Binding Isotope Effects - Chemical Reviews (ACS Publications)

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Binding Isotope Effects †,‡ ́ Katarzyna Swiderek and Piotr Paneth*,† †

Institute of Applied Radiation Chemistry, Faculty of Chemistry, Lodz University of Technology, Zeromskiego 116, 90-924 Lodz, Poland ‡ Department of Physical Chemistry, University of Valencia, 46100 Burjasot, Spain 3. Conclusions Author Information Corresponding Author Notes Biographies Acknowledgments References

Y Z Z Z Z Z AA

1. ISOTOPE EFFECTS The term “isotope effects” comprises numerous aspects of the different behavior of molecules containing different isotopes. CONTENTS 1. Isotope Effects 1.1. Equilibrium Isotope Effects 1.2. Kinetic Isotope Effects 1.3. Notes on Nomenclature 1.4. Notes on Measuring of Isotope Effects 2. Applications of Binding Isotope Effects 2.1. Ligand-Binding Enzymes 2.1.1. α-(2→6)-Sialyltransferase 2.1.2. trans-Salidase 2.1.3. Thymidine Phosphorylase 2.1.4. Purine Nucleoside Phosphorylase 2.1.5. Sarcosine Dehydrogenase 2.1.6. Chorismate Mutase 2.1.7. Cortcosteroid-Binding Globulin 2.1.8. Hexokinase 2.1.9. Alcohol Dehydrogenase 2.1.10. Lactate Dehydrogenase 2.2. Ligand-Carrying Proteins 2.2.1. Hemoglobin and Myoglobin 2.2.2. Cytochrome P450cam 2.2.3. Hemerythrin 2.2.4. Hemocyanin 2.2.5. Taurine Dioxygenase, (S)-(2)-Hydroxypropylphosphonic Acid, Epoxidase, and 1-Aminocyclopropyl-1-carboxylic Acid Oxidase 2.2.6. Human Serum Albumin 2.3. Nonbiological Host−Guest Systems 2.3.1. Calix[4]resorcarene Hosts 2.3.2. Cyclodextrins 2.3.3. Cylindrical Molecular Capsule Host 2.3.4. Hemicarcerand 2.3.5. Deep-Cavity Cavitand Host 2.3.6. Self-Assembled Capsule 1·4BF4 2.3.7. Self-Assembled [Ga4L6]12− Host © XXXX American Chemical Society

A B B C C D E E F F I J K N O P P Q Q Q R R

Figure 1. Contributions of zero-point energies to EIEs.

R R S S S S S V X X

Figure 2. Energetics of a simplified enzymatic reaction. The perpendicular plane signifies modes orthogonal to the reaction coordinate.

Received: December 19, 2012

A

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These include radioactivity of 3H, 14C, and 35S or NMR activity of 1H, 13C, and 15N to name those most frequently employed in chemical studies. The above examples may be classified as qualitative isotope effects as the isotopic nuclei either have or do not have a particular property. Herein, we are concerned with isotope effects on dynamic processes that can be classified as quantitative because both isotopic species exhibit a given property but to a different extend. In particular, we discuss equilibrium and kinetic processes of (bio)chemical and physical interest. Consequently, we present basic theory underlying equilibrium and kinetic isotope effects to the extent that is necessary to follow the main discussion of this contribution. Most recent and detailed consideration of isotope effects can be found elsewhere.1

approximation is related to the second derivative of energy in the function of movement; thus the steeper is the parabola, the larger is the force constant and the stronger is the bond. Assuming that only zero-point energies (ZPE) are isotope sensitive, ΔGi − ΔGh can be approximated by: ΔG l − ΔG h = (ZPE El ·L − ZPE Ll ) − (ZPE Eh ·L − ZPE Lh ) = (ZPE El ·L − ZPE Eh ·L) − (ZPE Ll − ZPE Lh ) = ΔZPEE·L − ΔZPEL

In the considered case, ΔZPE is smaller than ΔZPE ; thus exp[−(ΔZPEE·L −ΔZPEL)/RT] and EIE are larger than unity. Such EIEs are called “normal”. Obviously, when the reaction in the opposite direction (E·L ↔ E + L) is considered, the EIE is smaller than unity; the isotope effect is then referred to as “inverse”. It should be noted that subtraction of eqs 1.2 and 1.3 describes an isotopic exchange:

1.1. Equilibrium Isotope Effects

The most straightforward definition of equilibrium isotope effects, EIEs, comes from considering equilibrium constants for isotopologues, that is, molecules differing only in isotopic composition. Consider reversible binding of ligand L to receptor E: E + L ⇄ E·L

E + L h ⇄ E·L h

(1.3)

1/2 ⎛ ME·L ML ⎞3/2 ⎛ IxEl·LI yEl·LIzEl·L IxLhI yLhIzLh ⎞ l h EIE = ⎜ E·L L ⎟ ⎜⎜ E·L E·L E·L L L L ⎟⎟ ⎝ Mh Ml ⎠ ⎝ Ix h I y h Iz h Ix lI y lIz l ⎠ 3n L − 6

∏

with equilibrium constants Kl and Kh defined, respectively, as: [E·L l] Kl = [L l][E] Kh =

i

(1.5)

Kl [E·L l]/([ L l][E ]) [E·L l][L h] = = Kh [E·L h]/([ L h][E ]) [E·L h][L l]

3n E·L − 6

sinh(uiLh /2)

3n L − 6

and EIE =

sinh(uiLl /2)

∏ i

sinh(uiEl ·L /2) sinh(uiEh·L /2)

(1.10)

where M are molecular masses, I are principal moments of inertia, ui = hνi/(kBT), νi are isotopic frequencies, and h and kB are Planck’s and Boltzmann’s constants, respectively. Equation 1.10, introduced by Bigeleisen, can be further simplified on the basis of the Teller−Redlich rule to:

(1.4)

[E·L h] [L h][E]

(1.9)

for which the equilibrium constant is equal to EIE. Thus, EIE can be defined as the deviation of the distributions of isotopes from the equal probabilities between compounds at thermodynamic equilibrium. On the basis of statistical thermodynamics, EIE can be calculated from partition functions:2

that is characterized by the equilibrium constant K. Throughout this contribution, we use E to denote a receptor because we mainly focus on active sites of enzymes. For isotopologues of the ligand containing light (l) and heavy (h) isotopes, eq 1.1 can be written as: (1.2)

L

L l + E·L h ⇄ L h + E·L l

(1.1)

E + L l ⇄ E·L l

(1.8) E·L

EIE =

∏ i

uiLh ·sinh(uiLl /2) uiLl ·sinh(uiLh /2)

3n E·L − 6

∏ i

uiEh·L ·sinh(uiEl ·L /2) uiEl ·L ·sinh(uiEh·L /2)

(1.6)

(1.11)

Brackets denote concentrations. The first equality in eq 1.6 defines EIEs. They can be determined from isotopic concentrations of free and bound ligand, but, by far, a better method employs so-called isotopic ratios RL = [Lh]/[Ll] and REL = ([E·Lh])/([E·Ll]) that can be measured very precisely using isotope ratio mass spectrometry. EIE can also be determined from the reaction energetics using the relationship ΔG = −RT ln K:

The simplification is valid under Born−Oppenheimer approximation assuming pure harmonic frequencies are used. Equilibrium isotope effects (EIEs) are connected with any physical process or chemical reaction that reached an equilibrium. Herein, we are summarizing studies on processes and reactions in which a ligand (substrate, inhibitor) binds to the binding pocket of a host molecule (zeolite, enzyme). This subclass of EIEs has been termed binding isotope effects, BIEs (see, however, notes on terminology below).

EIE = e−(ΔG l −ΔG h)/ RT

(1.7)

1.2. Kinetic Isotope Effects

where G is Gibbs free energy, ΔGi = − for i = l and h, R is the universal gas constant, and T is the absolute temperature. Equation 1.7 is also used in theoretical predictions of EIEs, especially when hydrogen isotopes are of interest. Consider a case when the isotopic atom is more strongly bonded in the free ligand than when it is bound to the receptor. This is illustrated by Figure 1 in which a parabola corresponding to the strength of a bond to the isotopic atom on the left (free ligand) is steeper than that on the right (ligand complexed with the receptor); recall that the strength of a bond in the harmonic GE·L i

GLi

Although the literature is rich in examples of kinetic isotope effects (KIEs), in this work only their most important aspects are described to explain the main concepts that allow the reader to follow some of the studies presented in the later parts. Furthermore, because the majority of studies of BIEs concern enzymatic systems only, KIEs on these processes are discussed. Applications of isotope effects to enzymatic systems started in the early 1960s3−6 and matured to become an important experimental tool in the mid 1980s.7,8 It is, however, only recently when theoretical studies of isotope effects on B

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ligands to host systems, although such studies, albeit scarce, have been reported.12−14 Obviously, the equilibrium binding presented in eq 1.12 can be expressed as the ratio of two rate constants, k1 and k−1, and thus isotope effects on these rate constants are kinetic isotope effects on binding:

enzymatic systems are becoming precise enough to support and/or substitute for the experimental results.1,9 The minimal scheme of an enzymatic reaction comprises binding of the substrate L to the enzyme to form the so-called Michaelis complex, which subsequently undergoes conversion to products within the enzyme active site: k1

k2

E + L XooY E·L → E + P

BIE =

(1.12)

k −1

In the steady-state approximation, the apparent rate constant of the reaction 1.12 is given by: kapp =

k1k 2 (k − 1 + k 2 )

(1.13)

and thus the apparent isotope effect depends on three rate constants: k1, rate of the binding substrate to the enzyme; k−1, rate of the release of the substrate from the enzyme; and k2, which can be either the microscopic rate of the chemical conversion in the active site of the enzyme or a net rate comprising all events after the Michaelis complex is formed. For enzymatic systems for which k−1 is much faster than k2, and thus the equilibrium between a free substrate and its complex with the enzyme is established, eq 1.13 simplifies to: k1·k 2 = K ·k 2 k −1

aKIE = KIE1

3nTS − 7

∏ i

∏ i

⎛ R ⎞ BIE = ⎜ L ⎟ ⎝ RE·L ⎠eq

(1.15)

(1.19)

and thus BIEs may be determined from the isotopic ratios of free and bound forms of the ligand at equilibrium conditions. In practice, however, these measurements are usually not so straightforward, and as with any studies of isotope effects the particular experimental protocol depends on the type of isotopic species used, its abundance, and chemical form. Details of available methodologies can be found elsewhere, for example, in a recent monograph on isotopic effects.1 In a simplest case of binding a ligand to an enzyme, the solution contains a mixture of free and bound ligand. It is usually convenient to work under conditions at which the concentration of the ligand exceeds that of the enzyme ensuring that all active sites are occupied and that free ligand molecules can be found in the solution. A substantial part of the ligand should be in the bound form, which makes the demand for the enzyme much higher than in typical enzymatic studies. To measure isotopic ratios of free and bound ligand, it is necessary to isolate the two forms from the solution. One technique used for this purpose is ultrafiltration of the solution through a membrane not permeable to the enzyme−ligand complex. However, filtration through a low cutoff membrane is usually slow, and the isotopic ratio of the free ligand may change in the course of the process. So only relatively rapid, isothermic processes that prevent equilibrium perturbation (such as pressure filtration) are preferred for the purpose of BIE measurements. On the other hand, use of centrifugal filtration,

uiLh ·sinh(uiLl /2) uiLl ·sinh(uiLh /2)

TS uiTS h · sinh(ui l /2) TS uiTS l · sinh(ui h /2)

(1.18)

We conclude this introduction with a brief glance at the experimental techniques used in measurements of binding isotope effects. In theory, experimental determination of BIEs is very simple. From eq 1.6, it follows that

KIE on a reaction (e.g., with rate constant k2 of eq 1.12) can be calculated from the equation analogous to eq 1.11 by excluding the reaction coordinate from the equilibrium constant: 3n L − 6

1+C

1.4. Notes on Measuring of Isotope Effects

where K is the binding equilibrium constant. When k2 is the rate constant of the chemical conversion, or other steps do not contribute to the net rate constant, the apparent kinetic isotope effect, aKIE, depends on two isotope effects: BIE and kinetic isotope effect (KIE) of the chemical step of an enzymatic catalysis, called intrinsic (iKIE):

k ν⧧ KIE = l = l⧧ kh νh

(KIE2)/(KIE−1) + C

where C = k2/k−1 is called commitment toward catalysis. Equation 1.18 simplifies to eq 1.15 when C is negligible. On the opposite, when C is very large, aKIE approaches KIE1, that is, the kinetic isotope effect on binding the ligand to the receptor. As binding usually involves weak, noncovalent interactions, these isotope effects were for many years neglected. Only a few studies have been aimed directly15 or indirectly16,17 at kinetic isotope effects on binding. In the remaining part of this Review, we will discuss only equilibrium isotope effects on binding and we will be using the BIE symbol to denote them.

(1.14)

aKIE = BIE·KIE 2 = BIE·iKIE

(1.17)

Kinetic isotope effects on binding processes have, however, seldom been used and discussed. In fact, when no assumption regarding the relative values of k2 and k−1 is made, the apparent kinetic isotope effect on the process described by eq 1.12 is given by:

klapp/khapp

kapp =

KIE1 KIE−1

(1.16)

⧧

where ν is the frequency of vibration along the reaction coordinate and TS stands for transition state. Figure 2 shows the energetics of a typical, albeit simplified enzymatic reaction, and illustrates that KIEs relate properties of the transition state to those of the reactant. Equation 1.15 signifies the importance of the appropriate accounting for binding isotope effects when KIEs are used in studies of mechanisms of enzymatic processes.10,11 1.3. Notes on Nomenclature

We have elected to reserve the term BIE for equilibrium isotope effects only. However, semantics of the phrase suggest that it should be used to describe any isotope effect on the binding process, regardless of whether it is an equilibrium isotope effect or a kinetic isotope effect. Furthermore, we are neglecting solvent isotope effects on the process of binding of C

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which removes irreversibly the solution from below the membrane, can lead to dissociation of the ligand from the enzyme complicating the analysis. The main alternative method used in BIE studies is equilibrium dialysis in which the membrane separates the part of the solution that contains only free ligand from the one that contains a mixture of both free and bound ligand. Opposite to the previous approach, it takes a long time to reach the equilibrium, while the separation in this arrangement may be rapid and easy. However, only (RL)eq can be easily determined. Measurements of BIEs in such cases are achieved by comparing (RL)eq to the isotopic composition of the original material and require additionally exact determination of the fraction of the bound ligand. The most popular methods for isotopic ratio determinations in BIE experiments are isotope ratio mass spectrometry (IRMS) and dual channel liquid scintillation counting (LSC). However, other specific methods such as conventional mass spectrometry (MS), gel chromatography, or fluorometric titration have also been reported. The choice of the method depends on the isotopes used in the experiment. Most of the BIEs studied in the Schramm’s group were determined using double counting LSC technique in which two radioisotopes of different energetic spectra, for example, 3H and 14C, are counted in different channels and the ratio of counts is taken as the isotopic ratio. In principle, aliquots from two compartments of the dialysis cell could be used directly in these methods if sufficiently radioactive samples are used. The main disadvantage to the above approach is the need of multiple isotopic synthesis because frequently one of the radioisotopes serves as a reporter for a stable isotope introduced at another position (so-called remote labeling procedure18). When the natural isotopic composition may be employed, the IRMS is the method of choice. Extreme precision of isotopic ratio determinations is obtained with this method at the expense of limited, gaseous forms of the sample, such as N2, CO2, or SF6, suitable for analysis. Thus, the isotope in question has to be converted to an appropriate gas prior to the analysis. This approach has been used extensively in Klinman’s laboratory for measurements of the isotope effect of an oxygen molecule binding to its carrier protein. A special vacuum line has been used to convert online dioxygen to carbon dioxide suitable for the IRMS analysis. If the isotopic position of interest cannot be easily converted into a suitable gaseous form, a traditional mass spectrometry can be employed. Anderson used this approach in measurements of BIEs on the complexation of NAD+ and oxamate with lactate dehydrogenase. Depending on the studied ligand, some extra steps, like derivatization in case of oxamate, might be necessary. Furthermore, isotopic synthesis is usually needed for these measurements.

Figure 3. Structures of CMP-NeuAc and UMP-NeuAc.

Table 1. Calculated Equilibrium Isotope Effects for Carboxylate Interactionsa

a

Adapted with permission from ref 22. Copyright 1998 American Chemical Society.

2. APPLICATIONS OF BINDING ISOTOPE EFFECTS Herein (see section 1.3), a BIE is defined as an EIE originating in a change of molecular interactions between an unbounded (usually dissolved in water) and a bounded ligand inside the host system. In many cases, this host system is a protein molecule, although there are examples of other nonbiological types of hosts for which BIEs have been observed. As was shown as early as in the 1980s by Northrop,7 BIE may reveal useful mechanistic information. Sommers and coworkers19 showed that a secondary tritium isotope effect of 1.23 on the slow dissociation of FdUMP from thymidylate

Figure 4. CMP-3F-NeuAc bonded in active site of sialyltransferase in crystallographic structure 2IHZ.23

synthetase supports the hypothesis of formation of a covalently bonded complex. Studies by Lewis and Wolfenden20 on the hydration of a series of antiproteolytic aldehydes and ketones led them to the conclusion that aldehyde binds to the active site of sulfur protease as thiohemiacetal and not either free aldehyde or covalent hydrate. This conclusion was reached by comparison of solvent and secondary deuterium IEs on D

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Figure 5. Structures of sialyl-lactose and sialyl-galactose with the numbering of sialyl ring atoms. Figure 7. Imm-H molecule bonded in active site of HsPNP (PDB ID 1RR651).

at the TS and contradicts the SN2-like mechanism. For the SN1like process, however, a larger 3,3-2H isotope effect is expected. This fact motivated studies of the preceding reaction step to solve the problem whether and how binding interactions at the carboxylate group contribute to the observed KIEs. Because no information was available that could allow for estimation of the magnitude of BIE for this enzyme, ab initio calculations were carried out. It was assumed that BIEs can be produced by the process of binding the CMP-NeuAc carboxylate group. On the basis of this assumption, three simple systems were modeled theoretically: the carboxylate group was considered protonated, ion-paired with Li+, and hydrogen bonded with a water molecule. These models did not reflect interactions with the sialyltransferase active site but were considered to provide evidence for the existence of BIE in this system. The results of calculations, presented in Table 1, show inverse BIEs of different size depending on the model for the 3,3-2H labeled hydrogen atoms, carboxylate 1-14C, and anomeric 2-14C carbon atoms, all of which should contribute to the observed KIEs. It can be noticed that the largest isotope effects were obtained for the protonated carboxylate group model, while a lack of BIE characterized the model with hydrogen-bond interactions between the carboxylate group and water molecule. The largest isotope effects, 0.962 and 0.986 for the 3,3-2H and 2-14C, respectively, when used to recalculate experimental KIE values lead to 1.088 for 3,3-2H and 1.014 for 2-14C (assuming k−1, release from the enzyme, is much faster than forward reaction k2; compare eq 1.15). At that time, specific molecular interactions that take place in the enzyme and that could be responsible for the origin of BIE were not known because the structure of α(2→6)-sialyltransferase remained unsolved until 2007.23 The crystal structure (PDB ID 2IHZ) revealed that in the active site of this enzyme the (modified) substrate, CMP-3F-Neu5Ac, and α-lactose are

Figure 6. Structure of thymidine molecule.

aldehyde binding to papain.20 In the following part of this section, we summarize the available studies of BIEs. 2.1. Ligand-Binding Enzymes

2.1.1. α-(2→6)-Sialyltransferase. Sialyltransferases transfer N-acetylneuraminic acid (NeuAc) from cytidine monophosphate N-acetylneuraminic acid (CMP-NeuAc).21 One of the most interesting features of sialyltransferases is the unique structure and reactivity of this donor substrate; CMP-NeuAc is different from aldoses and ketoses because instead of having a hydrogen atom or hydroxymethyl group bonded to the anomeric carbon, it carries a carboxylate group in this position.22 Horenstein and co-workers investigated the reaction catalyzed by α-(2→6)-sialyltransferase using the addition of non-natural sugar-nucleotide, UMP-NeuAc, which is thought to be a slow substrate for this enzyme. UMP-NeuAc is an analogue of CMP-NeuAc (see Figure 3) with the 4-amino group of the pyrimidine ring being replaced by the oxo group. Experimental and theoretical approaches presented in their papers provided the opportunity to determine BIEs. In their first work published in Biochemistry in 1998,22 the authors focused on KIE studies of rat liver α-(2→6)sialyltransferase. They have observed unusual KIE values; 3,3−2H kinetic isotope effects were too low (1.022−1.033), leading to a surprising value for the partial bonding at the anomeric carbon. Moreover, primary KIE of the carbon atom 2-14C was expected to be substantially different from unity. However, the none measurable KIE was observed for this position. This is inconsistent with the nucleophilic participation

Table 2. Carbon and Hydrogen BIEs and KIEs for TP-Catalyzed Reactions BIE42 on dT binding label 3

5- H 4-3H 1-14C

substrates 3

14

[5- H]dT; [5- C]dT [4-3H]dT; [5-14C]dT [1-14C]dT; [4-3H]dT

in the presence of

KIE on dT depyrimidation

SO42−

1.060 ± 0.002 0.997 ± 0.005 0.990 ± 0.004

phosphorolytic

41

1.061 ± 0.003 1.020 ± 0.003 1.139 ± 0.005 E

hydrolytic44

arsenolytic45

1.033 ± 0.003 1.040 ± 0.003 1.033 ± 0.002

1.019 ± 0.002 1.025 ± 0.003

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Table 3. [5′-3H] BIE Data for Human PNP enzyme native PNP His257Phe His257Gly His257Asp native PNP native PNP

ligand [5′-3H]-, [5′-3H]-, [5′-3H]-, [5′-3H]-, [5′-3H]-, [5′-3H]-,

V/K KIE

[5′-14C]Inosine [5′-14C]Inosine [5′-14C]Inosine [5′-14C]Inosine [5′-14C]ImmH [5′-14C]DADMe-ImmH

1.054 0.992 0.925 1.046

± ± ± ±

0.002 0.003 0.005 0.004

BIE 1.015 1.022 1.024 0.980 1.126 1.292

± ± ± ± ± ±

0.003 0.004 0.006 0.005 0.005 0.012

intrinsic KIE 1.046 0.968 0.859 1.069

± ± ± ±

0.004 0.005 0.007 0.007

the results for this system indicate that BIE values are very small and can be neglected. It should be kept in mind that experimental data were obtained for a rat enzyme, while the crystal structure corresponds to the bacterial enzyme. It seems that a more complex and adequate model that includes enzyme−substrate interactions in the proper active site should be used. Application of such a model can bring different results of BIEs and most likely can better explain the unique results of KIEs obtained experimentally. In 2000, the same group published experimentally measured large inverse BIE values equal to 0.944 ± 0.010 and 0.984 ± 0.007 9,9-3H for the hydrogen atoms at carbon C9 labeled with tritium in the glycol tail of UMP-NeuAc and CMP-NeuAc.24 Unfortunately, no clear explanation of the source of these effects was offered, and the lack of such explanation was ascribed to the lack of structural information about glycol tail− enzyme interactions. With the enzyme structure available, it can be now speculated that the hydrogen BIE at the C9 carbon originates in two types of interactions. The first one comes from weak interactions from Thr268 and Trp270 residues. The second contribution comes from solvent molecules because of the position of the glycol tail, which sticks out from the active site. The glycol tail is placed at the edge of the active site that is widely open to the solution surface. 2.1.2. trans-Salidase. Horenstein’s group has also studied a similar enzyme, trans-salidase.25 This enzyme catalyzes the transfer of the sialic acid NeuAc group from the host glycoconjugates to the parasite surface glycocojugates, leading to the formation of α(2→3) linked products that are thought to be involved in the host cell invasion and immune masking.26,27 In this case, KIE measurements were carried out for βdideuterium and primary 13C positions in the physiological substrate, sialyl-lactose, and a slow substrate, sialyl-galactose (structures of the latter two compounds are presented in Figure 5). Investigations of BIEs were done using two isotopic substrates labeled with either 3H or 14C remote labels. Measurements indicate that there is a small inverse tritium isotope effect equal to 0.993 ± 0.008 in the case of sialyl-lactose labeled in position 6, while for sialyl-galactose, there is a normal BIE equal to 1.024 ± 0.006. 2.1.3. Thymidine Phosphorylase. Human thymidine phosphorylase (TP) is an enzyme of interest because of its link to aggressiveness and invasiveness of several types of human cancers.28−35 TP is a highly specific N-ribosyl phosphorylase, catalyzing the phosphorolysis of 2′-deoxypyrimidine nucleosides. TP catalyzes the chemical reaction between thymine and 2-deoxy-α-D-ribose 1-phosphate leading to thymidine (dT) and phosphate.36−40 The structure of thymidine is shown in Figure 6. Schramm and co-workers41 have modeled the transition state structure for the phosphorolytic depyrimidation catalyzed by TP, which was found to be a near-symmetric SN2 nucleophilic

Figure 8. [5′-3H]-labeled inosine, Immucilin-H, and DADMeImmusilin-H. Adapted with permission from ref 52. Copyright 2008 American Chemical Society.

Figure 9. Structure of [4-2H3]sarcosine.

Figure 10. Equilibrium between conformations of (A) diaxial chorismate and (B) diequatorial in water and enzymatic environment.

bonded as presented in Figure 4. It is clear that the strongest interaction of the substrate carboxylate group corresponds to the hydrogen bond to an arginine. Distances between the oxygen atoms of the carboxylate group and nitrogen atoms of Arg63 are equal to 2.72 and 2.94 Å, respectively. Out of the three considered theoretically, the simplest model representing these interactions is a system in which both CMP-NeuAc and a water molecule are present. However, as it is shown in Table 1, F

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Table 4. Isotope Effects for (A) (diax-chorismate)aq = (diax-chorismate)enzyme and (B) (dieq-chorismate)aq = (diaxchorismate)enzyme for Hydrogen Atoms Calculated at T = 30 °C for Carbon and Oxygen Atoms at T = 22 °C (A)

(B)

AM1/CHARMM label

BIE

BIE × KIE

2

[4- H] [4-3H] [5-2H] [5-3H] [9-2H′] [9-3H′] [9-2H′] [9-3H′] [9-3H2] [1-13C] [7-18O]

AM1/OPLS-AA BIE

0.9889

1.1329

1.0436 1.0006

0.8515 1.0192

0.9504 0.9317 1.0085 1.0112 0.9932 0.9904 0.9706 0.9592 0.9511 1.0017

1.0032

1.0509

1.0013

B3LYP/OPLS-AA

BIE × KIE

BIE

0.8566 1.0210

0.8158 0.7494 1.0531 1.0756 0.9555 0.9380 0.9322 0.9062 0.8515 1.0009

1.0518

1.0099

1.1804

experimental

BIE × KIE

KIE

1.3322

1.003 ± 0.02063

0.8602 1.0109 1.0552

1.012 1.0043 1.0057 1.045 1.053

± ± ± ± ±

0.00463 0.000264 0.000264 0.00364 0.00264

Figure 11. Cortisol bounded in CBG protein (PDB ID 2VDY69).

Figure 13. The binding of Glc to HBH.

In addition to the 5-3H-BIE, 4-3H- and 1-14C-BIEs were measured to distinguish BIEs from KIEs. The 4-3H-BIE is unity, within experimental error. Therefore, the intrinsic 4-3H-KIE of 1.020 is a direct result of the geometry at the TS, rather than binding interactions. The hydrogen atom attached to C4 is remote from most interactions, which could cause a BIE, and is unlikely to be engaged in a hydrogen bond. The lack of 4-3HBIE also suggests that the enzyme does not substantially alter the conformation of the ribosyl ring upon thymidine binding. Thus, ground-state destabilization via modification of the deoxyribose ring geometry is unlikely to play a significant part in catalytic rate enhancement. At this time, an attempt has been made to explain the large value (1.139 ± 0.005) of the carbon kinetic isotope effect for [1-14C]thymidine by invoking large BIEs,43 which, however, in fact turned out to be small and did not provide any insight into the origin of this large KIE value. In 2010, Schramm and co-workers continued their work on TP, and two new reactions, hydrolytic44 and arsenolytic depyr-

Figure 12. Binary complex of HBH active site with the Glc (PDB ID 1CZA73).

displacement of thymine by inorganic phosphate. Additionally, they have measured KIE values. Subsequently, they have measured competitive binding of [1-14C]dT and [5-3H]dT and [4-3H]dT in the presence of the phosphate analogue, SO42−.42 BIEs together with KIE values for the reaction of phosphorolytic, hydrolytic, and arsenolytic depyrimidation of dT catalyzed by TP are presented in Table 2. Preliminary studies indicate that phosphorolytic depyrimidation of dT exhibits 6.0% BIE at the position 5 which accounts, within experimental error, for the entire 6.1% experimentally determined KIE. This means that measured [5-3H] isotope effect is introduced upon the formation of the Michaelis complex and thus it is of equilibrium rather than kinetic origin. G

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Table 5. Experimental Equilibrium Isotope Effect on Binding Glc to HBH Glc labels 3

3

Kα/3Kβ

EIE[α→β] 14

[1- H]+[2- or 6- C] [2-3H]+[2- or 6-14C] [3-3H]+[2- or 6-14C] [4-3H]+[2- or 6-14C] [5-3H]+[2- or 6-14C] [6,6-3H2]+[2-14C]

1.063 1.039 1.039 1.001 1.053 0.997

0.994 0.996 0.996 1.000 0.995 1.000

BIE [binary] 1.027 0.927 1.027 1.051 0.988 1.065

± ± ± ± ± ±

0.002 0.0003 0.004 0.001 0.001 0.003

BIE [ternary] 1.013 0.929 1.031 1.052 0.997 1.034

± ± ± ± ± ±

0.001 0.002 0.0009 0.003 0.0009 0.004

Table 6. Computed BIEs with Their Conjugations label

deprotonation

[1-3H] [2-3H] [3-3H] [4-3H] [5-3H] [6,6-3H2]

1.027 1.010 1.027 1.051 1.050

hydroxyl angle restriction

C5−C6 rotation

steric compression 0.917

1.025

1.004 0.990

0.984

total BIE 1.027 0.927 1.027 1.051 0.988 1.065

imidation,45 were studied. In these cases, KIEs were measured, and the obtained values are presented in Table 2. Surprisingly, these KIE values differ meaningfully from the previously reported. The [1-14C]thymidine KIE is much smaller and equal to 1.033 ± 0.002 and 1.025 ± 0.003 for hydrolytic and arsenolytic depyrimidation, respectively. Computational analysis clearly shows that arsenolytic depyrimidation proceeds via the same concerted mechanism as phosphorolytic depyrimidation, opposite to hydrolytic depyrimidation for which the stepwise mechanism was proposed. The comparison of [1-14C]thymidine KIEs measured for phosphorolytic and arsenolytic depyrimidation shows a surprisingly large difference of over 11%. Moreover, the meaningful change in KIE can be

Figure 15. NADH bonded in the cavity of LADH (PDB ID 1P1R87).

found for [5-3H]thymidine KIE where the difference is about 4.1%. Unfortunately, no explanation for these large deviations was offered. Furthermore, more recent studies did not include reevaluation of BIEs; thus analysis of BIEs contribution to overall KIEs for hydrolytic and arsenolytic depyrimidation cannot be discussed.

Figure 14. Models for ATP binding in the ternary complex proposed by A. Aleshin et al. (upper scheme) and V. Schramm et al. (lower scheme). H

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Table 10. BIE and EIE Effects for [4-2H]NADH in Reaction Catalyzed by M4 and H4 Isoforms of LDH with Explicit Water Modela complex

BIEa

ligand

EIEa

BIE × EIE

M4-NADH··· H4-NADH··· M4-NAD+··· H4-NAD+···

0.9871 0.9880 1.0265 1.0262

···pyruvate ···pyruvate ···L-lactate ···L-lactate

0.9739 0.9650 0.9973 1.0062

0.961 0.954 1.024 1.033

a EIE denotes the isotope effect upon ligand binding step, while BIE denotes the isotope effect upon the cofactor binding step.

Figure 16. Top: Active site of lactate dehydrogenase with oxamate. Bottom: Structure of ligands capable to be bound in the active site of LDH. Ligand in red balls, cofactor in green balls. Adapted with permission from ref 100. Copyright 2011 American Chemical Society.

Figure 17. Heme molecules with O2 molecule bound in the pocket of Hb and Mb proteins.

Table 7. Results of BIE for [1-18O]Oxamate Reported in 1994

Table 11. Summary of Measured Isotope Effects for Hb and Mb Proteins

enzyme model AM1 (full)a

water model TIP4P (full) TIP4P (cut) SCRF SM2/SM3 COSMO experiment

AM1 (cut)b

PM3 (cut)b

0.9999 0.9988 0.9975 1.0075

1.0015 1.0007 1.0216

0.9860 0.9849 0.9837 0.9936 0.9810 0.9840 ± 0.0027

Force field was calculated for all atoms. bForce field was calculated only for oxamate atoms.

a

Table 8. BIEs of Oxamate Heavy Atoms in Chain A (Open) and Chain B (Close Active Site) monomer O5 N6 O1 and O3 C2

dimer

tetramer

chain A

chain B

chain A

chain B

chain A

chain B

0.9942 1.0013 0.9877

0.9953 0.9994 0.9816

0.9912 1.0021 0.9790

0.9920 0.9969 0.9796

0.9908 0.9989 0.9760

0.9933 0.9971 0.9819

1.0002

0.9985

1.0001

0.9979

0.9998

0.9988

2.1.4. Purine Nucleoside Phosphorylase. Human purine nucleoside phosphorylase (HsPNP) is an enzyme that catalyzes the reversible phosphorolysis of purine nucleosides to generate the corresponding purine base (e.g., inosine) and ribose 1-

Figure 18. OxyP450cam active site (PDB ID 2A1M114).

Table 9. Calculated 11-2H- and 7,8,9-2H3-BIE Values for Nonreactive Complexes That Can Be Used for Distinguishing the Isoforms of LDH LDH···

···NADH-L-lactate

···NADH-D-lactate

labeled

M4

H4

M4

H4

[11-2H] [7,8,9-2H]

0.813 0.842

0.879 0.830

0.916 0.757

0.970 0.880 I

···NAD+-pyruvate M4 0.870

···NAD+-D-lactate

H4

M4

H4

0.911

0.947 0.820

0.940 0.862

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of histidine to the unusually large 5′-3H-KIE observed in PNP reaction, and also to assess the importance of the binding step. It has been hypothesized that His257 is responsible for positioning of the O5′ atom as it is shown in Figure 7 and contributes to catalysis dynamics.50 Obtained KIE and BIE results for all types of mutations together with the native HsPNP are shown in Table 3. Normal BIEs of 2% were determined for the native enzyme, His257Phe and His257Gly, indicating that [5′-1H]inosine binds more tightly than [5′-3H]inosine. In contrast, a small inverse BIE of 2% was found for His247Asp, indicating that in this case the tritiated substrate is slightly preferred in the Michaelis complex. The conclusion regarding the magnitude of the 5′-3H-BIE is that its origin is more complicated than it was thought. Despite the fact that 1.5% BIE for the native HsPNP could be explained as the interaction with His257, this interpretation failed when mutated His257Gly, His257Phe, and His257Asp were studied because similar BIE has been found for these mutants. Therefore, the orientation of the 5′-OH group must be a dominant factor in Michaelis complexes. It has been assumed that two factors affect the magnitude of these BIEs: polarization and orientation of 5′-OH relative to one of the C5′-H orbitals. Obtained intrinsic KIEs (Table 3) were larger than the corresponding BIEs, indicating that the V/K KIEs are dominated by TS chemistry, rather than binding of inosine. This finding is in contrast to the results reported by this group for the TP enzyme where the BIE was found to be equal to the V/K KIE. Subsequently, BIEs discussed above were compared to those measured for [5′-3H]ImmH and [5′-3H]DADMe-ImmH, which are the TS analogues. This comparison allowed for the analysis of the bond distortions experienced at the TS with those that occur during the binding.52,53 The structure of inosine with TS analogues is presented in Figure 8. As it can be seen in Table 3, ImmH and DADMe-ImmH yieled large BIEs of 13% and 29%, respectively, which is much more than 1.5% BIE and 4.7% KIE measured for inosine. This suggests that both TS analogue inhibitors of HsPNP undergo larger bond vibrational distortions than occurred in the TS. Also, this is what is expected when the binding of the TS analogue converts a dynamic excursion, which forms the TS into a collapsed protein conformation. It has been assumed that large BIEs for ImmH and DADMeImmH, as previously assigned by authors, originate from two factors: the degree of hyperconjugation between orbitals of the C5′−H bonds and the neighboring electron density at C4′ and O5′, and the polarization. 2.1.5. Sarcosine Dehydrogenase. Sarcosine dehydrogenase (SDH) is a mitochondrial flavoenzyme involved in the conversion of sarcosine to glycine. SDH is one of the major folate-binding proteins in rats and humans. In addition, SDH has a covalently bound flavin-adenine dinucleotide (FAD) that is reduced to FADH2.54−56 Abeles and co-workers57,58 were the first to carry out experiments with a completely deuterated methyl group of sarcosine (Figure 9). They have studied the effect of 2H on the dehydrogenation reaction. In the process, they have also determined how the substitution of 2H for 1H affects the binding of the sarcosine to the enzyme. The Michaelis constants KM for both 1H- and 2Hsubstrates were determined as equal to 1.4 × 10−3 and 3.0 × 10−3 M, respectively. A small KM indicates high binding affinity; however, the relation between the forward and backward rates

Figure 19. Active site of hemerythrin (PDB ID 1HMO).123

Figure 20. The active site of Hc protein (PDB ID 1OXY127).

Table 12. Calculated 18O-BIE and Experimental 18O-BIEs and KIEs 18

entry

FeII + O2 → •−

O-BIE (calc)

1

Fe −OO

2

FeIII−OOH

3 4

FeIV−OOtBu Fe−alkylperoxo

1.0080 1.0093 1.0172 1.0137 1.0187 1.0129

5

FeIVO

1.0287

III

18

O-BIE (exp)

1.0054 (Mb) 1.0113 (Hr) ND ND ND

18

O-KIE (exp) ND

1.0120 (HppE) ND 1.0102 (TauD) 1.0215 (ACCO)

phosphate in the presence of inorganic orthophosphate as the second substrate. This enzyme is involved in purine-salvage pathways and has been proposed as a promising target for the design and development of antimalarial and antibacterial drugs.46,47 Using KIEs for the HsPNP-catalyzed arsenolysis, Lewandowicz and Schramm48 have determined the TS structure. In their earlier studies of TP, observed BIE significantly contributed to the overall KIEs on V/K. It was thus interesting to see if the same is true in the case of PNP. For this purpose, a series of BIEs were determined experimentally using the LSC technique.49 They have measured BIEs for [5′-3H]-, [5′-14C]inosine in the native enzyme and in its mutants where His257 was mutated individually to glycine (His257Gly), phenylalanine (His257Phe), and aspartate (His257Asp), to examine the contribution J

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Figure 21. Structure of caffeine and phenobarbitone isotopologues: (1) unlabeled caffeine, (2) [1-2H3]caffeine, (3) [3-2H3]caffeine, (4) [1,7-2H6]caffeine, (5) [3,7-2H6]caffeine, (6) [1,3,7-2H9]caffeine, (7) 5-(phenyl-[2H5])-phenobarbitone, and (8) unlabeled pheonobarbitone.

Table 13. Binding Isotope Effects of Caffeine and Phenobarbitone Isotopologues

a

structure number

inhibitor

2 3 4 5 6 7

[1-2H3]caffeine [3-2H3]caffeine [1,7-2H6]caffeine [3,7-2H6]caffeine [1,3,7-2H9]caffeine 5-(phenyl-[2H5])-phenobarbitone

BIE 1.20 1.34 1.71 1.82 1.06 0.56

± ± ± ± ± ±

0.12b 0.26b 0.29b 0.21a 0.19a 0.23b

Reference 142. bReference 143 Figure 23. Tetrasulfonate derivatives on calix[4]arene.

Table 14. BIEs for Encapsulation of Acetone and Thioacetone Guests hosts 1 guest

Y=H

Y = OH

acetone-d6 thioacetone-d6

1.08

1.08 1.12

Table 15. BIE by Complexation of Various Guest Compounds with α-, β-, and 6-Amino-6-deoxy-βcyclodextrins at T = 298 K host α-CD

Figure 22. Domain structure of HSA and location of Myr (myristate) and TIB (tri-iodobenzoic acid) binding sites. Adapted with permission from ref 147. Copyright 1998 Nature Publishing Group.

β-CD

of the decomposition of the Michaelis complex remained unresolved. Thus, although the Michaelis constant for [4-2H3]sarcosine is twice as large as the one for unlabeled sarcosine, only the maximum BIE of about 0.47 can be estimated, and most likely it is much lower due to the expected significant contribution of the forward reaction to the Michaelis constant. Studies on sarcosine bound to the dehydrogenase clearly demonstrated that at least two factors affect the observed KIEs. Isotopic selection in a biological system can arise not only from the difference in the reactivity of 2H−C and 1H−C bonds, but

am-β-CD

guest

BIE [KH/KD]

[2H10]1-butanol [2H11]hexanoic acid [2H15]octanoic acid [2H5]N-acetyl-L-phenylalanine [2H8]N-acetyl-L-phenylalanine [2H5]benzoic acid

1.09 1.04 1.14 1.07 1.08 1.08

also from the ability of the enzyme to discriminate between deuterium and protium substrates in the initial binding step. 2.1.6. Chorismate Mutase. B. subtilus chorismate mutase (BsCM) catalyzes the rearrangement of chorismate to prephenate, which is an important step in the shikimate pathway for biosynthesis of the aromatic amino acids phenylalanine and tyrosine in bacteria, fungi, and plants.59,60 K

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analyzed during the transfer of the substrate from water to the active site of the enzyme. Simultaneously, similar studies were done for the binding step of chorismate in the mutase where conformation change of the substrate was not taken into account as is presented in Figure 10A. It seems that the binding step of the chorismate molecule is very important for the reaction pathway, mainly because the TS exhibits a diaxial character. [7-18O]BIE × KIE values of 1.0509, 1.0518, and 1.0552 obtained at the AM1/CHARMM, AM1/OPLS-AA, and B3LYP/OPLS-AA levels, respectively, correlate well with the experimentally measured isotope effects equal to 1.045 ± 0.003 and 1.053 ± 0.002. However, other isotope effects of [1-13C] carbon, [5-3H], and [9-3H2] hydrogen atoms do not show such behavior. For example, 5-3H-BIE obtained with the B3LYP/ OPLS-AA approach deviates from the experimental data by as much as 30%. Table 4 lists results of computed BIEs together with the BIE × KIE values and experimentally observed KIEs. According to Marti et al., the products of BIE × KIE are believed to give the overall KIEs and to represent the best available estimates for the intrinsic KIEs for BsCM. Moreover, comparison of calculated BIE values presented in Table 4 gives a very important observation. For the binding step involving aqueous diaxial chorismate and the diaxial conformer in the BsCM, the calculated 5-3H-BIE is inverse and equal to 0.9889 at the AM1/CHARMM level, while for the binding step of aqueous diequatorial chorismate and the diaxial conformer in the BsCM the isotope effect is normal and equal to 1.1804 at the AM1/OPLS-AA and 1.3322 at the B3LYP/ OPLS-AA levels. A reverse situation is observed in the case of the [9-3H2] hydrogen atom, where normal 1.0436 BIE was obtained for the system without changing chorismate conformation, while results of calculation of BIEs that include diequatorial to the diaxial conformational change are inverse and equal to 0.9511 at the AM1/OPLS-AA and 0.8515 at the B3LYP/OPLS-AA levels. Finding the origin of these different results is not an easy task, and in fact authors did not focus on this comparison. Two possible explanations seem possible. The first is the difference in theory levels used for describing reaction A (see Figure 10), where CHARMM instead of OPLSAA force field was applied. The second is the fact that both labeled hydrogen atoms belong to the tail whose position changes significantly during the change of chorismate conformation. The first explanation seems more plausible because the difference between 5-3H-BIEs calculated at the AM1/OPLS-AA and B3LYP/OPLS-AA levels is about 20%,

Figure 24. Structure of α- and β-cyclodextrins.

Figure 25. Structure of the encapsulation complex of p-xylene and CCl4 in the dimeric capsule (C11H23) and isotopologues of p-xylene. Adapted with permission from ref 151. Copyright 2004 American Chemical Society.

Table 16. BIEs for Competitive Encapsulation

a

CH3-containing guest

CD3-containing guest

2 2 5 5

3 4 3 4

BIEa 0.76 0.76 0.79 0.83

± ± ± ±

0.04 0.04 0.04 0.05

BIE calculated from equilibrium constants.

Marti et al. have presented the results of KIEs for this reaction.61,62 Their studies focused mostly on KIEs, but calculations of BIEs were also carried out, because it was assumed that before arriving at the TS, a rearrangement of the conformation between diequatorial and diaxial forms of chorismate can take place. This conformation change was

Figure 26. Hosts and guests investigated in the Liu and Warmuth study with normal-phase HPLC recycle chromatogram. Adapted with permission from ref 153. Copyright 2005 John Wiley and Sons, Inc. L

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Figure 27. The protio and deuteron hosts with space-filling model of open C4v conformer of basket molecule for host 1. Reprinted with permission from ref 155. Copyright 2001 American Chemical Society.

Table 18. Relative Binding Affinities of [1H6]- and [2H6]Guests 2−5 to Capsule 4BF4a

Table 17. Binding Constants for Protiated and Deuterated Hosts in DMSO-d6a and Associated BIEs Ka/M−1 guest

protiated host

deuterated host

BIE (KH/KD)

adamantane cyanoadamantane bromocyclopentane iodocyclopentane bromocyclohexane iodocyclohexane bromocycloheptane iodocycloheptaneb bromocyclooctane iodocyclooctane 2-bromoadamantane exo-2-bromonorbornane

790 160 82 226 208 923b 419 2230 1330 5960 11 300 610

763 151 86 246 198 1390 448 3370 1230 7920 18 100 837

1.0354 1.0596 0.9535 0.9187 1.0505 0.6640 0.9353 0.6617 1.0813 0.7525 0.6243 0.7288

a

Errors associated with respective Ka determinations are ±10% for an average of at least two titrations. bPrevious determination (ref 156) reported value of 580 M−1.

T [K]

2

323 313 303 293 283 273 263 253 243 233 223

1.12 1.17 1.22 1.27 1.31 1.37 1.45 1.53

3

0.94 1.02 1.08 1.14 1.21 1.32 1.43 1.56

4 1.21 1.29 1.35 1.43 1.48 1.55 1.67 1.75

5

1.33 1.41 1.50 1.62 1.73

The resulting BIEs are listed in the summary Table 22.

a

which is equal to a difference between results obtained with AM1/CHARMM and AM1/OPLS-AA approaches. Differences

Figure 28. The capsule and the structure of the encapsulated complex of 4,4′-diacetoxybiphenyl 2 in capsule 4BF4 with all studied guest molecules. Adapted with permission from ref 157. Copyright 2009 John Wiley and Sons, Inc. M

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Table 20. BIEs on Exterior Guest Binding of [2Hn] at Different Temperatures in D2O and Thermodynamic Parameters ΔΔH, ΔΔS, and −TΔΔS in kcal/mol

Figure 29. (a) Schematic framework of host with bounded ligand. (b) Space-filling model of host. Reprinted with permission from ref 158. Copyright 2005 John Wiley and Sons, Inc.

Table 19. BIEs on Interior and Exterior Guest Binding of [2Hn] to the Host in D2O at 298 K BIE

a

interior

exterior

K0/K2 K0/K5 K0/K7 K0/K9 K7/K9

1.07b 1.00b 1.103b 1.14b

1.012a 1.021a 1.0302b 1.047b 1.017b

K0/K7

K0/K9

1.0302 1.028 1.025 1.026 1.0217 −0.05 −0.13 0.04

1.047 1.045 1.041 1.033 1.030 −0.12 −0.33 0.10

function is the distribution of plasma glucocorticosteroids to their target tissues and cells. CBG controls the bioavailability of corticosteroids in the blood by regulating the free cortisol concentration.65,66 Cortisol, presented in Figure 11, is a hormone involved in various important biological processes such as gluconeogenesis, lipid and protein metabolism, and growth.67,68 It is also a major component of the stress response system. Tritium or 14C-labeled radioactive steroids are used as tracers in hormone assays, receptor assays, and metabolic studies, because identical behavior of labeled and unlabeled forms is assumed. However, this assumption is valid only when BIEs are negligible. Lentjes and co-workers70 investigated whether radioactive labeled and unlabeled cortisol has the same binding affinity for CGB. For the binding studies, serum from healthy volunteers was used. To carry out measurements, they used ultrafiltration (UF), equilibrium dialysis (ED), and ED with UF methods. These experimental measurements of equilibrium constants showed differences in binding affinity for the unlabeled, [1,2,6,7- 3H]-, and [4-13C]cortisol only during the UF procedure; the equilibrium constant, Ka, for the unlabeled cortisol was 46 × 106 M−1, while for [1,2,6,7-3H]- and [4-13C]labeled cortisol the value was 5.8 × 106 and 0.49 × 106 M−1, respectively. Thus, Ka for the unlabeled cortisol was about 8 times higher than that for the tritium-labeled compound, and about 90 times higher than for 14C-cortisol. These results clearly indicate that the experimental protocol is erroneous because resulting BIEs far exceed reasonable values. In agreement with this conclusion, the results obtained with ED revealed no isotope effect, and similar results were obtained when ED was performed in the UF device. The authors

Figure 30. The benzyltrimethylphosphonium isotopologues [2Hn]. Reprinted with permission from ref 164. Copyright 2012 American Chemical Society.

ratio

T (K) 294 300 307 314 320 ΔΔH ΔΔS −TΔΔS (at 298 K)

Reference 163. bReference 164.

in 9,9-3H-BIE, depending on the method, are also similar and equal to 1%. 2.1.7. Cortcosteroid-Binding Globulin. Corticosteroidbinding globulin (CBG) is secreted by the liver, and its main

Figure 31. Diagram showing quantitatively changes in guest [2Hn] C−H and C−D ZPEs upon binding to interior (left) and exterior (right) of the host. Reprinted with permission from ref 164. Copyright 2012 American Chemical Society. N

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single value of measured BIEs for Glc hydrogen atoms. Additionally, to find a reasonable explanation for some surprising BIE results, they resorted to several theoretical methods that included semiempirical (PM3), HF (RHF/3-21G or RHF/6-31G**), and DFT (B3PW91/6-31G**) levels, and carried out calculations for model systems comprising 2propanol, ethanol, collision between 2-propanol and formaldehyde, 1-hydroxymethyl-tetrahydropyran, and cyclohexanol. All calculated BIEs with their components are presented in Table 6. The conclusion that can be generalized from these results is that every normal BIE, such as these obtained for hydrogen atoms attached to C1, C3, and C4 (numbering given in Figures 13 and 14), can be identified as coming from a hydrogen bond between the active site carboxylate, such as Glu742, Glu708, and Asp657, and the hydrogen atom, although, in the case of the hydrogen atoms at C6 with the largest isotope effect of 1.065, its main origin lies in the partial deprotonation of the neighboring hydroxyl group by Asp657. A surprising result was obtained for the hydrogen at carbon 2 for which the large inverse BIE was equal to 0.927. The position of this atom is within a hydrogen bond to Glu708, which would suggest that the normal BIE should be observed as in previous cases. However, steric interaction of this hydrogen with the backbone carbonyl group of Ser603, which seems to interact stronger than Glu708 residue, has been noticed. Contribution of steric interaction was confirmed by simple DFT calculations on the interaction of formaldehyde with 2propanol, which predicted an inverse value of about 6% at the distance of 2.43 Å. Analysis of the distance between Glu708 and the hydrogen atom at C2 (1.027 Å) confirmed that contribution of Glu708 in interaction with this hydrogen atom is much smaller. Finally, the analysis of BIE of a hydrogen atom attached to C5 was much more complicated and included results from calculations for rotation around the C5−C6 bond in the 1-hydroxymethyl-tetrahydropyran molecule that led to a small normal effect of 1.004. Additionally, it has been noticed that the position of Asn683 residue is not axial to this hydrogen atom, and this can be the origin of the inverse isotope effect as is shown in Table 6. On the basis of previous observations on binding Glc to the HBH active site, Schramm and Lewis studied how sugar binding contacts change in the ternary complex of Glc, HBH, and MgATP2− analogue, β,γ-CH2-ATP.76 The main target of these studies was to describe possible interactions in the ternary complex for which no crystal structure is available and to judge if the model of this complex proposed by Aleshin et al.77 was the right one. Aleshin et al. proposed that in the ternary complex, Asp657 is hydrogen bonded to a water molecule of hydrated Mg2+ ion instead of being bonded to the hydroxyl group at C4, as is shown in Figure 14. In the same figure, the alternative model of Glc and ATP binding in the HBH active site proposed by Lewis and Schramm is presented. The model proposed by Aleshin et al. was based on the analysis of experimental BIEs for Glc bounded in the ternary complex. BIEs obtained experimentally are listed in Table 5 As can be seen from the comparison of BIEs obtained for binary and ternary complexes (the last two columns in the table), values of BIEs of hydrogen atoms at C1, C5, and C6 change upon addition of MgATP2− analogue. The remaining BIEs do not change upon binding the ATP analogue to the active site, which strongly implies that the active site contacts to hydroxyl groups at C2, C3, and C4 as well as to CH2 do not change. Thus, BIEs

concluded that during centrifugation, CBG proteins accumulate with other serum proteins on the filter leading to wrong results. Following these findings, they suggested that results reported in the literature on free cortisol determinations, using radioactive labeled cortisol in a UF device in combination with centrifugation, should be revised. 2.1.8. Hexokinase. Human brain hexokinase (HBH) phosphorylates the glucose (Glc) that is transported into the brain by blood. HBH first binds glucose and then MgATP molecule. In the absence of MgATP, Glc forms a catalytically competent binary complex with the enzyme.71 Figure 12 presents such a binary complex. Schramm and Lewis published several articles about this enzyme, mostly focusing on the step of binding Glc in the active site of HBH. Initially they analyzed the conformational EIE using 13C NMR spectroscopy.72 They selected conformational EIE as the initial step describing Glc binding in the active site of HBH because HBH utilizes either α- or β-Glc, as it is shown in Figure 13. The existence of so-called “isotopepartitioning equilibrium” between several unbound conformers or isomers is possible, and, as a result, it may contribute significantly to the observed BIE. This could lead to the anomeric EIE to be interpreted as a BIE. Using inverse-degated H-decoupled 13C NMR spectroscopy, the isotope effects of 1.043 ± 0.004, 1.027 ± 0.005, 1.027 ± 0.004, 1.001 ± 0.003, 1.036 ± 0.004, and 0.998 ± 0.004 for [2- or 6-13C]Glc mixed with [1-2H]-, [2-2H]-, [3-2H]-, [4-2H]-, [5-2H]-, [6,6-2H2]Glc, respectively, were found. The anomeric EIEs were obtained as deuterium IEs. To measure BIE, they used tritium labeled Glc, and subsequently they recalculated EIE[α→β] values using the Swain−Schaad relationship:74 exp KH ⎛ KH ⎞ =⎜ ⎟ KT ⎝ KD ⎠

(2.1)

where Ki is the equilibrium constant for isotope i (H, hydrogen; D, deuterium; and T, tritium). The EXP value for hydrogen isotopes is assumed to be close to 1.44. Recalculated from deuterium isotope effects, values of tritium isotope effects for Glc are presented in Table 5. Subsequently, Schramm and Lewis measured BIEs for the binary complex of Glc with the HBH enzyme in the absence of MgATP2− using the ultrafiltration technique.75 Experimental results are listed in Table 5. The largest effects observed are 0.927 for [2-3H]Glc, 1.051 for [4-3H]Glc, and 1.065 for [6,6-3H2]Glc, indicating significant vibration changes experienced by every backbone hydrogen atom in Glc. To establish the contribution of EIE[α→β] to the total measured BIE for binary complex, Kα = 15.4 ± 3.0 μM and Kβ = 23.7 ± 3.1 μM were determined. The ratio of Kα to Kβ is 0.65, and the contribution of this “prebinding equilibrium” to the observed BIE is shown in Table 5. At the established affinity ratio of 0.65, the anomeric EIEs do not contribute significantly to BIEs; therefore, the authors concluded that the experimental BIEs must result from the isotopic fractionation during the binding. Thus, the BIE results can be interpreted in terms of binding equilibrium only. Apart from finding that EIE[α→β] does not contribute to BIE values, Lewis and Schramm presented, for the first time, the application of isotope effects to understanding hydrogenbonding interactions made between a substrate and the enzyme in the Michaelis complex. These authors deeply analyzed every O

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play an important role in the binding of the coenzyme to LADH prior to the binding of the second substrate. 2.1.10. Lactate Dehydrogenase. Lactate dehydrogenase (LDH) catalyzes reversible conversion of pyruvate to lactate in the presence of nicotinamide adenine dinucleotide. Human serum normally consists of five isoenzymes, which differ in molecular structure and in consequence in tissue specificity, affinity to ligands (substrates and inhibitors).91−95 In 1989, Anderson and co-workers96 showed that formation of the LDH-NAD+ binary complex is accompanied by a measurable isotope effect. They have measured the BIE of [4-2H]- and [4-3H]NAD+ using whole molecule isotope ratio mass spectrometry and 3H/14C scintillation counting methods. The obtained values equal to 1.10 ± 0.03 and 1.085 ± 0.01 for [4-2H]- and [4-3H]NAD+, respectively, clearly indicate that the bond between C4 and the hydrogen atom has a smaller ZPE when NAD+ is bound to the enzyme; that is, at least one of the vibrational force constants has been decreased by binding to the enzyme. Later in 1995, Anderson and co-workers16 extended studies of this system to the ternary complex of LDH-NADH and oxamate, a potent inhibitor of the enzyme. Figure 16 illustrates the binding of NAD+ and oxamate in the active site of LDH. Sites of isotopic labeling are indicated by red, and the numbers indicate the position as it is used in the discussion. As in the case of a binary complex, to obtain theoretical BIE values for [1-18O]oxamate, it was necessary to compute two separate systems composed of ligand aqueous solution and bounded in the active site of LDH. Oxygen BIEs have been modeled theoretically at the semiempirical level.17 The model of the LDH active site was very simple; it contained only important aminoacids from the active site: Asn138, Arg106, Arg169, His193, as well as a NADH molecule. However, during optimization only the position of oxamate atoms was allowed to be changed. Several solvent models of the oxamate−water system (explicit 22 water molecules described by TIP4P model as well as continuum SCRF, SM2/SM3, and COSMO models) were examined. Calculations yielded inverse values of BIE in the case of AM1 parametrization in agreement with the experimental value. The obtained results are collected in Table 7. Unfortunately, experimental and theoretical results, despite both predicting inverse BIEs, differ meaningfully by 2%. It should be noted that experimental measurements of [1-18O]oxamate BIE were carried out for LDH extracted from rabbit muscles, while the theoretical calculations were done using the available structure, which was obtained for dogfish LDH. This, together with a simple theoretical model of the active site, could lead to the above-mentioned discrepancies. Recent developments in QM/MM methodology provide an opportunity to carry out calculations for much larger models, including full tetrameric structure of LDH, which allows for verification of previously reported theoretical results. This new ́ theoretical approach was used by Swiderek and Paneth in their studies of IEs on inhibitor (oxamate) binding to LDH from rabbit muscles. The structure of this particular LDH (PDB: 3H3F)97 is unique because it contains simultaneously open and close conformations of the active site. It was thus possible not only to verify an experimental value of [1-18O2]oxamate BIE (see Table 8) but also to indicate that BIEs are very sensitive to the size (monomer, dimer, or tetramer) of the theoretical model.

should not be observed on the transition between binary and ternary complexes. However, BIE for hydrogen at C6 was found to change from 1.065 to 1.032. This change supports the model presented by Aleshin at al. in which a weakening of the hydrogen bond between the oxygen atom at C6 and Asp657 occurs. Yet, if this model was correct, the BIE change should be also observed for the hydrogen atom attached to C4, which is not the case; the experimentally determined value is unchanged between binary and ternary complexes, which suggests that conformational changes involving Asp657 are unlikely. Changes of BIEs for hydrogen atoms at C1 and C5 atoms while going from binary to ternary complexes were explained by ATP binding, which can shift the positions of Asn683 and Glu742. This can affect the strength of hydrogen bonding between Glu742 and the hydroxyl group at C1, as well as the steric contact of the hydrogen at C5 with Asn683. It seems that BIEs reported by Schramm and Lewis strongly support a lack of water molecule participation in the ternary complex of HBH, Glc, and MgATP analogue. In summary of their work, the authors suggest that experimentally obtained BIEs support the idea that HBH uses ground-state destabilization of glucose alone. 2.1.9. Alcohol Dehydrogenase. Horse liver alcohol dehydrogenase (LADH) has been known to be an effective catalyst of oxidoreduction reactions of a wide spectrum of substrates, for example, alcohols, aldehydes, or ketones.78−83 LADH requires NAD+ or NADH cofactors, which bind in an extended conformation across the C-terminal edge of the parallel β-sheet of the domain in such a way that each half of the dinucleotide is positioned on separate sides of the sheet, the adenosine half in a cleft at the surface of the domain and the nicotinamide half deep in the protein at the active site cleft.84−86 The binding site of NADH in LADH is presented in Figure 15. Isotope effects on the dissociation constants of NADH have been studied by a few groups to characterize cofactor binding steps. The first isotope effects on the Michaelis constant for NADH (vs NADD) have been reported by Mahler et al. in 1962.88 They obtained two different BIE values: 1.31 ± 0.64 and 0.50 ± 0.1 for (4R)- and (4S)-[4-2H1]NADH, respectively. Later, however, Taylor and de Juan, in their work from 1976,89 argued that KM constants obtained in the Mahler et al. experiments did not reflect the binding reaction, suggesting that the constant could be affected by the rate constants from other reaction steps. In the same article, they have reported the BIE value equal to 1.00 ± 0.02 for binding NADH in the active site of LADH. This result contrasted not only with the result obtained by Mahler but also was very different from results presented by Shiner and co-workers in 197190 where an inverse isotope effect of 0.58 ± 0.10 was calculated from the results of independent determinations of the dissociation constant for NADH and NADD using both gel exclusion chromatography and fluorometric titration. Explanation of these discrepancies can be sought in different experimental methods and conditions of BIE measurements. It seems that the method used in the 1971 experiment was extremely sensitive to a number of external conditions, and the gel filtration method required extreme instrumental sensitivity. It was concluded that the main reason for the difference in the observed values might be different pH conditions. Trusting their own results, Taylor and de Juan concluded that lack of BIE in their experiment indicated that strain involving the hydrogen in the C-4 position of the nicotinamide ring does not P

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that metal−oxygen interactions, as well as protonation at oxygen, have to contribute to the BIEs of oxygen bonded to heme in Hb and Mb proteins, and this motivated them to seek the experimental values. Additionally, they have carried out isotope effect calculations for O2 + 2e− + H+ ⇄ HO2•− reaction assuming that the final product of the reaction is hydrogen superoxide. Results of the measured BIEs of oxygen and calculations for HO2• are presented in Table 11. In the case of Hb and Mb, the combination of such techniques as X-ray crystallography,105 neutron diffraction,106 and infrared spectroscopy107−109 implicates a metal complexed oxygen molecule that is hydrogen bonded to a distal histidine (Figure 17). The studies were focused on this hydrogen bond created between oxygen and histidine suspecting its significant influence on the BIEs. Surprisingly, the measured isotope effects, 1.0039 ± 0.002 for Hb and 1.0054 ± 0.006 for Mb, turned out to be smaller than the value of 1.0103 calculated for the protonated superoxide. The authors attributed the reduction in the magnitude of experimental isotope effects for Hb and Mb, relative to protonated superoxide, to the increased bonding of the oxygen atom. To find interpretation for the obtained isotope effects values, they used information from Shaanan’s105 work who reported that in the α subunit of Hb, the distance between the nitrogen atom of the distal histidine side chain and the terminal oxygen atom of dioxygen bound to iron is 2.7 Å, shorter than in Mb where it is 3.0 Å (the β subunit of Hb shows longer distances between the nitrogen of distal histydine equal to 3.3 Å). These distances are in keeping with two structures of Hb and Mb from PDB (ID 1HHO103 and 1MBO104). The measured distances between O2 and a nitrogen atom of distal histidine for these crystallographic structures are presented in Table 11. Other explanations, like underestimation of the number of isotopically sensitive vibrations by the DFT calculations, have been offered for such systems.110 However, it should be pointed out that these calculations were performed using very crude models, and thus such conclusions would require much further work to be used as an argument. Using Shaanan results, the authors concluded that the net hydrogen bonding to Hb should be stronger than to Mb. This conclusion was supported by the fact that the obtained BIE in Hb protein is smaller than that in Mb protein by a small but significant difference of about 0.15%. In 2006, Klinman and coworkers111 remeasured the BIE for myoglobin, but this time for the enzyme from horse muscle. The obtained results are in good agreement with the previous data: 1.004 ± 0.002 and 1.003 ± 0.001 measured at 20 and 4 °C, respectively. 2.2.2. Cytochrome P450cam. The bacterial monooxidase cytochrome P450cam (CYP101) has a well-studied mechanism for molecular oxygen activation and camphor hydroxylation.112,113 Turnover by heme-containing P450cam is supported by a pair of electron-carrying proteins: the iron−sulfur cluster-containing putidaredoxin (Pdx) and the flavoprotein putidaredoxin reductase (PdR). In contrast to hemoglobin and myoglobin, where heme forms coordinate bonds to imidazole moiety of the histidine, in the case of P450cam the role of histidine is taken over by a cysteine with heme forming coordinate bonds to the thiolate, as is shown in Figure 18. The isotope effect on O2 binding to P450 was measured by the Klinman’s group111 by a modified procedure used previously for myoglobin and several other carrier proteins. With oxyP450cam, a BIE of 1.0048 ± 0.0003 was observed. The obtained result can be compared to the previously

It has been shown that the quaternary structure significantly affects the structure of the active site and including tetramer in theoretical calculations is essential to obtain correct results of BIEs at least for this enzymatic system. On the basis of these studies, it was shown that the calculated isotopic effects of a ligand binding to an active site are very sensitive to changes in geometry, and to the size of the theoretical model.98 In this case, the largest change was observed for the BIE of the nitrogen atom N6. BIE results computed for the closed conformation of the active site showed that [6-15N]oxamate BIE can change its character from being normal (BIE > 1) in the monomer model to being inverse (BIE < 1) in case of tetramer. Recently,99,100 studies on LDH were extended to examine new application for BIEs. These studies were focused on determining whether ligand BIEs in the active site of LDH are useful in distinguishing the H4 and M4 isoforms of LDH. BIEs were calculated theoretically for oxamate, pyruvate, L-lactate, and D-lactate (see Figure 16) bound in active sites of these two isoforms. Obtained BIE results indicated that all heavy atoms of four ligands interact with active sites of the isoforms of LDH in a very similar way, and only the deuterium BIEs could provide a useful tool for distinguishing the M4 and H4 isoforms. BIEs results for 7,8,9-H3- and 11-H-atoms labeled by deuterium are shown in Table 9. The 7,8,9-2H-BIE measurements seem to be useful in cases of three LDH complexes, with bounded NADH and D-lactate, NAD+ and pyruvate, and NAD+ and D-lactate; however, the largest difference between isoforms shows the LDH-NADH-D-lactate ternary complex with difference of about 12%. The remaining complexes give a difference of about 4%; only LDH-NADH-L-lactate is a complex for which the difference is about 1%. Additional theoretical studies of BIEs on the cofactor binding to the active site of LDH showed that these isotope effects do not distinguish the isoforms of this enzyme, but they highlighted the possibility for future KIEs interpretation. The 4-2H-EIEs for NADH and NAD+ cofactors, which describe the change in the isotopic ratio between cofactor bound in active site with or without the ligand, are listed in Table 10. Using a total value of the observed isotope effect defined as a product of BIE and EIE equal to 0.932 and 0.877 for M4 and H4 isoforms of LDH, respectively, for the LDH-NADH-L-lactate ternary complex, a 5% difference is obtained in 2H-BIE values that can be observed experimentally. Moreover, the presented results provide an important conclusion that BIE × EIE values are different from unity. This suggests that experimentally observed KIEs for pyruvate to lactate transformation should be smaller, while for the reverse reaction the observed KIEs should be larger than intrinsic KIEs. 2.2. Ligand-Carrying Proteins

2.2.1. Hemoglobin and Myoglobin. Hemoglobin (Hb) and myoglobin (Mb) are respiratory proteins that serve to transport and store molecular oxygen in living bodies. Hb consists of four polypeptide chains, while Mb is a single globin protein. Both contain the heme group embedded in the pocket of the globular protein.101 The heme forms coordinate bonds with the imidazole of the histidine residue of the pocketforming segment of the globin and becomes the oxygen binding site, as shown in Figure 17. Literature data indicate that in these types of oxygen carriers a formal reduction of dioxygen to superoxide takes place, which involves bond order changes. Klinman and Tiant102 assumed Q

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published value for sperm whale myoglobin of 1.0054 ± 0.0006 or the values of 1.004 ± 0.002 and 1.003 ± 0.001 for horse myoglobin. The explanation for the large similarity in obtained BIE values comes from the O−O stretching frequencies estimated for oxymyoglobin (∼1131 cm−1)115 and measured for oxyP450cam (1140 cm−1),116 which indicate a very similar O−O bond order in both complexes. In the same studies, the KIE of 1.0147 ± 0.0007 was determined, indicating that the reaction at the iron center is fully or partially rate limiting for kcat/KM(O2) in P450cam. 2.2.3. Hemerythrin. Hemerythrin (Hr) is one of the three major metalloproteins capable of reversibly binding dioxygen.117−119 It differs fundamentally from hemoglobin by possessing an active site containing two nonheme iron atoms linked by carboxylate groups and a μ-oxo bridging atom.120 Upon binding dioxygen, a charge is transferred from both iron atoms to dioxygen to form a peroxide complex,121,122 Fe2(III)− O22−, as is shown in Figure 19. Isotope effects on the vibration spectra of the bound oxygen provide the strongest evidence for the proton transfer to the peroxo anion and the existence of a hydrogen bond between the μ-oxo bridge and the protonated dioxygen species. In the same article where BIE of dioxygen formation (hemoglobin and dioxygen) myoglobin proteins were described, Klinman102 presented measurements for Hr. Experimental value equal to 1.0113 ± 0.0005 was compared to the computed values of BIEs to provide a more quantitative context for the interpretation of the oxygen isotope effect. In this case, isotope effect calculations for O2 + 2e− + 2H+ ⇄ H2O2 reaction were carried out. This is because Hr is believed to reduce O2 to peroxide.124 The obtained value of 1.0089 is in very good agreement with the measured one. The experimental value is slightly larger, consistent with the known structure in which the O−H bond of Fe(III)−OOH is weakened by the hydrogen bonding to the bridging oxygen. 2.2.4. Hemocyanin. Hemocyanin (Hc) is the latest protein included in the measurements of dioxygen BIEs in the work of Klinman’s group. Hemocyanin is an oligomeric blue copper containing respiratory proteins with an extremely high molecular weight and a complex quaternary structure that plays a significant role as the dioxygen carrier.125 Whereas in Hb, Mb, or Hr the dioxygen is bound by an iron atom, in Hc protein, the oxygen molecules are bound as peroxides between two copper atoms.126 Each copper atom is complexed by a set of three histidines, which form the connection to the protein backbone as presented in Figure 20. The measured BIE for the binding of dioxygen in the active site of Hc protein is equal to 1.0184 ± 0.0023. The X-ray structure of hemocyanin was not yet available by the time the measurements were carried out; thus the interpretation of experimental BIEs was based on the available structures of Cu2O2 complex in the active site of Hc protein, solved by Shiemke128 and Kitajima.129 As in other cases, the authors compared the experimentally obtained BIE value to theoretically calculated isotope effects. The measured value of the dioxygen BIE for this protein seemed to be the most interesting and controversial result, mostly because it is not in agreement with the computational data, as it was in the case of Hr protein. The comparison of the experimental BIE with the isotope effect calculated for O2 + 2e− + 2H+ ⇄ H2O2 and O2 + 2e− + H+ ⇄ HO2− reactions, for which obtained values are 1.0089 and 1.0343, respectively, indicates that the bonding of oxygen in

hemocyanin lies somewhere between fully protonated neutral peroxide and monoprotonated anionic peroxide intermediate. 2.2.5. Taurine Dioxygenase, (S)-(2)-Hydroxypropylphosphonic Acid, Epoxidase, and 1-Aminocyclopropyl1-carboxylic Acid Oxidase. Apart from Hr, which is a nonheme iron enzyme, Klinman and co-workers130 studied the 16 O/18O KIEs for O2-activiting enzymes to probe the early steps involved in O2 activation up to and including the ratedetermining step for three nonheme iron enzymes. These enzymes activate O2 at an iron center coordinated by a 2-His-1carboxylate facial triad: taurine dioxygenase (TauD), (S)-(2)hydroxypropylphosphonic acid (S-HPP), epoxidase (HppE), and 1-aminocyclopropyl-1-carboxylic acid oxidase (ACCO). TauD is an enzyme that catalyzes the hydroxylation of taurine in bacteria.131 HppE is a reductase-dependent enzyme that catalyzes the epoxidation of S-HHP, the last step in the biosynthesis of the antibiotic fosfomycin.132 ACCO is an ascorbate-dependent enzyme that catalyzes the last step of ethylene biosynthesis, an important plant hormone.133 As was the case in studies of chromosome P450cam, the 18O-BIEs were used as the upper limits for the measured 18O-KIEs. However, in the case of TauD, HppE, and ACCO, the BIEs for reactions involving no O−O bond cleavage were determined not experimentally but theoretically using previously published frequencies. The calculated 18O-BIEs are 1.0080, 1.0172, and 1.0287 for FeIII−OO•−,102 FeIII−OOH,134 and FeIVO species,135 respectively. In addition, 18O-BIEs of 1.0187 and 1.0129 were calculated for a Fe-alkylperoxo species, FeIII− OOtBu,136,137 respectively. All results are presented in Table 12. The interpretation of the measured 18O-KIEs using the calculated BIEs allowed the authors to obtain information on the first irreversible step of the O2 activation. As the result of the analysis by including 18O-BIE values for different reductants, they concluded that the measured 18O-KIEs for the three O2-activating nonheme iron enzymes, which use different reductants, have been directly related to each enzyme’s distinct chemical mechanism. For TauD, the 18O-KIE measurement provides direct evidence for the first irreversible step of O2 activation where observation suggests a rate-limiting formation of the peroxohemiketal intermediate. Similarly, a rate-limiting formation of an FeIII−OOH species is suggested for HppE. By contrast, in ACCO, the conclusion is that an FeIVO is formed in the first irreversible step. 2.2.6. Human Serum Albumin. Serum albumins are the major soluble protein constituents of the circulatory system and have many physiological functions.138 Their principal function is to transport fatty acids,139 but the most important property of this group of proteins is that they serve as transporters for a variety of compounds. Human serum albumin (HSA) is the one major drug binding protein in serum.140 Thus, the affinity of drugs toward albumin is of great importance. Many compounds, especially amphiphilic drugs and some endogenous substances, bind reversibly and with high affinity to HSA.141 Unfortunately, not too many binding isotope effects studies have been done until now on this system. One can find in the literature results of Brazier and co-workers who focused on studies of caffeine and phenobarbitone binding to HSA, which included BIE measurements.142,143 Their studies included five isotopologues of caffeine ([1-2H3]caffeine, [3-2H3]caffeine, [1,7-2H6]caffeine, [3,7-2H6]caffeine, and [1,3,7-2H9]caffeine) and one of phenobarbitone (5-(phenyl-[2H5])-phenobarbiR

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not be exhaustive and some other equilibrium isotope effects might be considered binding isotope effects. 2.3.1. Calix[4]resorcarene Hosts. Aoyama and co-workers149 studied C−H···π interactions in the complexation of highly hydrophilic guest molecules, acetone, and thioacetone, with calix[4]recorcatene host. The host presented in Figure 23 in which Y = H or OH and R = CH2CH2SO3−Na+ was used in BIEs measurements. Although the main focus of these studies was on thermodynamic parameters of the guest−host binding, three BIE values presented in Table 14 have been reported. The origin of normal BIEs in this case has been attributed to the effect of slightly larger polarizability observed for deuterated as compared to the corresponding nondeuterated molecules. Thus, these BIEs support the concept of describing C−H···π interactions between aromatic rings (soft bases) and C−H moieties (soft acids) in terms of the polarization-induced dipole with the charge-transfer character. 2.3.2. Cyclodextrins. In 2002, Inoue and Rekharsky150 studied α-, β-, and 6-amino-6-deoxy-β-cyclodextrins (α-, β-, and am-β-CDs) with a wide variety of guests (see Table 15). Figure 24 shows the structures of α- and β-cyclodextrins. The deuterated guests examined with a specific CD included [2H10]1-butanol, [2H11]hexanoic acid, and [2H15]octanoic acid with α-CD, [2H5]N-acetyl-L-phenylalanine and [2H8]N-acetyl-Lphenylalanine with β-CD, and [2H5]benzoic acid with am-βCD. BIE values for deuterated guests are listed in Table 15. It has been observed that all of the examined deuterated guests gave lower affinities toward α-, β-, or am-β-CDs than the nondeuterated isotopologues. The authors concluded that the consistently lower affinity of deuterated guests toward CDs originates from the physicochemical properties of the hydrophobic moiety of the deuterated guest molecules. Theoretical explanations of this behavior have been sought in the difference of C−D and C−H bond lengths, with the C−D bond being shorter than the C−H bond, what leads to a smaller inducted dipole for C−D than for C−H. It is an important observation because induced dipole plays an essential role in the van der Waals interactions upon guest inclusion by a CD. However, other effects such as hydrogen bonding or polarization-induced vibrational shifts of isotopic frequencies cannot be ruled out. 2.3.3. Cylindrical Molecular Capsule Host. The Rebek’s group observed inverse BIEs (KH/KD) within cylindrical cavitand hosts in mesistylene-d12 for encapsulation of p-xylene and CCl4.151 The host and studied isotopologues of p-xylene are presented in Figure 25. BIEs recalculated from NMR experiments are presented in Table 16. The values of BIE in the range of 0.75−0.83 show preference for encapsulation of deuterated rather than protiated CH3− group. This tendency is explained as being the result of the close interactions between the methyl group and the surrounding π-systems inside the capsule. Additionally, experimentally observed BIEs were modeled theoretically.152 In the theoretical model, the guest and the host were simplified to molecules of methane and benzene, respectively. An increase in C−H stretching frequencies of xylene upon encapsulation has been predicted. Isotopic fractionation was successfully explained by differences in ZPE levels. C−H···Ar (π-system) interactions represent the so-called “blue-shifting” hydrogenbonding systems inside the capsule. 2.3.4. Hemicarcerand. Warmuth and Liu153 studied BIEs for single isolated molecules inside a highly polarizable

tone). The structures of examined inhibitors are presented in Figure 21. Ligand concentrations, measured by GC/MS, were used to calculate the association constants (Ka) of isotopologues. Isotopic Ka values were directly recalculated to BIEs for the purpose of this Review. Final results are shown in Table 13. Interpretation of BIE results obtained for caffeine isotopologues is complicated because of large experimental errors, and at the first glance BIE values seem to be conflicting. For all four experimental values to be simultaneously correct, it is necessary to assume the maximum BIE for [1,3,7-2H9]caffeine of about 1.44 (experimental value of 1.06 plus double the standard deviation) and additivity of BIEs at different positions. With these assumptions, BIEs for [1-2H3]-, [3-2H3]-, and [7-2H3]caffeine are about 1.1, 1.15, and 1.2, respectively, with uncertainty of about 0.2 for each value. Any alternative interpretation requires questioning of the result obtained for either [3,7-2H6]- or [1,3,7-2H9]caffeine. Results for phenobarbitone isotopologues show that they bind differently to HSA. Moreover, 5-(phenyl-[2H5])-phenobarbitone has very high affinity to the carrier, higher than an unlabeled molecule, and higher than caffeine, which can result in the inhibition of caffeine binding. Another complication of the discussed results comes from the analysis of the HSA structure. HSA is an example of proteins that contain more than one binding site; according to the literature, there are five principal sites for medium or longchain fatty acids144−146 (see Figure 22). Brazier and co-workers have concluded that the total number of binding sites of all five deuterated isotopologues exceeds that of unlabeled ligand. The number of binding sites increases with deuteration from one for unlabeled caffeine to three sites for [1,3,7-2H9]caffeine. Thus, proposed interpretation supports the hypothesis of differences in the number of sites for each isotopologue, implying that isotopic substitution may modify the ligand affinity to different binding sites present in HSA and thus simple analysis of the obtained BIEs cannot be done. This interpretation, however, does not seem plausible, as it would require deuterium BIEs to substantially exceed reasonable limits even for primary KIEs. 2.3. Nonbiological Host−Guest Systems

BIEs play an important role not only in the biological systems, where their origin comes from the enzyme−ligand interactions, but also in so-called host−guest systems, that is, supramolecular systems where nonbonding interactions occur between guest (smaller) and host (larger) molecules. These systems can serve as models for interactions of ligands with receptors that might be considered as an intermediate between host−guest systems and the binding of molecules in enzyme active sites. The first isotope effect for a system of this type was the binding of helium in graphite observed by Baskin and co-workers.148Although the authors did not present any specific value of the BIE, their observation that the activation energy for the desorption of 4He is nearly 3 times that for 3He (21.0 and 8.1 kcal/mol, respectively) suggested the presence of a huge BIE. Recently, more groups have worked on BIEs in such systems. Opposite from clearly defined enzymatic systems, nonbiological host−guest systems are much harder to be unequivocally defined, and consequently comprehensive presentation is not simple. Thus, herein we present cases that we consider to be good examples, bearing in mind that this presentation might S

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Table 21. Summary of BIE Results for Protein-type Hosts (Arranged Alphabetically)

T

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Table 21. continued

U

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Table 21. continued

hemicarcerand-[2H6]p-xylene, in which the aryl protons were labeled. 2.3.5. Deep-Cavity Cavitand Host. In 2006, Gibb and coworkers154 studied C−H···X−R (X-halogen) host−guest interactions using isotope substitution of hydrogen atoms in deep-cavity cavitand155 (DCC), a new molecular basket host. The structure and the space-filling model of the studied host are shown in Figure 27. This host binds a variety of guest molecules. It has been shown earlier that the presence of one or more halogen atoms enhances the binding (R−I > R−Br > R−Cl). Therefore, the binding properties of protiated and deuterated hosts using a variety of halogenated compounds were studied. Results, obtained in DMSO using the NMR technique, shown in Table 17 allowed for identification of two general classes of guest molecules. Large guest molecules that filled the cavity

medium, which is represented by a hemicarcerand (see Figure 26). BIE of 1.013 for p-xylene labeled with 10 2H atoms was determined. This BIE is considered to originate primarily from the volume difference between the two isotopologues, which introduces a small structural change in the surrounding hemicarcerand that leads to the observed change in the binding energy of ΔΔG = 7.6(6) cal/mol. The BIE was measured by applying normal-phase HPLC recycle chromatography. The most important observation of this work is that the guest size plays a crucial role in modulating the hemicarceplex−surface interactions, and that even such subtle changes resulting from deuteration lead to a measurable change in the retention time has been drawn from the fact that partial separation of hemicarcerand-p-xylene and hemicarcerand-[2H10]p-xylene complexes was observed in the case of deuteration of the guest methyl groups, while it was absent for V

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Table 22. Summary of BIE Results for Host−Guest Systems (Arranged Alphabetically)

W

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Table 22. continued

supramolecular complexes with deuterated guest were thermodynamically more stable than those that contained light isotopes. Additionally, an increase of relative affinities with decrease of temperature was observed for all studied complexes. 2.3.7. Self-Assembled [Ga 4L 6] 12− Host. In 2010, Raymond’s group described a self-assembling tetrahedral [Ga 4 L 6 ] 1 2 − host, where L stands for 1,5-bis(2,3dihydroxybenzoamido)naphthalene158 illustrated in Figure 29, which is able to bind a variety of monocationic159,160 and neutral161,162 guest molecules. BIEs on the noncovalent host−guest interaction for these systems were determined163 by applying the 31P NMR titration method. The binding affinity of benzyltrimethylphosphonium isotopologues to the host was studied. Preliminary studies163 showed that deuterated guests bind more weakly to the exterior of the host. The origin of observed BIEs was discussed in the subsequent article164 in which the analysis of the thermodynamic differences in binding of isotopologues was explored. To investigate BIEs on the interior and exterior guest binding, a series of five different isotopologues of the guest ([2H0]-, [2H2]-, [2H5]-, [2H7]-, and [2H9]-) shown in Figure 30 were used. The results of these studies are collected and listed in Table 19. All of the measured BIEs on the guest encapsulation are greater than or equal to unity, what suggests that protium isotopologues are bound more strongly to the interior host than deuterium counterparts. The sole exception is [2H5]guest, which shows no measurable BIE (BIE ≈ 1). Obtained results lead to the conclusion that upon encapsulation the attractive

well bind stronger to deuterated host, while smaller guests are not influenced by deuteration. It was concluded that the difference between these two classes of guests depends on the halogen atom of the guest. While relatively small iodinated guests can differentiate between the protonated and deuterated hosts (BIE ≪ 1), the corresponding bromides do not (BIE ≈ 1). Differences in mobility of large and small guests are invoked to explain observed differences in Ka for protiated and deuterated hosts. This comparison demonstrates that smaller and more flexible guests have lower tendency to form hydrogen bonds, while lack of guest preorganization observed for larger molecules may lead to conformations that are “ill-suited” to halogen atom complexation in the crown. 2.3.6. Self-Assembled Capsule 1·4BF4. In 2009, Iwata and co-workers157 studied noncovalent isotope effects on encapsulation of different guests in a self-assembled capsule 1·4BF4. They found large isotope effects on the guest binding affinities and their temperature dependence for deuterated methyl groups at both ends of the guest molecules (Figure 28). Obtained by 1H NMR spectroscopy, BIE results are presented in Table 18. During the NMR experiment, the relative integration of methyl protons versus the aromatic protons adjacent to the acetoxy group of the encapsulated guests afforded the relative binding affinities for the temperature range from 252 to 323 K. Relative binding affinities were defined by the authors as the ratio of KD/KH (i.e., inverse of BIE). Experimentally obtained relative affinities were larger than unity, demonstrating that the X

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effects (KIEs) on enzymatic systems is most frequently performed within the frame of eq 1.12 or its more complicated forms corresponding to the actual kinetic scheme. Even when the commitment factor C is negligible, either due to the nature of the reaction or due to the experimental conditions (for more detailed discussion and examples, see refs 166, 167), the apparent (measured) value of the KIE differs from the intrinsic KIE (iKIE) by the value of BIE (see eq 1.15). iKIE is the isotope effect that is sought because it reports on the structural properties of the transition state, an entity not amenable to direct experimental scrutiny. Obviously, if the value of this isotope effect is wrong, so is the interpretation made based on it. Although equilibrium isotope effects (including BIEs) are usually small as compared to kinetic ones, this Review illustrates that they are frequently sufficiently large to provide a correction that is mandatory in the analysis of iKIEs. Other applications of BIEs, such as identification of the preferential binding to a particular isoenzyme form or differences in the binding affinities of labeled molecules that are used as tracers in studies of reaction pathways taking place inside living organisms, are case specific. In this Review, we have presented a number of theoretical calculations of BIEs that have been performed throughout the years. Some of these were done quite a long time ago, and some are very recent. Because the field of computational chemistry changes very dynamically, the quality of theoretical predictions requires a brief commentary. Studies of BIEs on binding oxamate to lactate dehydrogenase are an excellent example of these changes. Calculations performed in 1994 employed a semiempirical level of theory with the largest model comprising four amino acid residues that form the active site, a part of NADH and oxamate molecule.17 Table 7 illustrates how very fragile the results were, that is, how much they depended on the size of the model and on the model of the aqueous environment. These results span nearly the whole range of the possible values of isotope effects, and in fact one could choose those days the methodology that fit the experimental results. In contrast, in recent calculations, it was possible to study models comprising of hundreds of thousands of atoms and to compare behavior and show some important differences between monomeric, dimeric, and tetrameric forms of this enzyme. This was possible because of the development of hybrid QM/MM calculations that describe the crucial part of the model using quantum mechanical theories while the remaining part of the protein is treated with molecular mechanics. These calculations allow nowadays successfully addressing questions regarding reactivity of large (e.g., enzymatic) systems. It should be kept in mind, however, that QM/MM technology is still in its infancy, and a number of used simplifications are still debated. From the perspective of calculating isotope effects, the most severe problem is connected with diagonalization of the Hessian matrix necessary for calculations of harmonic normal modes of vibrations that are then fed into eq 1.11. Because operations on correspondingly large matrixes are usually not possible due to memory constrains, a smaller part of the model is used for the purpose of vibrational analysis. However, vibrational analysis is meaningful only when performed on a stationary point, the condition that the substructures selected for vibrational analysis may not, and in fact frequently do not, fulfill. We believe that the key to the future of theoretical calculations of isotope effects lays in finding appropriate methods of Hessian analysis.

interactions between the guest and aromatic walls of the host lower the vibrational force constants of C−H/D motions in the guest molecule. The contribution of the lower vibrational frequencies to the C−H and C−D ZPE levels for each transition is shown in Figure 31. The same behavior of the ZPE levels is observed in case of the guest binding to the exterior of the host molecule. However, BIEs on the exterior binding are smaller than those observed for the interior binding (see Table 19); in both cases, the trends observed are identical. Thus, it was concluded that the local noncovalent interactions between the host and the guest molecules on the exterior and interior of host are fundamentally the same. Also, despite the fact that host exterior is very hydrophilic, authors concluded that its large aromatic surfaces can be the source of the π-type interactions. The temperature dependence of BIEs on exterior binding has also been studied. Obtained results are shown in Table 20 and were used for the van’t Hoff analysis, which yielded thermodynamic parameters ΔΔH and ΔΔS. These thermodynamic parameters were used to differentiate between enthalpic and entropic contributions to the BIEs. Obtained results of ΔΔH and ΔΔS indicate that preferential association of the protiated isotopologues is driven by enthalpy, but their binding is entropically unfavorable.

3. CONCLUSIONS This Review presents equilibrium isotope effects on association constants of the host−guest systems with emphasis on biological ones, in which small chemical molecules (ligands) bind to proteins. We refer to them as binding isotope effects (BIEs), although this term is somewhat broader as discussed in section 1.3. Table 21 summarizes the results reported for the biological systems, while available literature on host−guest systems is collected in Table 22. Early studies of BIEs aimed at learning if isotopic substitution can change the pattern of binding or reaction channels.142,143 Since then, we have learned that this is not the case, although the primary deuterium kinetic isotope effect can be as large as 200,165 which experimentally may seem like different reactivity of the isotopologues. Nevertheless, it is clear that a large number of host−ligand systems exhibit non-negligible isotope effects on the binding step. As manifested by the results discussed herein, BIEs results can be used in two different ways. First, they can provide detailed information regarding the ligand−host interactions. In such cases, usually BIEs are measured experimentally, and subsequently their values are evaluated theoretically. Matching of the experimental values by the theoretical predictions is considered validation of the theoretical approach (although coincidental match cannot be excluded in some cases; see discussion below). Validated theoretical results are in turn used for the analysis of specific interactions of the ligand in the binding pocket. This includes identification of the hydrogenbond network, ionic contacts, charge distribution, ligand conformation, changes in the force constants upon going from free ligand in the (most frequently aqueous) solution, etc. To some extent, the information gained from BIEs is similar to the one that comes from the docking studies, although theoretical evaluation of BIEs is usually performed on a higher (QM or QM/MM) theory level than docking (usually MM). Second, and equally importantly, values of BIEs contribute to our understanding of (enzymatic) reactivity of the ligand− enzyme systems. The interpretation of the kinetic isotope Y

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In the light of the problems with the calculations mentioned above, it is reasonable to pose a question regarding the validity of theoretical predictions of isotope effects in general and BIEs in particular. Actually, the problem is not as severe as it may sound. For a frequency to affect an isotope effect, its force constant must change. This leads to two simplifications important in calculations of isotope effects. First, molecular vibrations are usually quite local. Therefore, frequencies remote from the isotopic site exhibit negligible isotopic shift and thus do not contribute to the isotope effect. Second, from among the frequencies affected by the mass of the isotopic atom, those whose force constants are not affected during the process cancel out between factors corresponding to reactants and either the transitions state (KIEs) or the products (EIEs). In the case of BIEs, these changes result from weak interactions between the host (enzyme) and the guest (ligand) such as bond polarization, rotational constrains, or hydrogen bonding. Thus, in fact usually only very few vibrations are really responsible for the size of the estimated isotope effect. Theoretical predictions of EIEs (including BIEs) have also the advantage of performing calculations only for stable compounds in contrast to calculations of KIEs, which require computing transition state properties that are not only more tedious but whose quality is difficult to assess. To stay on the fair side, it should be pointed out that experimental BIEs can also be very sensitive to experimental methods and conditions. Thus, extreme care should be taken in studying these isotope effects.

Technology. Recently, she has been contracted by the Spanish Ministry of Science as a researcher at the Department of Physical Chemistry, University of Valencia, under the supervision of Professor Iñaki Tuñoń .

Piotr Paneth obtained his degrees in Chemistry, M.Sc. (with honors), Ph.D. (under supervision of Prof. Wladyslaw Reimschüssel, with honors and individual award from the Minister of Science and Higher Education), and D.Sc. (habilitation, with individual award from the Minister of National Education) from the Lodz University of Technology (previously Technical University of Lodz, TUL). In 1996 he was awarded the Professor title by the President of Poland. His whole scientific career is connected with his Alma Mater where he moved through all ranks and is now appointed as a Full Professor. He received postdoctoral training at the University of Wisconsin-Madison, where he worked for 2.5 years under the supervision of Prof. Marion H. O’Leary. After obtaining D.Sc. (habilitation) degree, he spent another 2.5 years in Prof. O’Leary’s laboratory at the University of Nebraska-Lincoln where he later on was also a Visiting Professor. He spent another 2 years in foreign laboratories under grants from Svenska Institutet (University of Uppsala, Sweden with Prof. Olle Matsson), Fulbright Foundation (University of Minnesota at Minneapolis with Prof. Donald G. Truhar), Emerson Center (Emory University) and the Japanese Society for Promoting Science (Kyoto University, both with Prof. Keiji Morokuma), and CNRS (University of Nantes, France with Prof. Richard Robins). He served as Vice-Dean for Students Affairs and recently as the Dean of Faculty of Chemistry at TUL, where he is now Vice-Rector for Science. His entire scientific career is devoted to applications of isotope effects, with emphasis on heavy-atom kinetic isotope effects, to studies of mechanisms of enzymatic reactions and their chemical counterparts using both theoretical and experimental approaches. With Dr. Victor Anisimov he wrote a popular program ISOEFF for calculations of isotope effects. He contributed significantly to studies of biotic dehalogenations by means of chlorine isotope effects, the majority of which have been summarized in an article in Accounts of Chemical Research. He also coauthored a book on isotope effects, “Isotope Effects in the Chemical, Geological and Bio Sciences” published in 2010 by Springer. Currently, his scientific interests concentrate on exploring whether binding isotope effects can be useful in rational drug design. Recent recognition of his contribution to science includes two awards from the Minister of Health (2009, 2012) and the Jan Zawidzki Medal awarded by the Polish Chemical Society (2012). He is a volleyball addict for both playing and watching.

AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. Biographies

́ Katarzyna Swiderek obtained her M.Sc. in Chemistry from the Lodz University of Technology. Her Ph.D. studies (2007−2011), supervised by Professor Piotr Paneth, focused on theoretical studies of isotope effects on binding ligands to the active site of lactate dehydrogenase. During her Ph.D., she was twice awarded for the excellent poster presentation at MDMM conferences in 2008 and 2010. In 2008 she received AXIOM - Marie Curie Host Fellowships for 3 months to study at the Helmholtz Centre for Environmental Research-UFZ, Department of Isotope Biogeochemistry in Leipzig in Germany. In 2009 she obtained a scholarship from a project supported jointly by the European Social Fund and the Polish Government. In 2011 she received a research scholarship from the Lodz University of

ACKNOWLEDGMENTS We would like to thank the reviewers for insightful comments, which greatly enhanced this Review. This work was partly Z

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supported by grant 2011/02/A/ST4/00246 from the Polish National Science Center (NCN).

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