Effects of Hydrogen Bonding on 1H Chemical Shifts

Chapter 13 1

Effects of Hydrogen Bonding on H Chemical Shifts Yufeng Wei and Ann E . McDermott

Downloaded by UNIV OF PITTSBURGH on December 23, 2014 | http://pubs.acs.org Publication Date: August 20, 1999 | doi: 10.1021/bk-1999-0732.ch013

Department of Chemistry, Columbia University, New York, N Y 10027

The topic of "low-barrier hydrogen bonds" (LBHBs) and the question of how they are involved in enzyme function has been discussed heavily in the literature recently. Hydrogen bonds between two bases of nearly matched proton affinity often exhibit strongly perturbed bond lengths and spectroscopic parameters; it remains somewhat unclear exactly how the spectroscopic parameters reflect total energy or reactivity. In this study, we report H N M R chemical shift data and surveys of structural preferences for the well-studied O-H···O systems, and also for less studied, but biologically important Ν-Η···O systems, in particular the imidazole and imidazolium functionality. The H shifts also show interesting trends in comparison with O-H···O motifs, which will require further scrutiny. 1

1

Hydrogen bonds appear to be essential in all enzyme-catalyzed reactions, although why they are essential and how they promote function is an open question. In recent years a specific hypothesis for their involvement in catalysis has emerged: so-called low-barrier hydrogen bonds (LBHB) have been proposed to lower the transition state energy for many enzymatic reactions, including those of serine protease, citrate synthase, triosephosphate isomerase(TIM), A -ketosteroid isomerase, ribonuclease A (RNase A), and mandelate racemase.(7-5) The transition states or intermediates, but not the ground states, putatively benefit from a 10-20 kcal/mol L B H B interaction; this proposal has been the cornerstone for a hypothesis about enzyme reactivity.(2,4) The L B H B is defined as a particularly short hydrogen bond that forms when the two bases competing for a single proton have nearly matched proton affinities. The short bond gives the L B H B many special spectral properties and sensitivity to isotopic substitution: highly downfield Ή chemical shifts (16-22 ppm), small or inverted isotope effects in infrared vibrational frequencies (v /v =1.0), and low isotope fractionation factors (0.5-1.0) are observed.(6) Extensive studies and debate have appeared in the literature since the idea of L B H B was first proposed.(7-77) A key question in the debate is the energetics of a short hydrogen bond (or a LBHB) as contrasted with more typical hydrogen bonds between two groups of different proton affinity. 5

AH

AD

© 1999 American Chemical Society

In Modeling NMR Chemical Shifts; Facelli, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1999.

177

178 Several studies have shown that a pK match provides only moderate energy (~5 kcal/mol) in solution.(8,12-15) Ab initio calculations also confirmed this conclusion.(76) A linear correlation between A G and ΔρΛ^ was proposed in both experimental and computational studies where the dimensionless Br0nsted slope β is d

H B

8

defined as the slope relating log^f" and ΔρΚ . The experimental value for β was reported to be -0.7 in DMSO and 0.05-0.14 in water.(#,75,76) In contrast, gas phase studies showed 30-40 kcal/mol energy gains when the pK values are matched Ά


a

(implying β » I).(6) We have focused on similar questions regarding the solid or crystalline state, because we propose that the crystalline database is a relevant database for enzyme active sites and enzyme-substrate interactions. In particular, we are addressing the question of the bond lengths and proton chemical shifts when hydrogen bonds in the crystalline states involve matched vs. mis-matched pA 's, and we also discuss the question of their energies. N M R spectroscopy is probably the most popular spectroscopic tool used to study hydrogen bonding. The Ή chemical shift is a well-established indicator of hydrogen bonding; NMR signatures for hydrogen bonding were established very soon after the invention of NMR. The Ή shifts have also been used extensively by enzymologists. Strongly deshielded signals (ca. 16-20 ppm) and anomalous isotope effects and fractionation factors are observed in species with very short hydrogen bonds, for both small molecules(77-22) and enzymes [reviews;(Mildvan, A . S.; Harris, T. K . ; Abeygunawardana, C. Methods Enzymol. 1998, in press.) serine protease;(5,23-26) aspartate aminotransferase;(27,28) triosephosphate isomerase (TIM);(29) ketosteroid isomerase;(30,37) AKB-ligase(32)]. Many of these measurements for small crystalline compounds were performed using solid state NMR methods, such as Combined Rotation And Multiple Pulse Spectroscopy (CRAMPS).(33-37) Previous databases focused mainly on O-H—O systems; we have established an additional database of high resolution solid state Ή N M R chemical shifts of the imidazole-carboxylate hydrogen bonding system, which is much more relevant for enzymatic studies. In an effort to understand our N M R shifts, we have also summarized the hydrogen bonding structural trends of O-H—O and N - H - Ό systems by surveying the Cambridge Structural Database (CSO).(38-40) a

Results and Discussion l

H N M R chemical shifts in solid state. Harris, et. al, reported many Ή chemical shifts of acidic protons in carboxylic acids;(20) McDermott and Ridenour also reported some Ή chemical shifts in amino acids and small peptides.(27) In Figure la, we plot the Ή chemical shifts from literature(20,27) against the corresponding hydrogen bonding 0---0 distances from crystal structures from the CSD. We have organized the data according to the ρΚ difference between the partners. It is clear that the pK. matched and mis-matched species are distinct in terms of their chemical shifts and hydrogen bonding distances. All the matched species (COO-Η·· C O O ) are short in distance (2.4 - 2.6 Â) and deshielded in chemical shift (14 - 21 ppm). A good correlation can be found between Ή chemical shifts and hydrogen bond distances (R = 0.763). In contrast, the mis-matched species (COO-H-COOH) have longer distances (2.6 - 2.7 Â), and more shielded chemical shifts (12 - 14 ppm). The correlation between Ή chemical shifts and hydrogen bond distance in the mis-matched range is weak (R = 0.191). The outlying datum in the mis-matched group is for maleic acid, which adopts a short intramolecular hydrogen bond (2.502 À), and a deshielded H chemical shift (16.6 ppm). Despite this outlying point, we conclude that pK matched species exhibit special properties. Λ

d

2

2

l

d


179

20H


I

18H

16H CO ο i 14H χ: ϋ J 12

+* ï * ^ + I

Ι

1 1 1 1

> ' I

2.4

I j 11 ι ι

2.5

ι

ι ι 11 ι ι ι ι 11

i+fi

ApKa>1i

++ I I I

I j 11 ι ι

ι

ι ι ι ι ι

M

2.6 2.7 2.8 0 . . . 0 Distance/Â

I

II

ι

ι ι ι ι ι 11 ι ι

2.9

ι

ι 111 ι ι ι ι 11

3.0

20H Ε CL Q- 18 ω ϋ

12

U

1 1

2.4 Β

1 1

1

1

Ap/C = 10 a

• • ' i ' M I 11 i t ι 11111111 11111111 11 11 11 I I I [ 111 1111 ι 11 ι 11 ι 111111

2.5

2.6

2.7

2.8

2.9

3.0

Ν...O Distance/Â

Figure 1. Solid state Ή N M R chemical shifts of carboxylic acids and imidazoles are plotted against the hydrogen bonding distance: a) data for carboxylic acids (data from reference (2021)), circles are compounds with COO—Η · COO" motif, ApK « 0, and crosses are compounds with COO—Η - C O O H motif, ApK > 15; b) data for imidazoles (data from Table I), circles present cationic imidazoles (Im —H··· COO", ΔρΚ « 3), and crosses are neutral imidazoles (Im ··· COO", ΔρΚ » 10). a

a

+

Ά


Ά

180

Table I. Solid State Ή N M R Chemical Shifts of Imidazoles and Hydrogen Bonding Distances in Crystals Compound

Ή Chemical Shifts ô /ppm 12.8 13.5 12.9 13.4 13.3 13.3 12.4 11.2 12.3 16.4 14.7 13.3 13.3 16.7 12.5 16.9 13.6 13.5 13.5 16.6 15.7 14.7 13.2

N - -0 Â

CSD Refcode

H

Neutral


species

L-Carnosine DL-histidine (monoclinic) L-His-L-Leu L-histidine (monoclinic) L-histidine (orthorhombic) DL-histidine hydrochloride dihydrate L-histidine perchlorate L-histidine hydrochloride monohydrate L-histidine L-aspartate L-histidine acetate (monoclinic)

Cationic L-histidine hydrogen oxalate species L-His-Gly hydrochloride Gly-L-His hydrochloride DL-histidine glycolate L-histidine glycolate L-histidine squarate

2.698 BALHIS01 2.767 DLHIST 2.713 JUKMOR 2.733 LHISTD02 2.752 LHISTD13 DCHIST 2.726 2.933 G A S K A M 3.037 2.830 HISTCM12 2.642 2.687 LHLASP01 2.685 POPGUW 2.694 2.627 R A R X O X 2.910 2.650 RAVMAC 2.685 TEJGAO TEJVUZ 2.749 2.752 TEJWAG 2.651 2.704 2.709 TIWXEC 2.716

In this paper we report for the first time our studies of hydrogen bonding in the imidazole-carboxylate system, a common motif in enzyme active sites. The Ή solid state N M R data of polymorphic crystalline histidines were taken on a Chemagnetic CMX-400 spectrometer using the BR-24 sequence ,(34,36) with pulse length 2.2 ^s, and magic angle spinning (MAS) speed at 2.0 kHz. The results are listed in Table I along with the hydrogen bonding Ν · · Ό distances according to their ionization state. The reason we emphasize the ionization states is that the neutral imidazole species have quite different ρΚ values (pK ~ 14) from the cationic ones (pK ~ 7). In comparison with the carboxylic acids, which are the hydrogen bond acceptors in this system, the neutral imidazole species are far mis-matched in proton affinity (ΔρΚ ~ 9-11), while Ά

a

a

Ά

the cationic species are nearly matched (ΔρΚ. ~ 2-4). In Figure lb, Ή chemical shifts of imidazoles were plotted against the hydrogen bonding N---0 distance. The cationic species behave normally: the Ή chemical shifts become more deshielded when hydrogen bonding distances shrink. It is worth noting in comparison with these data that the Ή shifts for the Η in cationic imidazole of His-57 at the active site of cechymotrypsin exhibit a 18-19 ppm signal: 18.0 ppm for free enzyme at pH 4.1;(23) 18.7 ppm in iV-acetyl-L-Leu-L-Phe trifluoromethyl ketone inhibited complex at pH>7.6;(23) 18.9 ppm in N-acetyl-L-Leu-DL-Phe trifluoromethyl ketone inhibited complex at pH 7.0;(2 15), and carboxyl-carboxylate is d

d

&

matched (ApK « 0). As one can see in the histograms, which include both X-ray and neutron diffraction structures, the center of the distance distribution for all O-H—O cases is 2.8 A; in the carboxyl-carboxyl system, the center moves to 2.65 A; when the pK. values become closely matched in the case of carboxylate-carboxyl, the most probable 0—0 distance shortens to 2.5 A. Apparently it does not matter if the hydrogen bonding partners are syn or antU the hydrogen bonding distances are all in the same region. An analogous trend relating Ο—Ο distance to A p ^ can be seen for water species. The distribution for asymmetric and pK mis-matched H O - H — H 0 is a

d

a

a

2

+

centered at 2.8 Â, while H 0 - H — H 0 species, with ApK. ~ 0, is centered at 2.45 A , and includes the shortest 0—0 distances found in any O-H—O system. We looked at several chemical motifs to test whether the O-H covalent bond length is perturbed by interactions involving two pK. matched bases. Figure 3 displays the "stretching" of O-H bond lengths in O-H—O hydrogen bonding systems. We focused on structures involving two motifs, carboxyl and water. Only neutron diffraction data are included in these plots, because the hydrogen position in X-ray structures is poorly defined. The master plot of all O-H—O hydrogen bonds is wellknown and well documented.(6) As 0—0 distances shorten, O-H bond lengths are stretched. When we look at the individual systems in detail, we can isolate motifs that are "matched" or "mis-matched" in pK . The symmetric systems or "matched" cases (with A p ^ « 0), included carboxyl-carboxylate ( C O O - H - C O O ) and hydroxium2

2

d

d

a

a



182

Figure 2. Ο · Ο hydrogen bond length histograms indicate a difference in the intermolecular potential for various chemical species. Closely matched (symmetric) hydrogen bonds clearly adopt shorter 0 - - - 0 distances. Both X-ray and neutron diffraction data are from the CSD. From top to bottom: all Ο—Η ·*· Ο containing species; carboxyl-carboxyl, ΔρΚ > 15; carboxyl-carboxylate, àpK « 0; waterwater, ΔρΚ « 16; hydroxium-water, ΔρΚ « 0; carboxyl-water, ΔρΚ « 5; watercarboxylate, ΔρΚ « 10. The pK values used here are based on typical aqueous values. Ά

a

Ά

Ά

Ά

Ά

a


183

1.2

All O-H...Ο 1.1 1.0


0.9

^.2i

ApK

a

« 0

1.1 t:

1.01

5

0.91

CH+-ApK > a

H-O 15

"D

c ΐ

H

1.1

Δρ/Cg « 0

H

1.0τ

ApK

a

-

16

0.9τ 1.2 o-H ο

1.1

ApKg « 5

q H

P-H" ApK

1.0

a

« 10

0.9 '

i

ι ι l I I

I I I I I |

I l l

2.6

2.4

2.8

0...0

3.0

3.2

Distance/Â

Figure 3. Ο—H bond lengths in Ο—H---0 hydrogen bonds. The phenomenon of long Ο—H bonds appdars to be primarily for the cases in which ΔρΚ « 0. Neutron diffraction data are from the CSD. From top to bottom: all Ο — H - O ; carboxyl-carboxylate, ΔρΚ « 0 (circles), and carboxyl-carboxyl, àpK > 15 (crosses); hydroxium-water, ApK « 0 (circles), and water-water, àpK « 16 (crosses); carboxyl-water, ApK 5 (circles), and water-carboxylate, ApK « 10 (crosses). The pK values used here are based on typical aqueous values. Ά

Ά

a

a

a

a


a

a

184 +

water (Η 0 -Η···Η 0). The 0 · · · 0 distances are shortest in matched cases, from 2.4 2.6 Â, and O-H bond lengths are significantly stretched, 1.0 - 1.2 Â. The structurally similar, but mis-matched systems (asymmetric systems), including carboxyl-carboxyl (COO-H -COOH) and water-water ( H O - H - H 0 ) , have ApK. > 15. The O - ; 0 distances are long (>2.6 Â), and O-H bond lengths are in normal range (0.9 - 1.0 Â). In contrast to matched cases, the relation between O-H bond length and Ο—Ο distance is poor for the mis-matched cases. It could be argued that the Ο—Ο distances and O-H bond length are not perturbed so much by pK. match, but by the total charge of the system, because the shorter 0---0 distances and longer O-H bond lengths appear in charged species as described above. To distinguish the effects of p^T match from total charge, we selected two motifs: one is carboxyl-water (COOH—H 0), a neutral but near matched 2

2

Q

2

d

d


a

2

pair (ApK. ~ 5); the other is water-carboxylate (H 0—COO ), charged and more mis matched pair ( Δ ρ ^ ~ 10). The central distribution of Ο—Ο distances for the neutral, nearly p^T matched carboxyl-water motif is short (2.6 Â), compared with the charged, pK. mis-matched water-carboxylate system (2.8 A), as seen in Figure 2. In the plot correlating O-H and 0 · · Ό distances (Figure 3), the carboxyl-water system shows longer O-H bond lengths and shorter 0---0 distances than the water-carboxylate system. Apparently, it is the pK. match, not the total charge, that correlates with the perturbation of Ο—Ο distances and O-H bond lengths. N - H - Ό hydrogen bonding is more common than O-H—O bonding in enzyme active sites. Figure 4 shows the histograms of the distribution of N---0 distance in several N-H—Ο hydrogen bonding systems, including both X-ray and neutron diffraction structures. The p ^ values of the imidazolium-carboxylate (Im -H—COO") d

2

a

d

d

+

a

motifs are the most closely matched, with ApK. ~ 3. The center of the histogram of N---0 distances is 2.7 Â. The next two cases, ammonium-carboxylate ( R N d

+

3

H—COO-, R=H or C) and amide-amide, with ApK values about 5 and 15 respectively, exhibit N---0 histograms centered at 2.8 and 2.9 Â, respectively. The last case, the amide-water system, is generally not a good hydrogen bonding system, with ApK =17. The distribution of this system is pretty broad, compared with other systems, evenly ranging from 2.7-3.0 Â, with a small peak at 2.85 Â. The master plot of all N-H—Ο systems, is centered at 2.9 A . It is clear that when the pK matching condition achieved, the hydrogen bonding distance between the two heteroatoms ( N - O ) is shorter. The stretching of the N - H covalent bond in N-H—Ο systems, involving N - H bond lengths of 0.95-1.10 Â, is not very significant (Figure 5), in comparison with the O-H—O system, 0.85-1.20 Â (Figure 3) or in comparison with experimental error. The reason for the small variation in N - H bond lengths is probably that there are no or few exactly-matched structures reported in the CSD. We noted a difference between near-matched species (R N -H—COO", ApK. ~ 5) and mis-matched species a

a

a

+

3

d

(neutral aromatic heterocycles—COO-, ΑρΚ. ~ 10, and amide-amide, Δρ^Γ ~ 15). The data for near-matched species are mainly in the upper-left region in the master plot, and those for the mis-matched species make up the middle to right part of the master plot. The pK matching condition could still be an important factor in determining the length of N-H—Ο hydrogen bonds in crystalline state, but these data do not present a compelling cases. Future N M R studies will focus on N - H bond length for pK. matched systems. ά

3

a

d

Energetics of hydrogen bonding in crystals. As an indication of the formation energy of a hydrogen bond, we counted the percentage of structures with



185

Figure 4. Histograms of Ν ··· Ο hydrogen bonding distances. A systematic depen dence of Ν ··· Ο distance on A p ^ appears in these data. Both X-ray and neutron diffraction data are from the CSD. From top to bottom: all Ν—Η · · · O; imidazoliumcarboxylate, ΔρΚ « 3; ammonium-cargoxylate, ΔρΚ « 5; amide-amide, ΔρΚ « 15; amide-water, ΔρΚ « 17. The pK values used here are based on typical aqueous values. a

Ά

Ά

Β

a


Ά

186

1.2

•

1.1

•

All Ν-Η...Ο @§ ° ο Ο CCD

1.0

rPO


0.9 ""I""

I I I I I I I I I 11 1111 n ι 111111 Μ ι Η 111 I I n 111 11111 . i n

1

""!

1.2

Θ

1.1

Ο)

c φ

"D c Ο

ΠΒ

1.0

àpK ~5 a

0.9 • I • ι ι ι ι • ι • 11•••11 I I •111 I • I I I i 1 • ι I n 111 1

1.2-

1.1

1.0-

ΔρΚ^ΙΟ

0.9

1.2

ι

Aromatic Heterocycles Neutral species N-H...-OOC

m ΐ ζ

•

I " ι ι ι M ι ι ι I I I I I "I" I" "I ι 111 11 ι 1111 11 HI 11 11 11II I I Ι'ΊΤΙ 111 I I I I I

1 N-H- - - 0=\

1.1

1.01 ΔρΚ^Ιδ

0.9

Μ" Ή Μ ΐ |

2.6

Μ Μ , Μ

ι ι μ

2.8

1

1

1

1 1

'

1

1

1

' 1 1

1

' ' '1

1

3.0

3.2

Ν...Ο D i s t a n c e / Â Figure 5. Ν—Η bond lengths in Ν—Η *·· Ο hydrogen bonding systems. The phe nomenon of Ν—Η bond "stretching" is only weakly represented (if at all), probably because there are only few nearly matched systems that have been characterized by neutron diffraction. Neutron diffraction data are from the CSD. From top to bottom: all Ν—H -O; ammonium-carboxylate, àpK 5; neutral heterocyclecarboxylate, àpK « 10; amide-amide, àpK 15. The p ^ values used here are based on typical aqueous values. a

a

a

a


187 and without hydrogen bonding motifs in the CSD when the specific hydrogen bonding motifs were presence in the structure. The statistical data are tabulated in Table II. For the matched pK. cases, like Η 0 - Η · H 0 and COO-Η··-COO, the percentage of structures with hydrogen bonding was 8 0 % to 100%; for near matched cases ( R N H - - C O O ) , the percentage was about 7 0 - 8 0 % ; while for the mis-matched cases (amide--amide, COOH--COOH and Η 0 · · · Η 0 ) the percentage of structures with hydrogen bonding was only 2 0 - 4 0 % (concerning neutron diffraction data for amideamide motifs, a larger number of hydrogen bonds (70%) may be due to a lack of other hydrogen bonding possibilities). The percentage of "missed opportunities" for hydrogen bonding becomes larger when ΔρΚ. increases, which we loosely interpret to mean that a hydrogen bond with pK. match is energetically more favored than one with mis-matched pK. but not dramatically so. To extract an enthalpy from such a study would be ridiculous, but the enthalpy appears not to be dominant over other crystal packing considerations. +

2

d

2

+

3

2

2

ά


d

dl

Scheme 1

©

© NHo

Θ

NH - -O C 3

2

Κ

N

/

Proton transfer in hydrogen-bonded species

-HgN'

©

Θ

2

-HoN - - -H0 C

©

>-

2

symmetric

zwitterionic

HB

VK HB 2

Θ NH

3

C0

2

Θ

©

8c

H N 9

^a2^ ^a1

2

Proton transfer in isolated species

H N 3

©

0

2

H0 C 2

>-

© H B

We add a few comments on the linear relationship between the A G and ApK. (8,15,16) in the crystalline state. The following argument is based on the observation that formation of L B H B does not drive uphill proton transfers in the crystalline state under any known circumstances (and has not been reported in solution). Based on this observation, using a thermodynamic cycle, we conclude that β « 0 . 5 . Consider an amino acid which undergoes an equilibrium as illustrated in a thermodynamic cycle in Scheme 1, where the equilibrium constant for the reaction can be written as ^ „ (D d

K =

1

HB

Here Κ describes a proton transfer in the hydrogen bonded zwitterion pair to generate two symmetric hydrogen bonds or LBHBs. Equation (1) can be rewritten as (2) log Κ = 2(log K™ - log Ο - ApK a



188

Table II Hydrogen Bonding Preferences: Symmetric vs. Asymmetric

+

H 0 -H 0 Δρ# =0 COO-COOH Δρ# =0 R NH -COO3

2

Neutron Structures Only Both X-ray and Neutron Structures Total Number Number Percentage Total Number Number Percentage Number withHB without HB of HB Number withHB without HB of HB 15 13 2 86.7% 3 3 0 100%

3

363

278

85

76.6%

15

12

3

80%

1007

690

317

68.5%

34

29

5

85.3%

Amide-Amide

4964

2851

2113

42.6%

57

40

17

70.2%

COOH-COOH ΔρΚ >15 H 0-H 0

2402

861

1541

35.8%

57

13

44

22.8%

2492

678

1814

27.2%

44

10

34

22.7%

α

+

3

Apff «5 a

3

2

2


189

where ΔρΚ = pK - pK . Assuming a linear free energy correlation, we have logK" - \ogK" = βΔρΚ . Substituting this into equation (2), we get α

a2

3

al

B

α

\ogK = (2fi-l)bpK

(3)

a

It is well-known that amino acids are in the zwitterionic state in essentially every crystalline solid, not in a mixed neutral/zwitterionic form. Therefore the equilibrium strongly favors the reverse direction, i.e. log Κ « 0. Thus, we conclude


j3«0.5

(4)

This argument probably also applies to most solvent environments, as such mixed neutral/zwitterionic dimers are unknown: generally the species are either charged or neutral, but not in mixed dimers. We present this thermodynamic cycle because the resulting estimate for β is small compared some solution estimates.(5,75, i

Effects of Hydrogen Bonding on 1H Chemical Shifts

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