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A kinetic assessment of the enzymatic hydrolysis of potato ( Solanum tuberosum

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The biotechnology industry demands raw materials to prepare growth media for fermentative processes. These media contain a carbon source which can be obtained from potato, an abundant source of starch. This work deals with the modelling of the
  A kinetic assessment of the enzymatic hydrolysis of potato ( Solanum tuberosum ) R. Delgado a , A.J. Castro a , M. Va´zquez b , * a Division of Postgraduate Studies, Faculty of Chemical Engineering, Universidad Michoacana de San Nicola´s de Hidalgo, Morelia, Michoaca´n, Mexico b  Area of Food Technology, Department of Analytical Chemistry, Faculty of Veterinary, University of Santiago de Compostela, Campus de Lugo, 27002 Lugo, Spain a r t i c l e i n f o  Article history: Received 18 July 2008Received in revised form8 October 2008Accepted 6 November 2008 Keywords: a -AmylaseGlucoamylasePotatoEnzymatic hydrolysisKinetics a b s t r a c t The biotechnology industry demands raw materials to prepare growth media for fermentative processes.These media contain a carbon source which can be obtained from potato, an abundant source of starch.This work deals with the modelling of the enzymatic hydrolysis of potato using  a  -amylase and glu-coamylase. Several strategies were evaluated, including the use of those enzymes alone, in a mixture andunder different conditions of temperature, time and substrate concentration. Using  a  -amylase alone orglucoamylase alone, both enzymes reached the same hydrolysis yield (0.42 g/g). The hydrolysis usinga mixture of both enzymes allowed obtaining hydrolysates with reducing sugar concentrations up to14.1 g/L at 70   C. In this case, the yield of hydrolysis was increased up to 0.82 g/g. Considering theimportant effect and interactions of time and temperature, a statistical Box–Behnken design was con-ducted including substrate concentration, time and temperature as operational variables and reducingsugar concentration released as dependent variable. The conditions to obtain the maximum responsewere 6% DM of substrate concentration, 68   C and 180 min, where 32.62 g/L of reducing sugar concen-tration was predicted. Verification experiments gave a mean value of 33.57 g/L, confirming the accuracyof the model.   2008 Swiss Society of Food Science and Technology. Published by Elsevier Ltd. All rights reserved. 1. Introduction Many cereal seeds and tubers/roots store starch. Potato is anabundant material that mainly contains (fresh matter w/w):moisture (80  2%), starch (18  2%), cellulose and hemicelluloses(1.5  0.5%), glucose (0.4  0.3%) and proteins (2  1.5%) (Woolfe,1987). Its annual world production is around 300 million tons, andareas planted cover more than 18 million ha. Major producingcountries (and the world’s share of production) are China (20%),Russia(12%),India(8%),andUnitedStates(8%)(Miranda&Aguilera,2006).Biotechnology industries demand raw materials to preparegrowth media for the fermentative processes. These media containa carbon source which can be obtained from vegetables with highmonosaccharidecontents suchas sucroseof sugarcane ( Saccharumofficinarum ) (Patil et al., 2006; Sa´nchez & Cardona, 2008), highpolysaccharide contents such as cellulose and hemicelluloses of sugar cane bagasse (Al Arni, Zilli, & Converti, 2007; Cheng et al.,2008) or starch of potato ( Solanum tuberosum ) (C´uric´, Karlovic´,Tripalo, & Je  zek,1998; Liu, 2002). The polysaccharides (cellulose orstarch) should be transformed into monosaccharides by acid orenzymatic hydrolysis.Hydrolysates containing glucose can be obtained from potatostarch. The acid hydrolysis generates an acid solution that needsneutralization to be used for fermentative purposes while theenzymatic hydrolysis has the advantage that generates a glucosesolution that can be fermented without more treatments.Starch is generally composed of two kinds of   a  -glucan poly-mers: i) amylose, a linear polymer consisting almost exclusively of  a  -1,4-linked glucose residues and ii) amylopectin, which inaddition to linear chains of   a  -1,4-linked glucose, also contains a  -1,6-linked branch points (Hansen, Blennow, Pederson, Nørgaard,& Engelsen, 2008). Therefore, the amylose fraction is essentiallylinear, whereas amylopectin is highly branched. The amylosecontent is 26.9% for potato (Stawski, 2008).Gelatinization occurs when starch is heated in water. Aftercooling, the gelatinized starch forms a textural gel networkprovided the starch concentration has reached a critical concen-tration. Gelatinization allows enzymes to penetrate easily intostarch structures contributing to a more efficient reaction (Hansenet al., 2008). Two enzymes,  a  -amylase (E.C. and glucoa-mylase (E.C., have been applied as catalysts for enzymatichydrolysis of materials with high content of starch as chestnutpure´e (Lo´pez, Torrado, Fucin˜os, Guerra, & Pastrana, 2006).The  a  -amylase can hydrolyze starch into maltose, glucose andmaltotriose by cleaving the 1,4- a  - D -glucosidic linkages betweenadjacentglucoseunitsinthelinearamylosechain.Thisenzymecanbe obtained from several fungi, yeasts, bacteria and actinomyces. *  Corresponding author. E-mail address: (M. Va´zquez). Contents lists available at ScienceDirect LWT - Food Science and Technology journal homepage: 0023-6438/$34.00    2008 Swiss Society of Food Science and Technology. Published by Elsevier Ltd. All rights reserved.doi:10.1016/j.lwt.2008.11.001 LWT - Food Science and Technology 42 (2009) 797–804  However, fungal and bacterial sources have the main applicationsin food industry. Alkalophilic microorganisms, inparticular  Bacillus species like  Bacillus licheniformis , have attracted much interest inthe past few decades because of their ability to produce extracel-lular enzymes that are stable at high pH value (Baysal, Uyar, Dog˘ ru, & Alkan, 2008).Glucoamylase hydrolyses single glucose units from the non-reducing ends of amylose and amylopectin in a stepwise manner,and produces glucose as the sole end-product from starch andrelated polymers. Unlike  a -amylase, most glucoamylases are alsoable to hydrolyze the 1,6- a  -linkages at the branching points of amylopectin, although at a lower rate than 1,4-linkages (Gang-adharan, Sivaramakrishnan, Nampoothiri, Sukumaran, & Pandey,2008; Liu, 2002; Wang, Wang, Wang, & Ma, 2008). Glucoamylasesare produced by a diverse group of microorganisms, includingbacteria, yeasts and moulds; however the commercially usedenzymes are produced by species of   Aspergillus  and  Rhizopus (Norouzian, Akbarzadeh, Scharer, & Young, 2006).This work deals with the modelling and optimization of theenzymatic hydrolysis of dried potatoes with  a  -amylase andglucoamylase. 2. Materials and methods  2.1. Substrate and enzymes Potatoes supplied by local farmers (Diz, Dozo´n, Spain) werewashed,sliced,dried andgroundtobeused inthiswork. Thewaterextracted from potatoes was 80.35% of the fresh weight. The driedpotatoes contained a residual of 8.13% moisture.The enzymes used in this study were commercial  a  -amylase(Termamyl SC DS  ) and glucoamylase (Saczyme  ). They werekindlysuppliedbyNovozymesA/S,Bagsvaerd,Denmark.TermamylSC DS  was produced by submerged fermentation of   Bacilluslicheniformis . The commercial enzyme contains methionine,sodiumchlorideandsucroseasstabilisers.Saczyme  wasproducedby submerged fermentation of   Aspergillus niger  . The enzyme wasseparated and purified from the production organism. Thecommercial solution contains also sucrose and glucose as stabil-isers and potassium sorbate and sodium benzoate as preservatives.Dilutions of the commercial solutions were prepared to obtain theenzyme/substrate ratios needed.  2.2. Pretreatment  A 60 g solutionwas prepared of dried potato onwater (4% w/w)in sealed 250 mL bottles. The solution was heated to boiling withagitation of 500 rpm to allow gelatinization. Subsequently, 40 g of 0.15 M phosphate–citric buffer solution (pH 5.0) was addedobtaining a final solution of 2.4% of dried potatoes. The mixtureswere immediately used for the hydrolysis. In the experimentaldesign study the initial concentration of dried potato was varied toobtain the final substrate concentration needed in the range 2–6%.  2.3. Hydrolysis conditions The enzymatic hydrolysis of dried potato was carried out withagitation (600 rpm) and at different temperatures in a warmingplate with temperature controller. The enzyme/substrate ratio wasset up at 6 units (U)/g of dried potato (dry matter). The fraction of activity  a  -amylase/total enzymes was 0.35 U/U. These parameterswere taken from Lo´pez, Torrado, Fucin˜ os, Guerra, and Pastrana(2004). The ratio of liquid/solid was 40.9 g/g.In the kinetic studies, samples were taken and analyzed severaltimes until the reducing sugar concentration remained stable.  2.4. Overall process TheoverallprocessstudiedinthisworkisshowninFig.1.100 kgof potatoes were washed and sliced. Then they were dried at 60   Cwhere 85.35 kg of moisture was removed, yielding 0.1965 kg of dried potato/kg of fresh potato. The residual moisture was 8.13%.Thedriedpotatoesweregroundandtreatedat100   Cwithawater/solid ratio of 19.47 g/g, forming a gel. Then, it was mixed witha buffer solution to reach pH 5 and diluted enzyme solution wasadded to start the hydrolysis reaction. The water/solid ratio was40.9 g/g in the hydrolysis step. At the end of the reaction, thehydrolysate was filtered and the liquid (755.85 kg) is the glucosesolution that can be used as substrate for the growth of  Washing and slicingRaw potatoes,100 kgWater, 80.35 kgDried potatoes, 19.65 kg(moisture, 8.13 %)Potatoes, 19.65 kgWater, 349.96 kgCitric acid 0.15 M - Na2HPO4 0.3 M Buffer pH 5, 302.34 kgDiluted 1:55000 commercial α -amylase(Termamyl SC DS), 40.81 kgDiluted1:7500 commercialglucoamylase (Saczyme), 43.08 KgGrindingGelling pretreatment(boiling with agitationat 500 rpm)Sugar solution, 755.85 kgResidual sugars conc.,approx. 12-14 g/LEnzymatic hydrolysis40, 45, 55, 70 or 75°C0-180 min600 rpmDrying(60 °C) Fig. 1.  Overall process proposed for the pretreatment and enzymatic hydrolysis of potato. R. Delgado et al. / LWT - Food Science and Technology 42 (2009) 797–804 798  microorganism for different industrial purposes. Obviously, theconcentration of glucose depends on the hydrolysis conditions.  2.5. Analytical methods The composition of the dried substrate was obtained througha quantitative acid hydrolysis under standard conditions (Garrote,Domı´nguez, & Parajo´, 1999).The enzymatic activity of each enzyme was measured with themethod used by Lo´pez et al. (2006) with the difference that theydefined enzymatic activity units as the concentration of reducingsugarreleasedat40   Cduring10 minandweexpressedtheactivityunitastheconcentrationofreducingsugarreleasedat40   Cduring1 min.The glucose released by the hydrolysis was measured asreducing sugar concentration ( C  RS ) using the DNS (3,5-dini-trosalicylic acid) method. This method is adequate because glucoseis the unique reducing sugar of the starch (Lo´pez et al., 2004). This compound is reduced by glucose toward a coloured product(3-amino-5-dinitrosalicylic acid). The absorbance was measured at540 nm (V-670 spectrophotometer, Jasco, Tokio, Japan) andreducing sugar concentration was determined by a calibrationcurve using glucose as standard.  2.6. Modelling and statistical methods Adjustmentofexperimentaldatatomodelwasperformedusingthe solver utility of MS-Excel 2007 (Microsoft Corp., Redmond,Washington, USA). The model was statistically validated throughthe calculated values of regression coefficient ( r  2 ) and Fisher testprobability. The experiment design was analyzed using the DesignExpert  7.1.1 (Stat-Ease, Inc., Minneapolis, Minnesota, USA). 3. Results and discussion Thecompositionobtainedwas(drymatter):starchexpressedasglucan, 64.91  3.34%; xylan, 2.81  0.24%; araban, 0.47  0.36%.Klasson lignin was very low as can be expected (0.82  0.14%). Thelow concentration of lignin confirms that all the glucan detectedwas proceeded from the starch and not from cellulose which islinked with lignin and hemicelluloses. Acetyl groups were notdetected.  3.1. Determination of the  a  -amylase and glucoamylase activities Enzymeactivitiesof thelotsusedinthisworkweredetermined.The activity value of   a  -amylase (Termamyl SC DS  ) was 51,273U/ml and for glucoamylase (Saczyme  ) was 12,313 U/ml. Lo´pezet al. (2004) determined activities for other commercial  a  -amylase(Termamyl 120L (S)  ) and glucoamylase (AMG 300L   ), obtaininglower values, 734 U/ml and 245.9 U/ml, respectively. Therefore,Termamyl SC DS  a  -amylase was 70-fold more active than Ter-mamyl 120L (S)  and Saczyme  was 50-fold more active than AMG300L   . Therefore, Termamyl SC DS  solution was diluted 55,000-fold and Saczyme  solution was diluted 7500-fold to be in therange of unit needed in this study.  3.2. Enzymatic hydrolysis with  a  -amylase aloneor glucoamylase alone Enzymatic hydrolysis of dried potatoes was performed using a  -amylase alone or glucoamylase alone. The temperature was setupat70  Conthebasisof thestudyofhydrolysisofchestnutstarch(Lo´pez et al., 2004).In our study, 6 U/g (DM) of dried potatoes wereused. Samples at several times were taken, centrifuged andreducing sugars were analyzed in the supernatant. Fig. 2 shows theexperimental values obtained for glucose released expressed asreducing sugars (RS). Using  a  -amylase alone, 6.4 g/L was obtainedat 60 min. Longer times did not increased the concentration toomuch, reaching up to 7.3 g/L at 180 min. A similar result wasobtained using glucoamylase alone, where 6.1 g/L was obtained at60 min and 7.3 g/L at 180 min.Although models modifying the Michaelis–Menden equationcan be found in the literature (Lo´pez et al., 2004), due to the diffi-culty in finding a strict mechanism for hydrolysis reactions, it iscommon to simplify the models to determine the kinetics of thehydrolysis.Thehydrolysisofthedriedpotatoescanbestudiedasanirreversible first order reaction of decomposition of a poly-saccharide (starch as main component) toward glucose as it isshown in equation (1). ð C 6 H 10 O 5 Þ n þ n H 2 O / k n C 6 H 12 O 6  (1) The experimental data using both enzymes alone were fitted toa mathematical model adopted from the acid hydrolysis of sorghum straw (Herrera, Te´llez-Luis, Ramı´rez, & Va´zquez, 2003).Solving the differential equations, the following model predicts theconcentration of glucose (expressed as reducing sugars): C  RS  ¼  C  PRS  1  e  kt    (2) where  C  RS  is the reducingsugarconcentration released (g/L), C  PRS  isthe potential concentration of reducing sugars (g/L),  k  is the rate of reducing sugars released (min  1 ) and  t   is the reaction time (min). Time, min    R   S  c  o  n  c . ,  g   /   L 036912150306090120150180    R   S  c  o  n  c . ,  g   /   L 3691215Glucoamylase α -amylase Fig. 2.  Experimental (dots) and predicted (line) dependence of the reducing sugarsreleased during the hydrolysis of 24 g/L of dried potato using 6 U of   a  -amylase (Ter-mamyl SC DS  )/g or glucoamylase (Saczyme  )/g alone at 70   C.  Table 1 Kinetic and statistical parameters of reducing sugars released during the enzymatichydrolysis of dried potatoes at 70   C using  a  -amylase or glucoamylase.Enzyme  k  (min  1) C  PRS  (g/L)  r  2 Probability Fisher test a  -amylase 0.0434 6.9 0.9915 0.9936glucoamylase 0.0361 7.2 0.9935 0.9802 R. Delgado et al. / LWT - Food Science and Technology 42 (2009) 797–804  799  Table 1 shows the results of fitting to equation (2) to the enzy- matic hydrolysis catalyzed by  a  -amylase alone or glucoamylasealone at 70   C and the parameters for its statistical evaluation(coefficientof determination  r  2 and  F  -testprobability). The value of  C  PRS  was 6.9 g/L using  a  -amylase and 7.2 g/L using glucoamylase,closetotheexperimentalvalues.Thestatisticalparametersshoweda good agreement between experimental and predicted data. Fig. 2shows the values predicted by the model and experimental data.Thevalueoftherateofreducingsugarsreleasedwasslightlyhigherfor  a  -amylase than for glucoamylase.Considering a complete reaction, where the molecular weight(MW)ofstarchis162 $ n andthe n glucosemoleculesreleasedhavea MW of 180, the ratio of the stoichiometric factors is 180/162 g of released glucose/g of starch. Then the maximum concentration of glucose that can be obtained can be calculated as following: CM RS  ¼  180162  x S C  S  (3) whereCM RS  is maximumconcentration of reducing sugarsthat canbe obtained (g/L),  C  S  is dried potato concentration in the hydrolysismedia (gDM/L) and  x S  is the starch fraction in dried potato.In our study,  C  S  was 24 g/L and  x S  was 0.6491 g/g, consequentlythe maximum concentration of reducing sugars that can beobtainedis17.29 g/L.Accordingtothereducingsugarconcentrationobtained using  a  -amylase alone or glucoamylase alone, bothenzymes hydrolyzed only 42.22% of the maximum concentration,suggesting that a combination of both enzymes could give a higherdegree of hydrolysis.  3.3. Hydrolysis kinetics catalyzed by an  a  -amylaseand glucoamylase mixture A mixture containing a ratio of 0.35 U a  -amylase/0.65 Uglu-coamylasewastested.Theresults of the hydrolysiskineticsofdriedpotatoes (24 g/L) at several temperatures using 6 U/g of driedpotato with  a  -amylase fraction of 0.35 U per one total unit areshowninFig.3.Themaximumconcentrationofreducingsugarwasreached at 180 min for all temperatures. A positive effect of temperature over the maximum concentration of reducing sugarswas observed within the interval from 40 to 70   C, reaching up to14.1 g/L at 70  C. In this case, the yield of hydrolysis was 0.8155 g/g.Using a temperature of 75   C, the maximum value of the reducingsugar concentration observed was only 8.6 g/L while the yield of hydrolysis was 0.4974 g/g. It suggests that the enzymes initiate todenature at this temperature.The reducing sugar concentration using a mixture of   a  -amylaseand glucoamylase at 70  C was clearly higher than that using bothenzymes alone (93% higher). Note that the same enzyme activitywas used in both experiments (6 U/g).The experimental data of the reducing sugar concentrationobserved in Fig. 3 were fitted to the mathematical model proposedinequation(2). Table2 showstheresultsforfittingofexperimental data.Thestatisticalparametersshowedagoodagreement betweenexperimental and predicted data. The rate of reducing sugarsreleased ( k ) increased with the temperature. However, the 036912150306090120150180 Time, min    R   S  c  o  n  c . ,  g   /   L Fig. 3.  Experimental (dots) and predicted dependence (lines) of the reducing sugarsreleased during the hydrolysis of 24 g/L dried potato using 6 total units/g with a frac-tion of 0.35 U of amylase per total units at several temperatures: ( - ) 40   C, ( : ) 45   C,( A ) 55   C, ( C )70   C and ( 6 )75   C.  Table 2 Kinetic and statistical parameters of reducing sugars released during the enzymatichydrolysis of dried potatoes using a mixture of   a  -amylase and glucoamylase. T   (  C)  k  (min  1) C  PRS  (g/L)  r  2 Probability Fisher test40 0.0118 10.8 0.9928 0.997645 0.0119 12.2 0.9962 0.968755 0.0196 12.8 0.9870 0.950370 0.0225 13.8 0.9950 0.972675 0.0454 8.5 0.9933 0.9913 0246810121440506070060120180 Temperature, ºC    T   i  m  e ,    m   i  n    R  e   d  u  c   i  n  g  s  u  g  a  r  s  c  o  n . ,  g   /   L Fig. 4.  Prediction of the generalized model for the dependence of reducing sugarconcentration on time and temperature. 02040608010040506070060120180 Temperature, ºC    Y   i  e   l   d  o   f   h  y   d  r  o   l  y  s   i  s ,   %    T   i  m  e ,    m   i  n Fig. 5.  Prediction of the model for hydrolysis yield for the dependence on time andtemperature. R. Delgado et al. / LWT - Food Science and Technology 42 (2009) 797–804 800  potential concentration of reducing sugars ( C  PRS ) increased withthe temperature from 40 to 70  C, reaching values of 10.8–13.8 g/L,but decreased at 75   C with a value of 8.5 g/L. This confirms thesuggestion of the denaturation of the enzymes at 75   C.The maximum value obtained (14.1 g/L at 70   C and 180 min) isfarfromthemaximumconcentrationcalculatedusingequation(3),17.29 g/L. This can be due to that compared with other starches;potato starch has a higher concentration of covalently boundphosphate (Hizukuri, Tabata, & Nikuni, 1970). As amylolyticenzymes are incapable of bypassing the phosphorylated glucosylresidue, phosphoryl-oligosaccharides are released from the diges-tion of potato starch with amylase (Kamasaka et al., 1995). It islikely that this high phosphorus content in potato starch mightreduce the enzymatic digestibility of gelatinized starch.  3.4. Generalized kinetic model of hydrolysis The effects of the temperature on the rate of reducing sugarsreleased ( k ) and the potential concentration of reducing sugars( C  PRS ) were correlated as a linear function in the range of 40–70   C.The correlation coefficient  r  2 was 0.9116 for  k  and 0.8916 for  C  PRS .The probability of   F  -test was 0.9400 and 0.9271, respectively,showing the good agreement of the models.The results of the linear regressions tothese two functions wereincluded in equation (2) to obtain the generalized model of equation (4). C  RS  ¼ h 8 : 7  10  2 T  þ 7 : 8 i 1  e ð 3 : 9  10  4 T   4 : 2  10  3 Þ t    (4) Fig. 4 shows the response surface of the generalized model forthe dependence of   C  RS  on time and temperature in the range of thestudy. This kind of figure allows a visual evaluation of the models.Therefore, it is possible to select conditions under which thereducing sugarconcentration is the highest. Accordingto Fig. 4, themaximum concentration of reducing sugar was reached at 70   Cand 180 min, with a value of 13.9 g/L.The statistical evaluation between the model of equation (4)and the observed data of reducing sugar concentration ( C  RS ) gavea value of   r  2 of 0.9882 and an  F  -test probability of 0.9842. Thus, themodel can be considered valid.In order to provide a better understanding of the process,a derived model of equation (4) for the yield of hydrolysis can becalculated as  C  RS /CM RS . Fig. 5 shows the response surface for thehydrolysis yield in the range of study (40–70   C and 0–180 min).The effect of the time had more influence on the yield than that of temperature. However, an interaction between time andtemperature was observed. The maximum yield of hydrolysis(0.80 g/g) was predicted at 70   C and 180 min.  3.5. Response surface of the dependence of reducing sugar concentration on substrate concentration, temperature and time The previous results showed that the maximum concentrationof reducing sugars obtained was low (around 14 g/L) to be used forsome fermentative processes. Considering the important effectsand interaction of time and temperature, a new study was con-ducted including a new variable (substrate concentration) toincrease this concentration. The influence of substrate concentra-tion, temperature and time during the enzymatic hydrolysis of potato was assessed using the response surface methodologywhich has been successfully used to optimize biochemistry andbiotechnology processes related with food systems (Larraza´bal &Camacho, 2008; Roberto, Sato, Mancilha, & Tacheda,1995; Va´zquez& Martin,1998).The set of experiments followed a second-order, incomplete,factorial structure. The substrate concentration, temperature andtime were considered as operational variables (denoted  S  0 ,  T   and  t  ,respectively) and their effects on the selected dependent variable(reducing sugar concentration) were calculated. For computationpurposes, the normalized, dimensionless variables  x 1 ,  x 2 ,  x 3  weredefined as:  x 1  ¼  S  0  42 (5)  x 2  ¼  T   702 (6)  x 3  ¼  t   12060 (7)  Table 3 Variables involved in the experiments design (Box–Behnken) for the enzymatichydrolysis of dried potatoes using a mixture of   a  -amylase and glucoamylase.Nomenclature Units Variationlevels(a)  Fixed variables Agitation rpm 600Ratio enzyme/substrate U/g 6Fraction of activity a  -amylase/total enzymesU/total U 0.35(b)  Independent variables (factors) Dried potato concentration  S  0  % (w/w) (2, 4, 6)Temperature  T    C (68, 70, 72)Time  t   min (60, 120,180)(c)  Dimensionless, normalizedindependent variables Dried potato concentration  x 1  (  1, 0,1)Temperature  x 2  (  1, 0,1)Time  x 3  (  1, 0,1)(d)  Dependent variable (response) Reducing sugar concentration  C  RS  g/L   Table 4 Operational conditions assayed and experimental results achieved.Experiment Independent variables Dependent variableDimensional Dimensionless  C  RS S  0  T t x 1  x 2  x 3 1 6 70 60 1 0   1 19.092 4 72 60 0 1   1 12.533 4 70 120 0 0 0 16.074 2 68 120   1   1 0 9.115 6 70 180 1 0 1 29.326 4 72 180 0 1 1 20.527 2 70 180   1 0 1 10.718 6 68 120 1   1 0 27.659 4 68 180 0   1 1 23.1810 6 72 120 1 1 0 20.0411 2 72 120   1 1 0 9.4812 4 70 120 0 0 0 19.8213 4 70 120 0 0 0 17.1014 4 68 60 0   1   1 15.9315 2 70 60   1 0   1 6.99  Table 5 Summary of the sequential model sum of squares.Source Sum of squaresdf Meansquare F  -value  p -valueprobability > F  Mean vs Total 4421.7 1 4421.7Linear vs Mean 575.71 3 191.9 50.56  < 0.00012FI vs Linear 26.67 3 8.89 4.72 0.0353Quadratic vs 2FI 6.85 3 2.28 1.39 0.3483Cubic vs Quadratic 0.71 3 0.24 0.063 0.9749Residual 7.52 2 3.76Total 5039.16 15 335.94 R. Delgado et al. / LWT - Food Science and Technology 42 (2009) 797–804  801
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