Modeling cellulase kinetics on lignocellulosic substrates.

The enzymatic hydrolysis of cellulose to glucose by cellulases is one of the major steps involved in the conversion of lignocellulosic biomass to yield biofuel. This hydrolysis by cellulases, a heterogeneous reaction, currently suffers from some major limitations, most importantly a dramatic rate slowdown at high degrees of conversion. To render the process economically viable, increases in hydrolysis rates and yields are necessary and require improvement both in enzymes (via protein engineering) and processing, i.e. optimization of reaction conditions, reactor design, enzyme and substrate cocktail compositions, enzyme recycling and recovery strategies. Advances in both areas in turn strongly depend on the progress in the accurate quantification of substrate-enzyme interactions and causes for the rate slowdown. The past five years have seen a significant increase in the number of studies on the kinetics of the enzymatic hydrolysis of cellulose. This review provides an overview of the models published thus far, classifies and tabulates these models, and presents an analysis of their basic assumptions. While the exact mechanism of cellulases on lignocellulosic biomass is not completely understood yet, models in the literature have elucidated various factors affecting the enzymatic rates and activities. Different assumptions regarding rate-limiting factors and basic substrate-enzyme interactions were employed to develop and validate these models. However, the models need to be further tested against additional experimental data to validate or disprove any underlying hypothesis. It should also provide better insight on additional parameters required in the case that more substrate and enzyme properties are to be included in a model.

[1]  W. Steiner,et al.  Enzymatic hydrolysis of wheat straw after steam pretreatment: Experimental data and kinetic modelling , 1993 .

[2]  L. Ruohonen,et al.  Cello-oligosaccharide hydrolysis by cellobiohydrolase II from Trichoderma reesei. Association and rate constants derived from an analysis of progress curves. , 1996, European journal of biochemistry.

[3]  E G Koukios,et al.  Correlating the effect of pretreatment on the enzymatic hydrolysis of straw , 1992, Biotechnology and bioengineering.

[4]  D. Burk,et al.  The Determination of Enzyme Dissociation Constants , 1934 .

[5]  K. Sun,et al.  Kinetics of the Cellulase Catalyzed Hydrolysis of Cellulose Fibers , 2004 .

[6]  M. Ruth,et al.  Modeling the enzymatic hydrolysis of dilute-acid pretreated Douglas Fir , 1999 .

[7]  A A Huang,et al.  Kinetic studies on insoluble cellulose–cellulase system , 1975, Biotechnology and bioengineering.

[8]  M. Holtzapple,et al.  Neural Network Prediction of Biomass Digestibility Based on Structural Features , 2008, Biotechnology progress.

[9]  M. Penner,et al.  Substrate-velocity relationships for the Trichoderma viride cellulase-catalyzed hydrolysis of cellulose , 1990, Applied and environmental microbiology.

[10]  H. Ooshima,et al.  Kinetic study on enzymatic hydrolysis of cellulose by cellulose from Trichoderma viride , 1983, Biotechnology and bioengineering.

[11]  Srinivas Karra,et al.  Modeling Intrinsic Kinetics of Enzymatic Cellulose Hydrolysis , 2008, Biotechnology progress.

[12]  H. S. Fogler,et al.  Elements of Chemical Reaction Engineering , 1986 .

[13]  Charles E Wyman,et al.  Changes in the enzymatic hydrolysis rate of Avicel cellulose with conversion , 2006, Biotechnology and bioengineering.

[14]  A. Gusakov,et al.  Kinetics of the enzymatic hydrolysis of cellulose: 1. A mathematical model for a batch reactor process , 1985 .

[15]  C. Haynes,et al.  Surface Diffusion of Cellulases and Their Isolated Binding Domains on Cellulose* , 1997, The Journal of Biological Chemistry.

[16]  B. Dale,et al.  Enzymatic hydrolysis and recrystallization behavior of initially amorphous cellulose , 1985, Biotechnology and bioengineering.

[17]  Hugues Berry,et al.  Monte carlo simulations of enzyme reactions in two dimensions: fractal kinetics and spatial segregation. , 2002, Biophysical journal.

[18]  L. Xia,et al.  Kinetics of Simultaneous Saccharification and Lactic Acid Fermentation Processes , 1997, Biotechnology progress.

[19]  Christina L. Ting,et al.  A kinetic model for the enzymatic action of cellulase. , 2009, The journal of physical chemistry. B.

[20]  W. Liao,et al.  Kinetic modeling of enzymatic hydrolysis of cellulose in differently pretreated fibers from dairy manure , 2008, Biotechnology and bioengineering.

[21]  Weak lignin-binding enzymes , 2005 .

[22]  M. Moo-Young,et al.  Degradation of polysaccharides by endo and exo enzymes: A theoretical analysis , 1975 .

[23]  Charles E. Wyman,et al.  Mathematical modeling of cellulose conversion to ethanol by the simultaneous saccharification and fermentation process , 1992 .

[24]  Kinetic analysis and modeling of enzymatic hydrolysis and SSF , 2005 .

[25]  M. Penner,et al.  A simple individual-based model of insoluble polysaccharide hydrolysis: the potential for autosynergism with dual-activity glycosidases. , 1999, Journal of theoretical biology.

[26]  W. Steiner,et al.  A new approach for modeling cellulase–cellulose adsorption and the kinetics of the enzymatic hydrolysis of microcrystalline cellulose , 1993, Biotechnology and bioengineering.

[27]  W. Steiner,et al.  Adsorption of Trichoderma reesei cellulase on cellulose: Experimental data and their analysis by different equations , 1988, Biotechnology and bioengineering.

[28]  M. Rabinovich,et al.  The Structure and Mechanism of Action of Cellulolytic Enzymes , 2002, Biochemistry (Moscow).

[29]  M Tanaka,et al.  A model of enzyme adsorption and hydrolysis of microcrystalline cellulose with slow deactivation of the adsorbed enzyme , 1988, Biotechnology and bioengineering.

[30]  M. Holtzapple,et al.  The HCH‐1 model of enzymatic cellulose hydrolysis , 1984, Biotechnology and bioengineering.

[31]  Bernd Nidetzky,et al.  Hydrolysis of cellooligosaccharides by Trichoderma reesei cellobiohydrolases: Experimental data and kinetic modeling , 1994 .

[32]  C. Sheridan Europe lags, US leads 2nd-generation biofuels , 2008, Nature Biotechnology.

[33]  L. Lynd,et al.  Kinetic modeling of cellulosic biomass to ethanol via simultaneous saccharification and fermentation: Part II. Experimental validation using waste paper sludge and anticipation of CFD analysis , 2009, Biotechnology and bioengineering.

[34]  M. Penner,et al.  Apparent substrate inhibition of the Trichoderma reesei cellulase system , 1991 .

[35]  Enzymatic activity of cellulase adsorbed on cellulose and its change during hydrolysis , 1991, Applied biochemistry and biotechnology.

[36]  Jae Kuk Lee,et al.  Adsorption kinetics of exoglucanase in combination with endoglucanase from Trichoderma viride on microcrystalline cellulose and its influence on synergistic degradation , 1994 .

[37]  Maobing Tu,et al.  Weak lignin-binding enzymes , 2005, Applied biochemistry and biotechnology.

[38]  David K. Johnson,et al.  Biomass Recalcitrance: Engineering Plants and Enzymes for Biofuels Production , 2007, Science.

[39]  D. Wilson,et al.  Substrate heterogeneity causes the nonlinear kinetics of insoluble cellulose hydrolysis. , 1999, Biotechnology and bioengineering.

[40]  M. Savageau Michaelis-Menten mechanism reconsidered: implications of fractal kinetics. , 1995, Journal of theoretical biology.

[41]  L. Lynd,et al.  Toward an aggregated understanding of enzymatic hydrolysis of cellulose: Noncomplexed cellulase systems , 2004, Biotechnology and bioengineering.

[42]  M. Wada,et al.  Surface density of cellobiohydrolase on crystalline celluloses , 2006, The FEBS journal.

[43]  J. Howell,et al.  Kinetics of solka floc cellulose hydrolysis by trichoderma viride cellulase , 1975 .

[44]  A. Voragen,et al.  Synergism in cellulose hydrolysis by endoglucanases and exoglucanases purified from Trichoderma viride. , 1988, Biotechnology and bioengineering.

[45]  J. Saddler,et al.  Effect of enzymatic hydrolysis on the morphology and fine structure of pretreated cellulosic residues , 1993 .

[46]  P. Gao,et al.  Mechanism of cellobiose inhibition in cellulose hydrolysis by cellobiohydrolase , 2008, Science in China Series C: Life Sciences.

[47]  Rui M. F. Bezerra,et al.  Enzymatic kinetic of cellulose hydrolysis , 2005, Applied biochemistry and biotechnology.

[48]  F. M. Gama,et al.  Enzymatic depolymerisation of cellulose , 2007 .

[49]  C. Wyman,et al.  Study of the enzymatic hydrolysis of cellulose for production of fuel ethanol by the simultaneous saccharification and fermentation process , 1993, Biotechnology and bioengineering.

[50]  Raoul Kopelman,et al.  Rate processes on fractals: Theory, simulations, and experiments , 1986 .

[51]  Raoul Kopelman,et al.  Fractal Reaction Kinetics , 1988, Science.

[52]  Yoshimi Yamada,et al.  A kinetic equation for hydrolysis of polysaccharides by mixed exo‐ and endoenzyme systems , 1981 .

[53]  M. Fujii,et al.  Synergism of endoenzyme and exoenzyme on hydrolysis of soluble cellulose derivatives , 1986, Biotechnology and bioengineering.

[54]  N. Gilkes,et al.  Changes in the molecular-size distribution of insoluble celluloses by the action of recombinant Cellulomonas fimi cellulases. , 1994, The Biochemical journal.

[55]  Johan Karlsson,et al.  A model explaining declining rate in hydrolysis of lignocellulose substrates with cellobiohydrolase I (Cel7A) and endoglucanase I (Cel7B) of Trichoderma reesei , 2002, Applied biochemistry and biotechnology.

[56]  T. A. Jones,et al.  High-resolution crystal structures reveal how a cellulose chain is bound in the 50 A long tunnel of cellobiohydrolase I from Trichoderma reesei. , 1998, Journal of molecular biology.

[57]  Ruihong Zhang,et al.  Kinetic modeling for enzymatic hydrolysis of pretreated creeping wild ryegrass , 2009, Biotechnology and bioengineering.

[58]  T. Teeri,et al.  The Cellulases Endoglucanase I and Cellobiohydrolase II of Trichoderma reesei Act Synergistically To Solubilize Native Cotton Cellulose but Not To Decrease Its Molecular Size , 1996, Applied and environmental microbiology.

[59]  H. H. Beeftink,et al.  A generic model for glucose production from various cellulose sources by a commercial cellulase complex , 2007 .

[60]  J N Saddler,et al.  Factors affecting cellulose hydrolysis and the potential of enzyme recycle to enhance the efficiency of an integrated wood to ethanol process , 2000, Biotechnology and bioengineering.

[61]  P. Maini,et al.  A Century of Enzyme Kinetics: Reliability of the K M and v v max Estimates , 2003 .

[62]  Analysis and quantification of a mixed exo‐acting and endo‐acting polysaccharide depolymerization system , 1992, Biotechnology and bioengineering.

[63]  L T Fan,et al.  Kinetic studies of enzymatic hydrolysis of insoluble cellulose: Derivation of a mechanistic kinetic model , 1983, Biotechnology and bioengineering.

[64]  A. Converse,et al.  Kinetics of enzymatic hydrolysis of lignocellulosic materials based on surface area of cellulose accessible to enzyme and enzyme adsorption on lignin and cellulose , 1990 .

[65]  S. Allen,et al.  Kinetic dynamics in heterogeneous enzymatic hydrolysis of cellulose: an overview, an experimental study and mathematical modelling , 2003 .

[66]  Emily Waltz Will the current biofuels boom go bust? , 2007, Nature Biotechnology.

[67]  Tuula T. Teeri,et al.  Crystalline cellulose degradation : new insight into the function of cellobiohydrolases , 1997 .

[68]  Liisa Viikari,et al.  Hydrolysis of amorphous and crystalline cellulose by heterologously produced cellulases of Melanocarpus albomyces. , 2008, Journal of biotechnology.

[69]  L. Fan,et al.  Stochastic analysis of stepwise cellulose degradation , 1991 .

[70]  Mark F. Davis,et al.  Cellulase digestibility of pretreated biomass is limited by cellulose accessibility , 2007, Biotechnology and bioengineering.

[71]  Rui M. F. Bezerra,et al.  Discrimination among eight modified michaelis-menten kinetics models of cellulose hydrolysis with a large range of substrate/enzyme ratios , 2004, Applied biochemistry and biotechnology.

[72]  V. Bisaria,et al.  Studies on the mechanism of enzymatic hydrolysis of cellulosic substances , 1979, Biotechnology and bioengineering.

[73]  Bernard Henrissat,et al.  Cellulases and their interaction with cellulose , 1994 .

[74]  Kopelman,et al.  Steady-state chemical kinetics on fractals: Segregation of reactants. , 1987, Physical review letters.

[75]  J. Saddler,et al.  Substrate and Enzyme Characteristics that Limit Cellulose Hydrolysis , 1999, Biotechnology progress.

[76]  G. Pettersson,et al.  Acid hydrolysis of bacterial cellulose reveals different modes of synergistic action between cellobiohydrolase I and endoglucanase I. , 1999, European Journal of Biochemistry.

[77]  S. Mansfield,et al.  Cellulose hydrolysis – the role of monocomponent cellulases in crystalline cellulose degradation , 2003 .

[78]  K. Movagharnejad Modified shrinking particle model for the rate of enzymatic hydrolysis of impure cellulosic waste materials with enzyme reuse by the substrate replacement , 2005 .

[79]  M. M. Gharpuray,et al.  Structural modification of lignocellulosics by pretreatments to enhance enzymatic hydrolysis , 1983, Biotechnology and bioengineering.

[80]  G. Pettersson,et al.  Mechanism of substrate inhibition in cellulose synergistic degradation. , 2001, European journal of biochemistry.

[81]  M. Holtzapple,et al.  Structural features affecting biomass enzymatic digestibility. , 2008, Bioresource technology.

[82]  L. Lynd,et al.  A functionally based model for hydrolysis of cellulose by fungal cellulase , 2006, Biotechnology and bioengineering.

[83]  B. Henrissat,et al.  Synergism of Cellulases from Trichoderma reesei in the Degradation of Cellulose , 1985, Bio/Technology.

[84]  C. Wandrey,et al.  Characterization of a cellodextrin glucohydrolase with soluble oligomeric substrates: Experimental results and modeling of concentration‐time‐course data , 1989, Biotechnology and bioengineering.

[85]  M. Moo-young,et al.  Kinetics of enzymatic hydrolysis of cellulose: Analytical description of a mechanistic model , 1978, Biotechnology and bioengineering.

[86]  E. Koukios,et al.  Cross-synergism in enzymatic hydrolysis of lignocellulosics: Mathematical correlations according to a hyperbolic model , 1996 .

[87]  M. Lima,et al.  The role of cellulase concentration in determining the degree of synergism in the hydrolysis of microcrystalline cellulose. , 1988, The Biochemical journal.

[88]  E. Ross,et al.  Mathematical model for enzymatic hydrolysis and fermentation of cellulose by Trichoderma , 1979 .

[89]  Jack Saddler,et al.  Optimization of enzyme complexes for lignocellulose hydrolysis , 2007, Biotechnology and bioengineering.

[90]  V. Santos,et al.  Development of a generalized phenomenological model describing the kinetics of the enzymatic hydrolysis of NaOH-treated pine wood , 1996, Applied biochemistry and biotechnology.

[91]  F. Tjerneld,et al.  Enzymatic cellulose hydrolysis in an attrition bioreactor combined with an aqueous two‐phase system , 1991, Biotechnology and bioengineering.

[92]  F. Rombouts,et al.  Adsorption and kinetic behavior of purified endoglucanases and exoglucanases from Trichoderma viride , 1987, Biotechnology and bioengineering.

[93]  G. Johansson,et al.  Processive action of cellobiohydrolase Cel7A from Trichoderma reesei is revealed as 'burst' kinetics on fluorescent polymeric model substrates. , 2005, The Biochemical journal.

[94]  L. Lynd,et al.  Kinetic modeling of cellulosic biomass to ethanol via simultaneous saccharification and fermentation: Part I. Accommodation of intermittent feeding and analysis of staged reactors , 2009, Biotechnology and bioengineering.

[95]  L. Walker,et al.  Effect of Cellulase Mole Fraction and Cellulose Recalcitrance on Synergism in Cellulose Hydrolysis and Binding , 2006, Biotechnology progress.

[96]  M. K. Hayes,et al.  Hydrolysis of Cellulose by Saturating and Non–Saturating Concentrations of Cellulase: Implications for Synergism , 1988, Bio/Technology.

[97]  Y. Koo,et al.  Modeling and simulation of simultaneous saccharification and fermentation of paper mill sludge to lactic acid , 2005 .

[98]  A comparison of the Michaelis-Menten and HCH-1 models. , 1990, Biotechnology and bioengineering.

[99]  C. Eom,et al.  Statistical optimization of enzymatic saccharification and ethanol fermentation using food waste. , 2008 .

[100]  John N. Saddler,et al.  Effects of sugar inhibition on cellulases and β-glucosidase during enzymatic hydrolysis of softwood substrates , 2004 .

[101]  A. Converse,et al.  The effect of enzyme and substrate levels on the specific hydrolysis rate of pretreated poplar wood , 1991 .

[102]  Chandrika Mulakala,et al.  Hypocrea jecorina (Trichoderma reesei) Cel7A as a molecular machine: A docking study , 2005, Proteins.

[103]  Lee R. Lynd,et al.  Modeling simultaneous saccharification and fermentation of lignocellulose to ethanol in batch and continuous reactors , 1995 .

[104]  J. Ståhlberg,et al.  Adsorption and synergism of cellobiohydrolase I and II of Trichoderma reesei during hydrolysis of microcrystalline cellulose , 1994, Biotechnology and bioengineering.

[105]  Peter M. A. Sloot,et al.  Modelling and Simulation , 1988, Systems Analysis and Simulation 1988, I: Theory and Foundations. Proceedings of the International Symposium held in Berlin (GDR), September 12–16, 1988.

[106]  M. N. Karim,et al.  Model-Based Fed-Batch for High-Solids Enzymatic Cellulose Hydrolysis , 2009, Applied biochemistry and biotechnology.

[107]  I. S. Pretorius,et al.  Microbial Cellulose Utilization: Fundamentals and Biotechnology , 2002, Microbiology and Molecular Biology Reviews.

[108]  K. Oh,et al.  Bioconversion of cellulose into ethanol by nonisothermal simultaneous saccharification and fermentation , 2000, Applied biochemistry and biotechnology.

[109]  Hiroshi Ooshima,et al.  An extension of the Harano-Ooshima rate expression for enzymatic hydrolysis of cellulose to account for changes in the amount of adsorbed cellulase , 1995 .

[110]  Charlotte Schubert,et al.  Can biofuels finally take center stage? , 2006, Nature Biotechnology.

[111]  N. Pereira,et al.  Enzymatic hydrolysis optimization to ethanol production by simultaneous saccharification and fermentation , 2007, Applied biochemistry and biotechnology.

[112]  T. Wood Properties and mode of action of cellulases. , 1975, Biotechnology and bioengineering symposium.

[113]  K. Movagharnejad,et al.  A model for the rate of enzymatic hydrolysis of some cellulosic waste materials in heterogeneous solid–liquid systems , 2003 .

[115]  G. Pettersson,et al.  The initial kinetics of hydrolysis by cellobiohydrolases I and II is consistent with a cellulose surface-erosion model. , 1998, European journal of biochemistry.

[116]  Andreas S Bommarius,et al.  Cellulase kinetics as a function of cellulose pretreatment. , 2008, Metabolic engineering.

[117]  L. Fan,et al.  Kinetic studies of enzymatic hydrolysis of insoluble cellulose: (II). Analysis of extended hydrolysis times , 1983, Biotechnology and bioengineering.

[118]  J. N. Saddler,et al.  Evaluating the Distribution of Cellulases and the Recycling of Free Cellulases during the Hydrolysis of Lignocellulosic Substrates , 2007, Biotechnology progress.

[119]  Modelling the bioconversion of cellulose into microbial products: rate limitations , 1984 .

[120]  W. Steiner,et al.  Cellulose hydrolysis by the cellulases from Trichoderma reesei: a new model for synergistic interaction. , 1994, The Biochemical journal.

[121]  A. I. Antonov,et al.  Design of highly efficient cellulase mixtures for enzymatic hydrolysis of cellulose , 2007, Biotechnology and bioengineering.

[122]  K. Kadam,et al.  Development and Validation of a Kinetic Model for Enzymatic Saccharification of Lignocellulosic Biomass , 2004, Biotechnology progress.

[123]  Feng Xu,et al.  A new kinetic model for heterogeneous (or spatially confined) enzymatic catalysis : Contributions from the fractal and jamming (overcrowding) effects , 2007 .

[124]  Sun Bok Lee,et al.  Effect of compression milling on cellulose structure and on enzymatic hydrolysis kinetics , 1982, Biotechnology and bioengineering.

[125]  J. Ståhlberg,et al.  Isotherms for adsorption of cellobiohydrolase I and II fromtrichoderma reesei on microcrystalline cellulose , 1997, Applied biochemistry and biotechnology.

[126]  M. Holtzapple,et al.  Fundamental factors affecting biomass enzymatic reactivity , 2000, Applied biochemistry and biotechnology.

[127]  S. Al‐Zuhair The effect of crystallinity of cellulose on the rate of reducing sugars production by heterogeneous enzymatic hydrolysis. , 2008, Bioresource technology.

[128]  Stephen E. Wald,et al.  Kinetics of the enzymatic hydrolysis of cellulose , 1984, Biotechnology and bioengineering.

[129]  J. Schurz,et al.  Changes of structure and morphology of regenerated cellulose caused by acid and enzymatic hydrolysis , 1990 .

[130]  A. Stipanovic,et al.  Effect of digestion by pure cellulases on crystallinity and average chain length for bacterial and microcrystalline celluloses , 2007 .

[131]  F. Vahabzadeh,et al.  A model for the rate of enzymatic hydrolysis of cellulose in heterogeneous solid-liquid systems , 2000 .

[132]  M. Holtzapple,et al.  Effect of structural features on enzyme digestibility of corn stover. , 2006, Bioresource technology.

[133]  Xinhao Ye,et al.  Quantitative determination of cellulose accessibility to cellulase based on adsorption of a nonhydrolytic fusion protein containing CBM and GFP with its applications. , 2007, Langmuir : the ACS journal of surfaces and colloids.

[134]  Y. Zhuang,et al.  Optimization of cellulase mixture for efficient hydrolysis of steam-exploded corn stover by statistically designed experiments. , 2009, Bioresource technology.

[135]  J. Parajó,et al.  Cogeneration of cellobiose and glucose from pretreated wood and bioconversion to lactic acid: a kinetic study. , 1999, Journal of bioscience and bioengineering.

[136]  Rajesh Gupta,et al.  Mechanism of cellulase reaction on pure cellulosic substrates , 2009, Biotechnology and bioengineering.

[137]  J. Howell,et al.  Enzyme deactivation during cellulose hydrolysis , 1978 .

[138]  T. Wood,et al.  The cellulase of Trichoderma koningii. Purification and properties of some endoglucanase components with special reference to their action on cellulose when acting alone and in synergism with the cellobiohydrolase. , 1978, The Biochemical journal.

[139]  R. Maguire Kinetics of the hydrolysis of cellulose by beta-1,4-glucan cellobiohydrolase of Trichoderma viride. , 1977, Canadian journal of biochemistry.

[140]  M. Galbe,et al.  A review of the production of ethanol from softwood , 2002, Applied Microbiology and Biotechnology.

[141]  F. Tjerneld,et al.  Hydrolysis of microcrystalline cellulose by cellobiohydrolase I and endoglucanase II from Trichoderma reesei: adsorption, sugar production pattern, and synergism of the enzymes. , 1998, Biotechnology and bioengineering.

[142]  KINETIC MODELING OF SIMULTANEOUS SACCHARIFICATION AND FERMENTATION OF CELLULOSE , 1988 .

[143]  D. Kilburn,et al.  Cellulose-binding polypeptides from Cellulomonas fimi: endoglucanase D (CenD), a family A beta-1,4-glucanase , 1993, Journal of bacteriology.

[144]  L. Lynd,et al.  Determination of the number-average degree of polymerization of cellodextrins and cellulose with application to enzymatic hydrolysis. , 2005, Biomacromolecules.

[145]  G. Caminal,et al.  Kinetic modeling of the enzymatic hydrolysis of pretreated cellulose , 1985, Biotechnology and bioengineering.

[146]  P. Beltrame,et al.  Enzymatic hydrolysis of cellulosic materials: A kinetic study , 1984, Biotechnology and bioengineering.

[147]  M. Thoma,et al.  Modelling of the enzymatic hydrolysis of cellobiose and cellulose by a complex enzyme mixture of Trichoderma reesei QM 9414 , 1984, Applied Microbiology and Biotechnology.

[148]  L. Lynd,et al.  How biotech can transform biofuels , 2008, Nature Biotechnology.

[149]  Mark T Holtzapple,et al.  Enzymatic hydrolysis of lime-pretreated corn stover and investigation of the HCH-1 Model: inhibition pattern, degree of inhibition, validity of simplified HCH-1 Model. , 2007, Bioresource technology.

[150]  Farzaneh Teymouri,et al.  Understanding factors that limit enzymatic hydrolysis of biomass , 2005, Applied Biochemistry and Biotechnology.

[151]  M. Galbe,et al.  Effect of substrate and cellulase concentration on simultaneous saccharification and fermentation of steam-pretreated softwood for ethanol production. , 2000, Biotechnology and bioengineering.

[152]  Ye Sun,et al.  Hydrolysis of lignocellulosic materials for ethanol production: a review. , 2002, Bioresource technology.

[153]  W. Steiner,et al.  The effect of enzyme concentration on the rate of the hydrolysis of cellulose , 1989, Biotechnology and bioengineering.

[154]  Dae Ryook Yang,et al.  Cybernetic Modeling of Simultaneous Saccharification and Fermentation for Ethanol Production from Steam-Exploded Wood with Brettanomyces custersii , 2006 .

[155]  F. Agblevor,et al.  KINETICS OF ENZYMATIC HYDROLYSIS OF STEAM-EXPLODED COTTON GIN WASTE , 2008 .

[156]  E. Park,et al.  Empirical evaluation of cellulase on enzymatic hydrolysis of waste office paper , 2002 .

[157]  K. Schügerl,et al.  Modelling and simulation of cellulase adsorption and recycling during enzymatic hydrolysis of cellulosic materials , 1992 .

[158]  L. Fan,et al.  Kinetics of Hydrolysis of Insoluble Cellulose by Cellulase , 1980, Products from Alkanes, Cellulose and other Feedstocks.

[159]  H. Ooshima,et al.  Adsorption of cellulase from Trichoderma viride on cellulose , 1983, Biotechnology and bioengineering.

[160]  Mark Holtzapple,et al.  Inhibition of Trichoderma reesei cellulase by sugars and solvents , 1990, Biotechnology and bioengineering.

[161]  P. Kraulis,et al.  Investigation of the function of mutated cellulose‐binding domains of Trichoderma reesei cellobiohydrolase I , 1992, Proteins.

[162]  Göran Pettersson,et al.  Synergistic cellulose hydrolysis can be described in terms of fractal‐like kinetics , 2003, Biotechnology and bioengineering.

[163]  A. Converse,et al.  A synergistic kinetics model for enzymatic cellulose hydrolysis compared to degree-of-synergism experimental results. , 1993, Biotechnology and bioengineering.

[164]  J. Ståhlberg,et al.  A New Model For Enzymatic Hydrolysis of Cellulose Based on the Two-Domain Structure of Cellobiohydrolase I , 1991, Bio/Technology.

[165]  T. M. Wood,et al.  The degradation pattern of cellulose by extracellular cellulases of aerobic and anaerobic microorganisms , 1991 .

[166]  J. Asenjo Maximizing the formation of glucose in the enzymatic hydrolysis of insoluble cellulose. , 1983, Biotechnology and bioengineering.

[167]  K. Laidler THEORY OF THE TRANSIENT PHASE IN KINETICS, WITH SPECIAL REFERENCE TO ENZYME SYSTEMS , 1955 .

[168]  W. Steiner,et al.  Cellulose hydrolysis by the cellulases from Trichoderma reesei: adsorptions of two cellobiohydrolases, two endocellulases and their core proteins on filter paper and their relation to hydrolysis. , 1994, The Biochemical journal.

[169]  A. Converse,et al.  Substrate reactivity as a function of the extent of reaction in the enzymatic hydrolysis of lignocellulose. , 1997, Biotechnology and bioengineering.