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A Mathematical Model for the Inhibitory Effects of Lignin

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A Mathematical Model for the Inhibitory Effects of Lignin
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  A mathematical model for the inhibitory effects of ligninin enzymatic hydrolysis of lignocellulosics Roger H. Newman ⇑ , Alankar A. Vaidya, Sylke H. Campion Scion, Private Bag 3020, Rotorua Mail Centre, Rotorua 3046, New Zealand h i g h l i g h t s Cellulose conversion was calculated at cessation of cellulase activity. Steam-exploded pine feedstock provided data for a worked example. Conversion at relatively low enzyme loading characterized enzyme deactivation. Conversion at relatively high enzyme loading characterized cellulose occlusion. Enzyme requirements doubled when the temperature was raised from 30   C to 50   C. a r t i c l e i n f o  Article history: Received 20 August 2012Received in revised form 9 November 2012Accepted 16 December 2012Available online 23 December 2012 Keywords: SoftwoodSteam explosionEnzymatic hydrolysisEnzyme deactivation a b s t r a c t A new model for enzymatic hydrolysis of lignocellulosic biomass distinguishes causal influences fromenzyme deactivation and restrictions on the accessibility of cellulose. It focuses on calculating theamount of unreacted cellulose at cessation of enzyme activity, unlike existing models that were con-structed for calculating the time dependence of conversion. There are three adjustable parameters: (1)‘occluded cellulose’ is defined as cellulose that cannot be hydrolysed regardless of enzyme loading orincubation time, (2) a ‘characteristic enzyme loading’ is sufficient to hydrolyse half of the non-occludedcellulose, (3) a ‘mechanism index’ measures deviations from first-order kinetics. This model was used topredict that the optimal incubation temperature is lower for lignocellulosics than for pure cellulose. Forsteam-exploded pine wood after 96 h incubation, occluded cellulose was 24% and 26% at 30   C and 50   C,and the characteristic enzyme loadings were 10 and 18 FPU/g substrate, respectively.   2013 Elsevier Ltd. All rights reserved. 1. Introduction The lignin in lignocellulosic biomass inhibits enzymatic hydro-lysis, and the unique chemistry of softwood lignin makes soft-woods particularly challenging for bioconversion (Mabee et al.,2006). Mansfield et al. (1999) suggested that two distinct mecha- nisms are involved: lignin binds cellulases in non-productive com-plexes, while also blocking cellulose from being accessible tocellulases. This paper describes a mathematical model developedto assist in distinguishing between the two mechanisms, and usessoftwood biomass to illustrate use of the model.Lignin and other phenolic substances can inhibit enzymatichydrolysis through non-productive binding (Pan, 2008; Ximeneset al., 2010) or permanent deactivation (Ximenes et al., 2011). The distinction between the two mechanisms is important. Non-productive binding to the substrate or hydrolysis products slowsthe hydrolysis of cellulose to glucose, but the enzymes are eventu-ally released to continue the hydrolysis process. On the other hand,permanent deactivation, e.g. through denaturation or chemicaldeactivation reactions with the substrate, can lead to cessation of hydrolysis before all of the cellulose has been converted to glucose.Ximenes et al. (2011) studied the effects of phenolic substancesformed by degradation of lignin, e.g. vanillin, cinnamic acid and4-hydroxycinnamic acid, and reported considerable enzyme deac-tivation for substances that showed only traces of non-productivebinding. Sinitsyn et al. (1982) washed steam-exploded hardwoodand found that the wash water contained cellulase inhibitors. Theyalso found that adding the wash water to the washed wood re-sulted in markedly inferior glucose yields, with hydrolysis haltedafter incubation for 84 h. The latter observation indicated enzymedeactivation by water-soluble components of pretreated wood.Sewalt et al. (1996) suggested that deactivation of cellulase bylignin involves chemical reactions with quinone methideintermediates.Permanent deactivation can also occur in the absence of lignin,e.g. as a result of shear forces generated by agitation (Taneda et al., 0960-8524/$ - see front matter    2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.biortech.2012.12.122 ⇑ Corresponding author. Tel.: +64 7 343 5899. E-mail address:  Roger.Newman@scionresearch.com (R.H. Newman).Bioresource Technology 130 (2013) 757–762 Contents lists available at SciVerse ScienceDirect Bioresource Technology journal homepage: www.elsevier.com/locate/biortech  2012), particularly in the presence of air–liquid interfaces (Basuand Pal, 1956; Kim et al., 1982). Thermal deactivation can also beimportant. Studies of enzymatic hydrolysis of cellulose usually re-port incubation temperatures between 45   C and 50   C, maximiz-ing the initial rate of conversion of cellulose to glucose (Bakeret al., 1992; Tengborg et al., 2001). If the goal is to maximize thefinal degreeof conversion,rather thanthe initial rateof conversion,then a lower incubation temperature might be more appropriate(Eklund et al., 1990; Tengborg et al., 2001). It is important thatany mathematical model for deactivation incorporates the influ-ences of shear-force and thermal deactivation, as well as deactiva-tion by chemical reactions.Delignification is effective, but expensive (Cullis and Mansfield,2004). Cellulose microfibrils can be made more accessible by ther-mochemicaltreatment, during which lignin is depolymerized, relo-cated and repolymerized as droplets (Hansen et al., 2011).Accessibility is readily measured by adsorption of dyes or fluores-cently-labeled enzymes (Esteghlalian et al., 2001), and sometimeschanges during conversion (Kumar and Wyman, 2009). In this pa-per, the cellulose that never becomes accessible, even after an infi-nitely long incubation time, is referred to as ‘occluded cellulose’.The distinction between inaccessible cellulose and occluded cellu-lose is important. Cellulose that is initially inaccessible might be-come accessible through the action of enzymes, digesting layersof hemicelluloses that obstruct the movement of cellulase intothe pores of the substrate. Occluded cellulose never becomesaccessible, because it is surrounded by substances that are not di-gested by any component of the enzyme mixture.Numerous mathematical models have described the kinetics of enzymatic hydrolysis of cellulose over periods of hours or days(Zhang and Lynd, 2004; Zhou et al., 2009; Wang and Feng, 2010).Most of the models were based on an implicit assumption thatall of the available cellulose would eventually be consumed afterlong incubation times. Some models have showed that deactiva-tion can slow the release of glucose as conversion proceeds (Gusa-kov et al., 1992; Shen and Agblevor, 2008; Zhang et al., 2010; Yeand Berson, 2011). A different approach was taken in the mathe-matical modeling reported here. Instead of describing conversionas a function of time, the goal of the present work was to derivea mathematical relationship between enzyme loading and the ex-tent of conversion attained when enzymatic hydrolysis halts. Thiswas achieved by considering the ratio of rates of hydrolysis anddeactivation, so that incubation time was eliminated from theequations. 2. Theory  The model was kept at a semi-mechanistic level for simplicity.In other words, the details of reaction mechanisms were not incor-porated. As an example of a simplifying assumption, a single sym-bol  E   was used to represent ‘‘cellulase activity’’ in a broad sense.Commercial products contain mixtures of enzymes includingendoglucanases, exoglucanases and  b -glucosidases (Zhang et al.,2006). In this work, only enzyme activity associated with con-sumption of cellulose was considered relevant to the symbol  E  . Itwas assumed that cellobiose and other intermediate products wereeventually hydrolyzed to glucose by enzymes other than those in-cluded in the activity represented by  E  .The processwas assumed to start with enzymes added to a slur-ry of lignocellulosic substrate, bringing the enzyme concentrationto  E   =  E  0 , expressed in FPU (filter paper units) per liter, and the cel-lulose concentration to  C   =  C  0 , expressed in grams per liter. Theprocess was assumed to end when the enzyme was fully deacti-vated, i.e.,  E  1  = 0, leaving a concentration  C  1  of cellulose unre-acted. The percent conversion of cellulose was defined as: Conversion ð % Þ¼  A ð C  0  C  1 Þ C   10  ð 1 Þ Here A is the percentage of cellulose that can be hydrolyzed at rel-atively high enzyme loadings and long incubation times, i.e., 100  Ais the percentage of occluded cellulose. The rate of deactivation of the enzyme was assumed proportional to a function  f  ( E  ): d E  = d t   ¼ k d  f  ð E  Þ ð 2 Þ Here  k d  is a rate constant for deactivation, assumed to involve amixture of contributing processes including shear deactivation,thermal denaturation and chemical reactions with lignin. If deacti-vation is first order in  E  , as suggested by Gusakov et al. (1992), then  f  ( E  ) =  E  . If a portion of the enzyme is temporarily involved in non-productive binding,  f  ( E  ) might represent the non-bound portion.The form of   f  ( E  ) is not relevant here, as will be discussed further be-low. The rate of deactivation by lignin will, of course, depend on theshear forces applied during agitation, the temperature of incuba-tion, and the concentration of lignin, so it was assumed that allthese factors remain constant through the period of incubation.The function  f  ( E  ) includes deactivation by substrate componentsother than lignin, and deactivation mechanisms that do not involvethe substrate, such as thermal denaturation or deactivation at air–liquid interfaces as discussed in the Section 1. The rate of change of C was likewise assumed proportional to  f  ( E  ): d C  = d t   ¼ k h C  m þ 1  f  ð E  Þ ð 3 Þ Here  k h  is a rate constant for enzymatic hydrolysis. The exponent of  m  + 1 in Eq. (3) allows for a decline in reaction rate as conversionproceeds: the larger the value of the ‘mechanism index’  m , the stee-per the decline in reaction rate. If   m  = 0, conversion follows a kineticequation that is first-order in cellulose. Any decline in the reactionrate can then be attributed to enzyme deactivation. If   m  > 0, at leasta portion of the decline can be attributed to decreasing accessibilityof cellulose.Dividing Eq. (3) by Eq. (2) eliminates incubation timeand  f  ( E  ) from a differential equation: d E  = d C   ¼ k d k  1h  C   m  1 ð 4 Þ The elimination of   f  ( E  ) from Eq. (4) means that it is not necessary toconsider details of the conversion processes that are time depen-dent, e.g., the rate of exchange of enzymes between non-boundand non-productively bound states. A general relationship between enzyme loading and final con-version can be obtained by integrating Eq. (4) from the initial con-dition to the final condition. In the present work, just two values of  m  are considered:  m  = 0 or 1 in Models 1 and 2, respectively.In Model 1, any decline in reaction rate is attributed to deacti-vation of the enzyme rather than changes in accessibility of cellu-lose. Integration of Eq. (4) with  m  = 0 gives: E  0  ¼ k d k  1h  ð ln C  0  ln C  1 Þ ð 5 Þ Rearranging Eq. (5) and insertion into Eq. (1) gives: Conversion ð % Þ¼  A ð 1  exp ð k  1d  k h E  0 ÞÞ ð 6 Þ The initial enzyme loading  E  L   was expressed as FPU per gram of substrate, and defined as  E  L   =  E  0  X  / C  0 , where  X   is the mass fractionof cellulose in the substrate. A characteristic enzyme loading  e was defined as the value of   E  L   that is sufficient to achieve conver-sion of half of the cellulose, other than occluded cellulose, beforeenzyme activity ceases. Eq. (6) then becomes: Conversion ð % Þ¼  A ð 1  exp ð c  e  1 E L  ÞÞ ð 7 Þ Here  c   = ln(2) = 0.693, and: e ¼ cXC   10  k d k  1h  ð 8 Þ 758  R.H. Newman et al./Bioresource Technology 130 (2013) 757–762  In Model 2, the rate of enzymatic hydrolysis declines more stee-ply than in Model1. Integrating Eq. (4) with  m  = 1 and insertingtheresult in Eq. (1) gives: Conversion ð % Þ¼  AE  L  ð E  L  þ e Þ  1 ð 9 Þ Here  e  remains defined as the value of   E  L   required to achieve con-version of half of the cellulose, other than occluded cellulose, andin Model 2 the value of   e  is: e ¼  XC   20  k d k  1h  ð 10 Þ Eq. (9) is identical to an empirical relationship proposed by Sattleret al. (1989) in their study of enzymatic hydrolysis of steam-pre-treated willow wood. In both special cases of the general model,  e  involves a ratio of rate constants for deactivation and enzyme hydrolysis. Both rateconstants are expected to increase with temperature, but the rateconstant for a non-catalyzed reaction is expected to rise more stee-ply than that for a catalyzed reaction, so the value of   e  is expectedto be a function of incubation temperature. This prediction wastested by measuring cellulose conversion for two different incuba-tion temperatures and several different enzyme loadings. 3. Methods  3.1. Substrate Steam-exploded softwood was used as the substrate, because of the high lignin contents reported for similar substrates. Lignin con-tentsbetween39%and46%havebeenreportedforsteam-explodedand steam-pretreated woods from three different softwood species(Tengborg et al., 2001; Lu et al., 2002; Kumar et al., 2010). Pinus radiata  wood chips were obtained from a local sawmilland used to produce steam-exploded wood (SEW). The steamexplosion apparatus was built around a 75 mm diameter Type316 stainless tube with a ball valve mounted at each end, designedto be heated by steam injected directly into the tube. The lowerball valve discharged into a cyclone. A portion of 0.75 kg chips,with a moisture content of 60%, was impregnated with SO 2 (3% w/w) and heated with steam at 215   C for 3 min, and the lowerball valve was opened. The pulp was washed four times with waterto obtain a 54% yield of water-insoluble matter on an oven-driedbasis. It was freeze-dried, Wiley milled at 80 mesh and sievedthrough a 250 l m screen to reject coarse particles. Milling andsieving ensured uniform sub-samples for small-scale enzymatichydrolysis experiments. Preliminary enzymatic hydrolysis experi-ments on SEW that was neither freeze-dried nor milled showedpoor reproducibility, attributed to the sample size being too smallfor successful assembly of a collection of fragments to representthe mixture in the bulk supply.Extractives were determined using a FOSS Soxtec System 1043extraction unit with dichloromethane as the solvent. Lignin wasdetermined using methods based on TAPPI Standard Method T222 om-88 and TAPPI Useful Method UM 250. Fucose was addedto the hydrolysate from lignin analysis, as an internal standard,and the carbohydrates were analyzed by ion chromatograph usinga Dionex ICS 3000 instrument (Pettersen and Schwandt, 1991). Thecomposition of the freeze-dried SEW was: 53.6% glucosyl residues,36.2% Klason lignin, 5.5% extractives, 0.4% acid-soluble lignin, 0.2%mannosyl residues and 0.2% xylosyl residues. The composition wassimilar to published compositions for steam-exploded and steam-pretreated woods from other softwood species (Tengborg et al.,2001; Lu et al., 2002; Kumar et al., 2010). In particular, hemicellu-lose contents are typically <3%, most of the hemicelluloses havingbeen hydrolyzed during pretreatment.  3.2. Enzymatic hydrolysis Hydrolysis was performed on a 5 ml scale at 30   C or 50   C, pH4.8, in 0.05 M sodium citrate buffer containing 0.01% w/v sodiumazide, in 20-ml screw-capped glass tubes agitated at 180 rpm.Rotational motion was used, rather than shaking which caused tur-bulence and might have increased the rate of deactivation of en-zymes (Basu and Pal, 1956). Experiments were carried out induplicates or triplicates using a substrate concentration of 1.5%dry matter (DM). The SEW absorbed moisture from room air, andthis was allowed for in weighing out each portion of 75 mg sub-strate on a dry basis. The low substrate concentration was usedto avoid mass transfer problems encountered when agitating high-er consistency samples.Celluclast 1.5 l was supplemented with Novozym 188 to pro-vide additional cellobiase activity. The cellobiohydrolase in Cellu-clast 1.5 l converts cellulose to cellobiose, but is inhibited by thatcellobiose. Novozym 188 converts cellobiose to glucose and is, inturn, inhibited by that glucose (Hong et al., 1981). The enzymeswere mixed in an activity ratio of 1 FPU–1.25 IU, in order to ensureadequate conversion of cellobiose to glucose. In published experi-ments enzymatic hydrolysis of pretreated woods, ratios have usu-ally been chosen within the range 1:0.5–1:2.0 (Sinitsyn et al.,1982; Sattler et al., 1989; Gusakov et al., 1992; Esteghlalianet al., 2001; Lu et al., 2002; Cullis and Mansfield, 2004; Mabeeet al., 2006; Börjesson et al., 2007; Pan, 2008; Kumar and Wyman,2009; Kumar et al., 2010), although lower and higher ratios havealso been tested (Eklund et al., 1990; Tengborg et al., 2001; Inoueet al., 2008). Enzyme activities were measured by standard IUPACmethods (Ghose, 1987). Activity values were 67 FPU/ml for Cellu-clast 1.5 l and 498 IU/ml for Novozym 188. These activity valueswere similar to those published in other studies (Börjesson et al.,2007; Tengborg et al., 2001). Protein was analyzed by the methodof  Bradford (1976), using bovine serum albumin as the standard.The mixture of the two enzymes showed an activity-to-protein ra-tio of 1.7 FPU/mg.The samples for sugar analysis were taken at different timepoints up to 28 days. For each sample, enzymatic hydrolysis wasstopped by plunging the tube into boiling water for 5 min and thencooling it to room temperature in water. The mixture was thencentrifuged at 4000 rpm for 10 min at 25   C and the supernatantwas collected for glucose analysis by a YSI 2700 SELECT™ Bio-chemistry Analyzer (YSI Life Sciences) configured in single analytemode. The manufacturer’s specifications for precision indicatedthat the coefficient of variation should be <2% for 10 measure-ments of glucose concentration. Results were corrected for smallamounts of glucose introduced along with the enzyme solution.The standard deviation was used to calculate the 95% confidenceinterval for each mean value from duplicate or triplicate hydrolysisexperiments. 4. Results and discussion 4.1. Cessation of enzymatic hydrolysis For an enzyme loading of 5 FPU/g substrate, conversion of cellu-losetoglucosereachedaplateauatabout12%conversionafter24 hof incubation at 50   C (Fig. 1). Hydrolysis was not limited by occlu- sion of the cellulose, since treatment with larger enzyme loadingsresulted in conversion of 74% of the cellulose as discussed below. 4.2. Occlusion of cellulose Final conversion from cellulose to glucose was plotted againstenzyme loading, i.e.  E  L  , for incubation temperatures of 30   C and R.H. Newman et al./Bioresource Technology 130 (2013) 757–762  759  50   C (Fig. 2). For both incubation temperatures, Eq. (7) (Model 1, m  = 0) gave a better fit than Eq. (9) (Model 2,  m  = 1). This compar-ison was reflected in the root-mean-square-deviations (Table 1).Model 1 led to a correct prediction that the curves would reach aplateau at relatively high enzyme loadings, i.e.,  E  L   > 50 FPU/g sub-strate at 30   C or  E  L   > 100 FPU/g cellulose at 50   C (Fig. 2). Model2 led to a prediction that the curves would continue to rise steadilyon the right-hand side of  Fig. 2. That was not observed. The differ-ences between the qualities of the fits were, however, too small towarrant investigation of intermediate values of the mechanism in-dex, i.e., 0 <  m  < 1.Experiments carried out at longer incubation times pointed to alimitation in the model, in that the parameter  A  showed a smalldependence on incubation time (Fig. 3). The best-fit value forocclusion dropped from 100   A  = 26% at 96 h to 20% at 168 h and13% at 336 h of incubation. The slow increase in the apparent valueof   A  was attributed to slow diffusion of enzymes into poorly-acces-sible domains, rather than fully occluded domains. The indicatorfor deactivation showed little change, with best-fit values of  e  = 18, 18 and 20 FPU/g substrate after incubation times of 96,168 and 336 h, respectively.Sattler et al. (1989) studied enzymatic hydrolysis of steam-pre-treated willow wood and reported good fits to Eq. (9), i.e., Model 2.Their procedure for assessing the quality of the fit was reassessed.Sattler et al. (1989) plotted the reciprocal of conversion against thereciprocal of enzyme loading and reported linear plots, consistentwith the inverted form of Eq. (9): Conversion  1 ¼ e A  1 E  1L   þ A  1 ð 11 Þ Close inspection of their plots revealed slight deviations from line-arity. Results from the present work (Fig. 4) likewise showed a devi-ation from linearity for high enzyme loadings, i.e., at the left-handside of the plot. A broken line in Fig. 4 indicates extrapolation fromthelinear portionof the plot,as carriedout by Sattler etal. (1989)inorder to determine the intercept 1/  A  in Eq. (11). In Fig. 4, the inter-cept of the broken line on the vertical axis corresponds to  A  > 100%,yet the experimental data points curve away from broken line to-wards the intercept indicated by the solid curve. That intercept cor-responds to  A  = 76% as determined by direct least-squares fitting toModel 1 (Table 1). Clearly it is important to use direct least-squaresfitting rather than the procedure suggested by Sattler et al. (1989).It is also important to use enzyme loadings much greater than theloadings compatible with commercial processing, i.e., it is impor-tant to place multiple data points on the right-hand side of  Fig. 2or left-hand side of  Fig. 4. Sattler et al. (1989) and Lu et al. (2002) used wet substrates ob- tained by pretreating willow and Douglas fir, respectively, and re-ported that cellulose conversion rose to >90% at relatively highenzyme loadings. Luo and Zhu (2011) studied pretreated lodgepolepine and showed that air drying led to decreased enzyme digest-ibility, attributed to hornification and consequent loss of enzyme Fig. 1.  Enzymatic hydrolysis at 50   C and an initial enzyme loading of 5 FPU/gsubstrate. Error bars show 95% confidence intervals based on replication of data. Fig. 2.  Enzymatic hydrolysis by incubation for 96 h at 30   C and 50   C. Error barsshow 95% confidence intervals based on replication of data. Best-fit curves werebased on Model 1 ( m  = 0, solid line) and Model 2 ( m  = 1, broken line).  Table 1 Best-fit parameters for enzymatic hydrolysis of pine SEW. Model 100   A  (%)  e  (FPU/g substrate) RMSD a (%)Model 1, Eq. (7)30   C 24 10 1.450   C 26 18 1.1Model 2, Eq. (8)30   C 13 12 2.350   C 18 19 2.2 a Root-mean-square deviation of the best-fit curve from experimental datapoints. Fig. 3.  Enzymatic hydrolysis by incubation at 50   C. The incubation time (h) isshown beside each curve. Error bars show 95% confidence intervals based onreplication of data. Best-fit curves were based on Model 1 ( m  = 0).760  R.H. Newman et al./Bioresource Technology 130 (2013) 757–762
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