catalysts Article Catalyst Replacement Policy on Multienzymatic Systems: Theoretical Study in the One-Pot Sequential Batch Production of Lactofructose Syrup Pablo Silva 1 , Vanessa Arancibia 1 , Daniela Cid 1 , Oscar Romero 2 , Andrés Illanes 1 and Lorena Wilson 1, * 1 School of Biochemical Engineering, Pontificia Universidad Católica de Valparaíso, Avenida Brasil 2085, Valparaíso 2362803, Chile; pablo.silva@pucv.cl (P.S.); vanessa.arancibia@pucv.cl (V.A.); daniela.cid@pucv.cl (D.C.); andres.illanes@pucv.cl (A.I.) 2 Bioprocess Engineering and Applied Biocatalysis Group, Department of Chemical Biological and Environmental Engineering, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain; oscarenrique.romero@uab.cat * Correspondence: lorena.wilson@pucv.cl Abstract: One-pot systems are an interesting proposal to carry out multi-enzymatic reactions, though this strategy implies establishing an optimal balance between the activity and operability of the involved enzymes. This is crucial for enzymes with marked differences in their operational stability, such as one-pot production of lactofructose syrup from cheese whey permeate, which involves two enzymes—β-galactosidase (β-gal) and glucose isomerase (GI). The aim of this work was to study the behavior of one-pot sequential batch production of lactofructose syrup considering both enzymes immobilized individually, in order to evaluate and design a strategy of replacement of the catalysts   according to their stabilities. To this end, the modelling and simulation of the process was carried out, considering simultaneously the kinetics of both reactions and the kinetics of inactivation of Citation: Silva, P.; Arancibia, V.; Cid, both enzymes. For the latter, it was also considered the modulating effect that sugars present in D.; Romero, O.; Illanes, A.; Wilson, L. Catalyst Replacement Policy on the medium may have on the stability of β-gal, which is the less stable enzyme. At the simulated Multienzymatic Systems: Theoretical reaction conditions of 40 ◦ C, pH 7, and 0.46 (IUGI /IUβ-gal ), the results showed that considering the Study in the One-Pot Sequential Batch stability of β-gal under non-reactive conditions, meaning in absence of the effect of modulation, it is Production of Lactofructose Syrup. necessary to carry out four replacements of β-gal for each cycle of use of GI. On the other hand, when Catalysts 2021, 11, 1167. https:// considering the modulation caused by the sugars on the β-gal stability, the productivity increases up doi.org/10.3390/catal11101167 to 23% in the case of the highest modulation factor studied (η = 0.8). This work shows the feasibility of conducting a one-pot operation with immobilized enzymes of quite different operational stability, Academic Editor: Ulf Hanefeld and that a proper strategy of biocatalyst replacement increases the productivity of the process. Received: 29 July 2021 Keywords: multi-enzymatic reactions; one-pot; catalyst replacement policy; modulation factor; Accepted: 20 September 2021 sequential batch; lactofructose syrup; β-galactosidase; glucose isomerase Published: 27 September 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in 1. Introduction published maps and institutional affil- iations. The increasing use of enzymes as industrial catalysts [1–3], has evolved to the devel- opment of multienzyme processes [4–6], where two or more enzymes act coordinately to perform the conversion reaction [7]. An appealing proposal is to conduct the multi-step en- zymatic reaction in a single vessel (one-pot) [8–11]. This strategy implies that the enzymes Copyright: © 2021 by the authors. involved are able to act together without compromising their activity and operational sta- Licensee MDPI, Basel, Switzerland. bility, therefore reducing the intermediate product(s) inhibition, and avoiding unnecessary This article is an open access article separation and purification steps [12–15]. In this way, fewer unit operations are required, distributed under the terms and solvent consumption reactor volume and operation time are reduced, yield is increased, conditions of the Creative Commons and waste is considerably reduced [5]. However, the temperature and pH profiles of the Attribution (CC BY) license (https:// enzymes can differ significantly, as well as their operational stability [5,14,16]. Therefore, creativecommons.org/licenses/by/ compromised operation conditions should be established to optimally balance their activity 4.0/). and operational stability [14,17], which is a key determinant of reactor performance [18,19]. Catalysts 2021, 11, 1167. https://doi.org/10.3390/catal11101167 https://www.mdpi.com/journal/catalysts Catalysts 2021, 11, x FOR PEER REVIEW 2 of 15 profiles of the enzymes can differ significantly, as well as their operational stability Catalysts 2021, 11, 1167 2 of 15 [5,14,16]. Therefore, compromised operation conditions should be established to opti- mally balance their activity and operational stability [14,17], which is a key determinant of reactor performance [18,19]. InInthat thatdirection, direction,mathematical mathematicalmodeling modelingisisaapowerful powerfultooltoolforfor predicting predicting thethe process process output outputbefore beforeitsitsimplementation, implementation,allowingallowingto toexplore exploredifferent differentreactor reactorconfigurations configurations and and modes modesofofoperation operation totoearly onon early select thethe select most promising most promisingoptions that that options will later be validated will later be vali- experimentally dated experimentally[7]. Mathematical modelling [7]. Mathematical has beenhas modelling used beenin the used case of enzyme in the case of reactors enzyme toreactors identifytooptimal identifyoperation conditions, optimal operation maximizemaximize conditions, substrate substrate conversion into product, conversion into increase productivity, and maintain substrate conversion (and therefore product, increase productivity, and maintain substrate conversion (and therefore product product quality) during quality) reactor during operation within pre-established reactor operation margins of within pre-established variation margins [7,19]. [7,19]. of variation Immobilization of enzymes is another powerful tool for Immobilization of enzymes is another powerful tool for its industrial its industrial implementation, implementa- usually producing tion, usually a significant producing increase a significant in enzyme increase in enzyme stability andand stability facilitating thethe facilitating reactor reac- operation tor operation[4,20–22]. In theIncase [4,20–22]. the of one-pot case multienzyme of one-pot systems, multienzyme if eachifenzyme systems, is immo- each enzyme is bilized separately, immobilized the resulting separately, biocatalyst the resulting can becan biocatalyst handled independently be handled independently in a spinning in a spin- basket reactorreactor ning basket (Figure(Figure 1A) [5].1A) This [5].configuration allows allows This configuration an easyancontrol of the proportion easy control of the pro- ofportion each biocatalyst required, their activity and operational stability; of each biocatalyst required, their activity and operational stability; it alsoitallows indi- also allows vidual individual replacement of the spent immobilized enzyme according to its lifespan of[14]. replacement of the spent immobilized enzyme according to its lifespan of use use Since enzyme [14]. Since inactivation enzyme and its inactivation andreplacement is inevitable, its replacement modeling is inevitable, modelingand simulation and simulation is a powerful tool for is a powerful toolthe foreffective use of the effective the use ofbiocatalyst priorprior the biocatalyst to replacement to replacement and and the planning the plan- ofning reactor operation [23]. of reactor operation [23]. Figure 1. (A) Schematic representation of a spinning basket reactor with separate compartments Figure 1. (A) Schematic representation of a spinning basket reactor with separate compartments for for each immobilized biocatalyst. (B) Scheme of lactose hydrolysis with β-gal and glucose isomeri- each immobilized biocatalyst. (B) Scheme of lactose hydrolysis with β-gal and glucose isomerization zation with GI. with GI. A sound strategy for the upgrading of lactose is the production of lactofructose syrup A sound strategy for the upgrading of lactose is the production of lactofructose (LFS) by the sequential hydrolysis of lactose with β-galactosidase (β-gal) and the isomer- syrup (LFS) by the sequential hydrolysis of lactose with β-galactosidase (β-gal) and the ization of the resulting glucose by glucose isomerase (GI) (Figure 1B). The kinetics of both isomerization of the resulting glucose by glucose isomerase (GI) (Figure 1B). The kinetics enzymes have been well characterized, having significant differences in thermal stabiliza- of both enzymes have been well characterized, having significant differences in thermal tion [24–33]. [24–33]. stabilization The resultingThe product resultingis product a mixtureisofasugars mixture (fructose, of sugars glucose, galactose, (fructose, and glucose, residual lactose) with a sweetening power similar to sucrose [8,19,34]. galactose, and residual lactose) with a sweetening power similar to sucrose [8,19,34]. The The production of this syrup has production of thisbeen conducted syrup has been in aconducted sequentialin operation a sequentialin two separatein operation reactors for hy- two separate drolysis and isomerization; however, its production in a one-pot reactors for hydrolysis and isomerization; however, its production in a one-pot strategy strategy with co-immo- bilized with β-gal and GI has co-immobilized β-galbeen andrecently reported GI has been [8]. Itreported recently is well documented [8]. It is wellthat substrates documented and products of reactions, as well as some sugars, exert a modulation that substrates and products of reactions, as well as some sugars, exert a modulation effect on the stability effect of both enzymes [35–39]. In the case of β-gal, galactose exerts a positive on the stability of both enzymes [35–39]. In the case of β-gal, galactose exerts a positive modulation effect (protection)effect modulation while(protection) the lactosewhilemodulation the lactoseeffect is negative modulation andis glucose effect negativehas andno effect glucose [40,41]; in the case of GI, both glucose and fructose exert a positive has no effect [40,41]; in the case of GI, both glucose and fructose exert a positive modulation modulation effect [32,42]. effect [32,42]. Usingmodelling Using modellingand andsimulation simulation tools, tools, the the purpose purpose of of this this work work was was toto study study the the behavior of the one-pot sequential batch production of lactofructose behavior of the one-pot sequential batch production of lactofructose syrup considering both syrup considering both enzymes enzymes immobilized immobilized individually, individually, in order in order to evaluate to evaluate and design and design a strategy a strategy of cat- of catalyst alyst replacement replacement accordingaccording to theirtostabilities. their stabilities. β-gal Aspergillus β-gal from from Aspergillusoryzaeoryzae immobilized immobilized onto onto poly(methacrylate) poly(methacrylate) beads and beads and commercial commercial immobilizedimmobilized GI from GI from Streptomyces Streptomyces murinus (Sweetzyme) were selected for the purpose of this work, where different scenarios were considered in terms of the modulation effects exerted by lactose and galactose on β-gal, which is the less stable enzyme. Catalysts 2021, 11, x FOR PEER REVIEW 3 of 15 murinus (Sweetzyme) were selected for the purpose of this work, where different scenar- Catalysts 2021, 11, 1167 3 of 15 ios were considered in terms of the modulation effects exerted by lactose and galactose on β-gal, which is the less stable enzyme. 2.2.Results ResultsandandDiscussions Discussions 2.1. Selection of Operating Conditions 2.1. Selection of Operating Conditions Theperformance The performanceof ofaaone-pot one-potsequential sequentialbatch batchreactor reactorfor forLFS LFSproduction productionwas wassimu- simu- lated considering the thermal dependence of the kinetic and stability parameters lated considering the thermal dependence of the kinetic and stability parameters of β-gal of β-gal and GI at different GI/β-gal activity ratio and temperatures (see materials and GI at different GI/β-gal activity ratio and temperatures (see materials and methods). and methods). Thekinetics The kinetics ofof LFS LFS production production per per batch batch at at three three temperatures temperatures andand three three GI/β-gal activity GI/β-gal activity ratiosare ratios areshown shownin inthe theFigure Figure2. 2.As Asexpected, expected,fructose fructoseproduction productionincreases increases with with aa higher higher GI/β-gal activity ratio approaching more rapidly to its equilibrium concentration. GI/β-gal activity ratio approaching more rapidly to its equilibrium concentration. Simi- Simi- larly, increasing temperature favors fructose formation, given the thermophilic larly, increasing temperature favors fructose formation, given the thermophilic nature of nature of GI. On the other hand, it can be observed that the rate of lactose hydrolysis GI. On the other hand, it can be observed that the rate of lactose hydrolysis decreases at decreases at the higher the temperature higher temperature as aasresult of β-gal a result inactivation. of β-gal inactivation. Figure Figure 2. 2. Substrates Substratesandandproducts productsconcentrations concentrationsprofiles profiles during during the theone-pot one-pot production production of of lactofructose lactofructose syrup syrup in in batch batch at at different differenttemperatures temperaturesand andGI/β-gal GI/β-galactivity ratio. activity (Temperatures: ratio. (Temperatures: (1):(1): 40 °C, 40 ◦(2): 45 °C C, (2): 45and (3): 50 ◦ C and °C. (3): 50GI/β-gal activity ◦ C. GI/β-gal ratio: activity (A.1–A.3): 0.1; (B.1–B.3): ratio: (A.1–A.3): 0.3 and0.3 0.1; (B.1–B.3): (C.1–C.3): 0.5. Purple: and (C.1–C.3): lactose;lactose; 0.5. Purple: Green: Green: galactose; Blue: glucose; galactose; Red: fructose). Blue: glucose; Red: fructose). These Theseresults resultsreflect reflectthe theimportance importance ofofboth bothenzyme enzymeratioratioand andtemperature temperature on onreactor reactor behavior, behavior, andand the the need need toto identify identify conditions conditions that that maximize maximize thethe production production of of fructose fructose syrup. syrup.To To identify identify this this condition, condition,an an evaluation evaluation ofof the the effect effect of of temperature temperature andand enzyme enzyme ratio on the productivity ratio on the productivity was carried out. The effect The effect of GI/β-gal activity ratio on GI/β-gal activity ratio on the the productivity productivity of a batch of fructose syrup production for three different temperatures can of a batch of fructose syrup production for three different temperatures can be be found found inin the Supplementary Materials. An An optimum GI/β-gal GI/β-gal activity activityratio ratio for for each each temperature temperature resulting resulting in in 0.46, 0.46, 0.25, and 0.18 (IUGI/IUβ-gal) (IUGI/IUβ-gal) corresponding correspondingto to40, 40, 45, 45, and and 50 ◦ C,respectively 50°C, respectively(Figure (FigureS4). S4). In In order order toto select select the the temperature temperature forfor the the simulations, simulations, an an analysis analysis was was carried carried outout based on based on the the specific specific productivity productivity during during one one batch batch atat different temperatures. temperatures. Figure Figure 33 shows the variation of the specific productivity related to β-gal in one batch conducted at the optimum GI/β-gal activity ratio for each temperature. As it can be observed, specific productivities at 45 and 50 ◦ C are significantly lower than at 40 ◦ C, because the mass of β-gal Catalysts 2021, 11, x FOR PEER REVIEW 4 of 15 Catalysts 2021, 11, 1167 shows the variation of the specific productivity related to β-gal in one batch conducted at 4 of 15 the optimum GI/β-gal activity ratio for each temperature. As it can be observed, specific productivities at 45 and 50 °C are significantly lower than at 40 °C, because the mass of β- gal used is different at each temperature, being lower at 40 than at 50 °C. This shows the used is influence different at ◦ C. This shows the strong strong ofeach temperature,ofbeing the inactivation β-gallower atproductivity on the 40 than at 50 due to the thermal inacti- influence vation. of the inactivation of β-gal on the productivity due to the thermal inactivation. Figure 3. Specific productivity referred to β-galactosidase during one batch of lactofructose syrup Figure 3. Specific productivity referred to β-galactosidase during one batch of lactofructose syrup production at different reaction temperatures and at the corresponding optimal GI/β-gal activity ratio. production at different reaction temperatures and at the corresponding optimal GI/β-gal activity ratio. For the following simulations based on specific productivities, the temperature of 40 ◦ C and an IG/β-gal activity ratio of 0.46 (IUGI/IUβ-gal) were selected, which are For thethat conditions following simulations favor β-gal, the least based stableonenzyme specificinproductivities, this case. the temperature of 40 °C and an IG/β-gal activity ratio of 0.46 (IUGI/IUβ-gal) were selected, which are condi- tions that of 2.2. Effect favor β-gal, the Modulation least stable of β-gal enzyme Stability in this case.of Lactofructose Syrup in One-Pot on the Production Sequential Batch Operation 2.2. Effect It hasofbeen Modulation shownofthat β-gal Stability on substrates andtheproducts Production of ofreaction Lactofructose Syrup compounds (and other in One-Pot Sequential like some Batch polyolsOperation and sugars) may exert a modulation effect, usually protection, on en- zymeItstability has been[38,43]. shownIn thissubstrates that case, it hasandbeen reported products that galactose of reaction exertscompounds (and other a positive modulation like (protection), some polyols but lactose and sugars) may modulation is negative exert a modulation [41];usually effect, therefore, stability on protection, under en- non-reactive zyme conditions stability [38,43]. In doesthisnot adequately case, it has beenpredict the stability reported during reaction that galactose exerts asopositive that in many instances modulation thermal inactivation (protection), of enzymes is but lactose modulation is negative overestimated [8]. [41]; therefore, stability under Given the above, the eventual modulation effect that the non-reactive conditions does not adequately predict the stability during reaction sugars present in the reaction so that medium may have on the stability of β-gal was included, in many instances thermal inactivation of enzymes is overestimated [8]. β-gal being the less stable enzyme. Under non-reactive Given the above, conditions, the eventual the first order inactivation modulation effect that rate constant the sugars of A. oryzae present in the β-gal reac- was determined, − 1 ◦ tion medium mayobtaining have on the a value of 0.0098 stability h was of β-gal at 40included, C (see Supplementary β-gal being the Materials), less stable which is Under enzyme. highernon-reactive than the inactivation conditions,ratethe obtained first orderunder reactive inactivation conditions rate constant of [8];A.thus ory- reflecting the protective effect of the sugars. In addition, zae β-gal was determined, obtaining a value of 0.0098 h at 40 °C (see Supplementary −1 previous works have shown that the usewhich Materials), of modulation is higher thanfactors theisinactivation a good approximation rate obtainedtounder simulate the stability reactive conditions of enzymes under reactive conditions [38,44]. Therefore, it was decided [8]; thus reflecting the protective effect of the sugars. In addition, previous works have to evaluate the effect of different shown magnitudes that the of the global use of modulation (positive) factors is a goodmodulation approximation factor (η). to simulate the stability Simulation of the one-pot production of LFS in sequential of enzymes under reactive conditions [38,44]. Therefore, it was decided batch operation considering to evaluate the the operational effect of differentstability of bothofenzymes magnitudes the global with different (positive) global modulation modulation factor (η).factors (η) was carried out. The simulation considers one cycle of use of GI, since it is the most stable Simulation of the one-pot production of LFS in sequential batch operation consider- enzyme, and the results are shown in Figure 4. ing the operational stability of both enzymes with different global modulation factors (η) Catalysts 2021, 11, x FOR PEER REVIEW 5 of 15 Catalysts 2021, 11, 1167 was carried out. The simulation considers one cycle of use of GI, since it is the most5 stable of 15 enzyme, and the results are shown in Figure 4. Figure Figure 4. 4.Operational Operationalstability stabilityof of β-gal β-gal and GIGI in in terms termsofofreaction reactiontime timeand andnumber number ofof sequential sequentialbatches during batches duringthethe one- pot production one-pot production of of lactofructose syrup lactofructose syrupin in sequential sequential batch batchoperation. operation.Simulations Simulations were were performed performed considering considering 4040 °C,◦ C, pH 7, 10% (w/w) of initial lactose concentration and GI/β-gal activity ratio of 0.46 (IUGI/IUβ-gal). (A) η = 0; (B) η = 0.2; (C) η = 0.4; pH 7, 10% (w/w) of initial lactose concentration and GI/β-gal activity ratio of 0.46 (IUGI /IUβ-gal ). (A) η = 0; (B) η = 0.2; (D) η = 0.6; (E) η = 0.8. Operational stability of β-gal: blue lines; stability of GI: red lines. (C) η = 0.4; (D) η = 0.6; (E) η = 0.8. Operational stability of β-gal: blue lines; stability of GI: red lines. Asexpected, As expected, thethe simulation simulation in Figure in Figure 4 shows 4 shows thatnumber that the the number of cycles of cycles of use re- of use required byquired by β-gal β-gal with with respect to respect one cycle toof one GI cycle of GIasdecreases decreases a higher ηasis aconsidered. higher η isInconsidered. the absenceIn ofthe absence of(ηmodulation modulation = 0; Figure 4A),(η = 0; Figure it is 4A), that observed it is during observed onethat during cycle of useone cycle of GI, theofβ-gal use of GI, the has enzyme β-galto enzyme be replaced has to fourbetimes. replaced four times. Instead, when Instead, a η = 0.8when a η = 0.8 is is considered, oneconsidered, cycle of one use ofcycle GI willof match use of oneGI will cyclematch of β-galoneuse, cycle so of theβ-gal use, so the replacement replacement of both enzymes of both in would en- zymes would in this case be synchronic. this case be synchronic. Workingwith Working withcombi-crosslinked combi-crosslinkedenzyme enzyme aggregates aggregates (combi-CLEAs) (combi-CLEAs) of ofβ-gal β-galand andGI GIforfor thethe production production of lactofructose of lactofructose syrup fromfrom syrup lactose in one-pot lactose batchbatch in one-pot operation, Araya, operation, et al. [8] Araya, reported et al. that the [8] reported productivity that of fructose the productivity remained of fructose constant remained for five constant batches for five with batches an accumulated with an accumulated time of of time 50 50h. h.This Thisresult resultisissimilar similar toto the one one obtained obtained in inthis thiswork, work, considering η = 0.4 (Figure 4D). Indeed, the decrease in productivity from the first to the ninth sequential batch in our simulation was 18.34%, corresponding to an accumulated time during the nine batches of 48.6 (h). Catalysts 2021, 11, x FOR PEER REVIEW 6 of 15 Catalysts 2021, 11, 1167 considering η = 0.4 (Figure 4D). Indeed, the decrease in productivity from the first to 6 ofthe 15 ninth sequential batch in our simulation was 18.34%, corresponding to an accumulated time during the nine batches of 48.6 (h). The effect of operational stability and the global modulation factor on the productiv- ity ofThe eacheffect batchofwas operational stabilityand also evaluated anditsthe global modulation evolution is shown infactor on the5.productivity the Figure Productiv- of each batch was also evaluated and its evolution is shown ity decreases with the number of batches at all the evaluated conditions, as in the Figure 5. enzymes Productivity (es- decreasesβ-gal) pecially with the are number of batches progressively at all the so inactivated, evaluated that theconditions, time required as enzymes for each(especially batch in- β-gal) are creases. It progressively is important inactivated, to analyze the so that the time required productivity after eachforcycle each of batch increases. β-gal use; in It thisis important to analyze the productivity after each cycle of β-gal use; in this case, even though the productivity increases after β-gal replenishment, values obtained in case, even though the initial the productivity batchesincreases after β-gal are no longer reachedreplenishment, valuesinactivated since GI is already obtained into the initial batches a certain extent. are no longer reached since GI is already inactivated to a certain This situation worsens as the time of use of GI increases. After one cycle of use of extent. This situation GI, the worsens reductionasinthe time of usewas productivity of GI of increases. 63.8 and 71.7%, After the oneformer cycle of use of GI, thetoreduction corresponding an absence in productivity was of 63.8 and 71.7%, the former corresponding to an absence of modulation, and the latter to a modulation factor of η = 0.8. The results show that it is of modulation, and the latter to a modulation factor of η = 0.8. The results show that it is feasible to use feasible to use two catalysts with different stability in a one-pot process, when both are two catalysts with different stability in a one-pot process, when both are immobilized immobilized independently, which allows to replace the more unstable catalyst at the independently, which allows to replace the more unstable catalyst at the right time, without right time, without losing the residual activity of the second enzyme, thereby enabling a losing the residual activity of the second enzyme, thereby enabling a more cost-effective more cost-effective use of the catalysts. use of the catalysts. Figure 5. Evolution in productivity in sequential batch operation of lactofructose syrup production in one-pot considering one cycle of use of GI and one one or or several several cycles cycles of of use use of β-gal. Simulations of β-gal. ◦ were performed considering 40 C, pH 7, 10% (w/w) of initial lactose concentration and GI/β-gal activity ratio of 0.46 (IUGI /IUβ-gal ). (A) η = 0; (B) η = 0.2; (C) η = 0.4; (D) η = 0.6; (E) η = 0.8. Catalysts 2021, 11, x FOR PEER REVIEW 7 of 15 were performed considering 40 °C, pH 7, 10% (w/w) of initial lactose concentration and GI/β-gal Catalysts 2021, 11, 1167 activity ratio of 0.46 (IUGI/IUβ-gal). (A) η = 0; (B) η = 0.2; (C) η = 0.4; (D) η = 0.6; (E) η = 0.8. 7 of 15 Although other alternatives to compensate the enzyme inactivation have been dis- cussed in the literature, such as the addition of fresh enzyme, the increase of the reactor Although other alternatives to compensate the enzyme inactivation have been dis- temperature cussed in the [45,46] and thesuch literature, increase as theofaddition the residence of freshtime in continuous enzyme, reactor the increase of[19], none the reactor oftemperature them are compatible with the presented case of study. Moreover, the proposed [45,46] and the increase of the residence time in continuous reactor [19], none catalyst replacement of them arepolicy can bewith compatible applied to other multi-enzyme the presented case of study.systems Moreover, where the the enzymes proposed in- catalyst volved might have quite different stabilities [17]. replacement policy can be applied to other multi-enzyme systems where the enzymes In order involved to assess might the impact have quite different of the [17]. and the replacement of β-galacto- inactivation stabilities sidase on the production of LFS, the accumulated In order to assess the impact of the inactivation productivity was determined and the replacement (see Equa- of β-galactosidase tion (27)). The results show a decrease in accumulated productivity on the production of LFS, the accumulated productivity was determined (see Equation with the operation(27)). time (Figure 6). When inactivated β-gal is replaced by fresh enzyme, The results show a decrease in accumulated productivity with the operation time (Figure a slight increase in6). the accumulated productivity is observed because of the decrease of When inactivated β-gal is replaced by fresh enzyme, a slight increase in the accumulated the times required in the initial batches. productivity However, is observed since of because GIthe is partially decrease inactivated, of the times the reaction required times in the required initial batches. inHowever, the initial since batches GI are no longer is partially sufficient to inactivated, themaintain reactionthe initial times productivity. required This batches in the initial effect is are clearly noticeable after the first β-gal replacement and becomes less significant no longer sufficient to maintain the initial productivity. This effect is clearly noticeable in the following. As a result, the number of batches that can be performed depends after the first β-gal replacement and becomes less significant in the following. As a result, on the time ofthe β-gal use (see number Table S5). of batches thatFor canallbe η values studied, performed depends the onnumber the timeofofbatches β-gal use per β-gal (see Tableuse S5). decreases. For all η This valuesis astudied, clear effecttheof the batch number of duration batches per time, which β-gal useisdecreases. increasingThisbecause is a the clear GIeffect has not been of the replaced batch durationin the reactor time, whichand therefore has is increasing less and because the less activity. GI has not beenTherefore, replaced theinproductivity the reactor and values keep declining. therefore has less and less activity. Therefore, the productivity values keep declining. Figure Figure 6. 6. Variation Variation inin the the accumulatedproductivity accumulated productivityininthe theone-pot one-potproduction productionofoflactofructose lactofructose syrup syrup in sequential batch operation considering one cycle of use of GI and one or more cyclescycles in sequential batch operation considering one cycle of use of GI and one or more of β- of β-gal use. galSimulations use. Simulations were performed considering ◦ 40 °C, pH 7, 10% (w/w) of initial lactose were performed considering 40 C, pH 7, 10% (w/w) of initial lactose concentration and concen- tration and GI/β-gal GI/β-gal activity activity ratio ratio(IU of 0.46 of 0.46 (IUGI/IUβ-gal). Red line: η = 0; blue line: η = 0.2; green line: GI /IUβ-gal ). Red line: η = 0; blue line: η = 0.2; green line: η = 0.4; η = 0.4; purple line: η = 0.6; black line: η = 0.8. purple line: η = 0.6; black line: η = 0.8. 3. 3. Materials Materials andand Methods Methods 3.1. Materials 3.1. Materials This This study study was was conducted conducted using using the the commercial commercial immobilized immobilized GIGI Streptomyces fromStreptomyces from murinus under the trade name Sweetzyme ® IT, kindly donated by Novozymes (Bagsvaerd, murinus under the trade name Sweetzyme®IT, kindly donated by Novozymes (Bagsvaerd, Denmark), Denmark), andand the the commercial commercial soluble soluble from from β-galβ-gal Aspergillus Aspergillus oryzae,oryzae, under under the the trade trade name ® name Enzeco Fungal Lactase Concentrate, kindly provided by Enzyme Development Corporation (New York, NY, USA). In the case of β-gal, the enzyme was immobilized in a methacrylate heterofunctional support (Relizyme Resindion, Milano, Italy) [47,48] (more details in Supplementary Materials). All chemicals were purchased from Sigma-Aldrich (St. Louis, MO, USA). Catalysts 2021, 11, 1167 8 of 15 3.2. Modeling The operation of a one-pot sequential batch reactor was simulated with β-gal and GI immobilized separately for the production of LFS from lactose. For process modeling purpose, a perfectly stirred and isothermal basket type reactor was used throughout the operation, and internal diffusional restrictions of the catalysts were not considered. For each batch of LFS production, the evolution of substrate and products concentrations was obtained, determining the specific productivity and the residual activity of both immobilized enzymes. As previously reported [8], the composition of LFS on a dry basis was: 6% w/w lactose, 47% w/w galactose, 26% w/w glucose, and 21% w/w fructose). Both immobilized enzymes were recovered at the end of each batch and used in the next one without intermediate addition of fresh catalyst. The cycle of use of each immobilized enzyme was defined as the number of batches that could be carried out until its activity dropped to 30% of its initial activity, which was the criterion adopted for its replacement. The specific productivity of the whole cycle of use for each immobilized enzyme was also determined. The scheme of the reactions involved is shown in Figure 1B. 3.2.1. Enzyme Kinetics Rate equations and kinetic parameters were taken from the literature [28–30,49]. Hydrolysis of lactose by β-gal is competitively inhibited by galactose, so the rate equation corresponds to Equation (1). k ·e · Lac v1 = cat1 1  . (1) Km1 · 1 + Lac KI + Lac Temperature dependence of the kinetic parameters (k cat1 , K M1 and K I ) are represented by Arrhenius type equations: k cat1 = k cat01 ·exp(− Ea/RT ) , (2) K M1 = K M0 ·exp(−∆H ◦/RT ) , (3) ◦ K I = K I0 ·exp(−∆H I /RT ) . (4) Isomerization of glucose into fructose by GI is represented by reversible kinetics according to the steady-state hypothesis of Briggs-Haldane. At favorable conditions for GI, activity and operational stability, the equilibrium constant of the reaction is close to 1 so the glucose–fructose conversion at equilibrium is close to 50% [18]. The rate equation for glucose isomerization can be expressed in terms of the difference in glucose concentration and glucose concentration at equilibrium, as represented by Equation (5): VM2 ·( Glu − Glue ) v2 = . (5) K M2 + ( Glu − Glue ) where:   Glu0 = Glu + Fru = Glue + Frue = (1 + Ke )· Glue = 1 + Ke−1 · Frue , (6) 1 Kmr ·k cat2 ·e2   VM2 = 1 + , (7) K Kmr − Km f " ! !# Kmr ·Km f 1 Ke Glu0 K M2 = 1+ 1+ + . (8) Kmr − Km f Km f Kmr 1 + Ke Catalysts 2021, 11, 1167 9 of 15 As in the case of lactose hydrolysis with β-gal, kinetic parameters of the isomerization reaction with GI (k cat2 , Km f , Kmr , and Ke ) are represented by Arrhenius type equations: EaVm f   k cat2 = k cat02 exp , (9) R· T Ea,Km f   Km f = Km f 0 exp , (10) R· T   Ea,Kmr Kmr = Kmr0 exp , (11) R· T   E Ke = Ke0 exp − aK . (12) R· T In the case of GI, the affinity constant (KM2 ) depends on the initial concentration of glucose Glu0 ; therefore, the energy of activation and the frequency factor in KM vary with Glu0 . Dehkordi, et al. [49] observed that at constant temperature KM2 varied linearly with Glu0 , as expected, and reported a general equation for KM2 which is explicit in Glu0 and T: 7534 22,818 KM2 = 10.37·1010 exp− T Glu0 + 5.48·1032 exp− T . (13) Values of the kinetic parameters of β-gal and GI immobilized used in the simulation of the production of lactofructose syrup are presented in Table 1. In this work, pH 7 was considered for the one-pot production of LFS, which is a compromise between the pH optima of β-gal and GI. In fact, the activity of GI decreases significantly below pH 7, while β-gal is fairly active at pH 7 even though its optimum pH is lower [8]. Table 1. Values of the kinetic parameters of β-gal and immobilized GI used in the simulation of the production of lactofructose syrup. Enzyme Parameter Value Unit Reference k cat01 6.74 mol/(h·IU) Ea 7.02 kcal/mol K M0 1.01 × 107 M β-gal [29,30] ∆H ◦ 7.21 kcal/mol K I0 1.32 × 102 M ∆H ◦ I 5.52 kcal/mol k cat02 1.46 × 1015 mol/(h·IU) EaVm f 29.5 kcal/mol Km f 0 1.35 × 1021 M EaKm f 32.9 kcal/mol [49] GI Kmr0 5.27 × 1013 M EaKmr 21.2 kcal/mol Ke0 4.10 × 104 - EaK 7.03 kcal/mol 3.2.2. Enzyme Inactivation Kinetics of enzyme inactivation for each enzyme was performed at pH 7 and tem- peratures of 40, 50, and 60 ◦ C under non-reactive conditions. The results obtained (see Supplementary Materials) were fitting to a one-step first-order kinetics of inactivation. However, stability under operation conditions may vary depending on the presence of modulators of enzyme stability, such as substrates and products of reactions [40,41,43,50]. The equation for one-step first–order kinetics of inactivation under modulation can be expressed as: de − = k D ·(1 − η )·e . (14) dt Catalysts 2021, 11, 1167 10 of 15 Temperature dependence of the inactivation parameters is described by an Arrhenius type equation:  EaKD  k D = k D0 ·exp . (15) R· T The experimental data of inactivation of each of the immobilized enzymes under non-reactive conditions were adjusted by linear regression, using the function fminsearch of MATLAB® , to obtain the values of the parameters of the Arrhenius equation, as shown in Table 2, and then used for the calculation of the inactivation constants (k D ) of each immobilized enzyme at different temperatures, using Equation (15). Table 2. Parameters of the Arrhenius equation for the determination of the inactivation rate (kD ) of β-galactosidase and glucose isomerase. Parameters β-gal GI EaKD (Kcal/mol) 73.46 34.83 k D0 (h−1 ) 1.64 × 1049 5.98 3.2.3. Mathematical Model for the One-Pot Production of Lactofructose Syrup in Sequential Batch Operation The proposed model considers that the liquid phase in the reactor is completely mixed so that lactose concentration is the same at any point inside the reactor. The model was built up from a material balance of substrates and products considering enzyme inactivation throughout reactor operation. Since in this case there are two reactions in series, the product of the first reaction (glucose) becomes the substrate of the second. The following equations describe the system: dLac = −v1 ·γ1 , (16) dt dGal = v1 ·γ1 , (17) dt dGlu = v1 ·γ1 − v2 ·γ2 , (18) dt dFru = v2 ·γ2 , (19) dt dγ1 = −k D1 ·(1 − η )·γ1 , (20) dt dγ2 = −k D2 ·γ2 . (21) dt The operation curve of the one-pot sequential batch reactor (substrate conversion versus time) is obtained by the simultaneous solving of Equations (16)–(21). To do so, the proposed model was implemented in MATLAB® , version R2019a and the equations were solved using ode23s solver. Simulation of each batch during sequential batch operation was performed until reaching 90% conversion of lactose into glucose and 45% conversion of glucose into fructose. The GI/β-gal activity ratio is: e2 R= . (22) e1 The enzyme concentration of each enzyme, can be determined from the mass balance as: M ·a e1 =  cat 1  , (23) Vr · 1 + Ra·2a1   Mcat e1 e2 = − · a2 . (24) Vr a1 Catalysts 2021, 11, 1167 11 of 15 3.2.4. Reactor Operation Conditions The number of batches that can be performed within one cycle of use of an immo- bilized enzyme will depend on the process operating conditions, since the two enzymes have different kinetic properties and a great difference in operational stability. To enable the selective replacement of each immobilized enzyme, simulation was carried out consid- ering a compartmentalized basket enzyme reactor, where the immobilized enzymes were contained in separate compartments in order to be manipulated independently (Figure 1). The simulation of reactor operation was carried out at different temperatures, and kinetic and stability parameters were expressed as explicit functions of temperature using the above Arrhenius type equations. Each batch was performed at 0.3 M lactose (10% w/w) and pH 7, until reaching 90% lactose conversion and a minimum of 45% glucose isomer- ization (90% of the equilibrium conversion). Since the operating criterion adopted for sequential batch operation was a constant conversion of both reactions at the end of each batch, and there was no addition of fresh immobilized enzymes, the time for each batch progressively increases as the enzymes were inactivated. 3.3. Metrics Used in Reactor Operations The following parameters were used for describing reactor operation: Lactose conversion: the mass fraction of lactose hydrolyzed in the reactor: Lac0 − Lac x Lac = . (25) Lac0 Productivity: the mass of fructose produced per unit reaction time, calculated at 90% lactose conversion Vr · Fru· MWF q= . (26) t Accumulated productivity: the total mass of fructose produced in the m batches that make up the cycle of use of the immobilized enzymes, divided by the accumulated time of the m batches, calculated at 90% lactose conversion: Vr · MWF ∑1m Frui qa = . (27) ∑1m ti Accumulated specific productivity: the total mass of fructose produced in the m batches that make up the cycle of use of the immobilized enzyme, divided by the accumu- lated time of the m batches and the mass of immobilized enzyme (β-gal or GI) calculated at 90% lactose conversion: Vr · MWF ∑1m Frui Qj = . (28) (∑1m ti )· M j 4. Conclusions This work presents the design of a strategy of catalysts replacement in a multienzyme one-pot system operating in sequential batch operation, with each enzyme immobilized separately according to their respective stabilities. This strategy is useful when the stabili- ties of the enzymes differ significantly, since each enzyme can be individually replaced once the criterion for replacement has been reached, thus enabling a better use of each enzyme activity. However, this is not feasible when the enzymes are co-immobilized, where the less stable enzyme will determine the criterion for biocatalyst replacement, while the more stable enzyme may still be quite active. Having a mathematical model to simulate the one-pot reactor operation allows estab- lishing the strategies for the replacement of each immobilized enzyme considering their individual stabilities, therefore establishing a proper operational schedule for increasing productivity and thus boosting the profitability of the process. Catalysts 2021, 11, 1167 12 of 15 This work shows that it is feasible and convenient to carry out the one-pot sequential batch operation with the enzymes immobilized separately when the stabilities of the enzymes are significantly different. We envision that this strategy could be applied to any multienzyme system operating in a single pot for an effective use and replacement of the biocatalyst with the concomitant benefits in the economics of the process. Supplementary Materials: The following are available online at https://www.mdpi.com/article/ 10.3390/catal11101167/s1: detailed description of the material and method regarding enzymes activity assays and immobilization; Figure S1: Immobilization kinetics of β-gal; Figure S2: Effect of temperature on the stability of β-gal; Tables S1 and S2: Inactivation parameters of β-gal; Figure S3: Effect of temperature on the stability of GI; Tables S3 and S4: Inactivation parameters of GI; Figure S4: Effect of the GI/β-gal activity ratio (R) on the productivity (q) at different reaction temperatures; Table S5: Summary of the results the simulation of the one-pot production of lactofructose syrup. Author Contributions: Conceptualization, L.W., O.R. and A.I.; methodology, V.A., D.C. and P.S.; software, V.A., D.C. and P.S.; validation, P.S.; formal analysis, L.W., P.S. and A.I.; investigation, V.A. and D.C.; writing—original draft preparation, P.S., L.W., O.R. and A.I.; writing—review and editing, L.W., O.R. and A.I.; visualization, V.A. and D.C.; supervision, L.W., O.R. and A.I.; project administration, L.W., O.R. and A.I.; funding acquisition, L.W. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by FONDECYT-Chile (Grant number 1190709). Pablo Silva acknowledges funding from PUCV for a doctoral fellowship. Daniela Cid and Vanessa Arancibia acknowledges funding from VRIEA-PUCV (project no. 039.418/19). Data Availability Statement: The data presented in this study are available in the present article and in Supplementary Materials. Acknowledgments: We thank Ramiro Martinez, from Novozymes A/S, Spain, for supplying com- mercial enzymes. Conflicts of Interest: The authors declare no conflict of interest. Nomenclature β-gal: β-galactosidase GI: glucose isomerase a1 : specific activity of β-gal (IU/g) a2 : specific activity of GI (IU/g) e1 : enzyme concentration of β-gal (IU/L) e2 : enzyme concentration of GI (IU/L) Ea : activation energy (Kcal/mol) Fru: fructose concentration (M) Frue : equilibrium concentration of fructose (M) Gal: galactose concentration (M) Glu: glucose concentration (M) Glu0 : initial concentration of glucose (M) Glue : equilibrium concentration of glucose (M) ∆H◦ : standard enthalpy change of dissociation of β-gal-lactose into β-gal and lactose (Kcal/mol) ∆H◦ I : standard enthalpy change of dissociation of β-gal-galactose into β-gal and galactose (Kcal/mol) kcat1 : catalytic rate constant of β-gal (mol/(h·IU)) kD1 : thermal decay constant of β-gal (h−1 ) kD2 : thermal decay constant of glucose isomerase (h−1 ) kD’ : thermal decay constant under operational conditions (h−1 ) Ke : equilibrium constant of GI KI : inhibition constant of β-gal by galactose (M) Km1 : Michaelis-Menten constant for β-gal (M) Km2 : apparent Michaelis-Menten constant of GI (M) Kmf : Michaelis-Menten constant for fructose (mol) Kmg : Michaelis-Menten constant for glucose (mol) Catalysts 2021, 11, 1167 13 of 15 Lac: lactose concentration (M) Lac0 : initial concentration of lactose (M) q: productivity (g/h) qa : accumulated productivity of fructose (g/h) Qj : accumulated specific productivity of j catalyst (j =1: β-gal, j =2: GI) (g·g−1 ·h−1 ) R: universal gas constant (J/(mol·K)) T: temperature (K or ◦ C) t: time (h) η: modulation factor m1 : batch numbers in a use cycle of β-gal (−) m2 : batch numbers in a use cycle of GI (−) M1 : catalyst mass of β-gal (g) M2 : catalyst mass of GI (g) v1 : reaction rate of β-gal (mol/(g·h)) v2 : reaction rate of GI (mol/(g·h)) Vr : reaction volume (mL) Vm2 : maximum apparent reaction rate of glucose isomerization (mol/(g·h)) Vmf : maximum reaction rate for fructose isomerization into glucose (mol/(g·h)) Vmg : maximum reaction rate for glucose isomerization into fructose (mol/(g·h)) xLac: lactose conversion γ1 : residual activity of β-gal γ2 : residual activity of GI MWF : fructose molecular weight (g/mol) References 1. 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