Kinetics of Amycolatopsis mediterranei DSM 43304 lipase-mediated ...

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for the kinetic model building [10,11]. The description of this mechanism and the associated rate (r) is given by Eq. (1) [35]. ⎪⎧ [ ] [ ] [ ΙΑΑc] × [ Η ] ⎪⎫ 2Ο ν fν r ⎨ Αc × Η 2Ο − ⎬ ⎪⎩ keq r = ⎪⎭ (1) ⎛ { [ ] [ ] [ ΙΑΑ] ⎞ ν f km, Η Ο ν f k 2 m, ΙΑΑc ν ⎜ ⎟ f km, ΙΑΑ Αc + ν rkm, Αc ΙΑΑ × 1 + + [ ΙΑΑc] + [ Η 2Ο] + ν f [ Αc] × [ Η2Ο] ⎝ k' ΙΑΑ ⎠ keq keq ν f km, Η Ο ν f ν rk 2 m, Αc + [ Αc] × [ ΙΑΑc] + [ ΙΑΑc] × [ Η2Ο] + [ ΙΑΑ] × [ Η 2Ο] } k k k k eq i, Αc eq i, Η 2Ο where v f and v r are the maximal velocities for the forward and the reverse reactions, respectively, k eq is the equilibrium constant, k m,IAA , k m,Ac , k m,H2O and k m,IAAc are the Michaelis-Menten constants for isoamyl alcohol (IAA), acetic acid (Ac), water (H 2 O) and isoamyl acetate (IAAc), respectively, k’ IAA is the inhibition constant for IAA, and k i,Ac and k i,H2O are the dissociation constants for Ac and H 2 O from the specific enzyme-inhibitor complex, respectively. Owing to the mathematical complexity of this full-model involving ten adjustable parameters with associated problems of unidentifiability and indistinguishability of different parameters under normal experimental situations, a strategy to study the effect of dropping out some parameter(s) in order to produce a simpler model was implemented [11, 34]. Following the methodology of Paiva et al. [11], the Michaelis-Menten dissociation constant terms for each of the compounds (k m,x , where ‘x’ represents either [Ac], [IAA], [IAAc] or [H 2 O]) from the enzyme complex were considered for model reduction; the elimination of these parameters from the denominator of model rate constant would mean that such parameters assume high values in respect to the experimental data and there is no evidence of saturation in the concentration range studied or there is no affinity of the enzyme to the compound in question. In order to study the adequacy of this hypothesis, the model from Segel [35] was reformulated by eliminating the dissociation constants yielding simpler models. These models were separately fitted to the experimental data and F-tests were performed on the associated residual sum of squares with the aim of investigating the statistical likelihood of such simplifications. The results obtained in this comparison are presented in Table 1. Table 1. F-test results for model nesting Source model SSQ parameters Model (NP) df RSS a df Extra (σ) b Mean square (s 2 ) c F ratio d P value Full model vs. Nested-1 Eq- 1 793.49 10 53 – – 14.97 – – Eq-2 792.97 4 59 -0.52 6 -0.09 -0.01 0.99 a Residual sum of squares is the difference in the SSQ of models, b Extra degrees of freedom is the difference in the number of model parameters. c Mean square is the residual sum of squares divided by degrees of freedom (df). d F ratio is the full model (f) mean square divided by the mean square of the nested model (n), It can be concluded that, at p < 0.05 level of statistical significance, the resulting rate expression can be described by Eq. (2). ⎪⎧ [ ΙΑΑc] × [ Η ] ⎪⎫ 2Ο {( k cat f [ Et ]) × ( k cat r [ Et ])} × ⎨[ Αc] × [ ΙΑΑ] − ⎬ ⎪⎩ k eq ⎪⎭ r = (2) ( k f [ Et ]) ( k [ ])[ Αc] × [ ΙΑΑ] cat cat r Et + [ ΙΑΑc] × [ Η 2Ο] k The experimental concentration profiles were modeled using Eq. (2). Experimental points and the simulated curves obtained with the developed model are shown in Figure 1. The simulated curves follow reasonably well the experimental points, showing the kinetic model using Eq. (2) is able to describe the entire reaction progress under conditions of equimolar initial substrate concentrations as well as excess of one of the substrates (see Figure 1 for prediction and Table 2 for estimated parameters). eq
Concentration [mmol L -1 ] 300 280 260 240 Non-optimized condition 100 95 90 85 80 60 20 40 15 10 20 5 0 0 20 40 60 0 80 Conversion [%] Concentration [mmol L -1 ] Optimized condition 300 250 100 80 200 60 150 100 40 50 20 0 0 20 40 60 0 80 Conversion [%] Time [h] Time [h] Figure 1. Experimental and simulated ester production profiles. Enzyme loadings: 250 mg (х,▼), 500 mg (∆,▲), 750 mg (○,●), 1500 mg (□,■). Open symbol: isoamyl alcohol, Filled symbol: isoamyl acetate. Table 1. Parameter estimates of Eq-2 modelling using the kinetic data. Model parameter Value 95% confidence interval k cat , f [mol h g-1] 6.91×10-1 5.97×10-1 to 7.84×10-1 k cat , r [mol h g-1] 2.57×10-1 1.27×10-1 to 3.87×10-1 k eq [-] 7.02×10-2 6.37×10-2 to 7.68×10-2 RSS* [(mol L-1)2] 7.92×102 CONCLUSION R 2 adj 0.99 The present study investigated the direct esterification of isoamyl alcohol with acetic acid, in n-hexane, using a non-commercial Celite-immobilized A. mediterranei lipase. The selection of various reaction parameters that maximize equilibrium conversion yield at relatively low enzyme concentration was studied in detail. Optimized conditions for the synthesis of isoamyl acetate were 7.5% (w/v) of Celite-immobilized lipase, an acid/alcohol molar ratio of 2 with an initial addition of 1% (v/v) water at 50 °C and 200 rpm. Under these conditions the equilibrium conversion yield obtained was 59% in 12 h. A simplified model, based on a postulated Ping Pong Bi Bi mechanism, adequately described the kinetics of Celite-immobilized lipase catalyzed direct esterification of isoamyl alcohol with acetic acid. REFERENCES [1] Welsh F.W., Murray W.D., Williams R.E. 1999. Microbiological and enzymatic production of flavor and fragrance chemicals. Critical Reviews in Biotechnology, 9, 105-169. [2] Eisenmenger M.J. & Reyes-De-Corcuera J.I. 2010. Enhanced synthesis of isoamyl acetate using an ionic liquid– alcohol biphasic system at high hydrostatic pressure. Journal of Molecular Catalysis B: Enzymatic, 67, 36-40. [3] Razafindralambo H., Blecker C., Lognay G., Marlier M., Wathelet J.P., Severin M. 1994. Improvement of enzymatic synthesis yields of flavour acetates: the example of the isoamyl acetate. Biotechnology Letters, 16, 247-250. [4] Rizzi M., Stylos P., Rieck A., Reuss M.A. 1992. A kinetic study of immobilized lipase catalysing the synthesis of isoamyl acetate by transesterification in n-hexane. Enzyme & Microbial Technology 14, 709-714. [5] Romero M.D., Calvo L., Alba C., Daneshfar A., Ghaziaskar H.S. 2005. Enzymatic synthesis of isoamyl acetate with immobilized Candida antarctica lipase in n-hexane. Enzyme & Microbial Technolology, 37, 42–48. [6] Abbas H., Comeau L. 2003. Aroma synthesis by immobilized lipase from Mucor sp. Enzyme & Microbial Technology, 32, 589-595. [7] Ghamgui H., Karra-Chaâbouni M., Bezzine S., Miled N., Gargouri Y. 2006. Production of isoamyl acetate with immobilized Staphylococcus simulans lipase in solvent-free system. Enzyme & Microbial Technology, 38, 788-794. [8] Hari Krishna S., Prapulla S.G., Karanth N.G. 2000. Enzymatic synthesis of isoamyl butyrate using immobilized Rhizomucor miehei lipase in non-aqueous media. J. of Industrial Microbioliology & Biotechnology, 25, 147-154. [9] Oliveira A.C., Rosa M.F., Barros M.R.A., Cabral J.S.M. 2001. Enzymatic esterification of ethanol and oleic acid–a kinetic study. Journal of Molecular Catalysis B: Enzymatic, 11, 999-1005.
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