Probing the Electronic Structure of Peptide Bonds using Methyl Groups: Experimental Measures of...

Probing the Electronic Structure of Peptide Bonds Probing the Electronic Structure of Peptide Bonds using Methyl Groups: Experimental Measures of using Methyl Groups: Experimental Measures of

Resonance WeightsResonance Weights

aPhysics Lab, NIST, Gaithersburg, MDbChemistry Dept., University of Pittsburgh, PA

David F. Plusquellica and David W. Prattb

I II

_+

...... ..

..

Principal Resonance Structures of Peptide Bond

E = 30 kcal/mole * sin2ω

60% 40%

1.33 Å

L. Pauling et al., Proc. Natl Acad. Sci. USA 37, 205-211 (1951).R. B. Corey and L. Pauling, Proc Roy. Soc B 141, 10-20 (1953)

1.24 Å

Outcome I: Assigned Conformational Structures to > 10 systemsRotor axis angles, inertial constants and dipole moments

Outcome II: Determined V3 BarriersV3 barriers vary by more than 2-fold and therefore, sensitive to changes in structure that occur at the other end of the peptide bond.

Issues addressed• What are the principal factors responsible for the torsional barriers?• What influence do torsional motions have on relative weights of

resonance structures I and II?

Carbonyl Methyl Amide Methyl

Gas Phase FTMW Studies of Methyl Terminated Model Peptides

b

a

a

b

AGI

MAt

b

a

b

aEAA

I

EAAII

a

bAD

7eqPD

tCu

a

b

CS

C1

N-MethylAcetamideMAt

N-AcetylGlycineAGI

N-AcetylGlycineEthylEster EAAI & EAAII

Proline Dipeptide PDtCd

Model Peptides Investigated

Alanine DipeptideAD7eq

[J. Mol. Spec., 227, 28 (2004)]

[J. Mol. Spec., 228, 251 (2004)]

[J. Chem. Phys., 119, 5497 (2003)]

[J. Chem. Phys., 118, 1253 (2003)]

[in preparation]

Label Structure Symmetry V3 Barrier (cm-1)

Carbonyl Methyl

AGI CH3-[CONH]-CH2-C(O)OH Cs +57(1)

EAAI CH3-[CONH]-CH2-C(O)OC2H5 Cs +66(1)

EAAII CH3-[CONH]-CH2-C(O)OC2H5 C1 +66(1)

MAt CH3-[CONH]-CH3 Cs +73(1)

AD7eq CH3-[CONH]-CHCH3-[CONH]-CH3 C1 +98(1)

PDtCd CH3-[CON]-CHC3H6-[CONH]-CH3 C1 +333(5)

Amide Methyl

MAt CH3-[NHCO]-CH3 Cs +79(1)

AD7eq CH3-[NHCO]-CHCH3-[CONH]-CH3 C1 +84(1)

PDtCd CH3-[NHCO]-CHC3H6-[CON]-CH3 C1 +84(1)

Summary of the Experimentally Determined V3 Barriers

Torsional Barriers have their origin in electronic structure of peptide bond

Methyl Acetamide - MAt

anti

syn

anti

synMP2/aug-cc-pVTZ Predictions

Syn forms found to be more stable in previous theoretical work on biacetyl, propene, acetaldehyde, etc.*

* D. W. Pratt, et al., J. Am. Chem Soc. 109, 6591 (1987) J. A. Pople, et al., J. Am. Chem Soc. 98, 664 (1976)

What level of theory is needed?

CHARMm, MMAM1

AM1

Force Field and Semiempirical Models

CHARMm, MM

a

b

AGI

0 60 120

Level of Theory

Expt V3=57(1) cm-1

Basis HF DFT MP2

3-21G -184

6-31G -5.0

6-31G(d) +8.0 +89.0 +22.3

6-311G(d,p) +47.1 +104.0 +79.0

6-311++G(d,p) +53.7 +124.1 +90.9

HF/6-311++G(d,p) chosen level

V3E

anti V3 = Esyn - Eanti

V3T

anti

syn

Natural Bond Orbitals or NBOs

Prof. Frank Weinhold, http://www.chem.wisc.edu/~nbo5

1. Lewis interactions arising from electrostatic and exchange repulsion interactions of the NBOs of the idealized Lewis structure

Molecular e- density is decomposed in terms of bonding and anti-bonding orbital densities. Convenient way to separate energies associated with

*

*

2*

)2(

ˆ2

FE

E1

E2

} E

(2)

F is the Fock operator and εσ and εσ* are NBO orbital energies

Donor-Acceptor Interaction Energies fromSecond-Order Perturbation Theory

Rigorous separation made by deleting all anti-bonding and Rydberg orbitals and calculating new SCF energy

2. Non-Lewis stabilizing interactions arising from delocalization of the NBOs into empty Rydberg and antibonding (non-Lewis) orbitals

Carbonyl Methyl

E kcal/mole cm-1

V3E Lewis Non-Lewis V3 calc. V3 expt.

AGI anti -1.86 +2.02 +54 +57(1)

EAAI anti -1.90 +2.07 +59 +65(1)

EAAII anti -1.89 +2.06 +60 +66(1)

MAt anti -1.88 +2.07 +70 +73(1)

ADC7eq anti -2.85 +3.04 +67 +98(1)

PDtCd syn +6.33 -5.54 +278 +333(5)

Amide Methyl

MAt syn +1.88 -1.52 +126 +79(1)

ADC7eq syn +2.47 -1.98 +170 +84(1)

PDtCd syn +4.24 -3.75 +171 +84(1)

Lewis vs non-Lewis Contributions - HF/6-311++G(d,p)

Enon-Lewis

ELewis

EOpt

0

Enon-Lewis-=

EOpt - ELewis

ELewis

EOpt

synanti

V3{

Amide

ELewis

EOpt

0

Enon-Lewis-=

EOpt - ELewis

ELewis

EOpt

Enon-Lewis

anti syn

V3}

Carbonyl

Lewis Energy (LE) differences always favor syn configurationNon-Lewis (NLE) differences always favor anti configuration

-4

-3

-2

-1

0

1

2

3

4

0 10 20 30 40 50 60

Lewis and Non-Lewis EnergiesAlanine Dipeptide

Rel

ati

ve

En

erg

y / k

cal

/mo

le

Torsional Angle / o

Carbonyl MethylNon-Lewis

V3

Lewis

anti syn

-4

-3

-2

-1

0

1

2

3

4

0 10 20 30 40 50 60

Lewis and Non-Lewis EnergiesAlanine Dipeptide

Rel

ati

ve

En

erg

y / k

cal

/mo

le

Torsional Angle / o

Amide Methyl

Non-Lewis

V3

Lewis

syn anti

What are the principal contributions to the Lewis and non-Lewis energies differences?Why are the Lewis and non-Lewis interactions reversed?

Torsional Dependence of Lewis vs non-Lewis Differences

σC-H 3σC-H σC-N

πC=OσC=O σN-H

Lewis Interactions - Bonding PNBOs

Vicinal Lewis Orbital Energies – Carbonyl Methyl

anti syn

C-H

ip

C-H

op+7.45-4.14(x2)

C=O -2.57

+3.04

C-N

kcal/mole

C=O +0.44

= -0.08

Methyl Carbonyl of MAt

Vicinal Orbital Energies

Vicinal Bonds

σC-Hip - σC=O

anti

syn

anti syn

kcal/mole

nO

s

-2.43

nO

p

-2.70

= -3.31

-1.5

-1

-0.5

0

CCCCNNCCCCCCNOO

MA_6311ppss_HF_T1_DoS

L

D

Methyl Carbonyl of MAt

Remote Orbital Energies

N-H

+1.92

nN -0.54

Remote Lewis Orbital Energies - Carbonyl MethylRemote Bond

Remote Orbitals

nO (s-like)

nO (p-like)

Lewis Orbital Energies – Amide Methyl

nO

p +0.45

kcal/mole

C=O

+0.59

C=O

-1.41

Remote Orbital EnergiesAmide Methyl of MA

t

syn anti

nO

s +0.40

= -0.03

Remote Bonds

RemoteOrbitals

kcal/mole

nN -0.90

C-N +0.18

-1.73(x2)

+4.37C-H

op

C-H

ip

N-H

+3.19

Vicinal Orbital EnergiesAmide Methyl of MA

t

syn anti

= +3.38

Vicinal Bonds

VicinalOrbital

Carbonyl Methyl

kcal/mole

V3E Vicinal Remote Variational

AGI anti -0.08 -3.79 -1.86

EAAI anti -0.03 -3.92 -1.90

EAAII anti -0.01 -3.80 -1.89

MAt anti -0.08 -3.31 -1.88

AD7eq anti -2.71 -1.43 -2.85

PDtCd syn +8.24 +5.56 +6.33

Amide Methyl

MAt syn +3.38 -0.03 +1.88

AD7eq syn +1.22 +2.50 +2.47

PDtCd syn +1.27 +1.84 +4.24

Lewis Energy Difference Summary

Explains- the syn preference for amide methyl: vicinal Lewis energy differences dominate- the higher sensitivity of carbonyl methyl barriers to remote structural changes

Non-Lewis Interactions – PNBO Delocalizations

σN-H*

σC-H

πC=O*

3σC-H

σC=O*

σC-N*

Non-Lewis Energy Differences – Carbonyl Methyl

anti Carbonyl Methyl

σC=O* πC=0

* σN-C*

σCHip +4.60 <0.2 -4.29

σCHop -2.53 +0.29 +2.02

σCHop -2.53 +0.29 +2.02

Σ -0.46 +0.58 -0.25

Σ -0.13

AGI

anti σC-H σC=O* syn σC-H σC=O

*

Non-Lewis Energy Differences – Amide Methyl

syn Amide Methyl

σN-H* πC=0

* σN-C*

σCHip -3.78 -0.24 +4.21

σCHop +2.95 <0.2 -2.39

σCHop +0.45 <0.2 -1.49

Σ -0.38 -0.24 +0.33

Σ -0.04

AD7eq

NLE differences do not arise from direct interactions with the methyl top orbitals

Principal Delocalization: nN πC=0*

Indirect consequence of the methyl group interactions

Order of magnitude larger than any direct NLEσC-H σC=O

* 5 kcal/mole

nN πC=0* 100 kcal/mole

Carbonyl Methyl

kcal/mole

V3E Direct nN

πC=O*

Variational

AGI anti -0.13 +2.38 +2.02

EAAI anti -0.21 +2.42 +2.07

EAAII anti -0.25 +2.31 +2.06

MAt anti -0.17 +2.35 +2.07

AD7eq anti -2.91 +8.22 +3.04

PDtCd syn +1.49 -7.50 -5.54

Amide Methyl

MAt syn -0.42 -0.84 -1.52

AD7eq syn -0.04 -3.71 -1.98

PDtCd syn -0.12 -3.75 -3.75

Non-Lewis Energy Difference Summary

NLE difference should be related to the magnitude of the charge shifts

Torsional Dependence of Natural Charges

Natural charge shifts reflect changes in resonance character

Decrease in nN πC=0* Increase in nN πC=0

*

-0.010

-0.005

0.000

0.005

0.010

0 10 20 30 40 50 60

Natural ChargesAlanine Dipeptide

Rel

ati

ve

Na

tura

l C

ha

rge

Torsional Angle / o

O

C

N

Carbonyl Methyl

anti syn

-0.010

-0.005

0.000

0.005

0.010

0 10 20 30 40 50 60

Natural ChargesAlanine Dipeptide

Rel

ati

ve

Na

tura

l C

ha

rge

Torsional Angle / o

O

C

N

Amide Methyl

syn anti

Natural Resonance TheoryResonance weights decomposed from electron density

AGI V3E V3

T Δ

I 51.01 51.92 +0.91

II 22.06 21.18 -0.88

III 5.03 5.11 +0.08

Remaining 21.90 21.79 -0.11

1-e density operator represented in terms of an optimized resonance hybrid of density operatorsEach optimized resonance density is the determinant of the doubly occupied NBO for the chosen Lewis structure.

I

II

III

–

+•• ••

••

•• ••

•• –

+

••••

••

••••

Resonance Structural Weights

Resonance Structural weights (%)

Carbonyl Methyl

Lewis V3E V3

T Δ

AGI I 69.81 71.02 +1.21

II 30.19 28.97 -1.22

EAAI I 69.65 70.88 +1.23

II 30.35 29.11 -1.24

EAAII I 69.45 70.67 +1.22

II 30.54 29.33 -1.21

MAt I 68.76 69.94 +1.18

II 31.24 30.05 -1.19

Amide Methyl

MAt I 68.76 68.19 -0.57

II 31.34 31.81 +0.47

Carbonyl

Amide


I IIC IIN

dipolarcovalent

% Carbonyl Methyl Amide Methyl

AD7eq V3E Δ V3

E Δ

I 47.65 +2.10 47.65 -0.77

IIC 26.89 -2.06 26.89 -0.03

IIN 25.46 -0.04 25.46 +0.80

PDtCd Carbonyl Methyl Amide Methyl

I 47.40 -2.32 47.40 -0.77

IIC 26.31 +2.23 26.31 -0.01

IIN 26.28 +0.09 26.28 +0.79


I IIC IIN

dipolarcovalent

-2

-1

0

1

2

0 10 20 30 40 50 60

Resonance WeightsAlanine Dipeptide

Rel

ati

ve

Re

son

an

ce

Wei

gh

t /

%

Torsional Angle / o

IIN

I

IIC

Amide Methyl

syn anti

-2

-1

0

1

2

0 10 20 30 40 50 60

Resonance WeightsAlanine Dipeptide

Rel

ati

ve

Re

son

an

ce

Wei

gh

t /

%

Torsional Angle / o

IIN

I

IIC

Carbonyl Methyl

synanti

-2

-1

0

1

2

0 25 50 75 100 125

Rel

ativ

e R

eso

nan

ce W

eig

ht

of

I / %

V3 Expt / cm-1

Amide Methyl

Carbonyl Methyl

Correlation between V3 Barriers and

Lewis Structures

n

kkakkAR WFAA

1

2)(

)2()(00)(

n

kkkakkkakkkER WFWFAA 2

)()2(

)(00)(2

)()2(

)(10)()(

12000.0 20000.0

Torsional States

Inte

ns

ity

/ MHz

AA

EA

AE

Trot

~2K

Expt-AA-AE-EA

Expt

100% a-typeAAMA (14N2)

“Infinite-Barrier” Rotational Constants

A-state

E-state

0

50

100

0 120 240 360

En

erg

y /

cm

-1

/ degrees

Methyl Torsional Coordinate

V3=100 cm-1V=V

3/2 [1 - cos(3)]

AE

Experimental Evidence of Resonance Weight Changes

ΔI (amu A2)


EAAI EAAII AD7eq AD7eq PDtCd

Ia +0.02 +0.02 -0.08 -0.08 -0.01

Ib -0.06 -0.06 +0.00 +0.09 +0.09

Ic -0.04 -0.07 +0.02 -0.06 -0.01

Separate Fit Cases using the “high-barrier” Approximation

No improvement upon including- 4th order terms- denominator corrections

80 120 160 200 240 280

Wavefuntion Probability Amplitude

0

10

20

30

40

50

60

Methyl Torsional Angle

E-state

A-state

V3

T

V3

E

ΔI (amu A2) - HF/6-311++G(d,p)

EAAI EAAII

V3T - V3

E A – E V3T - V3

E A - E

Ia +0.04 +0.02 +0.05 +0.02

Ib -0.13 -0.06 -0.15 -0.06

Ic -0.09 -0.04 -0.10 -0.07

At top-of-barrier, A-state has ~7% larger

probability amplitude than E-state

Semi-Quantitative Agreement

Inertial Differences - HF/6-311++G(d,p)

Carbonyl Amide

AD7eq V3T -V3

E A-E V3T -V3

E A-E

Ia +0.10 +0.02 +0.09 +0.02

Ib -0.07 +0.00 -0.05 -0.05

Ic -0.22 -0.02 +0.26 +0.07

PDtCd High V3 Barrier

A +0.00 +0.00 +0.14 +0.01

B +0.00 +0.00 -0.09 -0.06

C +0.00 +0.00 +0.12 +0.02


Internal rotation models will need to include additional degrees of freedom to account for resonance character changes

Conclusions of MW Studies

Nine methyl torsional barriers have been investigated for 5 different model peptides

Non-Lewis energy differences favor the anti configurationLewis energy differences favor the syn configurationBoth are important resulting in low V3 barriers

Carbonyl Methyl Groups Non-Lewis energy differences dominate – anti minimum.Local steric interactions tend to cancel

Amide Methyl GroupsLewis energy differences dominate - syn minimumLocal steric interactions are most important

Acknowledgements

• Richard Lavrich, EPA• Michael Tubergen, Prof., Kent State Univ.• Jon Hougen, Richard Suenram, Frank Lovas,

Gerald Fraser and Angela Hight-Walker, NIST

• Isabelle Kleiner, CNRS, Paris, France

• Frank Weinhold, Prof., Univ. of Wisconsin

-10

-5

0

5

10

Carbonyl MethylDelocalization Energies

All othersn-*

AG EAAI

EAAII

MAt

AD7eq

PDtCd

E

/ k

cal/

mo

le

-10

-5

0

5

10

Amide MethylDelocalization Energies

All others

n-*

MAt

AD7eq

PDtCd

E

/ k

cal/

mo

le

Rotational Constants - HF/6-311++G(d,p)

EAAI EAAII

V3T - V3

E A - E V3T - V3

E A - E

A -21 -0.6 -25 -0.7

B +0.8 +0.03 +1.0 +0.03

C +0.4 +0.02 +0.6 +0.03

80 120 160 200 240 280

Wavefuntion Probability Amplitude

0

10

20

30

40

50

60

Methyl Torsional Angle

E-state

A-state

V3

T

V3

E


EAA1 b

a

EthylAcetAmidoAcetate

b

a

EAAS

ΔI (amu A2)

EAAI EAAII AD7eq AD7eq PDtCd

MeC MeC MeC MeN MeN

AR -0.60 -0.70 -0.08 -0.08 -0.01

BR +0.03 +0.03 +0.00 +0.09 +0.09

CR +0.02 +0.03 +0.02 -0.06 -0.01

Rotational Constants - HF/6-311++G(d,p)

Carbonyl Amide

AD7eq V3T -V3

E A-E V3T -V3

E A-E

A -7.7 -0.08 -6.8 -0.08

B +1.8 +0.00 +1.3 +0.09

C +3.0 +0.02 -3.4 -0.06

PDtCd High V3 Barrier

A -8.6 +0.00 -5.1 -0.01

B +2.9 +0.00 +1.8 +0.09

C -0.26 +0.00 -1.0 -0.01

Carbonyl E-state V3

T has more covalent character (I) than V3E

Amide E-stateV3

T has more ionic character (II) than V3E

0 60 1200 60 120

Non-Lewis energy differences increase at the MP2/6-311++G(d,p)

Carbonyl Methyl

anti

syn

II

Amide Methyl

anti

syn

V3 increases V3 decreases

I

I

II

HH

N

C

O

C

C

H

(d)

H

C

H

C

C

N

H

O

(c)

H

C

O

N

H

C

H

C

(b)

H

C

C

O

N

H

C

H

(a)

H

C

C

O

N

H

C

H

(a)

H

C

O

N

H

C

H

C

(b)

H

C

H

C

C

N

H

O

(c)

H

N

C

O

C

H

C

H

(d)

0 60

I

II

0 60

I

II

Gas Phase FTMW Studies of Methyl Terminated Model Peptides

Outcome I: Assigned Conformational Structures to > 10 systemsRotor axis angles, inertial constants and dipole moments

Outcome II: Determined V3 BarriersV3 barriers vary by more than 2 fold and therefore, sensitive to changes in structure that occur at the other end of the peptide bond.


Issues addressed• What are the principal factors responsible for the torsional barriers?• What influence do torsional motions have on relative weights of

resonance structures I and II?

O

Primary Peptide Structure - Biochemistry Primer

Primary structures

Alanine - Amino acid Dialanine - Polypeptides

+ = +

Water

NC H

Ramachandran Angles

ψφ

α-HelixParallel β-Sheet

Anti-parallel β-Sheet

Secondary Peptide Structure - Biochemistry Primer

φ ≈-140º ψ ≈+140º

φ ≈57ºψ ≈47º

Probing the Electronic Structure of Peptide Bonds using Methyl Groups: Experimental Measures of...

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