Modelling the enzymatic activity of two lipases isoenzymes commonly used in the food industry
Modelado de la actividad enzimática de dos isoenzimas lipasas comúnmente utilizadas en la industria alimentaria

Abstract

An in-depth analysis of the kinetics of two lipases isoenzymes (Lip1 and Lip2) in triacetin hydrolysis in absence and in presence of hexane was carried out. The addition of hexane led to an increase in enzymatic activities of both enzymes for all triacetin concentrations, and the kinetic data described a hyperbola which was consistent with the classical Michaelis–Menten model. Without hexane, the time-course of the triacetin hydrolysis by Lip1 and Lip2 did not follow a Michaelian behaviour. In this case, a first phase of low enzymatic activity (at triacetin concentrations from 0 to 250 mM) was followed by a rapid increase in velocity at triacetin concentrations ≥250 mM. The Michaelis–Menten model was unable to describe the first phase due to the linear (nonhyperbolic) relationship between the velocity and the triacetin concentration, meanwhile the logistic model provided a satisfactory description of the experimental data corresponding to the second phase of activity.

En este trabajo se llevó a cabo un profundo análisis de la cinética de dos isoenzimas lipasas (Lip1 y Lip2) en la hidrólisis de triacetina, en ausencia y en presencia de hexano. La adición de hexano a la mezcla de reacción incrementó las actividades enzimáticas de ambas enzimas para todas las concentraciones de triacetina, obteniéndose una relación hiperbólica compatible con el modelo clásico de Michaelis-Menten. En ausencia de hexano, la actividad de Lip1 y Lip2 no mostró un comportamiento Michaeliano, observándose una fase inicial de baja velocidad a concentraciones de triacetina entre 0–250 mM, seguida de un rápido incremento en la actividad enzimática ([triacetina] ≥ 250 mM). El modelo de Michaelis-Menten no pudo ser utilizado para describir la primera fase debido al incremento lineal (no hiperbólico) de la velocidad con la concentración de triacetina, mientras el modelo logístico describió adecuadamente la cinética de hidrólisis en la segunda fase.

Keywords:

• lipases
• food
• modelling
• triacetin
• hexane
• Michaelis–Menten model
• logistic model

Palabras clave:

• lipasas
• alimentos
• modelado
• triacetina
• hexano
• modelo de Michaelis–Menten
• modelo logístico

Introduction

Lipases are defined as triacylglycerol acylhydrolases (E.C.3.1.1.3) that catalyse the hydrolysis of fats and oils to mono- and di-acylglycerols, glycerol and free fatty acids. In contrast to carboxyl esterases (EC 3.1.1.1), catalysis occurs at the lipid–water interface, and most lipases showed a phenomenon known as interfacial activation (Saktaweewong et al., 2011). It describes an increase in the catalytic activity of the enzyme in presence of a hydrophobic interface as that formed by the tryacylglyceride. The activation has been associated to a conformational change of a lid or flap, consisting of an oligopeptide segment of the primary structure that covers the active site. In the inactive closed conformation, the flap covers the active site but in the presence of the interface the flap opens (active conformation) making the active site accessible to the substrate that enters the binding pocket (Rubin, 1994; Verger, 1997).

Lipolytic enzymes have attracted an enormous interest since more than 20 years ago and currently constitute the most important group of biocatalysts for biotechnological applications (Hasan, Shah, & Hameed, 2006; Schmid & Verger, 1998). That is mainly because although the naturally occurring triacylglycerides are the preferred substrates, lipases also catalyse the enantio- and regioselective hydrolysis of a wide range of natural and synthetic esters and also esterification, interesterification, and transesterification reactions in nonaqueous media (Schmid & Verger, 1998) Therefore, lipases have been selected for a number of potential applications in the food, detergent, pharmaceutical, leather, cosmetic, textile and paper industry (Bornscheuer, 2005; Hasan et al., 2006).

Currently, fat and oil modifications are one of the prime areas in food processing industry that demands novel economic and green technologies (Hasan et al., 2006). For oils and fats, it is well-known that the functional (e.g. melting points) and nutritional properties of triacylglycerols (e.g. digestion and absorption) depend not only on their fatty acid profiles, but also onfatty acid distributions in the glycerol backbone (Xu, 2000). Structured lipids are thus defined as triacylglycerol, which are modified to change the fatty acid composition and/or positional distribution in the glycerol backbone (Iwasaki & Yamane, 2000). Chemical interesterification is a mature technology in industry but only randomised products can usually be produced. However, application of lipases in lipid modification has found an enormous field of application as they show three main types of selectivity: (i)sn-1,3-regioselectivity, (ii) fatty acid selectivity and (iii) triacylglycerol selectivity (Kourist, Brundiek, & Bornscheuer, 2010). This explains why many nutritional and functional structured lipids have been produced enzymatically since more than 20 years ago (Xu, 2000).

The paradigmatic example is cocoa butter, an important major constituent of the chocolate, which melts between 32–35°C and re-crystallises during processing to a stable crystal mode. The uncertainty in the cocoa butter supply and the volatility in prices require manufacturers to seek alternatives to it. Cocoabutter equivalents are close to cocoa butter in composition and physical properties but are produced by enzymatic interesterification reactions from low valuable vegetable oils, mainly palm oil (Xu, 2000).

Candida rugosa lipases (CRLs) are amongst the most frequently used enzymes in biotransformations. In previous papers, we have purified and characterised three CRL isoenzymes sharing a high degree of homology at, namely, Lip1, Lip2 and Lip3 (Pernas, López, Pastrana, & Rúa, 2000; Rúa, Díaz-Mauriño, Fernandez, Otero, & Ballesteros, 1993), for which the crystal structures have been solved (Ghosh et al., 1995; Grochulski et al., 1993; Grochulski, Li, Schrag, & Cygler, 1994; Mancheño et al., 2003). Contrary to what is observed with “classical” esterases acting on soluble substrates, the lipase kinetic properties didn't describe a Michaelian kinetic (Verger & de Haas, 1976). In this way, many lipases, including CRL isoenzymes, can be activated by hydrophobic interfaces provided by the substrate (triacylglycerides) or non-catalytic interfaces such as those formed by detergents or organic solvents (hexane). Their activity on soluble triglyceride molecules is nearly marginal (Mancheño et al., 2003; Pernas, López, Rúa, & Hermoso, 2001; Pernas, Pastrana, Fuciños, & Rúa, 2009). That means that the activity increases significantly when the substrate forms a lipid–water interface (interfacial activation) (Verger & de Haas, 1976; Verger, 1997).

Therefore, in these cases, the use of the standard Michaelis–Menten model to fit the experimental velocity data could be very disadvantageous, because, the v _max and K_M values could be underestimated or overestimated (Houston & Kenworthy, 2000). This poor estimation of both variables can difficult the optimal operation and control policies when the enzymatic reaction is carried out in an industrial bioreactor (Bastin & Van Impe, 1995). For this reason, it is more adequate that the adoption of more suitable models resulting from a new proposed reaction mechanism or heuristic models that must provide the best fit of the experimental data as well as the optimum values for the model parameters (Taylor, 2002). However, only a few studies deal with the selection of models to describe the atypical rate-substrate concentration curves (Houston & Kenworthy, 2000).

Therefore, in the present study, the kinetic data from triacetin hydrolysis by Lip1 and Lip2 in presence and in absence of hexane, obtained in previous works (Mancheño et al., 2003; Pernas et al., 2001, 2009), were firstly modelled with the Michaelis–Menten model. Since Lip1 and Lip2 showed nonhyperbolic kinetics in absence of hexane, the enzymatic activity of these two lipases were then modelled by using a model developed in this work. Finally, sensitivity and robustness of both models were discussed in relation to the values of the mean relative percentage deviation modulus and the determination coefficient.

Materials and methods

Materials

Lipase type VII from Candida rugosa was purchased from Sigma Chemicals Co. (St Louis, USA). Triacetin was from Fluka (Deisenhofen, Germany). DEAE-Sephacel, Phenyl-Sepharose CL-4B, Sephacryl HR 100, PD-10 and Sephacryl S200 columns were from Pharmacia (Uppsala, Sweden). All chromatographic steps were run on a Pharmacia FPLC. All other chemicals were of analytical grade.

Lipase purification

Lip1 was purified from commercial crude preparations according to Rúa and Ballesteros (1994), whereas Lip2 was obtained from postincubates of the yeast as described in Pernas et al. (2000) and Sánchez et al. (1999).

Kinetic measurements

The interfacial activation of CRL isoenzymes was studied with triacetin as substrate using a titrimetrical pH-stat technique (Methrom, Switzerland) as described in Pernas et al. (2001). Activation occurs when triacetin forms emulsions above the solubility limit of this triacylglyceride in water. Briefly, assays were performed at 30°C in 5 mM Tris/HCl buffer (pH7.0) containing 0.1 M CaCl₂ and varying amounts of triacetin to cover a concentration range from 35 mM to 1 M. The pH was kept constant at pH 7. Kinetic assays were also carried out in the presence of 25% (v/v) hexane in the reaction media (Pernas et al., 2009). In any case, one activity unit was defined as the amount of enzyme, which released 1 μmol of fatty acids per min under assay conditions.

Protein concentration

It was determined by the Lowry method (Lowry, Rosebrough, Farr, & Randall, 1951) using BSA as standard.

Statistical analyses

Individual experiments were performed in triplicate and all data points are represented by the mean. Data sets were statistically analysed by using the software package SPSS Statistics 17.0 for Windows (Release 17.0.1; SPSS Inc., Chicago, IL, 2008).

Model parameters determination and model evaluation

The model parameters were obtained by using the nonlinear curve-fitting software of SigmaPlot (version 9.0, Systat Software, Inc., 2004), which minimised the deviations between model predictions and experimental data according to the sum of squares of errors (SSE) of the model fit:

where Δ _i, j represents the difference between the model and the experimental value, n and m represent the number of experimental data points and the number of variables, respectively.

The coefficients of the models with P values lower than 0.05 were considered statistically significant. Parameters were removed from the models when their asymptotic interval of confidence included zero.

The criteria used to evaluate the goodness-of-fit of each model were the determination coefficient (R ²) andthe mean relative percentage deviation modulus (RPDM) (Lomauro, Bakshi, & Labuza, 1985):

where X_i is the experimental value, X_pi is the calculated value, and N is the number of experimental data. The RPDM parameter is widely used to determine the quality of the fit, being a value of RPDM below 10%indicative of a good fit for practical purposes (Aguerre, Suarez, & Viollaz, 1989; Lomauro et al., 1985; Pérez-Guerra, Torrado-Agrasar, López-Macías, Fajardo-Bernárdez, & Pastrana-Castro, 2007).

Results and discussion

Modelling the enzymatic activity of the two lipases

The activity profiles of the two Candida rugosa lipases (Lip1 and Lip2) using triacetin without and with hexane are shown in Supplementary Figure 1. From the detailed observation of the results, it can be noted that in absence of hexane (upper part of Supplementary Figure 1), both enzymes displayed two activity pulses: being the first one at substrate concentrations from 0 to 250 mM and the second one at substrate concentrations from 250 to 1061 mM. In fact, the activity of both Lip1 and Lip2 enzymes showed a clear jump at triacetin concentrations of about 250 mM, at which, the first large-size droplets start to form as indicated by the increase in the turbidity of the solution (upper part of Supplementary Figure 1).

From the comparison between the activity of both enzymes, it can be observed that, in absence of hexane, from all the substrate concentrations, the increase in activity of Lip1 was smoother than for monomeric Lip2 (upper part of Supplementary Figure 1) but, in presence of hexane, Lip1 was considerably more active than Lip2 over the whole substrate concentration range (lower part of Supplementary Figure 1).

On the other hand, the addition of hexane to the reaction mixture led to an increase in enzymatic activities of both enzymes for all triacetin concentrations, particularly below the solubility limit (0.27 M) for this substrate (upper and lower parts of Supplementary Figure 1).

From a kinetic point of view, it can be noted that both enzymes showed a Michaelian behaviour only when triacetin was used as substrate in presence of hexane (lower part of Supplementary Figure 1), as itwas demonstrated with the Michaelis–Menten model(1):

where [S] was the initial triacetin concentration (M), v _max was the maximum rate of substrate conversion (U/mg) and K_M was the Michaelis constant (M) defined as the substrate concentration at which the rate is 50% v _max.

Thus, significant values for the parameters v _max and K_M with high R ² values and low RPDM values (lower than 10) were obtained (lower part of Supplementary Figure 1). In contrast, non-significant values were obtained for the parameters v _max and K_M for the kinetics in absence of hexane (upper part of Supplementary Figure 1), thus corroborating that in this case,the activity of Lip1 and Lip2 did not show a Michaelian behaviour (Verger, 1997; Verger & de Haas, 1976).

Conformational changes in lipases are an important part of the catalytic process, because these enzymes exist in two conformations, the inactive with the flap closed and the active or flap-open conformation. The transition between closed and open conformation, phenomenon know as interfacial activation, is triggered by the formation of the substrate lipidic interface. Several authors have reported that the addition of water insoluble organic solvents (such us hexane) increased the enzymatic activity of lipase acting on isotropic solutions of triacylglycerides giving rise to Michaelis–Menten type kinetics. These results correlated well with a conformational transition between the open and closed conformation of the lipase promoted by the highly hydrophobic hexane interface (Pernas et al., 2009).

The low activity over soluble substrates is then explained by the small fraction of active lipase molecules in the absence of the interface. Nevertheless, for those activated lipase molecules (by the substrate interface or in the presence of the hexane interface), a Michaelian dependence between hydrolysis rate and substrate concentration should be expected. On the other hand, when a lipidic interface is created, the equilibrium will shift towards the active open conformer and a jump in the hydrolysis rate is observed which frequently follows the characteristic allosteric shape as the substrate concentration increases. The existence of non-linear relationships between interfacial substrate and enzyme concentrations for several lipases and substrates (Brockman, Momsen, & Tsujita, 1988; Martinelle, Holmquist, & Hult, 1995) and/or cooperative effects in the adsorption of lipases to lipidic interfaces (Marangoni, 1994) might account for the observed sigmoidal activity/substrate concentration profiles.

Although for several lipases, the activity over water soluble substrates is only marginal (Verger, 1997), it is reasonable to assume that the overall hydrolysis rate at any substrate concentration will be the result of the catalysis of both soluble and insoluble substrate (the algebraic sum of rates if no interactions exist) by activated lipase molecules, the effective independent variable in lipolysis (Verger & de Haas, 1976). In other words, at any substrate concentration, a possible heuristic model to describe the lipolysis rate should involve the sum of Michaelian velocity (predominant at low substrate concentrations) and allosteric or autocatalytic velocity (predominant when the substrate interface is created in the system). Thus, using empirical logistic equations for the description of autocatalytic processes, the new model can be written as follows:

where and are, respectively, the apparent maximum rates (U/mg) for the Michaelian and autocatalytic processes, is the apparent Michaelis constant (M), m is the specific rate for the autocatalytic process (M⁻¹) and b is a dimensionless constant of the equation. Other term ([S]) is as previously described.

Although model (2) has not an underlying enzymatic mechanism, its mathematical form can be easily related with the lipase mode of action by reparameterising the logistic equation to make the substrate concentration explicit at , which is defined as . Thus, , and:

In this way, the parameters and could have pseudo-physical meaning (because a true reaction mechanism is not considered) with an operational and practical utility because they could be considered as theapparent affinities for substrate in each phase of the catalytic process. As the actual amount of activated lipases in the aqueous solution and that bound to the interface are unknown, and simply indicated the amount of substrate which permitted that each semimaximum velocity was reached. The sum of and is the potential maximum rate for the reaction. As the conversion of a lipase into its active conformation and its penetration into the interface is acritical step in the catalytic process, m parameter should include all factors related to the productive interaction lipase/interface. Thus, a high value of m should indicate a high interfacial activation, which is probably a function of the intrinsic structure of each individual lipase and interface.

Nevertheless, in Equation (3) it is not possible to obtain, as expected in an enzymatic reaction, a value of v = 0 for [S] = 0. To avoid this problem, it is necessary to subtract the intercept with the ordinate in the logistic part of model (3), as indicated as follows:

This model satisfies the essential initial and final conditions for the enzymatic reactions with both lipases. Thus, as occurred with the Michaelis–Menten model (1), when [S] = 0, v = 0, and when the overall maximum velocity of the reaction.

The results obtained with the use of model (4) are shown in Supplementary Figure 2 (upper part) and in Supplementary Table 1. Although the curves drawn through the experimental velocity seemed to indicate that this model describes adequately the trend observed in the experimental data obtained for each CRL isoenzyme (upper part of Supplementary Figure 2), the values obtained for v _max and K_M for Lip1 and Lip2were not statistically significant at P < 0.05 (Supplementary Table 1).

Thus, it is necessary to discuss the incapacity of model (4), comprised of the sum of two single models, for describing accurately the kinetic of enzymatic reactions exhibiting two serial enzymatic activity pulses. In this type of kinetics, the inefficacy of double models to fit the data, was found to be due to the difference in the amount and values of the experimental data belonging to the first and second pulse (Pérez-Guerra et al., 2010).

The different amount of experimental data in each activity pulse does not seem to be a cause to explain the non significant values obtained for v _max and K_M , because the first activity pulse had seven points for both enzymes, while the second activity pulse had eight (in case of Lip1) and nine (in case of Lip2) data points. However, the values of the experimental activities corresponding to the second activity pulse (from 1.3 to 26.6 U/mg for Lip1 and from 8.0 to 28.2 U/mg for Lip2) were considerably higher than those of the first activity pulse (from 0 to 0.8 U/mg for Lip1 and from 0 to 5.7 U/mg for Lip2). In these conditions, the least-squares technique used for fitting the model to the experimental data, that assumes constant error variance (Meyer, 1994), weighs the data corresponding to the second activity pulse, more heavily than those corresponding to the first activity pulse (Pérez-Guerra et al., 2010; Stanescu & Chen-Charpentier, 2009). For this reason, not statistically significant values for the parameters v _max and K_M could be obtained and consequently, model (4) should take the form of a simple Logistic model, whose expression is as follows:

Although from a practical point of view, a simple logistic model should not be used to describe a set of experimental data showing two pulses (Pérez-Guerra et al., 2007, 2010), model (5) was used to fit the kinetic data, in order to corroborate the above mentioned hypothesis on the inadequacy of model (4) to describe the formation of the two activity pulses observed in the enzymatic reactions of Lip1 and Lip2.

The results obtained (lower part of Supplementary Figure 2 and Supplementary Table 2) clearly showed that model (5) fits acceptably the experimental activity data, because significant values for the parameters , and m and in addition, R ² values higher than 0.98 were obtained (Supplementary Table 2). However, the values of RPDM were, in both cases, considerably higher than 10%. From the detailed observation of lower part of Supplementary Figure 2, it can be noted that model (5) did not fit satisfactorily the first seven experimental data for both enzymes. This observation is clearer for Lip2 than for Lip1 (see the circle in the right lower part of Supplementary Figure 2). In fact, the first seven data points produced, for both enzymes, the higher contributions (15.72 and 18.63%) to the overall RPDM values. This indicates that effectively, the experimental data belonging to the second activity pulse have a more weight in the fitting of the model than those belonging to the first activity pulse.

However, the non-significant values obtained for v _max and K_M when the double model (4) was used (Supplementary Table 1) also suggest that the failure of this model to fit the experimental data could be also due to the incapacity of the Michaelis–Menten model (1) for describing adequately the experimental data set corresponding to the first activity pulse. In an attempt for clarifying this hypothesis, model (1) was fitted to these latter experimental data. As can be seen in the upper part of Supplementary Figure 3, the use of the Michaelis–Menten model did not produce satisfactory results, because only the value of v _max for Lip1 was found to be significant. In addition, from the detailed observation of the plotted raw data, it can be observed that the velocity of catalysis show a linear (in case of Lip2) or almost linear (in case of Lip1) response, rather than a rectangular hyperbolic response, to increasing triacetin concentrations (lower part of Supplementary Figure 3). This means that the velocities of the reaction were directly proportional to the substrate concentration in this region and consequently, the enzymatic reaction with respect to substrate concentration is of first order in the first activity pulse. In fact, although the values for the K_M parameter (0.30 M for Lip1 and6.39 M Lip2) calculated with model (1) were notstatistically significant at P < 0.05 (upper part of Supplementary Figure 3), they were higher than the maximum TA concentration (0.25 M) corresponding to the first activity pulse for each enzyme.

In this case, when [S] ≪ K_M , the equation of Michaelis–Menten can be transformed in a linear Equation (6) as follows:

Since the quotient v _max/K_M is constant, it can be substituted into Equation (6) by a new constant, which could be named κ, therefore:

Substituting the Michaelis–Menten expression by Equation (7) into model (4) gives:

Model (8) satisfies the essential initial condition for any enzymatic reaction, because for [S] = 0, v = 0, but when [S] → ∞, it can be observed that v → ∞, and consequently, the final condition that implies that when [S] → ∞, v → v _max is not satisfied in this case. In fact, mainly for Lip2, a clear lack of fit was observed at higher substrate concentrations (Supplementary Figure 4).

Therefore, the models (4) and (8), which are based on the sum of the velocities in each activity pulse, are not applicable to describe the specific activities of Lip1 and Lip2 on triacetin without hexane.

For this reason, a new analysis of the experimental data was carried out by taking into account the following considerations. On the one hand, the linear increase in the specific activities, at a triacetin concentration of 0.27 M for both enzymes (Supplementary Figure 3) led to maximum specific activities of 0.98 U/mg for Lip1 and 6.11 U/mg for Lip2. On the other hand, at triacetin concentrations higher than 0.27 M, both the soluble and insoluble substrates are present in the reaction mixture. Therefore, the specific activities in the second activity pulse could be considered to be as the sum of the enzymatic activities on both the soluble and insoluble triacetin.

Since the kinetic behaviour of the two lipases is affected by the formation of micelles, in this case, the substrate-series data must be split in two and each set must be separately modelled by using the corresponding model. In this way, expression (7) must be used todescribe the first activity pulse observed for [TA] < 0.27 M, meanwhile the second activity pulse must be described by the following expression:

Where v ₀ is the minimum velocity of the second activity pulse, which corresponds with the maximum velocity in the first activity pulse. Other terms are as previously defined.

The results obtained showed that model (9) was able to describe satisfactorily the second activity pulse for both lipases because high R ² values (>0.99) and low RPDM values (<10%) were obtained (Supplementary Table 3). In addition, excellent agreement was found between model predictions and experimental results for enzymatic activity of Lip1 and Lip2 (Supplementary Figure 5). Thus, the first and second activity pulses were best mathematically described by using the strategy of modelling them separately with the expressions (7) and (9), respectively.

On the other hand, the values (28.0 ± 0.51 U/mg for Lip1 and 34.7 ± 10.07 U/mg for Lip2) and v ₀ (0.8 ± 0.21 U/mg for Lip1 and 7.6 ± 0.69 U/mg for Lip2) predicted by model (9) were in perfect agreement with the experimental maximum activity achieved for both enzymes (26.65 U/mg for Lip1 and 28.24 U/mg for Lip2) and the minimum velocity (1.0 U/mg for Lip1 and 6.1 U/mg for Lip2) in the second activity pulses in the hydrolysis of triacetin without hexane.

Conclusion

From the results obtained in this article, it can be concluded that the enzymatic activity of Lip1 and Lip2, that showed two activity pulses cannot be modelled by using heuristic double models (the sum of two simple models), because non-significant values were obtained for all the parameters. In this case, it is necessary to split the time-series data in two and each set must be modelled separately with the corresponding simple model. This approach allows to determine the reasons by which a simple model did not fit adequately a corresponding data set, and consequently to modify amodel (if necessary) in order to obtain further improvements in its predictions, by reducing the RPDM values and increasing the R ² values.

Supplementary material

The supplementary material for this paper is available online at http://dx.doi.org/10.1080/19476337.2011.601818

Supplementary Figure 1. Relationship between the specific activity (v) of the Candida rugosa lipases isoenzymes Lip1 and Lip2 and the concentration of triacetin ([TA]) in absence and in presence of hexane. The experimental data (○) are expressed as mean values of three experiments with three replicates each. The curves drawn through the experimental velocity data were obtained according to the Michaelis–Menten model (1). NS: Non-significant coefficients at P < 0.05.

Figura 1. Relación entre la actividad específica (v) de las isoenzimas lipasas Lip1 y Lip2 de Candida rugosa y la concentración de triacetina ([TA]) en ausencia y en presencia de hexano. Los datos experimentales (○) se expresan como la media de tres experimentos con tres réplicas cada uno. Las curvas dibujadas sobre los puntos experimentales representan las predicciones del modelo de Michaelis-Menten (1). NS: coeficientes no significativos a P < 0,05.

Supplementary Figure 2. Changes in velocity (v) for each lipase isoenzyme with the concentration of triacetin ([TA]) without hexane. The curves drawn through the experimental velocity data were obtained according to the models (4) and (5). The circle in the right lower part of the Figure indicates the lack of fitting produced between model (5) and the experimental data at low substrate concentrations.

Figura 2. Cambios en la velocidad (v) para cada isoenzima lipasa con la concentración de triacetina ([TA]) en ausencia de hexano. Las curvas dibujadas sobre los puntos experimentales (símbolos) son las predicciones de los modelos (4) y (5). El círculo en la parte inferior derecha de la figura indica el desajuste entre el modelo (5) y los datos experimentales a bajas concentraciones de sustrato.

Supplementary Figure 3. Changes in velocity (v) for each lipase isoenzyme with the concentration of triacetin ([TA]) without hexane, at substrate concentrations below the maximum solubility level of triacetin (0.27 M). The lines (Figures A and B) drawn through the experimental velocity data (symbols) were obtained according to the Michaelis–Menten model (1) and a linear equation, respectively. NS: Non-significant coefficients at P < 0.05.

Figura 3. Cambios en la velocidad (v) para cada isoenzima lipasa con la concentración de triacetina ([TA]) en ausencia de hexano, a concentraciones de sustrato inferiores al límite máximo de solubilidad de la triacetina (0,27 M). Las líneas (Figuras A y B) dibujadas sobre los puntos experimentales (símbolos) son las predicciones del modelo de Michaelis-Menten (1) y de la ecuación de una línea recta, respectivamente. NS: coeficientes no significativos a P < 0,05.

Supplementary Figure 4. Changes in velocity (v) for each lipase isoenzyme with the concentration of triacetin ([TA]) without hexane. The curves drawn through the experimental velocity data (symbols) were obtained according to the logistic model (8).

Figura 4. Cambios en la velocidad (v) para cada isoenzima lipasa con la concentración de triacetina ([TA]) en ausencia de hexano. Las curvas dibujadas sobre los puntos experimentales (símbolos) son las predicciones del modelo logístico (8).

Supplementary Figure 5. Changes in velocity (v) for each lipase isoenzyme with the concentration of triacetin ([TA]) without hexane for substrate concentrations above the triacetin solubility of 0.27 M. The curves drawn through the experimental velocity data (symbols) were obtained according to the Equation (9).

Figura 5. Cambios en la velocidad (v) para cada isoenzima lipasa con la concentración de triacetina ([TA]) en ausencia de hexano, para concentraciones de sustrato superiores al límite de solubilidad de la triacetina (0,27 M). Las curvas dibujadas sobre los puntos experimentales (símbolos) son las predicciones del modelo (9).

Supplementary Table 1. Parameter values (means ± standard errors) of the model (4) for the enzymatic reactions of the isoenzymes Lip1 and Lip2 on triacetin without hexane. NS: Non-significant coefficients at P < 0.05.
Tabla 1. Valores de los parámetros (medias ± errores estándar) del modelo (4) para las reacciones enzimáticas de las isoenzimas Lip1 y Lip2 en triacetina sin hexano. NS: coeficientes no significativos a P < 0,05.

Parameters	Lip1	Lip2
v max (U/mg)	NS	40.0 ± 17.46
KM (M)	NS	NS
(U/mg)	25.09 ± 2.945	15.3 ± 2.03
m (M^−1)	11.34 ± 1.360	48.4 ± 18.18
(U/mg)	0.57 ± 0.007	0.3 ± 0.01

Supplementary Table 2. Parameter values (means ± standard errors) of the logistic model (5) for the enzymatic reactions of the isoenzymes Lip1 and Lip2 on triacetin without hexane. NS: Non-significant coefficients at P < 0.05.
Tabla 2. Valores de los parámetros (medias ± errores estándar) del modelo logístico (5) para las reacciones enzimáticas de las isoenzimas Lip1 y Lip2 en triacetina sin hexano. NS: coeficientes no significativos a P < 0,05.

Parameters	Lip1	Lip2
(U/mg)	26.45 ± 0.272	28.93 ± 0.741
m (M^−1)	10.31 ± 0.313	15.63 ± 1.642
(M)	0.57 ± 0.004	0.32 ± 0.007
R ^2	0.9990	0.9897
RPDM	19.81	21.71

Supplementary Table 3. Parameter values (means ± standard errors) of model (9) for the enzymatic reactions of the isoenzymes Lip1 and Lip2 on triacetin without hexane in the second activity pulse.
Tabla 3. Valores de los parámetros (medias ± errores estándar) del modelo (9) para las reacciones enzimáticas de las isoenzimas Lip1 y Lip2 en triacetina con hexano en el segundo pulso de actividad.

Parameters	Lip1	Lip2
(U/mg)	27.28 ± 0.592	34.70 ± 10.068
m (M^−1)	9.64 ± 0.463	15.89 ± 4.186
(M)	0.56 ± 0.004	0.30 ± 0.038
v 0 (U/mg)	0.82 ± 0.210	7.60 ± 0.688
R ^2	0.9994	0.9916
RPDM	6.47	5.11