Quantitative Effects of SubstrateâEnvironment Interactions on the Free

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Quantitative Effects of Substrate-Environment Interactions on the Free Energy Barriers of Reactions Deliang Chen, Yibao Li, Xun Li, Wei Guo, Yongdong Li, Tor Savidge, and XiaoLin Fan J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b01094 • Publication Date (Web): 08 May 2019 Downloaded from http://pubs.acs.org on May 8, 2019

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The Journal of Physical Chemistry

Quantitative Effects of Substrate–Environment Interactions on the Free Energy Barriers of Reactions

Deliang Chen,†,* Yibao Li, † Xun Li, † Wei, Guo, † Yongdong Li, † Tor Savidge,‡,§,* Xiaolin Fan†,*

†

Jiangxi Key Laboratory of Organo-Pharmaceutical Chemistry, Chemistry and Chemical Engineering College, Gannan Normal University, Ganzhou, Jiangxi 341000, P. R. China; § Department of Pathology & Immunology, Baylor College of Medicine, Houston, TX 77030, US; § Texas Children’s Microbiome Center, Texas Childrens Hospital, Houston, TX 77030, US; *

: Email: [email protected]; [email protected]; [email protected]

1 ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ABSTRACT:

Quantifying the effects of the intermolecular noncovalent interactions between

substrates and reaction environments on the free energy barriers (FEBs) of both enzymatic and solution reactions is vital for understanding the origin of the enormous catalytic power of enzymes. However, such a task is difficult to accomplish. Using a theoretical derivation approach and experimental validations, we established models to quantify the effects of intermolecular noncovalent interactions on the FEBs of both enzymatic and solution reactions. We found that noncovalent interactions similarly affect the FEBs of enzymatic and solution reactions. We also found that the noncovalent interactions of the substrate atoms undergoing a charge density alteration largely affect the FEBs of reactions. These effects strongly correlate with the H-bonding capabilities of the environmental atoms of the noncovalent interactions. The proposed models make it possible to quantify the catalytic power contributed by substrate–environment interactions and provide guidance for the catalysis of reactions by altering the H-bonding capabilities of the environmental atoms. This study may facilitate enzyme engineering and provide a novel approach for exploring the catalysis of both enzymatic and solution reactions.


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■ Introduction Enzymatic reactions control most biological processes. Therefore, determining the origin of the enormous catalytic power of enzymes is critical to understanding biological systems, 1-4 developing potent enzyme inhibitors,5-7 and exploiting this information for catalyst design.8-10 Enzymes accelerate reactions by bringing the atoms that take part in the reactions to their optimal distances and orientations for effective function 11,

12

and by reducing free energy

barriers (FEBs). Many proposals developed for explaining the enormous catalytic power of enzymes, such as electrostatic interaction13-15 desolvation,16 and electrostatic stress,17 are related to the reduction of FEBs (RFEBs) via noncovalent interactions. However, the factors described in proposals for explaining the catalytic power of enzymes also reduce the catalytic power of enzymes. For example, in the ketosteroid isomerase (KSI)-catalyzed isomerization of 5-androstene-3,17-dione (5-AND) (Figure 1A), the electrostatic interactions of the substrate oxygen atom largely reduce the FEB.18 In contrast, halogenases remarkably catalyze halide alkylations by preventing electrostatic interactions between the substrates and bulk water 16 (Figure 1B). Moreover, the factors affecting enzymatic reactions similarly affect solution reactions. For example, electrostatic substrate–water interactions accelerate some solution reactions (Figure 1C) and decelerate others (Figure 1D). Thus, the intermolecular noncovalent interactions between substrates and their reaction environments greatly influence the FEBs of both enzymatic and solution reactions. But how the intermolecular noncovalent interactions affect the FEBs of reactions is not well-understood, and why enzymatic reactions have much lower FEBs than their reference solution reactions is not fully clarified.



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Figure 1. Examples demonstrating the effects of electrostatic interactions on enzymatic and solution reactions. (A) Isomerization of 5-androstene-3,17-dione (5-AND) catalyzed by ketosteroid isomerase (KSI). The electrostatic interactions between the substrate oxygen atom and polar hydrogen atoms from KSI reduce FEB more than the corresponding electrostatic interactions in the reference solution reaction. (B) Halide alkylation catalyzed by halogenase. Halogenase largely accelerates the reaction by reducing the electrostatic interactions between the substrate (S+ and X-) and water. (C) Electrostatic interactions can accelerate solution reactions. The addition of bromine

to

1-pentene

is

largely

accelerated

by

electrostatic

substrate–water

interactions.19 (D) Electrostatic substrate–solvent interactions can greatly decelerate solution reactions. The reaction rate of the halide-exchange reaction between radioactive iodide ion and iodomethane is approximately 13,000-fold greater in acetone than in water.20, 21


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To resolve this issue, it is vital to develop generic models that reveal the effects of noncovalent interactions on the FEBs of both enzymatic and solution reactions. Because of the similarity between enzymatic and solution reactions, the models should be quantitative so that the differences between enzymatic and solution reactions can be revealed accurately. Thus, the aim of this study is to develop generic models for quantifying the effects of intermolecular noncovalent interactions on the FEBs of both enzymatic and solution reactions. The models are developed by a theoretical derivation approach, and then validated on experimental data. We found that the effect of an intermolecular interaction between a substrate atom and an environmental atom on the FEB of the reaction strongly correlates with the change in H-bonding capability of the substrate atom and strongly correlates with the H-bonding capability of the environmental atom. The proposed approach is useful for exploring the catalysis of enzymatic and solution reactions.

■ Results and Discussion Theoretical derivation for quantifying the effect of noncovalent interactions on FEBs Challenges to accurately quantifying the effect of noncovalent interactions on FEBs. The effect of noncovalent interactions on the FEB of a reaction is complicated. For example, in the addition of bromine to 1-pentenethe in bulk water (Figure 1C), the charge density alterations of bromine atoms cause the change in the electrostatic interactions between the bromine atoms and water, which consequently causes the change in van der Waals interactions and entropies. It is challenging to obtain the effect of the noncovalent interactions on the FEB accurately by



summing the effects of the electrostatic interactions, van der Waals interactions and entropies. To meet this challenge, we seek a parameter that can quantify the relative free energies of the ground state (GS) and transition state (TS) of the reaction, directly providing the effect of noncovalent interactions on the reaction FEB. A good candidate parameter is the standard free energy change (ΔG) when a substrate transits from the gas state to the reaction environment (ΔGtrans, Figure 2A). (Note: unless otherwise specified, all ΔGs in this study are standard free energy changes caused by changes in noncovalent interactions). As shown in Figure 2A, the effect of the substrate-environment interactions on the FEB of the reaction can be obtained from the ΔGtrans values of both the GS and TS directly.

Figure 2: Theoretical approach for quantifying the reductions in free energy barrier (RFEBs) contributed by the intermolecular noncovalent interactions of the atoms undergoing charge density alterations. Unless otherwise specified, all ΔGs are standard free energy changes caused by the changes in noncovalent interactions. Grey symbols represent


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depolarized atoms or groups; colored R and R‡ represent the GS and TS of the substrate atom with a charge density alteration; Sub: substrate. (A) Thermodynamic cycle for demonstrating that the ΔG of transferring a substrate from the gas state to the reaction environment (ΔG trans) can quantify the effect of noncovalent substrate-environment interactions on the reaction FEB. (B) Thermodynamic cycle for calculating the H-bonding capability of the polar atom X.

Terms

ΔG1 and ΔG2 are the ΔGs for transferring the polar X and depolarized X from water to non-polar hydrocarbon. (C) Thermodynamic cycle for deriving the RFEB by the noncovalent interaction of R with bulk water (RFEBaqu, upper). HR and HR‡ are H-bonding capabilities of R and R‡. ΔG6 is zero because the noncovalent interaction during this reaction is constant. (D) (upper) The RFEB by the unrestrained interaction between R and an interacting atom Y in a solution reaction; (lower) the RFEB by the restrained interaction between R and Y in the enzymatic reaction. Terms ∆Greorg_GS and ∆Greorg_TS are standard free energy differences between restrained R…Y and unrestrained R…Y for the GS and TS, respectively.

Meeting the challenge: Introducing the H-bonding capability(a free energy parameter). As we cannot obtain the ΔGtrans of substrates, we adopt a similar free energy parameter called the H-bonding capability. The H-bonding capability of a polar atom is the ΔG of the process for depolarizing the polar atom in bulk water (Figure 2B) and was used to explore the effects of protein–ligand interactions on ligand binding affinities in a previous study. 22 Quantitatively, it equals the difference between the ΔG for transferring the polar atom from bulk water to a non-polar solvent (ΔG1, Figure 2B) and the ΔG for transferring the depolarized atom from bulk water to the non-polar solvent (ΔG2). To quantify the effect of substrate–environment interactions on the FEB of a reaction, we focus on substrate atoms whose charge density alters between the GS and TS (hereafter called the reacting atom), because the noncovalent interactions of substrate atoms with constant atomic charge density alteration have little effect on FEBs (Figure S1). In this study, the reacting atom is symbolized by “R” in the GS and “R‡” in the TS. The environmental atom t that noncovalently interacts with the reacting atom is called



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the interacting atom. The interacting atoms in the enzyme and aqueous solutions are symbolized by “E” and “W”, respectively.

Effect of noncovalent interactions on the FEBs of solution reactions. We first focus on the noncovalent interaction between R and bulk water and explore how the change of the interaction from the GS to the TS affects the FEB (Figure 2C, upper). The RFEB due to the change in the interaction (RFEBaqu) is the opposite of the ΔG caused by the same interaction change (ΔGaqu). This ΔGaqu can be derived from the ΔGs of depolarizing R and R ‡ in bulk water using the thermodynamic cycle shown in Figure 2C. Thus, RFEBaqu equals the difference between the H-bonding capability of R‡ (HR‡) and the H-bonding capability of R (HR) RFEBaqu = −ΔGaqu = HR‡ − HR

(1).

Equation (1) is the generic model for quantifying the RFEB due to the intermolecular noncovalent interaction of a reacting atom with the bulk water. It indicates that the interactions of reacting atoms with bulk water can either accelerate or decelerate solution reactions depending on how the charges of the reacting atoms change. If R ‡ has a higher charge density than R, then HR‡ is larger than HR indicating that the reactions involving an increase in charge density of reacting atoms are accelerated by aqueous solution. Conversely, the reactions with a reduction in charge density of the reacting atoms are decelerated by aqueous solution. Experimental data (Figure 1C&D) also indicate that the solution reactions can be accelerated or decelerated remarkably by bulk water depending on how the charge densities of the reacting atoms change. Thus, Equation (1) offers qualitative and quantitative descriptions of the effect of bulk water on the FEBs of solution reactions.


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We next explore how the noncovalent interaction between R and an imaginary generic interacting atom (Y), which has the same concentration as the hydrogen atoms or the lone-pair electrons in bulk water, affects the FEB of the solution reaction (Figure 2D, upper). Both equation (1) and the H-bond pairing principle reported previously22 indicate that the RFEB contributed by the interaction between R and Y in solution (RFEBsol) is directly proportional to the H-bonding capability of Y (Figure S2): RFEBsol = (HR‡ − HR) HY/HW = ksolHY

(2)

where HW is the H-bonding capability of the hydrogen or lone pair electrons of water (7.02 kJ/mol);22 HY is the H-bonding capability of Y; and ksol is (HR‡ − HR)/HW. Equation (2) describes how a solution reaction is affected by the noncovalent interaction of a reacting atom. Specifically, whether an interaction of a reacting atom accelerates or decelerates its reaction depends only on the charge density alteration of the reacting atom, but the magnitude of the acceleration or deceleration depends on both the charge density alteration of the reacting atom and the H-bonding capability of the interacting environmental atom. Effect of noncovalent interactions on the FEBs of enzymatic reactions. Unlike the interacting atoms in solution that are unrestrained, the interacting atoms in enzymatic reactions are restrained, and their interactions with substrate reacting atoms are close to their optimal geometries from the GSs to TSs. This phenomenon is referred as “electrostatic preorganization” in previous studies.23, 24 The RFEB contributed by a restrained R…Y interaction (RFEBrestr or RFEBenz, see Figure 2D, bottom) differs from that contributed by the corresponding unrestrained R…Y interaction (RFEBunrestr or RFEBsol). This difference can be obtained from the free energy differences between the restrained and unrestrained interactions, as depicted in the thermodynamic cycle of Figure 2D: 9 ACS Paragon Plus Environment


RFEBrestr = RFEBunrestr + ∆Greorg_GS − ∆Greorg_TS

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(3)

where ∆Greorg_GS and ∆Greorg_TS are the standard free energy differences between the restrained R…Y and unrestrained R…Y in the GS and TS, respectively. When stronger interactions are closer to their optimal geometries in solution, then the energy for restraining stronger interactions decreases. Thus, ∆Greorg_TS is less than ∆Greorg_GS if R‡ has a larger charge density than R, or it is larger than ∆Greorg_GS if R‡ has lower charge density than R. Therefore, electrostatic preorganization reduces FEB (RFEBrestr > RFEBunrestr) only when the reacting atom has a larger charge density in the TS than in the GS. If the reacting atom has a lower charge density in the TS than in the GS, then the corresponding electrostatic preorganization increases FEB (RFEBrestr < RFEBunrestr) and is unfavorable. Reactions involving a reduction in the charge density of reacting atoms can be significantly accelerated by the enzymes (e.g. halogenases can accelerate halide alkylations up to 1017-fold).16 Thus, we expect the effect of electrostatic preorganization on the FEBs of enzymatic reactions to be insignificant and RFEB restr is close to RFEBunrest. Based on the above theoretical derivation, we summarize the effect of intermolecular noncovalent interactions on the FEBs of both enzymatic and solution reactions. First, the effect of electrostatic preorganization towards FEBs of enzymatic reactions is small, and thus noncovalent interactions exert similar effects on the FEBs of enzymatic and solution reactions. Second, only the noncovalent interactions of the substrate atoms undergoing a charge density alteration affect the FEBs of reactions. These effects strongly correlate with the H-bonding capabilities of the interacting atoms in the environments. Experimental Validation


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Validating the small effect of electrostatic preorganization on the FEBs of enzymatic reactions. To validate the models, we first validate the small contribution of electrostatic preorganization towards RFEB by comparing the experimental RFEBrestr and RFEBunrest data contributed by interactions of the substrate oxygen atom in the isomerization of 5-AND (Figure 3). The RFEB of the isomerization of 5-AND catalyzed by KSI wild-type (WT) or mutant can be calculated accurately from the infrared spectral shifts of the C=O group of inhibitor 19-nortestosterone in the oxyanion hole of the KSI WT or mutant. 18 The reported C=O infrared spectral shifts were used to calculate the RFEB by unrestrained interactions between the C=O group and bulk water (RFEBunrestr, Figure S3). The RFEBunrestr was higher than 2.0 kcal per mol of interactions (>4.0 kcal per mol of C=O groups) (Figure 3, upper). Based on the experimental FEBs of the reactions catalyzed by Y16F KSI and Y16S KSI reported in a previous study, 18 we obtained that the corresponding experimental RFEB restr is 2.4 kcal/mol(Figure S4). Thus, the ∆Greorg_GS − ∆Greorg_TS for a C=O…HOH interaction is

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