probing the electronic structure of peptide bonds using methyl groups: experimental measures of...
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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
Resonance Structural Weights
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
Resonance Structural Weights
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)
Carbonyl Methyl Amide Methyl
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
Semi-Quantitative Agreement
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
Semi-Quantitative Agreement
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.
Carbonyl Methyl Amide Methyl
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