorization was completely inhibited by the laccase inhibitor sodium azide (0.5 mM). Enzyme inactivation method is a good method which averts the undesirable color formation in the reaction mixture after decolorization. High thermostability and efficient decolorization suggest that this crude enzyme could be effectively used to decolorize the synthetic dyes from effluents.     

Production of lactose-free galacto-oligosaccharide mixtures: comparison of two cellobiose dehydrogenases for the selective oxidation of lactose to lactobionic acid

Galacto-oligosaccharides, complex mixtures of various sugars, are produced by transgalactosylation from lactose using beta-galactosidase and are of great interest for food and feed applications because of their prebiotic properties. Most galacto-oligosaccharide preparations currently available in the market contain a significant amount of monosaccharides and lactose. The mixture of galacto-oligosaccharides (GalOS) in this study produced from lactose using recombinant beta-galactosidase from Lactobacillus reuteri contains 48% monosaccharides, 26.5% lactose and 25.5% GalOS. To remove efficiently both monosaccharides and lactose from this GalOS mixture containing significant amounts of prebiotic non-lactose disaccharides, a biocatalytic approach coupled with subsequent chromatographic steps was used. Lactose was first oxidised to lactobionic acid using fungal cellobiose dehydrogenases, and then lactobionic acid and monosaccharides were removed by ion-exchange and size-exclusion chromatography. Two different cellobiose dehydrogenases (CDH), originating from Sclerotium rolfsii and Myriococcum thermophilum, were compared with respect to their applicability for this process. CDH from S. rolfsii showed higher specificity for the substrate lactose, and only few other components of the GalOS mixture were oxidised during prolonged incubation. Since these sugars were only converted once lactose oxidation was almost complete, careful control of the CDH-catalysed reaction will significantly reduce the undesired oxidation, and hence subsequent removal, of any GalOS components. Removal of ions and monosaccharides by the chromatographic steps gave an essentially pure GalOS product, containing less than 0.3% lactose and monosaccharides, in a yield of 60.3%.     

Continuous enzymatic production of lactobionic acid using glucose-fructose oxidoreductase in an ultrafiltration membrane reactor

Glucose-fructose oxidoreductase from Zymomonas mobilis catalyzed the oxidation of various aldose sugars to the corresponding aldonic acids. The enzyme was used for the selective and high-yield conversion of lactose to lactobionic acid in batch, fed-batch and continous reaction mode. A productivity of 110 g L d was obtained in an ultrafiltration membrane reactor, operated for 70 h.     

Recombinantly produced cellobiose dehydrogenase from Corynascus thermophilus for glucose biosensors and biofuel cells

Cellobiose dehydrogenase (CDH) is an emerging enzyme in the field of bioelectrocatalysis. Due to its flexible cytochrome domain, which acts as a built‐in redox mediator, CDH is capable of direct electron transfer (DET) to electrode surfaces. This rare property is employed in mediatorless “third generation” biosensors. The ability of Corynascus thermophilus CDH to oxidize glucose under physiological conditions makes it a promising candidate for miniaturized glucose biosensors or glucose powered biofuel cell anodes. We report for the first time the electrochemical application and characterization of a recombinantly produced CDH in a glucose biosensor. Recombinant CDH from C. thermophilus (rCtCDH) was expressed by the methylotrophic yeast Pichia pastoris (376 U L^–1, 132 mg L^–1). A comparative characterization of rCtCDH and CtCDH shows identical pH optima, K_M values and heme b midpoint potentials. In contrast, the specific activity of rCtCDH (2.84 U mg^–1) and consequently the turnover numbers were ～five‐times lower than for CtCDH, which was caused by a sub‐stoichiometric occupation of catalytic sites with flavin‐adenin‐dinukleotid (FAD). The performance of rCtCDH‐modified electrodes demonstrates the suitability for electrochemical studies. This opens the possibility to engineer the substrate specificity of C. thermophilus CDH for specific carbohydrates by rational engineering or directed evolution.     

Oxygen-reducing enzyme cathodes produced from SLAC, a small laccase from Streptomyces coelicolor

The bacterially-expressed laccase, small laccase (SLAC) of Streptomyces coelicolor, was incorporated into electrodes of both direct electron transfer (DET) and mediated electron transfer (MET) designs for application in biofuel cells. Using the DET design, enzyme redox kinetics were directly observable using cyclic voltammetry, and a redox potential of 0.43 V (SHE) was observed. When mediated by an osmium redox polymer, the oxygen-reducing cathode retained maximum activity at pH 7, producing 1.5 mA/cm2 in a planar configuration at 900 rpm and 40 degrees C, thus outperforming enzyme electrodes produced using laccase from fungal Trametes versicolor (0.2 mA/cm2) under similar conditions. This improvement is directly attributable to differences in the kinetics of SLAC and fungal laccases. Maximum stability of the mediated SLAC electrode was observed at pH above the enzyme's relatively high isoelectric point, where the anionic enzyme molecules could form an electrostatic adduct with the cationic mediator. Porous composite SLAC electrodes with increased surface area produced a current density of 6.25 mA/cm2 at 0.3 V (SHE) under the above conditions.     

Enzymatically oxidized lactose and derivatives thereof as potential protein cross-linkers

The enzyme galactose oxidase [EC 1.1.3.9] was applied to convert lactose, lactylamine and lactobionic acid into their corresponding 6'-aldehyde compounds. The potential protein cross-linking ability of these oxidized lactose and derivatives thereof was investigated using n-butylamine as the model compound. First, oxidized lactose gave double Maillard reaction products that were stable under mild alkaline conditions. Second, reductive amination of lactose followed by enzymatic oxidation gave cross-links that were stable under both neutral and alkaline conditions. Third, stable cross-links were obtained through enzymatic oxidation and amidation of lactobionic acid.     

Novel Interaction between Laccase and Cellobiose Dehydrogenase during Pigment Synthesis in the White Rot Fungus Pycnoporus cinnabarinus

When glucose is the carbon source, the white rot fungus Pycnoporus cinnabarinus produces a characteristic red pigment, cinnabarinic acid, which is formed by laccase-catalyzed oxidation of the precursor 3-hydroxyanthranilic acid. When P. cinnabarinus was grown on media containing cellobiose or cellulose as the carbon source, the amount of cinnabarinic acid that accumulated was reduced or, in the case of cellulose, no cinnabarinic acid accumulated. Cellobiose-dependent quinone reducing enzymes, the cellobiose dehydrogenases (CDHs), inhibited the redox interaction between laccase and 3-hydroxyanthranilic acid. Two distinct proteins were purified from cellulose-grown cultures of P. cinnabarinus; these proteins were designated CDH I and CDH II. CDH I and CDH II were both monomeric proteins and had apparent molecular weights of about 81,000 and 101,000, respectively, as determined by both gel filtration and sodium dodecyl sulfate-polyacrylamide gel electrophoresis. The pI values were approximately 5.9 for CDH I and 3.8 for CDH II. Both CDHs used several known CDH substrates as electron acceptors and specifically adsorbed to cellulose. Only CDH II could reduce cytochrome c. The optimum pH values for CDH I and CDH II were 5.5 and 4.5, respectively. In in vitro experiments, both enzymes inhibited laccase-mediated formation of cinnabarinic acid. Oxidation intermediates of 3-hydroxyanthranilic acid served as endogenous electron acceptors for the two CDHs from P. cinnabarinus. These results demonstrated that in the presence of a suitable cellulose-derived electron donor, CDHs can regenerate fungal metabolites oxidized by laccase, and they also supported the hypothesis that CDHs act as links between cellulolytic and ligninolytic pathways.     

Comparison of fungal laccases and redox mediators in oxidation of a nonphenolic lignin model compound.

Several fungal laccases have been compared for the oxidation of a nonphenolic lignin dimer, 1-(3, 4-dimethoxyphenyl)-2-(2-methoxyphenoxy)propan-1,3-diol (I), and a phenolic lignin model compound, phenol red, in the presence of the redox mediators 1-hydroxybenzotriazole (1-HBT) or violuric acid. The oxidation rates of dimer I by the laccases were in the following order: Trametes villosa laccase (TvL) > Pycnoporus cinnabarinus laccase (PcL) > Botrytis cinerea laccase (BcL) > Myceliophthora thermophila laccase (MtL) in the presence of either 1-HBT or violuric acid. The order is the same if the laccases are used at the same molar concentration or added to the same activity (with ABTS [2, 2'-azinobis (3-ethylbenzothiazoline-6-sulfonic acid)] as a substrate). During the oxidation of dimer I, both 1-HBT and violuric acid were to some extent consumed. Their consumption rates also follow the above order of laccases, i.e., TvL > PcL > BcL > MtL. Violuric acid allowed TvL and PcL to oxidize dimer I much faster than 1-HBT, while BcL and violuric acid oxidized dimer I more slowly than BcL and 1-HBT. The oxidation rate of dimer I is dependent upon both kcat and the stability of the laccase. Both 1-HBT and violuric acid inactivated the laccases, violuric acid to a greater extent than 1-HBT. The presence of dimer I or phenol red in the reaction mixture slowed down this inactivation. The inactivation is mainly due to the reaction of the redox mediator free radical with the laccases. We did not find any relationship between the carbohydrate content of the laccases and their inactivation. When the redox potential of the laccases is in the range of 750 to 800 mV, i.e., above that of the redox mediator, it does not affect kcat and the oxidation rate of dimer I.     

Purification and characterization of a carbohydrate: acceptor oxidoreductase from Paraconiothyrium sp. that produces lactobionic acid efficiently

A carbohydrate:acceptor oxidoreductase from Paraconiothyrium sp. was purified and characterized. The enzyme efficiently oxidized beta-(1-->4) linked sugars, such as lactose, xylobiose, and cellooligosaccharides. The enzyme also oxidized maltooligosaccharides, D-glucose, D-xylose, D-galactose, L-arabinose, and 6-deoxy-D-glucose. It specifically oxidized the beta-anomer of lactose. Molecular oxygen and 2,6-dichlorophenol indophenol were reduced by the enzyme as electron acceptors. The Paraconiothyrium enzyme was identified as a carbohydrate:acceptor oxidoreductase according to its specificity for electron donors and acceptors, and its molecular properties, as well as the N-terminal amino acid sequence. Further comparison of the amino acid sequences of lactose oxidizing enzymes indicated that carbohydrate:acceptor oxidoreductases belong to the same group as glucooligosaccharide oxidase, while they differ from cellobiose dehydrogenases and cellobiose:quinone oxidoreductases.     

Comparison of Fungal Laccases and Redox Mediators in Oxidation of a Nonphenolic Lignin Model Compound

Several fungal laccases have been compared for the oxidation of a nonphenolic lignin dimer, 1-(3,4-dimethoxyphenyl)-2-(2-methoxyphenoxy)propan-1,3-diol (I), and a phenolic lignin model compound, phenol red, in the presence of the redox mediators 1-hydroxybenzotriazole (1-HBT) or violuric acid. The oxidation rates of dimer I by the laccases were in the following order: Trametes villosa laccase (TvL) > Pycnoporus cinnabarinus laccase (PcL) > Botrytis cinerea laccase (BcL) > Myceliophthora thermophila laccase (MtL) in the presence of either 1-HBT or violuric acid. The order is the same if the laccases are used at the same molar concentration or added to the same activity (with ABTS [2,2′-azinobis (3-ethylbenzothiazoline-6-sulfonic acid)] as a substrate). During the oxidation of dimer I, both 1-HBT and violuric acid were to some extent consumed. Their consumption rates also follow the above order of laccases, i.e., TvL > PcL > BcL > MtL. Violuric acid allowed TvL and PcL to oxidize dimer I much faster than 1-HBT, while BcL and violuric acid oxidized dimer I more slowly than BcL and 1-HBT. The oxidation rate of dimer I is dependent upon both k_cat and the stability of the laccase. Both 1-HBT and violuric acid inactivated the laccases, violuric acid to a greater extent than 1-HBT. The presence of dimer I or phenol red in the reaction mixture slowed down this inactivation. The inactivation is mainly due to the reaction of the redox mediator free radical with the laccases. We did not find any relationship between the carbohydrate content of the laccases and their inactivation. When the redox potential of the laccases is in the range of 750 to 800 mV, i.e., above that of the redox mediator, it does not affect k_cat and the oxidation rate of dimer I.     

Lactobionic and cellobionic acid production profiles of the resting cells of acetic acid bacteria

Lactobionic acid was produced by acetic acid bacteria to oxidize lactose. Gluconobacter spp. and Gluconacetobacter spp. showed higher lactose-oxidizing activities than Acetobacter spp. Gluconobacter frateurii NBRC3285 produced the highest amount of lactobionic acid per cell, among the strains tested. This bacterium assimilated neither lactose nor lactobionic acid. At high lactose concentration (30%), resting cells of the bacterium showed sufficient oxidizing activity for efficient production of lactobionic acid. These properties may contribute to industrial production of lactobionic acid by the bacterium. The bacterium showed higher oxidizing activity on cellobiose than that on lactose and produced cellobionic acid.