Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

What can we learn from NMR about Hydrogen Bonds?


identifies individual H-bonding groups




sees opening and closing, changes, i.e. dynamics




poses (answers?) questions about covalency

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

What can we learn from NMR about Hydrogen Bonds?


General knowledge about H-bonds








NMR observables for H-bonds







Definition History Hydrogen bond energies Hydrogen bond geometries Chemical shift Hydrogen exchange Scalar Couplings

NMR experimental data on H-bond couplings



DNA/RNA Proteins








Are H-bonds covalent?








Folding Temperature dependence and stability H
-H-bonds H-bond cooperativity

Pauling's suggestion Compton scattering experiment What is covalency? Relation to H-bond couplings

Conclusions

Literature


W. M. Latimer, and W. H. Rodebush. Polarity and ionization from the standpoint of the Lewis theory of valence. J. Am. Chem. Soc. 1920; 42: 1419–1433.




M. L. Huggins. Electronic structures of atoms. J. Phys. Chem. 1922; 26: 601–625.




L. Pauling. The nature of the chemical bond. 1939.




G. A. Jeffrey, and W. Saenger. Hydrogen bonding in biological structures. Springer-Verlag, Berlin, 1991.




G. C. Pimentel, and A. L. McClellan. The hydrogen bond. W. H. Freeman, San Fransico, California, 1960.




M. L. Huggins. 50 Years of Hydrogen Bond Theory. Angew. Chem. Intl. Ed. 1971; 10(3): 147–152.




G. A. Jeffrey. An introduction to hydrogen bonding. Oxford University Press, New York, 1997.




T.W. Martin and Z.S. Derewenda. The name is bond – H bond. Nat. Struct. Biol. 1999; 6:403–406.




T. Steiner. Die Wasserstoffbrücke im Festkörper. Angew. Chem. 2002; 114: 50–80.




S. Grzesiek, F. Cordier, V. Jaravine, and M. Barfield. Insights into biomolecular hydrogen bonds from hydrogen bond scalar couplings. Progr. NMR Spectroscopy 2004; 45: 275–300.

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

H-bond definition


Pimentel and McClellan (1960): "a hydrogen bond exists if (1) there is evidence of a bond and (2) there is evidence that this bond sterically involves a hydrogen already bonded to another atom"




Biomolecules:



usually O-H···O, N-H···O, O-H···N, N-H···N (lone pair of O/N acts as acceptor) but also C-H…O, H -> aromatic
electrons

"It is now recognized that the hydrogen atom, with only one stable orbital, can form one covalent bond, that the hydrogen bond is largely ionic in character …" Linus Pauling The nature of the chemical bond, 3rd ed., 1960 

+



D – H ••• A

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

“It seems to me that the most important addition to my theory of valence lies in the suggestion of what has become known as the hydrogen bond.” Gilbert N. Lewis, Valence and the structure of atoms and molecules, 1923.

“I believe, that as the methods of structural chemistry are further applied to physiological problems it will be found that the significance of the hydrogen bond for physiology is greater than that of any other single structural feature.” Linus Pauling, The nature of the chemical bond, 1939.

"The discovery of the Hydrogen Bond could have won someone the Nobel Prize, but it didn't" (Jeffrey and Saenger)




















1919 Huggins, PhD thesis (not published): electron pair bonds 1920 Latimer and Rodebush, 1922 Huggins: hydrogen nucleus between two electron octets constitutes a weak bond 1922 Bragg: structure of ice 1928 Pauling: paper on the shared electron chemical bond 1933 Bernal and Fowler: seminal paper on the structure of water 1933 Astbury: model of
- and -keratin involving attractions between NH and CO 1937 Huggins: model of protein inter-chain hydrogen bridges (peptide plane not planar) 1939 Pauling: planarity of peptide bond 1939 Pauling: one chapter on H-bonds in 'The nature of the chemical bond' 1943 Huggins: models of sheets and helices in proteins (peptide plane not planar) 1951 Pauling, Corey, Branson: accurate models of helical and extended polypeptide chains

References can be found in Martin and Derewenda, 1999 and Huggins, 1971

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

Astbury, 1933

Huggins, 1937

Hydrogen bond energies

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

Electrostatic+exchange+mixing long range dominated by electrostatics short range dominated by covalency total

From Jeffrey + Saenger, 1991, pg. 19

Which Functional Form Is Appropriate for Hydrogen Bond Energies of Amides? Kang, J. Phys. Chem. B 2000, 104, 8321-8326

L-J: 6-9, 6-12, 10-12

ELennard-Jones = D/rm-B/rn EMorse =  {e-2
(r-r0) - 2e-
(r-r0)}

Morse

ab initio MP2/6-31G**

N-H…O=C

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

kT (20˚C) = = 0.6 kcal/mol = 2.6 kJ/mol

Steiner, 2002, pg. 55

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

Energy Summary








In contrast to covalent bonds which are of the order of 100–600 kJ mol–1 in bond energy, the energies of the usual “weak” H-bonds are approximately an order of magnitude smaller (i.e.
30 kJ mol-1). The overwhelming importance of H-bonds in biology and chemistry stems from the very moderate energies needed for their formation and rupture. This makes it possible that H-bonds play an essential role in many common enzymatic and chemical reactions occurring in many common solvents, such as water, at ambient temperatures. The potential energy function of an H-bond seems most adequately described by the form of a Morse potential. For long hydrogen bond lengths the electrostatic interactions clearly dominate, for short lengths also covalent interactions play a role.

Hydrogen bond geometries

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

Steiner, 2002, pg. 60

Donor directional preference

Steiner, 2002

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

Acceptor directional preference

Steiner, 2002, pg.62

Influence on covalent bond length

rDH

rHA

Steiner, 2002

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

Geometry Summary












In general, distance and directional preferences are not very strong. It is a very important property of the weak hydrogen bond that the possible bond distances and bond angles cover a rather wide range. Apparently, the energy minimum is relatively shallow with respect to a variation of bond distances and angles. Therefore a variety of different H-bond geometries can be realized with relative ease. This property enables the H-bonds to act as a very adaptive “glue” and contrasts with covalent bonds that display distinct preferences with respect to bond distances and angles . For the donor geometry, a preference exists for rather straight H-bonds, i.e. the DH…A angle is usually in the range of 180 +/- 20 degrees For the acceptor geometry, a certain preference exists such that the X-A direction coincides with the free electron pair of the acceptor. However the preference is weak. Shorter H-bonds have more directional preference than longer ones The D-H distance increases as the H…A distance gets shorter, i.e. the proton is pulled towards the acceptor for short H-bonds

NMR observables for H-bonds: Proton chemical shift H-bond formation usually results in chemical shift changes for all the nuclei involved in the H-bond. As the chemical shift is intrinsically related to the local electronic environment, these chemical shift perturbations indicate a redistribution of the electron density upon H-bond formation. For H-bonding to an electronegative acceptor atom such as oxygen or nitrogen, there is always a change in the isotropic chemical shift of the H-bonded hydrogen nucleus to higher frequencies (downfield shift). This downfield shift is a result of a number of not yet fully understood and partially competing factors, including a decrease in the electron density around the hydrogen nucleus and deshielding effects from the electronic currents of the acceptor atom. A large number of examples can be given for such proton downfield shifts on H-bond formation with oxygen or nitrogen acceptors. E.g., downfield shifts of the amide proton in proteins have long been recognized to be correlated to shorter H-bond lengths. Likewise, the formation of H-bonds in nucleic acid base pairs results in downfield shifts for the imino and amino protons. In certain systems, proton downfield shifts upon H-bond formation have been observed to be as large as 15–20 ppm.

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

H-bond formation in ethanol (H3C-CH2OH) HO 1 M ETOH in CDCl3

HO

H2C

HO 1 mM ETOH (monomeric) in CDCl3

H3C undiluted ETOH

Dependence of 1H chemical shift on H-bond length in proteins


 =  - random coil Wagner, Pardi, Wüthrich JACS 1983

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

H-bond formation of imino protons in DNA 12 mer

not H-bonded

12 mer

H-bonded

12 mer (forming hairpin)

ppm

NMR observables for H-bonds: hydrogen exchange

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

Hydrogen exchange: basic idea H O Exchange H O

O H N

Closed structure

H N

Open structure

W. Englaender, Encyclopedia of NMR, 1996

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

W. Englaender, Encyclopedia of NMR, 1996

W. Englaender, Encyclopedia of NMR, 1996

HX is acid- and base-catalysed

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

Hydrogen exchange: basic experiment H H

H H

H

H H

H2O

H

D

D2O

Transfer to D2O

D2O

Observe exchange

(Dry+redissolve or mix)

Thioredoxin dissolved in D2O 1H-15 N

NMR correlation spectrum

O

After 5 min

C

O N

C


C

Cheng + Dyson, Biochemistry, 1995, 34, 611

15N

H

Chemical shift

1HN

ppm

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

Thioredoxin dissolved in D2O

After 5 min

After 700 h

15N

Cheng + Dyson, Biochemistry, 1995, 34, 611

Chemical shift

1HN

ppm

Intensity of 1H-15N amide resonance = population of protonated amide

Hydrogen Exchange in Thioredoxin dissolved in D2O

Amide of Ile38

Oxidized protein

Reduced protein

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

H-exchange: example staphyloccocal nuclease (J. Markley)

Summary hydrogen exchange











Amide hydrogen exchange times can vary from milliseconds to > years The fact that the hydrogen nuclei exchange gives evidence of local and global unfolding of macromolecules The exchange of individual amide hydrogens is most easily studied by NMR Hydrogen exchange is extensively used to elucidate macromolecular folding and unfolding mechanisms

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

NMR observables for H-bonds: hydrogen bond scalar couplings (HBCs)

Scalar Couplings

Scalar couplings are mediated via the electron cloud of a molecule. Thus they can only be observed between nuclei that are connected by chemical bonds. The energy of the orbital motion of electrons is affected by the magnetic moment of the nucleus of the atom, and of course in a molecule the electrons of the constituent atoms interact with each other. Thus the orientation of nuclear spin A, acting via the electrons of the bonds between them, will affect the local magnetic environment of nucleus B. Since A has two possible orientations the nucleus B will have two possible and slightly different energies; in a sample consisting of a large number of molecules half the molecules will be in each state. Thus in a resonance experiment two Larmor frequencies will be seen for B and it will appear as a doublet. The effect is known as spin-spin splitting, scalar coupling, or J-coupling; the separation of the two components of the signal from B is expressed as J Hz.

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

Example of a scalar coupling: from Abragam pg. 486.

Scalar couplings can be used to transfer magnetization in multidimensional correlation experiments (COSY)

Example: 1H-15N COSY of a protein correlating 1H and 15N nuclei separated by one chemical bond

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

H-bond scalar couplings in a U-A base pair

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

Hoogsteen Watson-Crick DNA triplex

J. Feigon

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

N-H•••O=C h3 J

NC'

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

Dependence on H-bond Geometry and Dynamics

Dependence on 1H chemical shift Wagner, Pardi, Wüthrich JACS 1983, 105, 5948

proteins

nucleic acids

2

3

d [Å]

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

Dependence of h3JNC' on distance

N-H•••O=C h3J

NC'

= -5.9·104 Hz exp(-4·R NO/Å)


RNO = -0.25 Å
h3JNC'/h3JNC'

Cornilescu et al. JACS 121 (1999) 6275

Density functional calculations E() = KE() + PE() + XC( )  = electron density KE = kinetic energy PE = potential energy XC = exchange/correlation (Pauli principle ) 1998 Nobel Prize in Chemistry Walter Kohn (density functional theory, DFT) John Pople (computational methods – Gaussian)

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

M. Barfield

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

Pople and Santry LCAO model of H-Bond coupling

N-H···O=C H-bonds: DFT and LCAO model

M. Barfield JACS, 124, 2002, 4158

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

N-H···O=C H-bonds: DFT and LCAO model

h3 J

NC'


-360 Hz exp(-3.2 rHO)cos2(
2)

M. Barfield JACS, 124, 2002, 4158

Protein G h3JNC' H-bond couplings predicted vs. measured

M. Barfield

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

Influence of dynamics on H-bond couplings (predicted from DFT)

Tudor domain, Markwick et al. JACS 125 (2003) 644

200-ps MD average static NMR struct.

h3 J

NC'

static X-ray struct.

[Hz]

h3 J

NC'

(measured)

= A exp(-r/ro)cos2(
2)

Prediction of h3JNC' from MD and LCAO formula (Protein G)

300-ps MD average RMSD = 0.10 Hz

h3 J

NC'

static X-ray struct. RMSD = 0.15 Hz

[Hz]

h3 J

NC'

(measured)

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

Protein G H-bond angular distribution from MD x-ray structure

strand 1 Y3

L5

L7

rHO


helix Q32

x-ray structure energy minimized

Y33

A34

N35

D36

Applications to protein stability

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

Linear thermal expansion:
L = 1/r dr/dT = 2·10-4/K

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

H-bond couplings and H-exchange

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

C
H • • • O = C H-bonds O N

C

C

H

H

Huggins (collagen), Chem. Rev., 1943 Derewenda et al., JMB,1995

~2.4 Å

~2.0 Å

O C

N H

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

C  H • • • O = C H-bonds

BPTI, 0.86 Å, 1g6x, Addlagatta et al., 2001

Vargas et al., JACS 2000: C-H ••• O=C:
H298 = 3.0 kcal/mol N-H ••• O=C :
H298 = 5.3 kcal/mol

13C

H

O

13C'

M. Barfield DFT: h3JCACO ~ 0.2 – 0.6 Hz

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

O

Protein G: Selective H(NCA)CO N 3hJ

CACO

= 0.3 Hz

0.2 Hz

0.2 Hz

C

H C


N

D


H

O C


C

N

Protein G: -sheet bifurcated H
•••O•••HN-bonds anticorrelation

h3J

NC'

h3J

C
C'

h3 J

Distance

observed h3JC
CO

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

H-bond Cooperativity

H-bond cooperativity observed from h3JNC' correlations

+



+


-

Juranic & Macura, JACS, 123 (2001) 4099

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

– h3JNC' [Hz]

Ligand-induced H-bond strain and cooperativity in SH3 peptide binding

Linda Nicholson

Are hydrogen bonds covalent?

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

Pauling's partial covalency hypothesis Ice: O – H

–

O

1Å

1.76 Å

H

:O

61 %

based on

:O

34 %

distance/bond order

O

5%

relation

A

O

B

O:-

H+

C

O:

H

–

J. chim. phys. 46, 435, (1949) The nature of the chemical bond, Chapter 12

The compton scattering experiment by Isaacs et al.

E. D. Isaacs, A. Shulka, P. M. Platzman, D. R. Hamann, B. Barbellini, C. A. Rulk, Phys. Rev. Lett. 1999, 82, 600-603

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

Density of wavefunction coherence H…O distance

O-O distance

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

Critique of the Compton-scattering experiment by analysis of electronic wavefunctions electron density at acceptor decreases due to ice formation

- - - isolated H 2O –– ice

calculations give same Compton scattering profile as experiment

Romero et al. phys. stat. sol. (b) 220, 703 (2000)

H-bond couplings indicate a correlated motion of (s-)electrons on donor and acceptor

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

What is covalency?


In the absence of electron pairing between radicals, it is not clear which part of the total interaction energy should be called "covalent". Coordinate-covalent bonding is usually defined as the sharing of an electron pair of one fragment with an empty orbital of the other (Ghanty et al., JACS, 2000,122,1210-1214). The energy of this charge-transfer (CT) should be significant relative to other energies. For H-bonds this would mean that the acceptor donates some density from its free electron pair to an unoccupied orbital of the acceptor.




The partitioning of donor and acceptor wave functions and energies into different contributions, particularly in the case of DFT calculations, is difficult. A number of papers address this question (Umeyama and Morukawa, JACS, 1977, 99, 1316; Ghanty et al., JACS, 2000,122,1210; Arnold and Oldfield, JACS, 2000, 122, 12835; Wilkens et al., JACS, 2002, 124, 1190). The general outcome is that the answer is not "black or white". Most of the energy for H-bonds in biomolecules stems from pure electrostatics. However there is some contribution from covalency. Biomolecular H-bonds are in a transition region (Arnold and Oldfield, JACS, 2000, 122, 12835) where this covalent contribution switches from not significantly covalent for the weaker H-bonds (e.g. amide-carbonyl, normal protein backbone) to partially covalent for the stronger H-bonds (e.g. imino-aromatic N, normal nucleic acid base pairs). recent theoretical results indicate that for biomolecules the transition from not significant to partial covalency happens somewhere between amide-carbonyl (normal protein backbone) and imino-aromatic N (normal nucleic acid) H-bonds (Arnold and Oldfield, JACS, 2000, 122, 12835)




Natural Bond Order Analysis of H-bond Energy + Couplings

Lone pairacc

NH N

H

N'


E = 27 kcal/mol: repulsive
h2JNN = 4.2 Hz

Lone pairacc

NH N

H

N'


E = -35 kcal/mol: attractive!!!
h2JNN = 4.85 Hz Wilkens et al., JACS, 124 (2002) 1190

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Aufbaustufe E4: 2485 Biomolecular Interactions and Structures, 12.5.2005, Stephan Grzesiek

Conclusions


NMR can be used to detect changes in individual hydrogen bonds, like opening, stretching etc.




the hydrogen bond network adapts to external changes like ligand binding or temperature variations




the hydrogen bond scalar couplings and the Compton scattering experiment prove a correlated motion of electrons on donor and acceptor, but not necessarily a covalent character of the H-bond




the main energy contribution for H-bonds stems purely from electrostatics. However the covalent for biomolecular H-bonds switches from not significant to significant from the weaker H-bonds (such as amide->carbonyl in a normal protein backbone) to the stronger H-bonds (such as imino->aromatic N in normal nucleic acid base pairs)

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