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. 2020 Sep 23;5(39):25077–25086. doi: 10.1021/acsomega.0c02401

The Energetic Origin of Different Catalytic Activities in Temperature-Adapted Trypsins

Yuan-Ling Xia †,§, Yong-Ping Li ∥, Yun-Xin Fu †,‡,*, Shu-Qun Liu †,*
PMCID: PMC7542600  PMID: 33043186

Abstract

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Psychrophilic enzymes were always observed to have higher catalytic activity (kcat) than their mesophilic homologs at room temperature, while the origin of this phenomenon remains obscure. Here, we used two different temperature-adapted trypsins, the psychrophilic Atlantic cod trypsin (ACT) and the mesophilic bovine trypsin (BT), as a model system to explore the energetic origin of their different catalytic activities using computational methods. The results reproduce the characteristic changing trends in the activation free energy, activation enthalpy, and activation entropy between the psychrophilic and mesophilic enzymes, where, in particular, the slightly decreased activation free energy of ACT is determined by its considerably reduced activation enthalpy rather than by its more negative activation entropy compared to BT. The calculated electrostatic contributions to the solvation free energies in the reactant state/ground sate (RS/GS) and transition state (TS) show that, going from BT to ACT, the TS stabilization has a predominant effect over the RS stabilization on lowering the activation enthalpy of ACT. Comparison between the solvation energy components reveals a more optimized electrostatic preorganization to the TS in ACT, which provides a larger stabilization to the TS through reducing the reorganization energy, thus resulting in the lower activation enthalpy and hence lower activation free energy of ACT. Thus, it can be concluded that it is the difference in the protein electrostatic environment, and hence its different stabilizing effects on the TS, that brings about the different catalytic activities of different temperature-adapted trypsins.

1. Introduction

Temperature is one of the main environmental factors affecting the distribution, physiology, and survival of organisms. Enzymes of the extremophilic organisms adapted to the extremely high/low temperatures should maintain a sufficient catalytic efficiency (kcat/km) to guarantee the normal metabolism and growth of organisms. The catalytic efficiencies of homologous psychrophilic and mesophilic enzymes are roughly identical at the living temperatures of their respective source organisms,1 while their catalytic rate constants (kcat; referred to as the catalytic activity hereafter) are obviously different at the room temperature, with the psychrophilic enzyme having a higher catalytic activity than the mesophilic counterpart. According to the transition state theory, a key problem encountered by an enzyme is that the rate constant would decrease exponentially as the temperature decreases if the activation free energy remains unchanged:

1. 1

where κ is a transmission coefficient, T is the temperature, k and h are the Boltzmann and Planck constants, respectively, and ΔG‡ is the activation free energy, which can be decomposed into the entropic (ΔS‡) and enthalpic (ΔH‡) contributions according to ΔG‡ = ΔH‡ – TΔS‡. Furthermore, it can be deduced from eq 1 that, if an enzyme is capable of maintaining a sufficiently high catalytic activity at low temperatures, the catalyzed reaction should have a low ΔG‡/T or ΔH‡/T value or a high ΔS‡ value.

Many studies have attempted to ascertain the origin of different catalytic activities between different temperature-adapted homologs. Several experimental studies revealed that protein flexibility is likely to be positively correlated with the increased catalytic activities of the psychrophilic α-amylases,2 xylanase,3 and DNA ligases1 compared to those of the respective mesophilic/thermophilic counterparts. Many studies conducted using combined experimental and computational approaches also revealed a collective increase in both the catalytic activity and structural flexibility of the homologous enzymes as the habitat temperature of the source organisms decreases.4−12 Interestingly, it has been found that the isotopically substituted heavy enzymes, within which all carbon, nitrogen, and nonexchangeable hydrogen atoms, are replaced with their heavier isotopes: 13C, 15N, and 2H, reduced the catalytic rate constant due to the increased mass and slower motions of proteins coupled to the reaction coordinate.13−19 Therefore, it is generally believed that an increase in the catalytic activity of the psychrophilic enzyme requires enhanced protein flexibility, especially at a low temperature that strongly slows down molecular motions.7

Although the above studies have shed light on the relationship between the catalytic activity and structural flexibility of enzymes, understanding the origin of different catalytic activities needs to compare the thermodynamic activation parameters (i.e., activation free energy ΔG‡, activation enthalpy ΔH‡, and activation entropy TΔS‡) between different temperature-adapted homologous enzymes. Thanks to computational methods, such as the empirical valence bond (EVB) approach20 and the linear response approximation (LRA) treatment,21 we can now reliably calculate the catalysis-relevant thermodynamic parameters and probe the energetic origin of different catalytic activities between different adapted homologous enzymes.

The EVB method can reproduce the experimentally determined activation free energy values through approximating the potential energy surface of a reaction with a calibrated Hamiltonian.20,22,23 Furthermore, the activation enthalpy and entropy can be extracted from an Arrhenius plot, where a series of activation free energy values at different temperatures can be obtained using the EVB method.20,21,24 The LRA treatment provides a good estimation for the change in the free energy between two potential energy surfaces and, hence, offers the unique ability to evaluate the electrostatic contribution to the solvation free energy (referred to as the electrostatic solvation energy or LRA energy in this paper) of a specific state,21 which can be used to detect whether the catalysis is due to reactant state/ground state destabilization (RSD/GSD) or to transition state stabilization (TSS) via comparing the energy magnitude of the reactant state/ground sate (RS/GS) or the transition state (TS) between two reaction systems.25,26

Interestingly, studies using the LRA approach have revealed that the TSS is responsible for the catalytic effects of most studied enzymes due to the preorganized electrostatic environment in the protein structure,25,27 although the RSD was also observed to reduce the activation free energy in certain natural enzymes28−30 and the engineered enzymes derived from the directed evolution experiments.26 Nevertheless, as for the different temperature-adapted homologous enzymes, the questions of how large the difference in the activation free energy is between them and how the difference is brought about still remain obscure.

Here, we employed two different temperature-adapted homologous enzymes, the psychrophilic trypsin from Atlantic cod (Atlantic cod trypsin, ACT)31 and the mesophilic trypsin from bovine (bovine trypsin, BT),32 as a comparative model system to quantify the difference in the activation free energy between them and to explore the origin of the activation free energy difference. The psychrophilic ACT has been experimentally shown to have about a three-fold higher catalytic activity than the mesophilic BT towards the synthetic substrate benzoyl-Arg-p-nitroanilid at room temperature.31 In this study, we first calculated the activation free energies of the two enzymes using the EVB method, yielding the energy values consistent with the experimentally determined ones; then, we extracted the activation entropy and the activation enthalpy from the calculated Arrhenius plots of these two enzymes; finally, the LRA approach was used to calculate the electrostatic solvation energies of the reaction fragments in the RS and TS for both enzymes to judge whether RSD or TSS is responsible for the increased catalytic activity of ACT. Our results indicate that the lower activation free energy of ACT originates from its lower activation enthalpy, which in turn is predominantly determined by its larger magnitude of TSS, although ACT has a more stable RS and more unfavorable activation entropy than BT.

2. Results

2.1. Activation Free Energies of ACT and BT

Accurately estimating the activation free energies of different temperature-adapted homologous enzymes is a prerequisite for understanding the difference in the catalytic activity and probing the origin of the difference. Therefore, we first calculated the activation free energies for ACT and BT at 300 K using the EVB method.

Figure 1 shows the calculated free energy profiles along the generalized reaction coordinate for the rate-limiting acylation reactions of the psychrophilic ACT and mesophilic BT. The corresponding free energy profile for the reference acylation reaction catalyzed by imidazole in water,33 which was used to calibrate the EVB potential, is also shown in Figure 1. It is clear that both enzymes have similar free energy profiles despite being quite distinct from that of the reference reaction in water. The activation free energy (i.e., a change in free energy from the RS to TS) of the reference reaction in water is significantly higher than those of ACT and BT, indicating the large catalytic effect on the acylation reaction by both enzymes. Compared to BT, ACT has a slightly lower activation free energy, confirming its higher catalytic activity. Specifically, the calculated values for ACT and BT at 300 K are 16.40 ± 0.48 and 17.26 ± 0.94 kcal·mol–1, respectively, which are in excellent agreement with the energy values of 16.75 and 17.41 kcal·mol–1 converted from the experimental rate constants toward a small synthetic substrate benzoyl-Arg-p-nitroanilid, kcat(ACT) = 3.44 s–1 and kcat(BT) = 1.13 s–1, respectively.31 As a result, our EVB calculations have reproduced the experimental activation free energies with high accuracy for ACT and BT.

Figure 1.

Figure 1

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Calculated free energy profiles at 300 K for the tetrahedral intermediate formation in the acylation step of Atlantic cod trypsin (ACT; blue) and bovine trypsin (BT; red) and in the imidazole-catalyzed reference reaction in water (wat; black). RS, TS, and PS represent the reactant state, transition state, and the product state of the tetrahedral intermediate, respectively. Energy gap in kcal·mol–1 is the generalized reaction coordinate.

2.2. Active Site Configurations along the Reaction Coordinate

In order to compare the differences in the active site configurations of the RS, TS, and product state (PS) between ACT and BT, the corresponding structures were extracted from the MD/EVB simulations and shown in Figure 2. As shown in Figure 2, the geometric configurations of the active site in each of the three states are very similar between ACT and BT, although slight differences can be found in the distances between certain atoms and in the side-chain orientations of the catalytic triad residues.

Figure 2.

Figure 2

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Active site structures of ACT and BT in the reactant state (RS), transition state (TS), and product state (PS). These structures were extracted from the MD/EVB simulations driving the acylation reaction from the RS to the PS via the TS along the reaction coordinate. The catalytic triad residues (Asp102, His57, and Ser195) and part of the substrate are shown in a stick model, with the carbon, nitrogen, oxygen, and hydrogen atoms colored green, blue, red, and gray, respectively. The distances between selected atoms (see the text for details) are labeled as Å.

In the RS, the hydroxyl hydrogen and oxygen atoms of the nucleophilic residue Ser195 point to the His57 imidazole Nε2 atom and the substrate carbonyl carbon atom of the scissile peptide bond, respectively, with the distances between the mentioned atoms (2.5 and 3.2 Å, respectively) being the same in both enzymes; the two carboxylate oxygen atoms of the catalytic Asp102 coordinate to the protonated imidazole Nδ1 atom but with their distances being slightly different between ACT and BT due to different orientations of the carboxylate groups. In the transient TS, the transfer of Ser195 hydroxyl hydrogen to the imidazole Nε2 atom was observed to be accompanied by an apparent reduced distance of the Ser195 hydroxyl oxygen to the substrate carbonyl carbon atom (i.e., 2.5 Å in the TS compared to 3.2 Å in the RS) and by a slight orientation adjustment of the imidazole ring in both enzymes, implying a concerted process of proton transfer and a nucleophilic attack.34 In the PS, His57 imidazole Nε2 has already captured the hydrogen atom from the Ser195 hydroxyl, and the hydroxyl oxygen has accomplished the nucleophilic attack on the substrate carbonyl carbon atom, thus forming the protonated imidazole ring and the tetrahedral intermediate, respectively, in both enzymes; interestingly, small concerted adjustments of the His57 imidazole and Ser195-linked tetrahedral intermediate, which lead to an approach of the newly obtained proton toward the nitrogen atom of the substrate leaving group, can also be observed in both enzymes.

Taken together, the geometric configurations of the active site in the RS, TS, and PS are, respectively, very similar between ACT and BT, which makes it unlikely to pinpoint the source of the difference in the activation free energy between them. To this end, we turned to examine the origin of their different catalytic activities by decomposing the activation free energy into its enthalpic and entropic components.

2.3. Arrhenius Plots and Separation of Activation Enthalpy and Entropy

Although our EVB calculations have revealed that the psychrophilic ACT has a slightly lower activation free energy value than the mesophilic BT at 300 K, ascertaining the source of such difference necessitates the decomposition of the activation free energy into its individual energy contributions: the activation enthalpy and the activation entropy. The best way to do this is to obtain a sufficiently accurate Arrhenius plot that describes the relationship between the activation free energy and temperature.35,36

Figure 3 shows two forms of Arrhenius plots constructed based on calculating the activation free energy profiles at eight different temperatures ranging from 275 to 310 K. Figure 3a plots the values of ΔG‡/T against the reciprocal temperature 1/T, with the slopes of the best-fit straight lines obtained from the linear regression of the data points representing the activation enthalpies (ΔH‡) of ACT and BT at 300 K, i.e., 12.65 and 19.46 kcal·mol–1, respectively. The activation entropies (TΔS‡) of ACT and BT thus are −3.75 and 2.20 kcal·mol–1, respectively, according to ΔG‡ = ΔH‡ – TΔS‡. Therefore, the psychrophilic ACT has lower activation enthalpy and more negative activation entropy than BT.

Figure 3.

Figure 3

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Calculated Arrhenius plots of psychrophilic ACT (blue) and mesophilic BT (red). (a) Form of Arrhenius plots of ΔG‡/T vs 1/T, with slopes of the fitted lines representing the activation enthalpies of the two enzymes. (b) Form of Arrhenius plots of ΔG‡ vs T. Error bars correspond to the standard deviations.

The lower activation enthalpy of ACT means that it costs less energy (ΔH‡) to climb the activation barrier than BT does, thus benefiting to lowering the activation free energy. For ACT, the negative activation entropy means that its TS becomes more ordered in terms of the degree of freedom of the reaction system when compared to its RS, which is unfavorable for lowering the activation free energy; on the contrary, the positive activation entropy of BT means that its TS is more disordered than its RS, thus making a favorable contribution to lowering the activation free energy. Thus, going from BT to ACT, the decreased activation enthalpy (ΔΔH‡ = −6.81 kcal·mol–1) is counteracted by the reduced activation entropy (TΔΔS‡ = −5.95 kcal·mol–1), ultimately leading to a small reduction in the activation free energy (ΔΔG‡ = −0.86 kcal·mol–1). Despite such remarkable enthalpy–entropy compensation, it can still be seen that it is the decreased activation enthalpy, rather than the decreased activation entropy, that makes a positive contribution to the decreased activation free energy of ACT compared to BT.

Figure 3b shows the calculated activation free energy values against the temperature T for both enzymes. It is clear that the energy values of the psychrophilic ACT are lower than those of the mesophilic BT at any of the tested temperatures, and, interestingly, the values of ACT and BT decrease considerably and increase slightly, respectively, as the temperature falls, resulting in a trend amplifying the difference in the activation free energy between the two enzymes. These results explain why ACT has a higher catalytic activity than BT at room temperature31 and why, in general, psychrophilic enzymes exhibit much higher catalytic activities than their mesophilic/thermophilic counterparts at low temperatures.7,37

Taken together, these two forms of computationally constructed Arrhenius plots not only characterize the distinctly different changing trends in activation free energies of ACT and BT with changing temperature but also, more importantly, reveal that the difference in the activation enthalpy, rather than that in the activation entropy, is the determinant for the lower activation free energy of ACT compared to BT.

2.4. Electrostatic Solvation Energies in the RS and TS

Compared to BT, although the lower activation free energy of ACT is due to its lower activation enthalpy, the source of different activation enthalpies of the two enzymes needs to be elucidated further. Here, we calculated using the LRA approach, the electrostatic solvation energies (i.e., LRA energies) of the reacting fragment/EVB region in the RS and TS of both ACT and BT (Table 1 and Figure 4) to judge whether the lower activation enthalpy of ACT is due to RSD or to TSS.

Table 1. LRA Energies (or Electrostatic Solvation Energies in kcal·mol–1) of the Reacting Fragment in the RS (Reactant State) and TS (Transition State) for ACT and BTa.

  ACT
 BT
  RS TS RS TS
⟨UQ – U0⟩QW + P –18.6 ± 1.1 –79.1 ± 5.4 –18.0 ± 1.7 –80.6 ± 5.1
⟨UQ – U0⟩0W + P –6.5 ± 1.8 –21.5 ± 2.7 –3.8 ± 2.5 –11.4 ± 2.9
ΔGsolvelec –13.0 ± 1.2 –50.3 ± 2.2 –11.9 ± 1.6 –46.0 ± 2.0
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a

W and P represent water and protein, respectively, both of which are defined as the generalized solvent in this paper; U denotes the interaction potential between the solute (i.e., the reacting fragment/EVB region) and the generalized solvent, with the subscripts Q and 0 denoting the charged and uncharged states, respectively; ⟨ ⟩Q and ⟨ ⟩0 represent the average over the configurations generated by MD runs for the charged and uncharged solutes, respectively.

Figure 4.

Figure 4

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LRA energies (or electrostatic solvation energies) of the reacting fragment in the RS (reactant state) and TS (transition state) for ACT and BT. The numbers represent the LRA energy values in kcal·mol–1; TSS represents the transition state stabilization of ACT relative to BT; RSS represents the reactant state stabilization of ACT relative to BT (which makes a negative contribution to lowering the activation enthalpy of ACT) or, conversely, the reactant state destabilization (RSD) of BT relative to ACT.

As can been seen from Table 1 and Figure 4, both enzymes have a significantly lower LRA energy value (ΔGsolvelec) in the TS than in the RS. This seems to be counterintuitive but is not surprising, as the LRA energy is neither the solvation free energy itself nor the absolute free energy of the TS or RS, while it merely accounts for an electrostatic (enthalpic) contribution to the solvation free energy of the reacting fragment in a given state. However, the LRA energy difference between the RS and TS for different enzyme systems can still reflect the difference in the activation free energy/enthalpy between them.26,27 For ACT and BT, the differences in LRA energy values between the RS and TS (i.e., ΔΔGsolv = ΔGsolvelec (TS) – ΔGsolv (RS)) are −37.3 and −34.1 kcal·mol–1, respectively, consistent with the observed trend that ACT has lower activation enthalpy than BT in particular and, in general, psychrophilic enzymes have lower activation enthalpy than their mesophilic counterparts.38

Figure 4 clearly demonstrates that, when compared to BT, ACT has a relatively lower LRA energy value in the RS (−13.0 vs −11.9 kcal·mol–1) while a considerably lower value in the TS (−50.3 vs −46.0 kcal·mol–1), indicating that ACT stabilizes (solvates) the RS more than BT does and stabilizes the TS much more than BT does. The fact that a large favorable TSS magnitude (−4.3 kcal·mol–1) overcompensates for a small unfavorable RS stabilization magnitude (RSS; −1.1 kcal·mol–1) indicates that the electrostatic TSS of ACT dominates the difference between the LRA energy difference (−3.2 kcal·mol–1; calculated as ΔΔΔGsolvelec = ΔΔGsolv (ACT) – ΔΔGsolvelec (BT)) of ACT (−37.3 kcal·mol–1) and BT (−34.1 kcal·mol–1) and, therefore, determines the lowered activation enthalpy of ACT (12.65 kcal·mol–1) compared to BT (19.46 kcal·mol–1). It is also worth noting that, as shown in Table 1, the difference in the TS’s ΔGsolv between ACT and BT is associated with the average over the configurations generated by MD runs for the uncharged TS (⟨UQ – U0⟩0W + P). Since this term represents the effect of the environment (protein and water surrounding the reacting fragment) preorganization, the lower value in the TS of ACT indicates a better preorganized electrostatic environment and hence a lower reorganization energy (calculated as 0.5 (⟨UQ – U0⟩0 – ⟨UQ – U0⟩QW + P)27) in the ACT than in BT.

In summary, our LRA calculations reveal that, when compared to BT, the lower activation enthalpy of ACT is due to its larger magnitude of TSS, which in turn originates from its more optimized electrostatic environment surrounding the reacting fragment in the TS.

3. Discussion

At room temperature, the experimental rate constant of the psychrophilic ACT is about three-fold higher than that of the mesophilic BT31 and, according to the transition state theory (eq 1), such an increased catalytic activity should result from a decreased activation free energy of ACT compared to BT at the same temperature. Encouragingly, our MD/EVB simulations reproduce the activation free energies (i.e., 16.40 ± 0.48 and 17.26 ± 0.94 kcal·mol–1 for ACT and BT, respectively, at 300 K) that correspond accurately to the experimental rates of both enzymes. In a previous work,35 the activation free energies of BT and another psychrophilic anionic salmon trypsin (AST) were calculated using the same approach as in this paper, with the obtained values at 300 K being 19.0 ± 1.4 and 18.2 ± 0.8 kcal·mol–1, respectively. The possible reasons for the different energy values of BT are that the different initial atomic coordinates for BT were used, i.e., PDB ID 4I8G32 with the resolution of 0.8 Å in this study and 3BTK39 with 1.85 Å resolution in ref (35), and different MD/EVB simulation protocols/parameters were used, e.g., different force fields, atomic charges of the EVB region, water sphere radii, long-range electrostatic treatments, and relaxation MD simulation time scales. At any rate, both calculated values for the warm active BT reflect the relative difference in the catalytic activity with respect to the respective cold-adapted counterparts, ACT and AST.

The very similar geometric configurations in each of the three key states (i.e., RS, TS, and PS) for ACT and BT are not surprising, as the two enzymes catalyze the acylation reaction with an identical mechanism by a completely conserved catalytic triad Asp102−His57−Ser195; furthermore, those residues spatially close to the triad are highly conserved so as to provide similar structural environments for the active centers of the two enzymes. In addition, the backbone root mean square fluctuation (RMSF) values of the catalytic triad residues calculated from the MD/EVB simulation trajectories are collectively low and very similar for ACT (Asp102: 0.236, His57: 0.263, and Ser195: 0.269 Å) and BT (Asp102: 0.239, His57: 0.260, and Ser195: 0.268 Å), indicating the similar high-rigidity of their active centers. Interestingly, the similar high-rigidity of the active sites was also observed for the psychrophilic, mesophilic, and thermophilic citrate synthases.36 Therefore, the geometric and dynamical properties of the active site are very similar between ACT and BT and unlikely to cause different catalytic activities of these two different adapted enzymes.

Decomposition of the activation free energy into its enthalpic and entropic contributions via constructing Arrhenius plots is the only way to probe the origin of different activation free energies between ACT and BT. Furthermore, Arrhenius plots can provide direct information about the temperature dependence of the activation free energy and hence of the catalytic rate. It should be noted that the Arrhenius plots (Figure 3) constructed based on the 60 independent EVB/FEP/US simulations at each of the eight temperature points have sufficient high accuracy since the standard deviations of all calculated ΔG‡ values are relatively small (around or within ± 1.0 kcal·mol–1) and the R2 values of the fitted lines are all greater than 0.98.

Our observation that the lower activation enthalpy and the more unfavorable activation entropy of the psychrophilic ACT compared to the mesophilic BT is in agreement with previous studies demonstrating that the cold-adapted enzymes have a reduced activation enthalpy and more negative activation entropy than their warm-active counterparts.7,31,35,36 In fact, according to eq 1 of the transition state theory, such characteristic trends regarding the activation enthalpy and entropy for psychrophilic enzymes should be completely universal without exception.35,38 More specifically, it can be deduced from eq 1 that (i) at the same (low) temperature, the maintenance of a higher catalytic activity (kcat) by a psychrophilic enzyme requires a lower value of ΔG‡/T when compared to its mesophilic counterpart; (ii) as the temperature falls, the psychrophilic enzyme requires a smaller magnitude of the change in ΔG‡/T to avoid the exponential decrease of the catalytic activity; and (iii) although a more positive activation entropy (ΔS‡) is beneficial to increasing the catalytic activity, this does not occur for the psychrophilic enzyme due to the enthalpy–entropy compensation, i.e., a decrease/increase in enthalpy is accompanied by a concomitant decrease/increase in entropy.40,41 It is worth noting that the magnitude of the ΔG‡/T change in response to one unit of change in the 1/T value is the activation enthalpy ΔH‡ (i.e., the slope of the fitted line as shown in Figure 3a), which actually represents the sensitivity of the catalytic activity to the changing temperature, with a lower ΔH‡ value making the rate constant more insensitive to the falling temperature. Our computational simulations have explicitly reproduced all these characteristic relationships among the thermodynamic activation parameters for the psychrophilic and mesophilic trypsins (Figure 3). Nevertheless, here we highlight that it is a greater magnitude of reduction in ΔH‡ that overcompensates for the (unfavorable) decreased TΔS‡, ultimately leading to a small but lower ΔG‡ of ACT compared to BT.

What is the origin of the different activation enthalpies for ACT and BT? To address this problem it is important to keep in mind that the enthalpic change (ΔH‡) from the RS to TS in a catalytic reaction is essentially determined by the corresponding change in the potential energy (ΔU‡), i.e., ΔH‡ = ΔU‡ + pΔV‡, where the pressure–volume term (pΔV‡) is negligible. Although the decomposition of the activation potential ΔU‡ into the contributions from the reacting fragment (i.e., interactions among atoms within the reacting fragment and interactions between the reacting fragment and its surroundings) and from the surrounding environment (i.e., interactions among atoms within the surroundings) is a feasible way to ascertain the trend–decisive energy term,35 a more efficient approach is to directly evaluate the electrostatic contributions to the solvation free energies of the reacting fragment in the RS and TS. It should be noted that the electrostatic solvation energy is actually the electrostatic interaction energy (or the electrostatic contribution to the binding free energy) between the reacting fragment and its surroundings and, hence, does not account for the entropic contribution to the solvation/binding free energy. Using the LRA approach, Warshel et al. have repeatedly demonstrated that the electrostatic interactions between the reacting fragment and its surroundings are of overwhelming importance in determining the stability of the RS or TS and hence the catalytic effect of enzymes.21,25−27,42 Hence, it is reasonable to use the calculated LRA energy as a measure of stability of the RS or TS, and further, to judge whether the decreased activation enthalpy of ACT is due to RSD or TSS.

Our calculated LRA energies reveal that, although the psychrophilic ACT provides better stabilization to both the RS and TS than the mesophilic BT does (Figure 4), a much larger magnitude of stabilization to the TS than to the RS determines that the decreased activation enthalpy of ACT comes from the electrostatic TSS effect. The calculated TSS effect is consistent with the experimental study demonstrating that the transition state analogs bind more strongly to the psychrophilic trypsin (AST) than to the mesophilic BT.43 Our LRA calculations also reveal that ACT has better preorganized environments (reflected by ⟨UQ – U0⟩0W + P) to both the RS and TS than BT, while the electrostatic preorganization to the TS is much better in ACT than in BT. This explains why ACT solvates/stabilizes its RS slightly more than BT does while it stabilizes its TS much more than BT does. In addition, the better electrostatic preorganization to the TS in ACT results in lower reorganization energy than that in BT (28.8 vs 34.6 kcal·mol–1). Since the energy needed to reorganize the environment dipoles toward the charged TS contributes substantially to the activation free energy/enthalpy,27,44,45 the lower reorganization energy means that ACT costs less energy to climb the activation barrier than BT does. Since the reorganization of the environment dipoles occurs outside the reacting fragment, it is likely that the mobility/flexibility in other protein regions distant from the active center could influence the reorganization energy. Interestingly, Åqvist and coworkers have repeatedly demonstrated that the increased protein surface mobility in the psychrophilic enzymes could be directly related to their decreased activation enthalpies compared to the mesophilic counterparts,35,46−51 implying the importance of the protein surface in regulating the reorganization energy along the reaction path.

4. Conclusions

This work probes the energetic origin of the different catalytic activities observed between two different temperature-adapted trypsins using the combined methods of MD/EVB free energy simulations, Arrhenius plot constructions, and LRA solvation energy calculations. Our results show that psychrophilic ACT has a slightly lower activation free energy, a considerably lower activation enthalpy, and more negative activation entropy than the mesophilic BT, in agreement with the characteristic trends with respect to the changes in the thermodynamic activation parameters between the psychrophilic and mesophilic enzymes. We concluded that the origin of different catalytic activities for different temperature-adapted trypsins is the preorganized electrostatic environment of the protein structure, where the psychrophilic ACT has a better electrostatic preorganization that results in TSS and hence the lower activation enthalpy, which in turn overcompensates for the unfavorable activation entropy, ultimately resulting in the slightly lower activation free energy and hence a higher catalytic activity of ACT compared to BT.

5. Materials and Methods

5.1. Enzyme–Substrate Complexes

Atomic coordinates of the psychrophilic ACT and mesophilic BT were retrieved from the Protein Data Bank (PDB; http://www.rcsb.org) with PDB IDs of 2EEK and 4I8G,32 respectively. In order to obtain the enzyme–substrate complexes, a tripeptide Pro–Arg–Ala (corresponding to the P2, P1, and P1′ substrate residues, respectively) was docked into the substrate-binding site of the two proteases using the AutoDock 4.0 program52 with the orientations of P2, P1, and P1′ residues in a trypsin–trypsin inhibitor complex (PDB ID: 4BNR(53)) as the reference. The enzyme–substrate complex structures of ACT and BT are shown in Figure S1.

5.2. EVB Calculations

The structures of the enzyme–substrate complexes were employed to model the enzyme-catalyzed reaction using the empirical valence bond (EVB) method.20 The corresponding free energy profiles were calculated using the free energy perturbation/umbrella sampling (FEP/US) approach25,54,55 implemented in the MOLARIS-XG package.56

The trypsin-catalyzed peptide bond hydrolysis reaction consists of two steps involving sequential formations of two tetrahedral intermediates. The formation of the first tetrahedral intermediate, which involves a proton transfer from Ser–OH to His–imidazole and the subsequent nucleophilic attack of Ser–O– on the carbonyl carbon of the peptide bond (Figure 5), is the rate-limiting acylation step of the reaction.33 Therefore, it is sufficient to use two diabatic valence bond states, i.e., the structures before the proton transfer and after the nucleophilic attack, as the reactant state/ground state (RS/GS), and the product state (PS) of the hydrolysis reaction, respectively, in the EVB calculation.35,46

Figure 5.

Figure 5

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Schematic description of the acylation step catalyzed by trypsin. Shown are the catalytic triad residues (Asp, His, and Ser) and the tripeptide substrate (Pro–Arg–Ala) involved in the reaction. The structures before proton transfer (reactant) and after the nucleophilic attack (tetrahedral intermediate product) were treated as the two EVB diabatic states, respectively. EVB atoms and their numbers are shown in red, with atomic numbers corresponding to those listed in Table S1.

Each structure of the two enzyme–substrate complexes was divided into an EVB region (or reacting fragment) and a classical region. The former consists of partial groups of the catalytic triad in the enzyme and parts of the substrate (the region colored red in Figure 5), and the latter is composed of the rest of the complex and the solvent. The two complex structures were solvated by a 20 Å radius water sphere centered on the center of the EVB region, using the surface-constrained all atom solvent (SCAAS) model,57,58 and then surrounded by a 2 Å grid of Langevin dipoles. The ENZYMIX force field57 was assigned to the complex except for the EVB region, whose atomic changes in the RS, TS, and PS were taken from a previous study (Table S1).59 Long-range electrostatic interactions were treated using the local reaction field (LRF) method57,60 with a direct cutoff of 10 Å, and no cutoffs were applied to interactions involving the reacting fragment. Each system was first relaxed by a 700 ps MD simulation at 300 K with a time step of 1 fs, and then 60 different structures were chosen at an interval of 10 ps from the last 600 ps trajectory for the subsequent FEP/US simulations. In the FEP/US simulations, each of the 60 starting structure was driven adiabatically from the RS to PS along the reaction coordinate via 51 mapping frames, with each frame being simulated for 10 ps with a time step of 1 fs at 300 K to obtain the mapping potential. Finally, the complete reaction free energy profile was generated by patching together the overlapped free energy functions derived from the 51 mapping potentials. The EVB parameters (off-diagonal term H12 of the EVB Hamiltonian and the gas-phase energy difference Δαgas between the two VB states) were adjusted to reproduce the ab initio results of the imidazole-catalyzed methanolysis of formamide in water,33 and the obtained calibrated values were 80.5 and 164.5 kcal·mol–1 for H12 and Δαgas, respectively.

5.3. Arrhenius Plot Constructions

It has been repeatedly shown that the computationally constructed Arrhenius plots can reproduce the experimentally determined activation enthalpies and entropies of different enzyme-catalyzed reactions.35,46,49−51 In order to obtain the activation entropies and enthalpies of ACT and BT, their Arrhenius plots were constructed as follows: the activation free energy values (ΔG‡) of each enzyme were calculated using the EVB method at eight different temperatures (T = 275, 280, 285, 290, 295, 300, 305, and 310 K), at each of which 60 independent FEP/US simulations were performed as described in the previous section, resulting in a total simulation time of 244.8 ns for each enzyme; then, two forms of Arrhenius plots were constructed by plotting the values of ΔG‡/T against 1/T and the values of ΔG‡ against T, respectively. The slope of the fitted line derived from the least squares linear regression of ΔG‡/T vs 1/T thus corresponds to the activation enthalpy (ΔH‡) of an enzyme, and the activation entropy (TΔS‡) can be calculated based on the equation ΔG‡ = ΔH‡ – TΔS‡.

5.4. LRA Calculations

The line response approximation (LRA) treatment21 was used to evaluate the electrostatic contributions to the solvation free energies (or binding free energies) of the reacting fragment/EVB region in both the GS and TS for the two systems, where the EVB region and its surroundings (including both the protein and water) were considered as the solute and an effective/generalized solvent, respectively. Specifically, the LRA electrostatic solvation energy (ΔGsolvelec or LRA energy) of a given state was calculated by changing the charges of the EVB atoms from 0 (uncharged state) to the actual EVB charges (charged state) using the following equation:25,61,62

5.4. 2

where W + P designates water + protein (i.e., the generalized solvent), U is the interaction potential between the generalized solvent and the solute, UQ and U0 thus represent the potential energy surfaces of the charged and uncharged states, respectively, and ⟨ ⟩Q and ⟨ ⟩0 represent the average over the trajectories propagated on the potential energy surfaces of the charged and uncharged states, respectively.

For ACT and BT, their LRA energies of the EVB region in both the RS and TS were calculated using the POLARIS module implemented in the MOLARIS-XG package to explore the origin of the difference in the catalytic activity between these two trypsins in terms of the magnitudes of RSD and TSS. Specifically, the frames in the RS and TS of each enzyme were first extracted from the previously generated 60 independent MD/FEP/US trajectories and then subjected to the LRA calculations, in which five MD simulations (each for 20 ps at 300 K with a 1 fs time step) were performed to sample conformations of the RS and TS in both the charged and uncharged forms, based on which the LRA energies for both RS and TS were calculated.

Acknowledgments

This work was supported by a grant (2019KF007) from the State Key Laboratory for Conservation and Utilization of Bio-Resources in Yunnan, Yunnan University, the National Natural Sciences Foundation of China (31370715), the Program for Donglu Scholar in Yunnan University, and the Scientific Research Fund Project of the Education Department of Yunnan Province (2020 J0010).

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.0c02401.

  • Cartoon representations of the enzyme–substrate complex structures of the two different temperature-adapted trypsins and their backbone superposition; atomic charges of the reacting fragment for the reactant state (RS), transition state (TS), and product state (PS) (PDF)

Author Contributions

⊥ Y.-L.X. and Y.-P.L. contributed equally to this work.

The authors declare no competing financial interest.

Supplementary Material

ao0c02401_si_001.pdf (361.2KB, pdf)

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