Reaction Equilibrium of the Ï-Transamination of (S)-Phenylethylamine

Article pubs.acs.org/OPRD

Reaction Equilibrium of the ω‑Transamination of (S)‑Phenylethylamine: Experiments and ePC-SAFT Modeling Matthias Voges,†,§ Rohana Abu,‡,§,∥ Maria T. Gundersen,‡ Christoph Held,*,† John M. Woodley,‡ and Gabriele Sadowski† †

Laboratory of Thermodynamics, Department of Biochemical and Chemical Engineering, TU Dortmund, Emil-Figge-Strasse 70, 44227 Dortmund, Germany ‡ Department of Chemical and Biochemical Engineering, Technical University of Denmark, DK-2800, Kgs. Lyngby, Denmark S Supporting Information *

ABSTRACT: This work focuses on the thermodynamic equilibrium of the ω-transaminase-catalyzed reaction of (S)phenylethylamine with cyclohexanone to acetophenone and cyclohexylamine in aqueous solution. For this purpose, the equilibrium concentrations of the reaction were experimentally investigated under varying reaction conditions. It was observed that the temperature (30 and 37 °C), the pH (between pH 7 and pH 9), as well as the initial reactant concentrations (between 5 and 50 mmol·kg−1) influenced the equilibrium position of the reaction. The position of the reaction equilibrium was moderately shifted toward the product side by either decreasing temperature or decreasing pH. In contrast, the initial ratio of the reactants showed only a marginal influence on the equilibrium position. Further experiments showed that increasing the initial reactant concentrations significantly shifted the equilibrium position to the reactant side. In order to explain these effects, the activity coefficients of the reacting agents were calculated and the activity-based thermodynamic equilibrium constant Kth of the reaction was determined. For this purpose, the activity coefficients of the reacting agents were modeled at their respective experimental equilibrium concentrations using the equation of state electrolyte PC-SAFT (ePC-SAFT). The combination of the concentrations of the reacting agents at equilibrium and their respective activity coefficients provided the thermodynamically consistent equilibrium constant Kth. Unexpectedly, the experimental Km values deviated by a factor of up to four from the thermodynamic equilibrium constant Kth. The observed concentration dependency of the experimental Km values could be explained by the influence of concentration on activity coefficients. Further, these activity coefficients were found to be strongly temperature dependent, which is important for the determination of standard enthalpy of reactions, which in this work was found to be +7.7 ± 2.8 kJ·mol−1. Using the so-determined Kth and activity coefficients of the reacting agents (ePC-SAFT), the equilibrium concentrations of the reaction were predicted for varying initial reactant concentrations, which were found to be in good agreement with the experimental behavior. These results showed a non-negligible influence of the activity coefficients of the reacting agents on the equilibrium position and, thus, on the product yield. Experiments and ePC-SAFT predictions showed that the equilibrium position can only be described accurately by taking activity coefficients into account.

1. INTRODUCTION Biocatalysis is today established as a useful complement to synthetic methods for the production of many interesting chemical compounds.1 Many of these syntheses benefit from the excellent characteristics of enzyme-catalyzed reactions, such as high selectivity under mild reaction conditions, particularly for the synthesis of optically pure chiral pharmaceutical intermediates.2 The number of biocatalytic applications continues to grow in many industry sectors. This is mainly due to the development of protein engineering technologies3−5 that make new enzymes and pathways available. Despite this, the applicability of a surprisingly large number of potentially interesting enzymes is still limited to laboratory scale. One of the reasons for this is the fact that many interesting biologically mediated reactions are thermodynamically limited processes. In nature, such reactions may run in the reverse direction dependent upon the conditions, but from a synthetic perspective this may not be useful. Such reactions are therefore hampered by low reaction yields.6 Thus, thermodynamic assessment is one of the first steps evaluating enzymatic reactions.7 Remarkably, the area of equilibrium thermody© XXXX American Chemical Society

namics of biological systems has gained relatively little attention, and until now, surprisingly little thermodynamic information has been available in the scientific literature.8,9 Although there are a number of reports of thermodynamic properties (e.g., enthalpy changes upon reaction, equilibrium constants, and Gibbs free energies), unfortunately these data are limited and scattered across a range of conditions, such as temperature, pH, ionic strength, buffer, and cofactor types.10 This poses many challenges for the implementation and optimization of enzymatic reactions in process design.11 Such challenges are exacerbated by the fact that the terminology used to describe the thermodynamics of biological systems is not always consistent with that used to describe the thermodynamics of chemical systems.12 For example, the term “apparent” equilibrium constant has usually been reported for biological systems instead of the more usual activity-based equilibrium constant. The term apparent implies that the thermodynamic activity of a reacting agent is set to be equal to Received: March 3, 2017

A

DOI: 10.1021/acs.oprd.7b00078 Org. Process Res. Dev. XXXX, XXX, XXX−XXX

Organic Process Research & Development

Article

Figure 1. Cyclohexanone (CHO) amination with (S)-1-phenylethylamine (PEA) to cyclohexylamine (CHA) and acetophenone (ACP) catalyzed by the ω-transaminase (ω-TA) in the presence of the cofactor pyridoxal-5′-phosphate (P5P) at pH 7.

amino acid residues located in the substrate binding pocket.26 High enantioselectivity makes the enzyme-catalyzed reaction an attractive alternative to the chemically catalyzed route, which frequently suffers from poor enantioselectivity.27 However, a key challenge when running this reaction in the synthetically valuable direction (creating, rather than resolving, a chiral center) is the thermodynamically limited product yield at equilibrium, since the reaction equilibrium does not favor the product of the reaction.28 Most studies have, to some extent, successfully overcome the thermodynamic constraints in such reactions by the application of equilibrium shifting strategies such as use of an excess of a cosubstrate or coupling cascades.29 Remarkably, very little information on thermodynamics was quantified in these studies. In order to address this paucity of data, recently, we reported experimentally determined equilibrium constants for ω-transaminase reactions in order to better understand the dependence of the thermodynamics on the types of molecules used, and in particular the amine donor. Nonetheless, the effect of the activity coefficients of the reacting agents in aqueous solution was neglected,30,31 and this motivated us subsequently to consider the impact of this in the present work. Hence, the objective of this work was to determine the activity-based thermodynamic equilibrium constants for such transaminase reactions and to compare them with the apparent concentration-based equilibrium constants. In this work we have used the amination of cyclohexanone (CHO) with (S)-1phenylethylamine (PEA) to cyclohexylamine (CHA) and acetophenone (ACP) catalyzed by ω-TA as a model reaction for that purpose. The reaction scheme is illustrated in Figure 1. The synthetic direction toward PEA is economically more attractive (a chiral center is synthesized), while the thermodynamic equilibrium of the reaction favors the direction toward CHA and ACP. However, since this work focuses on the equilibrium, the direction of the reaction to reach equilibrium is freely selectable for experimental investigations. The direction of the reaction in this work is defined in Figure 1. At pH 7, the amines are present as protonated species and thus are represented as charged species in Figure 1.

the respective molal or molar concentration of a reacting agent at equilibrium.13 Indeed, concentration and thermodynamic activity are often assumed to be equivalent (and equal) due to the general use of dilute aqueous solutions for enzymecatalyzed reactions. 12 However, this is a very critical assumption, since it has been shown that the “apparent” equilibrium constant strongly depends upon reaction conditions such as pH, reaction media, and reactant concentrations.14−16 The difference between the apparent equilibrium constant and the thermodynamic equilibrium constant is expressed in the activity coefficients of the respective reacting agents. This property reflects deviations between real behavior and the ideal mixture, caused by molecular interactions between all components in a reaction mixture. Unfortunately, the large majority of the available equilibrium constants available in the literature are the apparent values. These apparent values (or sometimes Debye−Hückel corrected equilibrium constants) have frequently been used to describe metabolic pathways.17−19 In metabolic pathways, the concentrations of the reacting agents are usually very low, so in this case, the apparent equilibrium constants and the thermodynamic equilibrium constants may indeed be similar, justifying such an approach. However, in vitro reaction concentrations can be significantly higher. The problem is made worse by the fact that activities are difficult to measure experimentally due to the complex environment in biological systems (e.g., pH, ionic strength20). For all these reasons, the possibility to quantitatively predict activity coefficients of reacting agents is very attractive. Recently, the thermodynamic model ePC-SAFT21,22 was used for that purpose, with the intent of focusing on biologically mediated reactions.14−16,23,24 Although this is not the only approach possible, ePC-SAFT allows calculation of the activity coefficient by considering specific interactions in biological solutions caused by hydrogen bonding and charges. Interestingly, Hoffmann and co-workers found that the value of the activity coefficient significantly deviates from unity by 3- to 6fold even at dilute reactant concentrations (2−10 mmol·kg−1) in a feruloyl esterase-catalyzed reaction.14 A similar finding was also reported for the isomerization of glucose-6-phosphate at low reactant concentrations, 1−50 mmol·kg−1.24 Since the activity coefficients deviate from unity, this infers nonideal behavior in such systems even at low concentrations of reacting agents. Hence, neglecting nonideality in a biological reaction contributes to potentially erroneous assumptions in calculating equilibrium constants. In order to contribute to further progress in this research area, the asymmetric synthesis of optically pure chiral amines was studied in this work. The enzyme ω-transaminase (EC 2.6.1.18) was used, which is able to catalyze the transfer of an amine group between a donor molecule and an acceptor ketone with unprecedented enantioselectivity.25 The kinetics of the ωtransaminase (ω-TA) reaction strongly depend on pH, whereas the substrate selectivity is controlled by the pKa of the charged

2. THEORETICAL BACKGROUND Theoretically, the thermodynamic activity-based equilibrium constant (Kth) of a (bio)chemical reaction is the value that characterizes the thermodynamic equilibrium of a reversible reaction at a given temperature and pressure. The value of Kth for the transaminase reaction considered in this work (Figure 1) is defined as the ratio of the activities of products (CHA and ACP) over the activities of reactants (PEA and CHO) at equilibrium in the forward reaction: K th =

∏ aiν

i

i

B

=

aCHA+ ·aACP a PEA+ ·aCHO

(1) DOI: 10.1021/acs.oprd.7b00078 Org. Process Res. Dev. XXXX, XXX, XXX−XXX


Article

Table 1. Compounds Used in This Work with Their CAS Number, IUPAC Name, Supplier, Purity, and Purification Methoda

a

Compound

CAS No.

IUPAC name

Supplier

Purity, mass based

Purification

(S)-(−)-1-Phenylethylamine Acetophenone Cyclohexanone Cyclohexylamine Pyridoxal-5′-phosphate Trizmabase Sodium hydroxide Hydrogen chloride Dimethyl sulfoxide 4′-Bromoacetophenone Magnesium sulfate Ethyl acetate Acetic anhydride Triethylamine

2627-86-3 98-86-2 108-94-1 108-91-8 54-47-7 77-86-1 1310-73-2 7647-01-0 67-68-5 99-90-1 7487-88-9 141-78-6 108-24-7 121-44-8

1-Phenylethan-1-amine 1-Phenylethan-1-one Cyclohexanone Cyclohexanamine (4-Formyl-5-hydroxy-6-methylpyridin-3-yl)methyl phosphate 2-Amino-2-(hydroxymethyl)propane-1,3-diol Sodium hydroxide Hydrogen chloride Dimethyl sulfoxide 1-(4-bromophenyl)ethan-1-one Magnesium sulfate Ethyl acetate Acetic anhydride N,N-Diethylethanamine

M F S F S S S S S S S S S S

≥0.98 ≥0.990 ≥0.99 ≥0.99 ≥0.98 ≥0.999 ≥0.97 ≥0.37 ≥0.99 ≥0.98 ≥0.995 ≥0.998 ≥0.98 ≥0.99

None None None None None None None None None None None None None None

S = Sigma-Aldrich Chemie GmbH, M = Merck KGaA, F = Fluka Chemie GmbH.

In eq 1, ai is the activity and νi the stoichiometric coefficient of component i. The generic activity coefficient γi expresses the deviation of the behavior of component i between the mixture and the pure component; that is, the reference state “pure component” was used in this work. The activity ai of component i can also be written as the product of the concentration and the respective activity coefficient. In this work, following the usual thermodynamic convention, molality was used (mol·kg−1 water, denoted as mi) and the molalitybased activity coefficient (denoted as γmi). However, considering the stoichiometry of the ω-transamination in this work, Km can also be calculated straight from the mole fraction (denoted as xi) of the reacting agents and Kγ from the mole-fractionbased activity coefficients (denoted as γi) as shown in eqs 3 and 4. Hence, Kth can be expressed as the product of the molalitybased Km value (eq 3) and the activity-coefficient-based Kγ value (eq 4), as shown in eq 2.

K th = K m·K γ

Km =

Kγ =

EQ EQ mPEA + · mCHO

m m γPEA +· γ CHO

EQ Σ,EQ mCHA ·mACP EQ Σ,EQ mPEA ·mCHO

=

=

Λ PEA+(pH) =

ΛCHA+(pH) =

EQ EQ x CHA +· xACP EQ EQ x PEA +· xCHO

mPEA+ Σ mPEA

mCHA+ Σ mCHA

⎞−1 ⎛ 10−pK a,PEA 1 =⎜ + ⎟ ⎠ ⎝ 10−pH

⎞−1 ⎛ 10−pK a,CHA =⎜ + 1⎟ ⎠ ⎝ 10−pH

(6)

(7)

Replacing molalities of the ionic species of PEA and CHA present at pH 7 (PEA+ and CHA+) in eq 3 by eqs 6 and 7 and taking the stoichiometry and mole balances of the equimolal initial molalities into account yields the following expression for Km:

(3)

γCHA+·γACP γPEA+·γCHO

(5)

Since CHA and PEA can be present as different ionic species Σ,EQ according to the pH of the reaction media, mΣ,EQ CHA and mPEA represent the sum of the molalities of the single positively charged ionic species and the neutral ionic species of CHA and CHO, respectively. The fractions ΛPEA+ and ΛCHA+ of the single positively charged ionic species PEA and CHA were calculated using their pKa values as shown in eqs 6 and 7. Due to low solute concentrations in the reaction medium, it is reasonable to assume that the pKa values of PEA and CHA are constant and the density of the reaction mixture is the density of pure water, which does not change during reaction.

(2)

EQ EQ mCHA + · mACP

m m γCHA +· γ ACP

K ′m (pH) =

(4)

In general, Kth only depends on the temperature, and its dependency is described by the van’t Hoff equation as shown previously.15 However, both the Kth and Km values of the ω-TA reaction shown in Figure 1 do not depend on the pH value and are valid for the reaction with the ionic species of the reacting agents present at pH 7 (PEA+, CHO, CHA+, ACP). However, the reacting agents can be protonated/deprotonated and be present at different ionic species dependent upon the pH of the reaction media and the acid dissociation constant pKa of the reacting agents (pKa,PEA = 9.0,32 pKa,CHA= 10.633,34). Due to that and equilibrium constraints, the measured equilibrium molalities of the sum of all ionic species of PEA and CHA change as a function of pH. Thus, if a reacting agent is present as more than one ionic species at a given pH, the concentration of these ionic species is often summed up, which leads to the “apparent” biochemical equilibrium constant K′m, which is a function of the pH value (eq 5).

Km =

Σ,EQ 2 ΛCHA+·(mCHA ) t=0 Σ,EQ 2 Λ PEA+·(mCHO − mCHA )

(8)

In this work, the Km values for the ω-TA reaction were measured experimentally at varying reaction conditions (initial molalities of reacting agents and temperature) at pH 7, and K′m values were experimentally measured at varying pH values at 30 °C. In these reaction mixtures, either PEA and CHO or CHA and ACP were present before the reaction was started (see section 3). Furthermore, the activity coefficients of the reacting agents and the Kγ values were predicted using ePC-SAFT (see section 4) in order to obtain the thermodynamic constant Kth according to eq 2.

3. MATERIALS AND METHODS 3.1. Materials. In this study lyophilized ω-transaminase (ATA-81) was used, provided from c-LEcta GmbH (Leipzig, C



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phase was transferred to a GC vial. For derivatization, 15 μL of triethylamine and 10 μL of acetic anhydride were also added into the GC vial. The concentrations of reactants and products were analyzed by gas chromatography on a Clarus 500 (PerkinElmer) with a 25 m × 0.25 mm CP-Chirasil-Dex CB column (Agilent J&W GC scientific). Samples (2-μL) were injected with a 30:1 split ratio and a thermal gradient from 120 to 200 °C for 14 min. 1.4 mL/min helium was used as a carrier gas, and the FID detection was carried out at 250 °C. In order to obtain Km, the starting molalities and the ACP molality at equilibrium were used. The calibration range of ACP was between 0 and 25 mM.

Germany). Further chemicals used in this work are summarized in Table 1. 3.2. Reaction Equilibria. Reactions were carried out at a 3 mL scale in a 4 mL vial containing 1 mg/mL ATA-81, 1 mM pyridoxal-5′-phosphate, and 5% (v/v) dimethyl sulfoxide in 100 mM Tris-HCl buffer at pH 7. The reaction conditions (pH and temperature) were selected based on the typical reaction conditions of ω-transaminase reactions, which can be found in the literature.35,36 The reaction mixtures were continuously mixed in a thermoshaker (HCL, Bovenden, Germany) at constant temperature (30 and 37 °C) and agitation (450 rpm). All reactions were run in both directions (forward and reverse) until the equilibrium was reached at the same position on both sides. Reaction equilibrium was reached at 48 h (see also Figure 2). The same procedure was used for determining the Km

4. EPC-SAFT MODELING 4.1. Theory. In this work, the activity coefficients of the reactants and products of the reaction were determined by means of ePC-SAFT at the same conditions (temperature, pH, reaction medium) as used in the experiments. ePC-SAFT calculates the residual Helmholtz energy of a system Ares as the sum of different contributions, which are considered to be additive and independent from each other (eq 9). Depending on the molecule, different contributions can be added “modular” to model interactions and to predict thermodynamic nonidealities. First, the types of interactions (and, thus, the types of contributions in eq 9) for every component are defined. For example, only CHA and PEA need the “ion” contribution, and components that associate use the association term (all components in this work) and otherwise not.

Figure 2. Time-dependent experimentally determined molality of PEA in the forward reaction (circles) and the reverse reaction (squares) with the initial molality of 25 mmol·kg−1 of reactants (forward reaction: PEA + CHO; reverse reaction: CHA + ACP). The reactions were run at 30 °C in 100 mM Tris-HCl buffer at pH 7. Dashed lines are to guide eyes.

Ares = Ahc + Adisp + Aassoc + Aion

(9)

In general, a molecule is described as a chain composed of spheres, which can interact with other chain molecules by repulsive forces (Ahc), attractive van-der-Waals forces (Adisp), formation of hydrogen bonds (Aassoc), and Coulomb forces (Aion). Ahc, Adisp, and Aassoc were used as in the original PCSAFT model.37 Aion was used as described by Cameretti et al.38 A maximum of five parameters for each component i are required: the number of segments mseg i , the segment-diameter σi, the dispersion-energy parameter between two segments ui/ kB, and the association-energy parameter κAiBi/kB and the association-volume parameter κAiBi for an associating molecule with N association sites. Mixture properties based on the pure-component parameters (eqs 10 and 11) are described by means of combining rules as proposed by Lorentz and Berthelot and were applied for each pair of components i and j, where kij (eq 11) is a binary interaction parameter that corrects deviations from the

values as a function of pH (7, 8, and 9) and temperature (30 and 37 °C). The initial reactant molalities were varied between 5 and 50 mmol·kg−1. All reactions were carried out in duplicate for each reaction condition. 3.3. Analytics. After reaching equilibrium, aqueous NaOH (5 M, 100 μL) was added to a reaction mixture, thereby stopping the reaction. The reacting agents were extracted from their aqueous reaction media to organic solvent prior to gas chromatography (GC) analysis. For the extraction step, 400 μL of ethyl acetate as well as 4-bromo-acetophenone (150 mM; 20 μL) as internal standard were added. The aqueous phase was wasted, and magnesium sulfate was added to the organic phase in order to remove any water residues. The water-free organic

Table 2. ePC-SAFT Pure-Component Parameters for All Components Considered in This Work as Well as Their Binary Interaction Parameters with Water Component +a

PEA CHOa CHA+ a ACPd watere DMSOg

miseg

σi

ui/kB

Niassoc

εAiBi/kB

κAiBi

4.1687 3.0169 3.2263 3.3911 1.2047 2.9223

3.4963 3.6445 3.6466 3.6583

275.94 308.54 279.69 322.00 353.94 355.69

1:1 1:1 1:1 1:1 1:1 1:1

559.86 0 516.11 0 2425.7 0

0.0056 0.0451 0.0050 0.0451 0.0451 0.0451

f

3.2778

kij (with water) a,b a,c

0.0330d −0.065h

This work. bkij = 0.000257 × T [K] − 0.096380. ckij = 0.000505 × T [K] − 0.22353241. dReference 16. eReference 39. fσwater = 2.7927 + 10.11 exp(−0.01775 × T [K]) − 1.417 exp(−0.01146 × T [K]). gReference 40. hReference 41. “+” denotes positively charge; that is, the component was assigned with charge qi = +1 for ePC-SAFT modeling. a

D



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Table 3. Experimental Data and Validation of the ePC-SAFT Parameters Fitted in This Work Pure component

a

Aqueous binary mixture

Component

exp. data

ARDa [%]

T range [K]

exp. data

ARDa [%]

T range [K]

PEA CHO CHA

ρ0, p047−49 ρ0, p0LV50 ρ0, p0LV50

0.01; 0.6 1.7; 3.9 0.8; 1.7

303−460 272−592 256−586

LLE51 γ∞43

0.9 3.1

293−361 298−373

46

NP

ARD = 100 × 1/NP ∑k = 1 (1 − ykpred /ykexp )

noncharged species of CHA in aqueous solution since Bernauer et al.43 corrected the experimental data by taking into account the degree of protonation of CHA in the aqueous solution. The resulting pure-component parameters, the kij with water, as well as the ePC-SAFT parameters for water, ACP, and DMSO, are listed in Table 2. Using these parameters yields average relative deviations (ARD) between ePC-SAFT modeling and experimental data in a typical range of values compared to similar components.44,45 These ARD values are summarized in Table 3. Note that none of the parameters (listed in Table 2) were fitted to experimental reaction data. However, preliminary modeling results showed that the experimental results could be described more quantitatively using a weak dispersion interaction between ACP and CHA. Thus, dispersion interaction between ACP and CHA was not considered for ePC-SAFT modeling. 4.3. Prediction of Kpred and K′pred Values. Using the m m pure-component and binary ePC-SAFT parameters as listed in Table 2, Km values at pH 7 and 30 °C were calculated from predicted equilibrium molalities of the reacting agents for varying initial reactant molalities. First, the thermodynamic equilibrium constant Kth that only depends on temperature was calculated according to eq 2 by means of one experimental Km value and the corresponding ePC-SAFT predicted Kγ value. With the knowledge of Kth, the OF(λ) (eq 14) was minimized in order to determine the extent of reaction at equilibrium λ.

geometric mean of the pure-component dispersion-energy parameters. σij = 0.5(σi + σj)

(10)

0.5

uij = (uiuj) (1 − kij)

(11)

Based on these parameters, ePC-SAFT determines the fugacity coefficient φi of component i, which can be used to determine generic activity coefficients according to eq 12 for the reactants and products. γi =

φi(xi) φ0i(xi = 1)

(12)

φi is the fugacity coefficient of component i in the mixture, and φ0i is the fugacity coefficient of pure component i. The mole-fraction-based activity coefficient γi can be converted into molality-based activity coefficients γmi by the relation xiγi = miγmi. The so-determined activity coefficients can then be used in eq 4 in order to obtain Kγ. 4.2. Parameter Estimation. The pure-component ePCSAFT parameters of ACP,16 of water,39 and of DMSO40 as well as the binary interaction parameters (kij) between water and ACP16 and between water and DMSO41 are available from the scientific literature. These are listed in Table 2. In the present study, the ePC-SAFT parameters of CHO, CHA, and PEA were fitted to experimental density data and vapor-pressure data of pure components. For that purpose, the objective function OF (eq 13) was minimized using a Levenberg− Marquardt algorithm: NP(p0LV ) i

OF =

∑ k=i

⎛ pLV,pred ⎞ i ⎟ + 1 − ⎜⎜ 0LV,exp ⎟ p ⎝ 0i ⎠k

NP(ρ0i )

∑ m=i

OF(λ) = 1 −

⎛ ρ pred ⎞ 1 − ⎜⎜ 0iexp ⎟⎟ ⎝ ρ0i ⎠m

= min(< 10−6) (14)

At given Kth (determined in section 5.2, see Figure 3), eq 14 requires the activity coefficients of the reacting agents in order to predict Kγ(λ) values, which are accessible by ePC-SAFT.

(13)

= min

K th pred K m (λ ) · K γ (λ )

LV,exp

The experimental vapor-pressure data p0 and density data ρ0exp were taken from the literature (for references, see Table 3). CHA and PEA are present as protonated species in aqueous solutions at pH 7. This was accounted for by using the PC-SAFT parameters listed in Table 2 (determined with eq 13) and additionally assigning one single positive charge to CHA and PEA. The additional proton was considered in the molecular weight of CHA and PEA for modeling respectively. This procedure was taken from the literature.42 Even in their charged state, dispersion and association interactions were considered. The relative dielectric constant required in the expression for Aion was set to the value of pure water in this work (76.6 at 30 °C and 74.2 at 37 °C). The kij value between water and CHO was fitted to experimental LLE data, and the kij value between water and CHA was fitted to experimental activity coefficients at infinite dilution. The resulting kij values are given in Table 2. It has to be noted that the activitycoefficient data of CHA from the literature corresponds to the

Figure 3. Experimental Km values (gray squares), the corresponding ePC-SAFT predicted Kγ values (white triangles), and the resulting Kth values (black diamonds) versus the initial reactant molality of CHO (and PEA equimolal) at 30 °C and pH 7. Activity coefficients obtained using the ePC-SAFT parameters given in Table 2. E



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Table 4. Km Values of the ω-TA Reaction at Different Initial Equimolal Molalities and at Different Ratios of Initial Molalities in 100 mM Tris-HCl at pH 7a

a

No.

T [°C]

1 2 3 4 5

30 30 30 30 37

6 7

30 30

−1 mt=0 CHO [mmol·kg ]

5.053 9.987 25.000 50.553 9.979

± ± ± ± ±

0.172 0.225 0.340 0.695 0.181

0 0

−1 mt=0 PEA [mmol·kg ]

4.956 10.014 25.019 49.489 10.009

± ± ± ± ±

−1 mt=0 CHA [mmol·kg ]

0.511 0.294 0.463 0.929 0.015

0 0 0 0 0

−1 mEQ ACP [mmol·kg ]

0 0 0 0 0

10.214 ± 0.288 50.568 ± 0.963

0 0

−1 mt=0 ACP [mmol·kg ]

4.816 9.593 23.828 47.345 9.574

49.514 ± 0.294 10.474 ± 0.181

± ± ± ± ±

0.012 0.016 0.076 0.205 0.011

48.267 ± 0.028 9.201 ± 0.009

Km* [−] 699 554 406 325 520

± ± ± ± ±

111 10 65 52 25

278 ± 24 279 ± 9

A complete table with all equilibrium molalities is shown in the Supporting Information. Asterisk indicates calculated according to eq 3.

Table 5. ePC-SAFT Predicted Mole-Fraction Activity Coefficients of the Reacting Agents at Equilibrium and Corresponding Kγ Values, Experimental Km Values, and Resulting Kth Values of the Same Reaction Numbers as in Table 4

a

No.

T [°C]

γCHO [−]

γPEA [−]

γCHA [−]

γACP [−]

Kγ [−]

1 2 3 4 5

30 30 30 30 37

97.9 97.2 95.2 92.0 96.1

7018.9 6794.8 6318.8 5744.9 5583.4

46.1 45.8 46.0 47.4 52.9

3505.7 3536.7 3629.1 3783.7 2843.8

0.235 0.245 0.277 0.340 0.280

Km [−] 699 554 406 325 520

± ± ± ± ±

108 10 15 52 25

Kth [−] 164.55 136.13 112.90 110.70 145.60

± ± ± ± ±

25.42 2.45a 4.16 17.66 7.00a

These values for Kth at 30 and 37 °C were used in the subsequent sections.

reaction at 30 °C and pH 7. At initial equimolal concentrations (25 mmol·kg−1) of CHO and PEA in the forward direction, the same equilibrium position was reached as for the reverse direction of the reaction (initial feed of CHA and ACP). Similar observations were made using different initial molalities of reactants (5, 10, and 50 mmol·kg−1) as presented in Table 4. The values of Km as well as the extent of reaction were calculated from the molality of reactants and products at equilibrium mEQ. Table 4 shows that the Km value decreased with an increase in initial reactant molality. This observation indicates that the Km value calculated from the measured molalities at equilibrium is not a constant but rather depends on the composition of the reaction media (e.g., molalities of reactants). In turn, this means Kγ differs from unity, since Kth is a constant for a constant temperature. This is caused by the thermodynamic nonideality of the reaction media, meaning the activity coefficients of the reacting agents differ from unity. In addition, the temperature dependence of Km was investigated at pH 7 and is also shown in Table 4. The Km value decreased with increasing temperature. The temperature dependency on the reaction equilibrium is discussed in section 5.2.2. In addition to the investigation at equimolal initial reactant molalities, the influence of the ratio of the initial reactant molalities on Km was studied. For that purpose, ACP and CHA were present when the reaction was initialized while mt=0 PEA and mt=0 CHO were zero. The Km values at pH 7 and 30 °C at a ratio of initial molalities of 5:1 and 1:5 (CHA:ACP) are shown in Table 4. It can be seen that the Km value does not depend on the ratio of initial molalities. 5.2. ePC-SAFT Predictions. 5.2.1. Prediction of Kγ Values and Determination of Kth. The activity coefficients of the reacting agents were predicted using ePC-SAFT at equilibrium molalities taken from the experimental results at 30 and 37 °C at pH 7. This allowed determination of Kγ values according to eq 4, and combined with the experimental Km value finally yields the thermodynamic equilibrium constant Kth. Figure 3 shows the experimental Km values, the corresponding Kγ values, and the resulting Kth (=Km·Kγ) values for the different initial

According to the stoichiometry of the reaction, the molalities of reactants and products were expressed as a function of the extent of reaction λ as shown in eqs 15−18. t=0 EQ mPEA +(λ) = m PEA+ − λ

(15)

EQ t=0 mCHO (λ) = mCHO −λ

(16)

EQ t=0 mACP (λ) = mACP +λ

(17)

t=0 EQ mCHA +(λ) = mCHA+ + λ

mt=0 PEA+,

mt=0 CHO,

(18)

mt=0 CHA+

mt=0 ACP,

and correspond to the initial molalities of the reacting agents. The molalities at equilibrium EQ EQ EQ pred mEQ PEA+, mCHO, mACP, and mCHA+ were used to calculate Km (λ) values according to eq 3. The pH dependency of K′m was predicted by calculating mΣ,EQ CHA at equilibrium using one Km value at pH 7 and 30 °C, eqs 6−8 and the objective function (OF, eq 19) for a given pH: Σ,EQ,pred Σ,EQ,pred OF(mCHA ) = |K m(pH7) − K mpred(mCHA )|

= min(< 10−6)

(19)

mΣ,EQ,pred CHA

Finally, and the initial equimolal molalities of CHO and PEA were used to calculate K′pred m (eq 20). pred K ′m (pH) =

Σ,EQ,pred 2 (mCHA ) t=0 (mCHO

Σ,EQ,pred 2 − mCHA )

(20)

5. RESULTS AND DISCUSSION 5.1. Experimental Km Values at pH 7. The Km values of the ω-AT reaction at pH 7 were calculated based on eq 3 from the experimentally measured equilibrium molalities of the reacting agents. In order to be sure the measured molalities were equilibrium molalities, time-dependent concentrations were analyzed. Figure 2 illustrates that equilibrium was reached after 48 h of reaction. In the experiments, the reactants were allowed to reach equilibrium from both directions of the F



Article

equimolal molalities at pH 7 and 30 °C. However, for the investigations and results in all subsequent sections, one Kth was used. This Kth of the reaction was determined from one experimental Km at initial equimolal reactant molalities of 10 mmol·kg−1 at 30 °C and the corresponding ePC-SAFTpredicted Kγ values (No. 2 in Table 5). This data point was chosen for the determination of Kth due to the lowest experimental uncertainty in Km. The experimental Km value was found to be 554 ± 10, Kγ was found to be 0.245, resulting in a value for Kth of 136.1 ± 2.4. This value was used in all subsequent sections for 30 °C. First, it becomes obvious that the Kth and Km values of the ωTA reaction differ by a factor of up to four at the conditions under investigation. That is, the use of Km values instead of the use of the thermodynamic constant Kth will cause an incorrect characterization of the equilibrium and also of other standard data that can be derived from these values (e.g., standard enthalpy of reaction or standard Gibbs energy of reaction). As observed already in Table 4 and mentioned in section 5.1, the experimental Km values are decreasing with increasing reactant molalities. Figure 3 illustrates that this decrease is caused by increasing Kγ values with increasing reactant molality. Thus, the experimental behavior observed from Table 4 is correctly predicted qualitatively by ePC-SAFT. This further shows that Km and Kγ values are strongly concentration dependent. It can be seen from Figure 3 that Kγ doubles by changing the initial equimolal molality of CHO and PEA from 5 to 50 mmol·kg−1, which can still be considered low concentrations. Furthermore, the Kth values (calculated as the product of the predicted Kγ values and the measured Km values) are almost constant within their experimental uncertainties. This is consistent with the definition of the thermodynamic equilibrium constant Kth that solely depends on temperature. In addition, these results validate the applicability of the ePCSAFT parameters estimated in section 4.2. The PC-SAFT predicted activity coefficients of the reacting agents at equilibrium for the corresponding Km values from Table 4 are shown in Table 5. An investigation of the activity coefficients in Table 5 allows an analysis of the reason behind the concentration dependence of the experimentally observed Km values. It can be observed that upon increasing concentration of all reacting agents for equimolal initial molalities at 30 °C (Nos. 1−4 in Table 5) the activity coefficients of ACP and CHA increase while the activity coefficients of PEA and CHO decrease. This causes the increase of Kγ with increasing concentration (as illustrated in Figure 3). As a consequence, the experimentally observed Km values have to decrease in order to fulfill the criterion of a constant value for Kth. This is in agreement with the experimentally determined Km data. 5.2.2. Influence of Temperature on Kth. The Kth of the reaction was determined from the experimental Km at initial equimolal reactant molalities of 10 mmol·kg−1 at 30 °C and of 10 mmol·kg−1 at 37 °C (Nos. 2 and 5 in Table 5) and the corresponding ePC-SAFT predicted Kγ values listed in Table 5. At 30 °C the experimental Km value was found to be 554 ± 10, and Kγ was found to be 0.245, resulting in a value for Kth of 136.1 ± 2.4. Accordingly, Kth at 37 °C was found to be 146 ± 7. These Kth values allow determination of the standard enthalpy of reaction ΔRh°. For this purpose, the activity coefficients of the reacting agents have not been assumed to be temperature independent. Considering line Nos. 2 and 5 in Table 5, it becomes obvious that the activity coefficients predicted with

ePC-SAFT are strongly temperature dependent. This is important since the concentrations of the reacting agents in line Nos. 2 and 5 in Table 5 are very similar; thus, the difference of the activity coefficients is attributed almost entirely to temperature. The standard enthalpy of reaction ΔRh° can then be obtained from the slope of the dependence of ln(Kth) on the reciprocal temperature, as shown in Figure 4, and by assuming that ΔRh° is independent of temperature. For the ω-TA reaction, ΔRh° was found to be +7.7 ± 2.8 kJ·mol−1, meaning the reaction is endothermic.

Figure 4. ln(Kth) versus the reciprocal temperature of the ω-TA reaction. Symbols: ln(Kth) of this work; solid line: van’t Hoff equation.

5.2.3. Prediction of Km Values at 30 °C and pH 7. In this section ePC-SAFT is used as a tool to predict the equilibrium molalities of the ω-TA reaction and, thus, the Km values (eq 3) of the reaction at experimental conditions. With the knowledge of Kth, the Km values at pH 7 and 30 °C were predicted (as described in section 4.3) at different equimolal initial molalities and compared to the experimental Km values from Table 4. The result of such a prediction is illustrated in Figure 5. It can be seen that both experimental Km and predicted Kpred m values decrease with increasing initial equimolal molalities of the reactants CHO and PEA. The dependency of the experimental Km mean values on the initial molalities shown

Figure 5. Km values versus initial molality of CHO at different initial equimolal molalities of CHO and PEA in 100 mM Tris-HCl buffer at pH 7 and 30 °C. Experimental Km values are represented by squares, and ePC-SAFT predicted Kpred m values are represented by the line. ePCSAFT calculations were performed with the parameters in Table 2. G



Article

Table 6. Experimental K′m Values at pH 7, 8, and 9 with 10 mmol·kg−1 Initial Reactant Molalities in 100 mM Tris-HCl at 30 °C pH [−]

−1 mt=0 PEA [mmol·kg ]

−1 mt=0 CHO [mmol·kg ]

−1 mt=0 CHA [mmol·kg ]

−1 mt=0 ACP [mmol·kg ]

−1 mEQ ACP [mmol·kg ]

K′m [−]

7 8 9

9.987 ± 0.225 9.984 ± 0.212 9.990 ± 0.669

10.014 ± 0.294 10.012 ± 0.057 10.020 ± 0.136

0 0 0

0 0 0

9.593 ± 0.016 9.579 ± 0.019 9.485 ± 0.064

554 ± 10 523 ± 50 332 ± 89

the density of the reaction mixture was the density of pure water and did not change during reaction. The pH dependency of K′m was predicted by calculating mΣ,EQ CHA at equilibrium as described in section 4.3. In Figure 6 the calculated K′pred m values are compared to the experimental K′m values determined from the experimental molalities at different pH.

in Figure 5 is almost equivalent to an exponential function (exponential function not shown). However, the exponential relation between Km and initial equimolal molalities is solely valid in the molality range under investigation for equimolal molalities at pH 7 and 30 °C. Therefore, the extrapolation by means of an exponential relation of Km to initial CHO molalities smaller than 5 mmol·kg−1 would lead to extreme high and questionable Km values. In addition, the ratio of the initial molalities can also influence Km values15,16 in a way that cannot be described by the exponential relation between Km and initial molalities that was measured for equimolal initial molalities. For the prediction of Km values for initial molalities of CHO and PEA that are not in the molality range under investigation, ePC-SAFT can be used. Figure 5 illustrates that the predicted Kpred m values are in good agreement with the experimental Km values, and ePC-SAFT allows predicting the influence of initial molalities almost quantitatively, considering that the used ePCSAFT parameters were not fitted to the Km values. In turn, as already shown in Figure 3, this means that Kγ values increase with increasing initial equimolal molalities of reactants. Thus, the influence of reacting-agent molalities on Kγ (and therewith also on Km) must not be neglected if the equilibrium position is predicted. In addition, these results validate the estimated ePCSAFT parameters in section 4.2. Interestingly, in a recent study of the alanine aminotransferase reaction using the same class of enzyme, the influence of activity coefficient on the Km values, modeled by ePC-SAFT, was low for equimolal initial reactant molalities up to 100 mmol·kg−1 compared to the reaction of this work. This is probably caused due to the similar structure of reactants and products in the alanine aminotransferase (EC 2.6.1.2) reaction15 compared to the structure of reactants and products of the reaction of this work. From the experimental Km values (Table 4), it could be seen that Km does not depend on the ratio of initial molalities. This observation was also made by the ePC-SAFT predicted Kpred m values (data not shown). Summing up, the Km values of the ωTA reaction do not strongly depend on the ratio of initial molalities of the reacting agents in comparison to the results of the alanine aminotransferase reaction in a previous work.15 In turn, this means that Kγ values do also not strongly depend on the ratio of the initial molalities of the reacting agents in the range under investigation. 5.3. Influence of the pH Value on K′m Values. To investigate the effect of pH on the equilibrium position, experiments were run at different pH values (7, 8, and 9) at an initial reactant concentration of 10 mmol·kg−1 and 30 °C. The experimental K′m of the ω-TA reaction was found to be pHdependent, where K′m decreased with an increase in pH (Table 6). K′m values were also predicted as a function of pH, based on the experimental Km value at pH 7 and 30 °C (554; see Table 4), the pKa values of the reacting agents, and the initial molalities according to eqs 5−8 and eq 19. Due to low solute concentrations in the reaction medium, it was reasonable to assume that the pKa values of PEA and CHA were constant and

Figure 6. K′m values of the reaction at 30 °C with initial molalities of PEA and CHO of 10 mmol·kg−1 as a function of pH. Solid line: values (see section 4.3); symbols: experimental K′m predicted K′pred m values.

It can be observed that experimentally obtained K′m and predicted K′pred m values are in very good agreement for the pH range under investigation. K′m and K′pred both decrease with m increasing pH, meaning that the yield is reduced for pH values higher than pH 7.

6. CONCLUSION An experimental equilibrium study on the ω-TA reaction from PEA and CHO to ACP and CHA was carried out to investigate influencing factors on the position of the reaction equilibrium and on the maximum product yield, and understand the role of the activity coefficients of the reacting agents. The position of the reaction equilibrium was shifted toward the product side by decreasing temperature, decreasing reacting agent concentrations, and decreasing pH. In contrast, the initial ratio of the reactants showed only a marginal influence on the equilibrium position. In addition, the activity coefficients of the reacting agents were predicted by means of ePC-SAFT. The ePC-SAFT modeling results show that the activity coefficients and, thus, Kγ values deviate from unity, meaning a strong nonideal behavior of the reacting agents in the reaction medium. In contrast, the activity-based equilibrium constant Kth calculated from the experimental Km values and the modeled Kγ values had constant values for the reaction conditions under investigation, which is consistent with the definition of a concentration-independent Kth. Kth was found to be 136.1 ± 2.4 at 30 °C. For the reaction under investigation, the experimental Km values deviated by a factor of up to 4 from the thermodynamic equilibrium constant Kth. The observed concentration dependH



Article

Niassoc piLV pKa R T ui/kB xi y

ency of the experimental Km values could be explained by the influence of the concentrations of all reacting agents on the activity coefficients of the aromatic compounds (ACP and PEA). Further, these activity coefficients were found to be strongly temperature dependent, which is important for the determination of standard enthalpy of reactions, which in this work was found to be +7.7 ± 2.8 kJ·mol−1. Comparing experimental and modeled data, it can be concluded that equilibrium reactions can be described more accurately by taking the activity coefficients of the reacting agents into account. Based on this, more reliable analysis of the thermodynamic feasibility of a reaction and of maximum product yield are possible.

■

Greek Characters

εAiBi/kB γi κAiBi ρ σi φi λ νi Σ Λ

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.oprd.7b00078. Experimental molalities and the predicted activity coefficients of all reacting agents at equilibrium (PDF)

■

0 property of pure component i,j component indices ij binary mixture of components i and j

AUTHOR INFORMATION

*E-mail: [email protected].

Superscript

ORCID

∞ ′ t=0 assoc disp EQ exp hc mod pred res

Christoph Held: 0000-0003-1074-177X Gabriele Sadowski: 0000-0002-5038-9152 Present Address ∥

(R.A.) Faculty of Chemical & Natural Resources Engineering, Universiti Malaysia Pahang, 26300 Kuantan, Malaysia. Author Contributions §

M.V. and R.A. contributed equally.

Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the German Science Foundation (DFG) HE 7165/2-1as well as by the Cluster of Excellence RESOLV (EXC 1069) funded by the Deutsche Forschungsgemeinschaft (DFG). R.A. acknowledges the Malaysian Ministry of Education and Universiti Malaysia Pahang for financial support of part of this work.

ACP CHA CHO ARD EoS ePC-SAFT GC LLE OF P5P PEA SAFT TA

Latin Characters

Km Kγ kB kij M mi miseg NP

infinite dilution apparent value at experimental conditions at initial condition association dispersion at reaction equilibrium experimental hard chain modeled ePC-SAFT predicted residual

Abbreviations

NOMENCLATURE

A ai ΔRg° ΔRh° Kth

association-energy parameter of component i [K] activity coefficient of component i [−] association-volume parameter of component i [−] mass density [kg/m3] segment diameter of component i [Å] fugacity coefficient of component i [−] extent of reaction [mol·kg−1] stoichiometric coefficient of reacting agent i [−] sum of all ionic species of one reacting agent [−] fraction of one ionic species of one reacting agent [−]

Subscript

Corresponding Author

■

number of association sites [−] vapor pressure of component i [kPa] negative decimal logarithm of acid dissociation constant ideal gas constant [J/(mol·K)] temperature [K]/[°C] dispersion-energy parameter of component i [K] mole fraction of component i [−] measured value [−]

Helmholtz energy [J·mol−1] activity of component i [−] standard Gibbs energy of reaction [kJ·mol−1] standard enthalpy of reaction [kJ·mol−1] activity-based (thermodynamic) equilibrium constant [−] molality-based equilibrium constant [−] activity-coefficient ratio [−] Boltzmann constant [J·K−1] binary interaction parameter between components i and j [−] molecular weight [g·mol−1] molality of component i (mole component i per kg solvent) [mol·kg−1] segment number of component i [−] number of data points

■

acetophenone cyclohexylamine cyclohexanone average relative deviation equation of state electrolyte Perturbed-Chain Statistical Associating Fluid Theory gas chromatography liquid−liquid equilibrium objective function pyridoxal-5′-phosphate (S)-1-phenylethylamine Statistical Associating Fluid Theory transaminase

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