Developing the rate equations for two enzymatic Ping-Pong reactions in series: Application to the bio-synthesis of Bis(2-ethylhexyl) azelate

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Highlights

  • The kinetic equations of two bisubstrate Ping-Pong reactions in series was developed.

  • To obtain the kinetic equations the approximation to stationary state was applied.

  • The bio-synthesis of bis(2-ethylhexil) azelate was used to check the model.

  • The reaction was carried out in a batch reactor and catalysed by Novozym® 435.

  • A user’s software was developed to fit the experimental data to the model.

Abstract

In this work, the rate equations of two simultaneous bisubstrate Ping-Pong in series reactions have been developed for the first time. To obtain these equations, the approximation to the stationary state has been applied and, for the total balance of enzyme, all the intermediate complexes of the two reactions, which are present simultaneously in the reaction medium, have been taken into account.

To check the kinetic equations obtained, the synthesis of bis(2-ethylhexyl) azelate by transesterification from diethyl azelate and 2-ethylhexanol, in the presence of the immobilized lipase Novozym@ 435, has been used as reaction model. The reaction has been carried out in solvent-free conditions in a batch reactor. A design model of the reactor has also been developed and solved by applying a numerical method. The model equations have been implemented in user’s software in Visual Basic for Applications. In that software a routine, based on a very well-known procedure to minimize the sum of the square errors, has also been implemented. By using this software, the model parameters have been determined by fitting the experimental data to the model. A high determination coefficient was obtained, which validated both the kinetic equations and the reactor’s design model.

Graphical abstract

Variation of substrates and products concentrations along the reaction time:

♦ [2-Etilhexanol] (Mol L−1); ▲ [Diethyl azelate] (Mol L−1); ● [Ethyl 2-ethylhexyl azelate] (Mol L−1); + [Bis(2-ethylhexyl) azelate] (Mol L−1); x [Sum of azelates]; () kinetic model.

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Introduction

Along the last century, the field of enzymatic reactions has experimented an important increase and, as a consequence, most of the mechanisms and kinetic equations involved in the enzymatic processes have been well established. Currently, not only a high number of publications in the high impact journals, but also excellent books, on the more common mechanisms and kinetic equations related with mono-substrate or bi-substrate enzymatic reactions, with or without inhibition, can be consulted [1,2]. But new reactions of interest continuously appear and new mechanisms and kinetic equations must be developed to better understand their behaviour.

In this sense, it is observed that, in the last years, important efforts have been made to find alternatives to traditional lubricants. In this way, esters of branched alcohols and dicarboxylic acids have shown good properties to be used as an alternative friendly with the environment, because they are biodegradable and can be obtained through enzymatic processes, which are very selective and don’t need high level of energy consumption.

Between these esters, adipates and sebacates have been some of the more commonly used [[3], [4], [5], [6], [7], [8], [9], [10], [11], [12]], being the direct esterification between the dicarboxylic acid and the alcohol, or the transesterification from other ester, the more common ways to be obtained. The reaction is carried out, generally, in the presence of a bio-catalyst, in solvent free systems or in not aqueous solvents. As the main characteristic, it must be pointed out that the overall reaction takes place by way of an intermediate semi-ester, which is synthesized in a first reaction and after, in a second reaction, act as an in situ new substrate to give, finally, the di-ester, which is the product of interest. As a result, the global process can be considered as the coupling of two consecutive reactions, which is a new field to be studied, as it has been made in this work.

Some examples of these reactions are, for the adipates, the bio-synthesis of bis(2-ethylhexyl) adipate, [3], dilauryl adipate, [5], dimethyl adipate [6], and dioctyl adipate, [7], and for sebacates, bis(2-ethylhexyl) sebacate and bis(3,5,5-trimethylhexyl) sebacate, [4]. Despite the adipic and sebacic acids have been the first dicarboxylic acids used to obtain esters with lubricant properties, recently the azelaic acid has been also tested, because most of its esters can be used in the plasticizer industries, [[13], [14], [15]].

As bio-catalysts, the most commonly used were Novozym@ 435 and Lipozyme@ IM, [3,4]. Also, lipase from Candida rugosa immobilized on Mg, Zn and Ni of layered double hydroxides, [6], and an immobilized lipase from Thermomyces lanuginosus, [12], were used. And related to the reaction conditions, most of these studies were carried out in “solvent-free” medium, [8,12], which makes it possible to obtain the pure final product without the solvent removal, reducing the cost of the process.

Regarding the kinetics of these processes practically no works can be found that provide detailed reaction mechanisms and kinetic equations. Most of the studies, based on the application of the Surface Response Methodology, [5,9,10,15], have been developed to optimize the experimental conditions of the bio-synthesis of these compounds. Also, some other optimization studies, based on the neural network theory, have been applied [7,14]. Until now, only one work has been found where, from data of initial reaction rates, a bisubstrate ping-pong mechanism with inhibition by methanol was proposed [9]. Although this is, probably, the first study about the esters of dicarboxylic acids that proposes a classic kinetic equation, the equation derived from the mechanism only takes into account the final product, and the intermediate semi-ester was not considered.

Some other reactions catalysed by lipases to obtain esters from monocarboxylic acids and monohydroxylic alcohols have been studied, [[16], [17], [18], [19]], and, in most of them, the bisubstrate ping-pong equation has been used.

Other aspect that must be taken into account is the determination of the kinetic parameters of the kinetic model for these reaction types. In this sense, some works [20,21], where problems that include the bisubstrate ping-pong kinetics are solved, are of interest, mainly the second one [21], where the group of non-linear differential equations of the model are solved by means of numerical calculation.

In this work, taken into account that the first substrate to be attached to the enzyme must be an acyl donor, the kinetic equations of two simultaneous bisubstrate Ping-Pong in series reactions have been developed by the first time. To obtain these equations, the approximation to the stationary state has been applied and, for the total balance of enzyme, all intermediate complexes of the two reactions, which are present simultaneously in the reaction medium, have been taken into account. Additionally, to check the kinetic equations obtained, the synthesis of bis(2-ethylhexyl) azelate by transesterification from diethyl azelate and 2-ethylhexanol, in the presence of the immobilized lipase Novozym@ 435, has been used as reaction model, and the experimental results obtained in a batch reactor have been fitted to the model, using user’s software in Visual Basic for Applications, with good degree of agreement.

Section snippets

Reactions

According to the nomenclature adopted in this work, and taken into account that the reaction chosen to check the kinetic model has been the enzymatic synthesis of bis(2-ethylhexyl) azelate, by transesterification from diethyl azelate and 2-ethylhexanol, the reactions that take place can be represented as follows:Reaction1;A+BLipaseR+PReaction2;A+PLipaseR+Q

In this reaction scheme the product R, ethanol in the reaction type selected, disappears from the reaction medium by vaporization due

Chemicals

Diethyl azelate (90 %), 2-ethylhexyl alcohol (99.6 %), methyl myristate (99 %) and n-heptane (>96 %), were purchased from Sigma Aldrich. Bis(2-ethylhexyl) azelate (75 %) was purchased from TCI Europe NV.

The lipase-based bio-catalyst, Novozym@ 435 was kindly provided by Novozymes Spain S.A.

Other reagents and products were of analytical grade.

Experimental procedure

The reaction was carried out under solvent free conditions. Experiments were conducted in a jacketed stirred batch reactor of 50 cm3 total volume. The

Progress curves

The experimental results obtained are depicted in Fig. 2A–C, for 0.25, 0.50 and 1.00 g of enzyme, respectively. In these Figures, the progress curves of the concentrations of both substrates, as well as the intermediate product, the final product and the sum of the different compounds of azelate, are shown. The dots are the experimental values and the solid lines are the ones calculated with the model.

Regarding Fig. 2A, it can be seen that, with 0.25 g of enzyme, after a total reaction time of

Conclusions

In this work, the kinetic equations of two simultaneous bisubstrate Ping-Pong in series reactions have been developed by the first time. To obtain these equations, the approximation to stationary state has been applied and, for the total balance of enzyme, all intermediate complexes of the two reactions, which are present simultaneously in the reaction medium, have been taken into account.

To check the kinetic equations obtained the synthesis of bis(2-ethylhexyl) azelate by transesterification

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

This work was supported by the grant MCIU/AEI/UE-FEDER RTI2018-094908-B-I00 from Ministerio de Ciencia, Innovación y Universidades of Spain. Authors thank to R. Martínez Gutiérrez, from Novozymes España S.A., who friendly provided the biocatalyst.

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