Multi-enzyme cascade reaction in a miniplant two-phase-system: Model validation and mathematical optimization

Biotechnological application of multiple enzymes in different phases for target com-pounds synthesis poses a significant challenge for industrial process development. At the same time, a growing demand for natural flavors and fragrances opens up possi-bilities for novel biotechnological processes to replace current chemical synthesis routes, with additional advantages such as avoiding harsh reaction conditions and toxic chemicals, and less by-products in the system. Within complex biotechnological processes, the key for unfolding their industrial application potential in bioprocess engineering lies in their mathematical modeling. In this contribution, a multi-enzyme cascade reaction in a two-phase system implemented in a miniplant-scale reactor setup is mathematically modeled for the example of the flavoring agent cinnamyl cinnamate. Using our validated model and a mathematical optimization tool based on a genetic algorithm, optimization runs are performed to demonstrate the potential of computer-aided process development for complex biotechnological processes.


| INTRODUCTION
The worldwide market for flavors and fragrances generates a 30 billion U.S.-dollars revenue volume per year, and grows at a 5% annual rate. 1 Natural flavor production is of increasing importance, predominantly in Europe and North America. The U.S. Food & Drug Administration defines natural flavors as those deriving their chemicals from animal or plant sources, as opposed to artificial flavors that use synthetic chemicals in the production process. 2 Industrial biotechnology can fulfill naturality prerequisites through novel, sustainable processes. At the same time, its potential to replace current chemical synthesis routes remains controversial across different fields of study such as the production of specialty and fine chemicals. [3][4][5][6][7][8] Here, a promising approach to the synthesis of flavors and fragrances is the development of in vitro multi-enzyme cascade reactions. [8][9][10][11][12] These combine the benefits of enzymatically catalyzed reactions (e.g., high selectivity, mild reaction conditions) with the concept of process integration, thereby achieving benefits such as in situ cofactor regeneration, flexible design of new reaction routes, or the shift of unfavorable reaction equilibria. 13,14 In literature, cascade reactions with up to 10 reaction steps and eight enzymes have been successfully established, albeit usually limited to the application in an aqueous phase. 10,13 Few examples show the application in both aqueous and organic phases: they, however, make use of process integration (extraction steps) solely in order to enhance reaction turnover, without implementing additional reaction steps in the organic phase. 15 In previous papers, our research group conclusively proved the applicability of multi-enzyme cascade reactions in a multiphase system for the production of specialty chemicals through the example of cinnamyl cinnamate with integrated cofactor regeneration and integrated intermediate extraction. 11,16,17 As a consequent step toward productionscale process development, within this line of research we successfully implemented a continuous production process for the flavoring agent cinnamyl cinnamate in a 3 L miniplant reactor setup. 11,18 Cinnamyl cinnamate is extracted as a natural component from Balsam of Peru, and used as a flavoring agent in cosmetic products and perfumes. 19 Currently, two main chemical production processes are in use: styrene oxidative carbonylation with carbon monoxide, oxygen and aliphatic alcohols in the presence of palladium and sodium propionate, or cinnamic aldehyde synthesis in absolute ether with aluminum ethylate. 19,20 Contrary to the conventional chemical approach, in this study we investigate an innovative production process for cinnamyl cinnamate that fits the criteria of both the U.S. Department of Health and Human Services 2 and the European Union 21 for labeling the product as a "natural flavor." An important requirement to scale new production processes up for industrial application from an economic and/or ecological point of view is the possibility of a mathematical description of said process for continuous process control and development. 8,[22][23][24] However, due to the use of various enzymes and multiple phases, the mathematical description of complex biotechnological processes such as multienzyme cascade reactions constitutes an obstacle to biotechnological process development. 8 Therefore, this study takes on the challenge of introducing a mathematical model to describe a complex biotechnological production process implemented in a miniplant. Our model is implemented in Aspen Custom Modeler ® V8.8 (ACM, Aspen Technology, Inc.), and validated using experimental data obtained from the miniplant. In this study, we present the cinnamyl cinnamate-producing multi-enzyme cascade reaction sequence and discuss our mathematical model as well as experimental results for the miniplant. Furthermore, a mathematical optimization tool is used to perform simulation runs with the validated model, while simultaneously varying the process conditions to find optimal process operating windows, thereby proving the benefits of computer-aided process development in biotechnology.

| PROCESS DESCRIPTION
As the first step of process development toward a potential industrial application, the multidisciplinary studies and laboratory-scale analyses conducted by our research group and presented in previous peerreviewed papers, 11,16 resulted in the in vitro multi-enzyme cascade reaction sequence for the production of cinnamyl cinnamate from cinnamyl aldehyde in a multiphase system ( Figure 1).  phase is subsequently pumped through a fixed bed reactor, containing 12.8 g of Novozym ® 435 and tempered to 60 C according to the enzyme provider's information (Figure 2d). Since the lipase is commercially available and proved to be stable for extended times of operation, 23,25 no exchange of lipase batches was necessary. Therefore, the application of a simple-tooperate and well-established fixed bed reactor was preferred over an additional SpinChem ® reactor in the organic phase.

| MATHEMATICAL MODEL
In order to simulate the multi-enzyme cascade reaction sequence in the miniplant, a customized mathematical model is developed and solved in Aspen Custom Modeler ® V8.8 (Aspen Technology, Inc.) using an equation-oriented approach for simulating. As shown in F I G U R E 1 Multi-enzyme cascade reaction sequence for the production of cinnamyl cinnamate from cinnamyl aldehyde with integrated co factor regeneration and in situ intermediate extraction in a two-phase system 11

| Aqueous phase
A bi-bi mechanism with competitive inhibition for both the ADHcatalyzed reaction of cinnamyl aldehyde (CAL) to cinnamyl alcohol (COH) and the FDH-catalyzed reaction of formate to CO 2 are implemented in the model according to initial rate measurements as presented by Engelmann et al, 26 describing the ADH reaction rate according to Equation (1) and the FDH reaction rate according to Equation (2). The corresponding values for the constants are listed in Table 1.
The kinetic Equations (1) and (2) describe the reaction rates of free enzymes. During the immobilization process, a decrease in enzyme activity can be observed and is described by an efficiency factor η eff. 16 Remaining enzyme activity after immobilization for both FDH and ADH was determined to be 4% of the respective free enzyme activity. Additionally, as described in literature, a loss of activity over time was observed for the ADH, significantly affecting the reaction rates. 27 This time-dependent activity loss reaches values up to 68% and is described in the model by the deactivation factor f deac .
The effective reaction rates for the dehydrogenases can be obtained after multiplying the respective kinetic equations with the enzyme mass, while considering the aforementioned activity losses, resulting in Equation (3) for the ADH and Equation (4)  10.14 ± 6.67 As expected due to the application of a phosphate buffer, 28 experimental results showed auto-oxidation of the cofactor NADH over time, as previously reported in literature. 29,30 In order to model the reaction system as precisely as possible, the auto-oxidation of NADH was measured at wavelengths of λ 1 = 340 nm and λ 2 = 292 nm in a time range of 48 hr using a VWR™ UV-1600PC Spectrophotometer. Additionally, absorption values at λ 3 = 260 nm increased analogous to NADH-oxidation during these experiments, indicating that NADH is oxidized to NAD + . In our mathematical model it is therefore assumed, that NADH auto-oxidizes to NAD + . The resulting NADHoxidation for this system is described through a function of exponential decay as shown in Equation (5). The empirical constants shown in Equation (5)   The mass balance of each component in the aqueous phase is therefore described through differential equations in dependency on the reactions of the respective enzymes, the feed streams, mass transfer to the organic phase, and the precipitated amount in each time step. Equation (6) shows the generalized form of the mass balance for any given component i in the volume specific form. Equations (7) and (8) show the modified forms of the mass balance for the cofactors NADH and NAD + respectively, considering the auto-oxidation of NADH instead of the non-existing precipitation of the cofactors.

| Phase interface
The mass transfer at the phase interface is important, in that it affects the concentrations of all components in both phases, thereby influencing all three enzymatic reactions. Experimental results show that the mass transfer rate in the centrifuge is significantly higher than the reaction rates of all three enzymes in the reactors (see Supporting Information). Therefore, the assumption of instantaneous mass transfer seems reasonable 31 : this leads to a concentration distribution between the two phases according to the partition coefficient for each component i as described according to Equation (9).
The partition coefficients were determined in concentration ranges of 0.02-1,000 mM in triplets and are listed in Table 2. As expected, the partition coefficients proved to be concentration-independent.
Analogous to the aqueous phase, component precipitation is described with storage terms for the extractive centrifugation step. Additionally, during this step, each one of the two phases is saturated with its counterpart.
The temperature in the extractive centrifuge influences the productivity of the final reaction step by affecting water saturation concentration in the organic phase, as described in previous studies. 11 Therefore, the linear temperature-dependent water saturation concentration of the organic phase is implemented in the model according to Equation (10). 11 w water− organic = 0:0015 Á T centrifuge + 0:0081 ð10Þ

| Organic phase
The immobilized-lipase-filled fixed bed reactor for the esterification reaction is modeled as a cascade of σ CSTR reactors 22  the lipase reaction rate is described according to a bi-bi mechanism with substrate excess inhibition of CAC for the present reaction system. Equation (12) shows the lipase reaction rate as implemented in the model, and the corresponding parameters are described in Table 3. 32 The reaction Equation (12)  Therefore, the model is to be used for mathematical optimization.
Prior to process simulation and optimization, however, our model needs to be validated using independent experimental data from the miniplant as the consequent second step of process development.
Since the developed mathematical model is designed to perform dynamic simulations, the start-up phase of the reactor setup has to be included in the validation process.
All experiments for model validation were performed in the miniplant described in Figure   In Figure  As can be seen in Figure 4, the intermediate concentration of Examples of enzyme-based process modeling and simulation exist that do not validate the model with independent experimental data, 31,36,37 or their validation is based on qualitative agreement between experimental and simulated values. 38  F I G U R E 4 Experimental and simulated data of experiment number 2 for model validation biological evolution, and it has been successfully applied to various chemical and biotechnological processes. 22,25,[43][44][45][46] In a first step, a randomly selected set of so-called "individuals" is created to form the initial population. Each individual represents a fully parameter- This results then in a Pareto front representing a set of optimal solutions, each one being a trade-off of the objective functions whereby no other solution can satisfy both objective functions better.
Exemplarily for these results, Figure 5 shows a multi-objective optimization run to increase the CCI space-time yield while decreasing the cofactor concentration after 50, 200, and 300 generations of the aforementioned algorithm cycles respectively: as can be seen in The optimal values shown in Figure 5

| CONCLUSION AND OUTLOOK
The wo rld-wide growing demand for natural flavors poses a chance for enzyme-based production processes to be implemented to specialty and fine chemicals industry. In vitro multi-enzyme cascade reactions are a promising part of such novel, enzyme-based approaches, in that they present a chance for process integration. Within our Future research will now further investigate the optimal operating settings for the miniplant-scale production process. Specifically, integration of the product separation step will be the focus of our work: promising results for cinnamyl cinnamate separation from the product mixture were already achieved using annular chromatography. Incorporating the downstream process into the mathematical model for process optimization will show the full potential of this novel process specifically, and the benefits of applying mathematical modeling and optimization to biotechnology in general.

ACKNOWLEDGMENTS
The authors thank the Deutsche Forschungsgemeinschaft (German