Combined co-solvent and pressure effect on kinetics of a peptide hydrolysis: an activity-based approach

Michael Knierbein a, Anton Wangler a, Trung Quan Luong b, Roland Winter b, Christoph Held *a and Gabriele Sadowski a
aLaboratory of Thermodynamics, TU Dortmund University, Emil-Figge-Str. 70, 44227 Dortmund, Germany. E-mail:
bPhysical Chemistry I, TU Dortmund University, Otto-Hahn-Str. 4a, 44227 Dortmund, Germany

Received 9th July 2019 , Accepted 26th September 2019

First published on 1st October 2019

The application of co-solvents and high pressure has been reported to be an efficient means to tune the kinetics of enzyme-catalyzed reactions. Co-solvents and pressure can lead to increased reaction rates without sacrificing enzyme stability, while temperature and pH operation windows are generally very narrow. Quantitative prediction of co-solvent and pressure effects on enzymatic reactions has not been successfully addressed in the literature. Herein, we are introducing a thermodynamic approach that is based on molecular interactions in the form of activity coefficients of substrate and of enzyme in the multi-component solution. This allowed us to quantitatively predict the combined effect of co-solvent and pressure on the kinetic constants, i.e. the Michaelis constant KM and the catalytic constant kcat, of an α-CT-catalyzed peptide hydrolysis reaction. The reaction was studied in the presence of different types of co-solvents and at pressures up to 2 kbar, and quantitative predictions could be obtained for KM, kcat, and finally even primary Michaelis–Menten plots using activity coefficients provided by the thermodynamic model PC-SAFT.


The demand for biocatalytic processes is rising within the chemical industry as they often present meaningful alternatives to chemically catalysed routes.1–3 Biocatalysis is already established for the production of active pharmaceutical ingredients (APIs),4 functional food5 and in the cosmetic, paper and textile industries.6,7 Enzyme-catalysed reactions are highly selective, allow catalysis under mild reaction conditions and enable the production of enantiopure products.8 Additionally, enzyme catalysis allows detoxifying hazardous reactions that use concentrated salts or acids or toxic solvents.9 However, the process window of enzyme-catalysed reactions is often limited as the influence of temperature, pressure, pH and the concentration and kind of solvent is often unknown or lead to unstable conditions,10,11 or low reaction rates.12 A conventional method to overcome these limitations without the need to increase the enzyme concentration is the addition of co-solvents13–17 and the application of high pressure18–20 to stabilize the enzyme and to increase reaction rates.21,22 Several approaches to quantify and explain the effects of pressure and co-solvents on enzyme-catalysed reactions are proposed in literature. In such works, the effects of co-solvents and pressure on enzyme kinetics are investigated experimentally and quantified empirically, only.23–26 To yield further insights into the origin behind the effects observed and to allow predicting them requires physical models. An already established approach is the use of molecular dynamics simulations to study the behaviour of solvent, substrate and enzyme on a molecular level. Especially the interaction between (co-)solvent and the amino acids of the enzyme's active site was studied in the literature.27–29 Gopal et al.30 investigated solvent/enzyme and additionally solvent/substrate interactions separately. Their results showed that enzyme-independent interactions between the substrate, solvent and co-solvent were the key elements to quantify co-solvent influences on the Michaelis constant KM of various reactions. This approach was further successfully used by other research groups.30–35 In a previous work from our group, an activity-based approach was applied to successfully predict co-solvent influences on the reaction equilibrium and the KM of the SPNA (N-succinyl-L-phenylalanine-p-nitroanilide) hydrolysis at ambient pressure.31 The ability to quantify co-solvent influences on the overall reaction is an urgent need.21,22 Besides Michaelis constants, this requires a non-empirical treatment for the catalytic constant kcat. However, such a treatment towards the prediction of pressure on the Michaelis constant as well as the influences of co-solvents and pressure on kcat is still missing.

This research gap is addressed in this work by presenting a thermodynamic approach to predict the combined influence of pressure and of co-solvents on the reaction kinetics of SPNA hydrolysis catalysed by α-chymotrypsin (α-CT), see Scheme 1.

image file: c9cp03868j-s1.tif
Scheme 1 The peptide SPNA is hydrolysed by α-CT to yield N-(3-carboxypropanoyl)phenylalanine (3-CP) and p-nitroaniline (4-NA).

α-CT catalyses the hydrolysis of the peptide SPNA into the products N-(3-carboxypropanoyl)phenylalanine (3-CP) and p-nitroaniline (4-NA), of which the latter is used as a precursor for the synthesis of azo dyes.36,37 α-CT is a digestive enzyme which catalyses the hydrolysis of different proteins by cleavage of peptide or amide bonds.38 While the industrial relevance of α-CT is discussed in the literature,39,40 the catalysis is still mostly seen as a model reaction to study pseudo one-substrate kinetics.41,42 The enzyme α-CT is known to be highly pressure stable, up to pressures in the multi-kilobar-range. Also, beneficial effects of various co-solvents on the reaction kinetics of α-CT have already been identified.26 Previous experiments have revealed combined effects of pressure and co-solvents on the reaction kinetics of α-CT.23,24 Based on these promising findings, we set out to develop and apply a thermodynamic activity-based framework that allows predicting the effects of both, pressure and co-solvents, on the Michaelis constant and catalytic constant of the SPNA hydrolysis at 293 K and pH 8. This required experimental data to validate the predictive framework.


Experimental procedure

The experimental measurements of the reaction kinetics were carried out using a high-pressure stopped-flow (HPSF) system (HPSF-56 of Hi-Tech Scientific), which operates up to 2000 bar. The increase in optical absorbance at 410 nm due to formation of the product 4-NA was recorded using the built-in absorbance spectrometer. The procedure has already been validated in the literature.23,24 All chemicals were used without further purification or analysis and are given in Table S1 (ESI).

Experiments were carried out at 293 K in 100 mmol kgwater−1 TRIS–HCl buffer at pH 8. The concentration of the enzyme α-CT was 8 μmol kgwater−1 and SPNA concentrations of 1, 2, 4 and 8 mmol kgwater−1 were investigated. Concentrations of the co-solvents were 0.5 mol kgwater−1 TMAO, 1 mol kgwater−1 urea, 2.1 mol kgwater−1 DMSO and 4.2 mol kgwater−1 DMSO. The kinetic experiments were carried out at 1, 500, 1000, 1500 and 2000 bar. The dead time of the instrument is 10 ms and the absorbance was measured after the rapid mixing process for 3 min.

Theoretical background

The hydrolysis of SPNA, as shown in Scheme 1, can be regarded as a pseudo-one substrate reaction.37,42–44 This assumption is valid as water is present in excess and thus, does not limit the reaction rate.45,46 According to this assumption, the reaction scheme is regarded as shown in eqn (1):
E + S ⇌ ES → E + P(1)
E characterizes the free enzyme, S the substrate, ES the enzyme–substrate complex and P the products of the reaction. Assuming Michaelis–Menten steady-state kinetics,47 the initial reaction rate normalized to the total enzyme concentration, ν′, can be expresses as shown below:45,46
image file: c9cp03868j-t1.tif(2)
In eqn (2), kcat characterizes the catalytic constant, KM the Michaelis constant, ν the observed reaction rate, mE the total enzyme molality and mS the initial substrate molality. Both, kcat and KM are concentration based and dependent on temperature, pressure and any co-solvent added to the reaction mixture.

In this work, an activity-based approach was used to analyse the reaction kinetics. Based on this approach (2) rewrites to:

image file: c9cp03868j-t2.tif(3)

Thermodynamic activities ai = mi·γi are used instead of concentrations. The advantage of using thermodynamic activity is that the kinetic constants do not depend on co-solvent.31–33,48 In order to successfully apply the activity-based approach according to (3), reaction kinetics have to be determined only for the reaction in the neat co-solvent free system. Further, the activity coefficients γi of SPNA and of α-CT are required, which were obtained in this work by the equation of state PC-SAFT. The PC-SAFT parameters for the enzyme α-CT were obtained from the enzyme's amino acid sequence and density data of aqueous amino-acid solutions (see Tables S2, S3 and Fig. S1, S2, ESI). It is known that co-solvent effects on KM are mainly caused by molecular interactions between solvent, co-solvent and substrate.49 Co-solvent effects on kcat also involve interactions of the enzyme, i.e. co-solvent/solvent/substrate/enzyme interactions, accessible via the second osmotic virial coefficient B22 (see Table S5, ESI). A detailed description of PC-SAFT and the prediction of activity coefficients is provided in the ESI (see chapter “Thermodynamic model PC-SAFT”).

Pressure effects on reaction properties (e.g. equilibrium constants) are commonly described by means of the Eyring equation.50 It was shown in literature51 that also KM depends exponentially on pressure according to:

image file: c9cp03868j-t3.tif(4)
where Δv# represents the binding volume.

Analogously, pressure effects on the reaction rate are quantified according to the eyring equation, relating kcat to the activation volume Δv.50

image file: c9cp03868j-t4.tif(5)
The activation volume denotes to the change in volume between the enzyme–substrate complex ES and the transition state of the enzyme–substrate complex.23,24 A smaller volume of the transition state consequently leads to a negative activation volume. Hence, higher pressure accelerates the reaction rate.19

Results and discussion

Co-solvent effects on KM and kcat

In a first step of this work, the experimentally observed catalytic constants kobscat of the α-CT catalysed hydrolysis of SPNA under neat conditions at pH 8, 1 bar and 293 K and under the co-solvent influence of 0.5 mol kgwater−1 TMAO, 1 mol kgwater−1 urea, 2.1 mol kgwater−1 DMSO and 4.2 mol kgwater−1 DMSO were measured according to the procedure described in the experimental section. Values for the experimental Michaelis constants KobsM were taken from our previous work.31 The experimental results on KobsM are shown in Fig. 1.
image file: c9cp03868j-f1.tif
Fig. 1 Experimentally determined (white bars) and PC-SAFT predicted (grey bars) Michaelis constants KM under the influence of different co-solvents at given molalities M for the α-CT catalysed hydrolysis of SPNA at 293 K, pH 8 and 1 bar.27 Values are given in Table S7 (ESI).

The experimental results show that the addition of 0.5 mol kgwater−1 TMAO to the reaction system has no significant effect on KobsM. In contrast, presence of 1 mol kgwater−1 urea or 2.1 mol kgwater−1 DMSO increases KobsM by about 40%. Accordingly, an even higher concentration of DMSO (4.2 mol kgwater−1) further increases KobsM by about 250%, which is considerably disadvantageous. Fig. 1 additionally shows PC-SAFT prediction results. It should be noted that PC-SAFT parameters (Tables S4, and S6, ESI) were taken from literature. These parameters stem from fitting to reaction-independent thermo-physical properties. Comparing the experiments with PC-SAFT predicted Michaelis constants KpredM, it can be concluded that PC-SAFT accurately predicts the experimental data. These predictions are based on the activity coefficient of SPNA as function of co-solvent concentration, independent of enzymatic interactions that were not considered for the predictions of KpredM. That is, the interactions between the substrate SPNA and the respective co-solvent are responsible for the observed dependency of KobsM on the kind and concentration of the added co-solvent, no interaction with the enzyme itself has to be invoked.

The co-solvent influence on kobscat at 1 bar and 293 K at pH 8 is depicted in Fig. 2. The experimental results show that addition of TMAO has no significant effect on kobscat. In contrast, urea and DMSO decrease kcat by about 18 to 25%, respectively. Interestingly, increased concentrations of DMSO do not further decrease kobscat within the experimental uncertainty.

image file: c9cp03868j-f2.tif
Fig. 2 Experimentally determined (white bars) and PC-SAFT predicted (grey bars) catalytic constant kcat under the influence of different co-solvents at given molalities M for the α-CT catalysed hydrolysis of SPNA at 293 K, pH 8 and 1 bar. Values are given in Table S7 (ESI).

Further, it can be seen from Fig. 2 that PC-SAFT predicts the co-solvent influences on kobscat in very good agreement with the experimentally determined values for all co-solvents studied. These predictions explicitly account for molecular interactions of the enzyme with the substrate, the solvent and the co-solvent, expressed as the activity coefficient of the enzyme. These interactions are obviously the key for predicting kcat.

To summarize the results at atmospheric pressure, the co-solvents urea and DMSO decreased the catalytic constant and increased the Michaelis constant in a significant way, and these effects could be predicted successfully with PC-SAFT. Most importantly, successful predictions required the interactions between co-solvent and substrate (for predicting Michaelis constants) as well as between co-solvent and enzyme (for predicting catalytic constants), expressed as activity coefficients, which are listed in Table S10 (ESI).

Pressure effects on KM and kcat

In addition to the co-solvent influence, the effect of high pressure on reaction kinetics was investigated in this work. First, we determined the pressure dependence of the kinetic constants KobsM and kobscat experimentally for neat (buffer) conditions at 293 K and 1500 bar (see Fig. S3 and Table S8, ESI). In accordance with the literature, KobsM and kobscat can be assumed to exponentially depend on pressure (eqn (4) and (5)). Consequently, knowing these kinetic constants at two pressures, e.g. 1 bar and 1500 bar, allows predicting the reaction kinetics at any other pressure. The plot of the experimentally determined and extrapolated kinetic constants is shown in Fig. 3. The results show that ln(KM) and ln(kcat) linearly depend on pressure over a wide pressure range between 1 bar and 2000 bar.
image file: c9cp03868j-f3.tif
Fig. 3 Logarithmic plot of the normalized Michaelis constant KM·KM,1bar−1 and the normalized catalytic constant kcat·kcat,1bar−1versus pressure p at 293 K and pH 8. Full circle: experimentally determined KM (1500 bar), full square: experimentally determined kcat (1500 bar). The lines represent the fit lines used to determine the respective values of KM·KM,1bar−1 (stars) and kcat·kcat,1bar−1 (triangles) at 500, 1000 and 2000 bar. Values are given in Tables S8 and S9 (ESI).

Using this information allows predicting pressure effects on the reaction in the neat (co-solvent free) buffer system. The results are shown in Fig. 4 as a primary plot, proving that pressure has a positive, accelerating effect on the enzyme-catalysed hydrolysis of SPNA. Further, primary plots were predicted with PC-SAFT by accounting for the pressure effect on KobsM (decreases with increasing pressure, indicating a higher affinity of the substrate towards the enzyme) as well as on kobscat (increases with increasing pressure). Both effects cause higher reaction rates at lower substrate concentrations (see Fig. 4).

image file: c9cp03868j-f4.tif
Fig. 4 Primary plot of the initial normalised reaction rate ν′ under neat (buffer) conditions plotted against the initial substrate molality mSPNA at different pressures at 293 K and pH 8. Lines: PC-SAFT predictions, symbols: experimental data (circles: 1 bar, squares: 500 bar, triangles: 1000 bar, diamonds: 1500 bar, stars: 2000 bar).

Combined co-solvent and pressure effects on KM and kcat

In a final step, the combined effects of pressure and co-solvents on the reaction kinetics were studied. KobsM values are shown in Fig. 5. In the neat buffer system, KobsM decreased by 32% upon a pressure increase from 1 bar to 2000 bar. Upon adding co-solvents, KobsM also decreased with increasing pressure. Thus, pressure is the dominating factor and overcomes the disadvantages of co-solvents, which all increased KM at 1 bar (see Fig. 1). However, the beneficial effect of pressure is strongly reduced upon adding DMSO, as KM decreased only by 4–8% at high pressure.
image file: c9cp03868j-f5.tif
Fig. 5 Pressure dependence of the Michaelis constant KM at 293 K and pH 8. Lines: PC-SAFT predictions, symbols: experimental data (circles: neat, squares: 0.5 mol kgwater−1 TMAO, triangles: 1 mol kgwater−1 urea, diamonds: 2.1 mol kgwater−1 DMSO, stars: 4.2 mol kgwater−1 DMSO). Values given in Table S7 (ESI).

The combined effect of pressure and co-solvents on kobscat are presented in Fig. 6. As a reference value it should be stated again that kobscat increases by 80% upon a pressure increase from 1 bar to 2000 bar in the neat system. An increase of the catalytic constant was observed even in the presence of co-solvents. However, upon addition of 4.2 mol kgwater−1 DMSO, a significantly lower pressure effect on kobscat was detected compared to all other systems studied. This means that adding DMSO decreases the pressure benefit on the catalytic constant similarly as it has been observed also for KM in Fig. 5.

image file: c9cp03868j-f6.tif
Fig. 6 Pressure dependence of the catalytic constant at 293 K at pH 8. Lines: PC-SAFT predictions, symbols: experimental data (circles: neat, squares: 0.5 mol kgwater−1 TMAO, triangles: 1 mol kgwater−1 urea, diamonds: 2.1 mol kgwater−1 DMSO, stars: 4.2 mol kgwater−1 DMSO). Values are given in Table S7 (ESI).

The effects of pressure and co-solvents on the reaction kinetics are not necessarily additive. Pressure may strengthen or weaken co-solvent effects. For all reaction systems it was observed that pressure decreases KobsM while increasing kobscat. In contrast to that, all co-solvents increase KobsM while decreasing kobscat. The effect of DMSO is the strongest among all co-solvents under investigation. The combined co-solvent and pressure effects show that pressure weakens the effect of urea on KobsM and kobscat while pressure strengthens the effect of DMSO on KobsM and kobscat. This is illustrated and explained in more details in the ESI (Fig. S4 and S5 and according text). Thus, a generally valid behaviour of the combined effects of pressure and co-solvent cannot be deduced. This even more highlights the importance of a predictive thermodynamic model such as PC-SAFT that allows predicting the combined pressure and co-solvent effects on the reaction kinetics. The predictions of combined effects were done by using the kinetic constants (Fig. 3) as an input to predict the activities of SPNA and of the enzyme at the desired pressure and co-solvent conditions. The predictions are shown in Fig. 5 (Michaelis constant) and in Fig. 6 (catalytic constant), respectively. The numerical values for the predictions are given in Table S7 (ESI). As can be clearly seen, the PC-SAFT predictions are in good agreement with the experimental observations. That is, PC-SAFT predicts decreased KpredM and increased kpredcat values upon increasing pressure correctly. Further, PC-SAFT correctly predicts that DMSO weakens the pressure-induced kinetic benefit, and that urea and TMAO only slightly affect the pressure effect on the reaction kinetics.

Prediction of primary Michaelis–Menten plots

As a final step, a primary plot was predicted with PC-SAFT for one reaction system under the influence of co-solvent at high pressure. The predictions are based on the Michaelis constant and catalytic constant, which were predicted as shown in Fig. 5 and 6. At these conditions, the kinetic constants KpredM and kpredcat deviate by less than 15% from the experimental values. Since co-solvent effects are most pronounced in the 4.2 mol kgwater−1 DMSO system, the PC-SAFT results predicted are shown here for this system including all pressures up to 2000 bar (see Fig. 7).
image file: c9cp03868j-f7.tif
Fig. 7 Primary plot of initial normalised reaction rate ν′ at 4.2 mol kgwater−1 DMSO conditions plotted against the initial substrate molality mSPNA at different pressures. Lines: PC-SAFT predictions, symbols: experimental data (circles: 1 bar, squares: 500 bar, triangles: 1000 bar, diamonds: 1500 bar, stars: 2000 bar).

Even for these extreme cases, PC-SAFT predictions agree very well with the experimental data. Hence, PC-SAFT allows predicting primary kinetic diagrams, requiring two experimental values under neat (buffer) conditions only, namely KobsM and kobscat at 1 bar and at 1500 bar in our case. The success of these predictions is based on the fact that for the considered reaction solvent-mediated molecular interactions as predicted by PC-SAFT (via introduction of activity coefficients) determine the reaction kinetics, only. PC-SAFT predictions are accurate also for other pressure and co-solvent conditions as shown in Fig. S6 and S7 in the ESI.


To conclude, we present for the first time an activity-based framework in order to predict the combined influence of pressure and co-solvents on the kinetic constants KobsM and kobscat of an enzymatic reaction. Primary plots (rate vs. substrate molality) of the enzyme reaction were predicted with PC-SAFT using thermodynamic parameters that were fitted to reaction-independent data, such as density, vapour pressure, and osmotic pressures. The predictions of KM are based on molecular solvent/co-solvent/substrate interactions, while predictions of kcat are based on enzyme/solvent/co-solvent/substrate interactions. We could show that co-solvent effects and pressure effects on the reaction kinetics of the hydrolysis reaction of SPNA can be divided into the substrate activity and the enzyme activity. The single effect of co-solvent, the single effect of pressure as well as the combined effect of co-solvent and pressure were quantified and rationalized by thermodynamic activities. The approach proposed here allows prediction of the initial reaction rate of an enzymatic reaction depending on the substrate concentration with satisfying accuracy, opening new avenues in process optimization and in the development of biocatalytic routes making use of temperature, pressure, and co-solvent modulation.

Conflicts of interest

There are no conflicts to declare.


Financial support from the DFG Research Unit FOR 1979 and the Cluster of Excellence RESOLV (EXC-2033 – Projektnummer 390677874) is gratefully acknowledged.

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Electronic supplementary information (ESI) available. See DOI: 10.1039/c9cp03868j
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