Odd–even effect for efficient bioreactions of chiral alcohols and boosted stability of the enzyme

We describe a holistic approach for achieving a nearly quantitative conversion for an enzymatic reaction while simultaneously increasing the long-term stability of the enzyme. The approach provided chemical control of bioreactions by utilizing newly synthesized tetrahydrothiophene-based ionic liquids (THT ILs). We showcased its power by using THT-ILs as additives at a low concentration (only 10 mmol L−1) in the alcohol dehydrogenase (ADH)-catalyzed synthesis of methylated 1-phenylethanol (Me-PE). We discovered an “odd–even” effect of the IL-cation chain length: Me-PE displayed beneficial interactions with THT ILs having odd-numbered chain lengths and deleterious interactions with those having even-numbered chain lengths. An intermolecular thermodynamic simulation of the bulk phase and critical micelle concentration investigations of the local surroundings of the THT-ILs proved the occurrence of these interactions, and these two methods confirmed the odd–even effect from different perspectives. Additionally, storing the ADH enzyme in pure THT IL at room temperature allowed for a boosted long-term stability of the enzyme (500 times greater than that in aqueous buffer) without the need for freezing.


SYNTHESES OF TETRAHYDROTHIOPHENE-ILS
The samples of the THT-ILs (1-alkyl-tetrahydrothiophene bis(trifluoromethanesulfonyl)imide, [C n THT][NTf 2 ] (n = 4 -8)) were prepared according to literature procedures. 1 The ILs were synthesized in two steps. The first step was the alkylation of tetrahydrothiophene, THT with the n-iodoalkane, C n H 2n+1 I to yield [C n THT]I. The [NTf 2 ]-ILs were then prepared by an anion exchange with Li[NTf 2 ] in an aqueous solution (Scheme S1). The anion purity of the THT-ILs was measured by ion chromatography. The purities are given in Table S1. Scheme S1. Synthesis of the tetrahydrothiophene-based ionic liquids. 99.6 a Sample were prepared by dissolving a defined mass of IL in a defined volume of eluent.
The UV-Vis spectra of the THT-ILs are shown in Figure S1. No absorption was detected for the wavelength used to track the ongoing ADH reaction ( ).

THERMODYNAMICS OF REACTION EQUILIBRIA
The general background on thermodynamic equilibria is based on the Gibbs free energy of a reacting system according ∆ to equation (1). The relationship between the free energy and the chemical potential in terms of a thermodynamic chemical equilibrium constant has been discussed in detail numerously before. Equation (2) links this relationship to the activity ℎ of the reactants and to , where and are the activity and the mole fraction-based equilibrium constants, respectively, is the mole fraction of reactant , the corresponding activity coefficient, and the stoichiometric factor of component taking part in the current E reaction. only depends on temperature. It has to be noted that the thermodynamic equilibrium constant as used in this work ℎ includes the activity of H + (equation (3)) due to the application of a Hepes buffer and thus a constant pH-value leading to a constant activity of H + .
As a benchmark for the prediction of the influence of the THT-ILs with ePC-SAFT, the conversion related to the substrate Me-ACP was used as described in equation (4).

EPC-SAFT MODELLING
To calculate the activity coefficients for modelling the THT-IL influence on conversion of the ADH reaction, and thus , the ePC-SAFT equation of state is used. The activity coefficients were determined according to equation (5) and are based on the standard state 'pure component': Both equations are based on the fugacity coefficient , which is calculated with equation (6), where Z is the compressibility factor and is the chemical potential.
The chemical potential, in turn, is calculated from the residual Helmholtz energy (equation (7)), which is a sum of four contributions. The first three contributions account for uncharged components; the hard-chain, dispersion and association terms.
Charged species additionally need the fourth term , which for ePC-SAFT 2 is based on the Debye-Hückel theory. In contrast to prior works on enzyme-catalyzed reactions, the term is varied and a concentration-dependent dielectric constant is incorporated according to equation (8). A detailed view on the new approach can be found in the literature. 3 = ℎ + + + =- To calculate the residual Helmholtz energy, ePC-SAFT requires up to five physically meaningful pure-component parameters for each component. These parameters are the number of segments , the segment-diameter , the dispersion-energy parameter between two segments , being the Boltzmann constant, and the association-energy parameter / / and the association-volume parameter for an associating component with N association sites. To consider mixtures for binary pairs and , combining rules from Berthelot and Lorentz are applied as shown in equations (9) and (10).
For the dispersion energy, is a binary interaction parameter correcting the energy between the pairs, giving a possibility to correlate the ePC-SAFT results to experimental data where necessary.

PARAMETER ESTIMATION FOR THT-ILS
For the parametrization of the THT-ILs, no association is assumed and the IL-ions are modelled individually. Thus, IL-ions are limited to three pure-component parameters. THT-ILs are a new kind of ILs and their IL-cations, in contrast to the [NTf 2 ] --anion, have not yet been parametrized. Due to the very low vapor pressure of ILs, only their pure liquid density at different temperatures is used for the fitting process. Minimizing the objective function (equation (11)) with a Levenberg-Marquardt algorithm, the pure-component parameters for [C 4 THT] + and [C 8 THT] + have been fitted. The pure-component parameters for the intermediate IL-cations [C n THT] + (n = 5, 6, 7) have then been linearly correlated, following the procedure already used in earlier publications. 4,5 The fitting was successful when the deviation to experimental data, also for the intermediate IL-cations, was minimal. The pure-component parameters for the IL-cations, as well as for the other reacting agents and solvents, are listed in Table S2.

PREDICTING THT-IL INFLUENCE ON REACTION EQUILIBRIUM
The effect of IL-additives on reaction equilibrium is predictively available through the thermodynamic equilibrium constant as described above. The predication is possible by minimizing the objective function described in equation (12) in an ℎ iterative process. In an iteration step i, the equilibrium constant is calculated from variation of the NADH concentration , and mass balance. Thereafter, ePC-SAFT is used to calculate . The steps are repeated until the criterion for the objective , function is met.

PURE-COMPONENT PARAMETERS FOR EPC-SAFT
Pure-component parameters for the THT-ILs have been fitted to liquid density data measured in this work (see Table S4). The approach used in this work is similar to prior work 4 It should be noted that these correlations are only valid until a maximum value of about = 200 g/mol as the ,dispersion energy must not approach infinity but a constant value for ILs with very high cation chain length.

SOLUTION PREPARATION
Solutions were prepared gravimetrically using the analytical scale XS205 DualRange (Mettler Toledo, uncertainty g).

-4
Millipore water with Hepes buffer (0.1 mmol/kg) was used as an aqueous basis for the ADH reaction, setting the pH-value to pH = 7 and periodically controlled via a pH-meter (Mettler Toledo, accuracy 10 -2 ). The substrates and the IL-additives, according to the required concentration under investigation (Table S5), were placed in 1.5 mL Eppendorf vials and mixed with the aqueous solution. The vials were then placed in a ThermoMixer (Eppendorf) at constant reaction conditions (1000 rpm and 298 K). Afterwards, the enzyme ADH was solved and the vial was left in the ThermoMixer for the reaction time.

REACTION-EQUILIBRIUM MEASUREMENTS
Reaction-equilibrium measurements for the ADH reaction with reactant Me-ACP was carried out by two different methods. First, a prepared solution was measured continuously in an Eppendorf Biospectrometer. Therefore, the stock solution was filled in a Cuvette SUPRASIL TYP 114-QS from Hellma Analystics. The enzyme was added, and the solution was carefully stirred (with 800 rpm) to ensure good mixing. Then, the cuvette was placed in the Biospectrometer (tempered to 298 K) and the extinction of NADH was measured at a constant wavelength of 340 nm. With ongoing reaction, the extinction of NADH reduces with the production of NAD + , thus giving an easily quantifiable approach. The other reactants and the THT-ILs experience no absorption at this wavelength. Second, duplicate measurements were performed in a ThermoMixer (Eppendorf) as described above. After the reaction equilibrium was reached, the equilibrium concentration of NADH was measured in the Biospectrometer. In total, the influence of THT-ILs on the ADH reaction was tested three times for every IL and concentration. An extinction over time plots for the reaction is exemplarily shown in Figure S2 for the neat reaction in buffer. All reactant concentrations in equilibrium are available through mass balances according to equations (16) to (18). All concentrations are measured in molarities [mol/L buffer].

VERIFYING REACTION EQUILIBRIA
To state the reach of real reaction equilibrium, two effects have to be discussed and validated. First, there is the possibility of a deactivated enzyme and second, a limitation of the substrate concentration. Both effects lead to a constant extinction level of NADH while the reaction is observed in the Biospectrometer, although the reaction equilibrium was not reached. A deactivation of the enzyme can be tested straight forward by adding new stock solution with solved, active enzyme. If the reaction equilibrium was reached, no further decrease in NADH extinction is observed, except for the extinction due to the addition of stock solution. For the second possibility, substrate should be added accordingly. Since NADH is a substrate itself, the NADH extinction initially increases but eventually reaches about the same value as before the substrate addition. Results for the ADH reactions for the neat reaction in aqueous buffer solution and with the THT-IL additives are shown in Table S6. Figure S2. Extinction E over time plot for the ADH reaction in aqueous buffer (neat) at 298 K and at  = 340 nm. Verification of equilibrium by addition of new substrate after 1800 s and subsequent reduction of the extinction to the value before substrate addition.

MEASURING THE CRITICAL MICELLE CONCENTRATION
For the investigation of the odd-even effect and the local surrounding of the THT-ILs, the concentration-dependent surface tensions (σ) of the THT-ILs were measured with a ring tensiometer in order to determine the respective CMCs. For this purpose, a stock solution of the respective THT-IL in water was prepared and a series of dilutions was performed.
Three measurements for each concentration and accordingly the mean values for the CMC was determined. The measurements were also repeated with the addition of the product Me-PE. The results for both systems are shown in Table S7. For the determination of the CMC, the data are plotted and the two value ranges are linearized. The concentrations of the critical micelle formation are given by the intersection. The CMC is obtained by delogarithmization. An exemplary application can be seen in Figure S3. The results are shown in Table S8.

ADH REACTION IN NEAT THT-ILS
The investigations described until this point address the effect of THT-ILs at rather low concentrations of about 10 mmol/L es per kg water. The question rises whether the reaction can be realized also in pure IL. Thus, the holistic approach in this article was extended to investigations of enzyme stability in the pure THT-ILs. The application of ILs to bioreactions has been successful for different enzymatic reactions and highly benefitted the conversion. However, the stability of the enzyme in presence of ILs at high concentration is usually a challenge, [8][9][10] which can be solved only by immobilization of the enzyme. 11 Accordingly, the influence of the pure THT-IL on the enzyme activity was investigated over a time span of 31 days ( Figure  S4).
Periodic sampling of the ADH solution was performed. Therefore, stock reactant solution was introduced to the reaction media and the reaction progress was monitored by UV-Vis detection of NADH. The results in Figure 4 prove that the reaction proceeds, but the kinetics is decreased compared to the reaction water. This is probably caused by transport limitation in the pure IL compared to water. In addition to the enhancement effect of [C 5 THT][NTf 2 ] on conversion, even after more than one month, the activity of the ADH was unaltered and the enzyme found to be stable. The difference in extinction peak heights is related to the different amount of reactants (Me-ACP and NADH) added to reaction medium at the specified times. For the activity analysis the reactants were added frankly as no quantification was necessary. For comparison, ADH in an aqueous buffer solution was found to be active only for 2 h at room temperature. In pure [C 5