Modeling of protein turns and derivation of NMR parameters related to turn structure
Megan ChawnerBRITE REU Program
Advisor: Dr. Dimitrios MorikisDepartment of Bioengineering
University of California, Riverside
Outline
• Background• My Project• Results• Conclusions• Acknowledgements
Protein Structure: All proteins are made up of twenty amino acid building blocks into a sequence = primary structure
Protein structure: sequence folds into -sheet, -helix, random coil loops and various types of turns stabilized by atomic interactions (e.g., H-bonds) = secondary structure
Anti-parallel-sheet
-helix
Primary structure: GPLLNKFLTT
Primary structure: EKQKPDGVFQE
Strand 1
Strand 2Inter-strandH-bonds
C=O(i)…H-N(i+4) H-bonds1 helix turn = 3.6 a.a.
Protein Structure: three-dimensional protein folds are stabilized by long range interactions = tertiary structure
Turns introduce reversibility in the direction of other elements of secondary structure, such as -helices or -sheets• 3 amino acids = -turn • 4 amino acids = -turn
-turn
-turn
i-1 i i+1
ii i
-sheetRamachandran plot() plotdefines secondary structure
-180
-120
-60
0
60
120
180
-180 -120 -60 0 60 120 180
-
-II
-I’
-II’
-VIII
-direct
-inverse
-180
-120
-60
0
60
120
180
-180 -120 -60 0 60 120 180
-
-II
-I’
-II’
-VIII
-direct
-inverse
Backbone torsion angles:
Turns
-helix
Amino Acid i Amino Acid i+1Amino Acid i Amino Acid i+1
N C C
OR
H
N C C
O
H
R
i ii+1 i+1
H Hi
N C C
OR
H
N C C
O
H
R
i ii+1 i+1
H Hi
Amino Acid i Amino Acid i+1Amino Acid i Amino Acid i+1
N C C
OR
H
N C C
O
H
R
i ii+1 i+1
H Hi
N C C
OR
H
N C C
O
H
R
i ii+1 i+1
H Hi
Protein Structure Determination: uses Nuclear magnetic resonance (NMR) spectroscopy to get NMR observables, which are converted to NMR-derived structural parameters • Nuclear Overhauser effects (NOEs) inter-proton distances• 3J(HN-H)-coupling constants -torsion angles
Karplus Equation (Karplus, 1959, J Chem Phys)
NOE equation (Wuthrich, 1986) ri,j inter-proton distancec rotational correlation time
)(fr
1)HH(NOE c6
j,i
ji
CcosBcosA)HH(J 2N3
o60
A=6.98, B=-1.38, C=1.72 (Wang and Bax, 1996, JACS)
NOE < 5 Å through-space interactions inter-proton distances3J(HN-H) = 3-chemical bond coupling through-bond interactions -torsions
Amino Acid i Amino Acid i+1
N C C
OR
H
N C C
O
H
R
i i
3J(HN-H)
i+1 i+1
H Hi
HN(i)-H(i)
HN(i)-HN(i+1)HN(i)-H(i+1)
3J(HN-H) = 3-bond -torsionNOE < 5 Å distance in space
H(i)-H(i+1)
H(i)-HN(i+1)
Relations of experimental observables and structural parameters
dN (i,i+1)
dNN (i,i+1)
dN (i,i)dN (i,i) d (i,i+1)
o60
3J(
HN-H
)
(Hz)
(o)
Cis=0o
=60o
=90o
=150o
Newman Projections
N
C=OC=O
HHC
N
C=OC=O
HHC
N
C=OC=O
HHC
N
C=OC=O
HHC
N
C=O
C=O H
H
C
N
C=O
C=O H
H
C
=-90o
=-30o
N
C=O
C=OC
N
C=O
C=OH
H
C
N
C=O
C=OC
N
C=O
C=OH
H
C
Trans=180o
=-120o
Solution of Karplus equation using MatLab
-helix
-sheet
N C
H
H
Cis
N C
H
HTrans
N C
H H
Cis
N C
H
HTrans
C
N C
C
Cis
C
N C
C
Trans
C
N C
C
Cis
C
N C
C
C
N C
C
Cis
C
N C
C
Trans
C
N C
C
C
N C
C
Trans
Chawner & Morikis, in preparation
My ProjectGoals: To use NMR-derived parameters (inter-proton distances and -torsion angles) to create databases of expected NMR observables (NOEs and 3J(HN-H)-coupling constants) for ideal - and - turns with statistical deviations.
Bottom line: we are back-calculating NMR observables. Remember, during structure determination, NMR-derived parameters are obtained from NMR spectroscopic observables, NOEs and 3J(HN-H)-coupling constants.
Use: Rapid protein turn structure identification by examination of raw NMR observables, without a complete structure calculation.
Color code:
Blue: N
Light blue: H
Gray: C
Red: O
Color code:
Blue: N
Light blue: H
Gray: C
Red: O
VIIIVIII
I I’
II’II
1
32
4
H-bond
C-C
I I’
II’II
1
32
4
H-bond
C-C
-turns
Computational modeling of ideal -and -turns according to torsion angles using DeepView
Classic -turn criteria
Distance: C(1)-C(4) < 7 ÅC=O(1)…H-N(4) H-bondedDistance: O(1)-N(4) < 3.3 Å Distance: O(1)-HN(4) < 2.4 ÅAngle: O(1)-H(4)-N(4) almost linear ± 35o
-180
-120
-60
0
60
120
180
-180 -120 -60 0 60 120 180
-
-II
-I’
-II’
-VIII
-direct
-inverse
-180
-120
-60
0
60
120
180
-180 -120 -60 0 60 120 180
-
-II
-I’
-II’
-VIII
-direct
-inverse
Torsion angles (o)
Type 2 2 3 3
I -60 -30 -90 0
II -60 120 80 0
I' 60 30 90 0
II' 60 -120 -80 0
VIII -60 -30 -120 120
Chawner & Morikis, in preparation
Torsion angles (o)
Type 2 2
Direct 70 -60
70 -70
85 -60
85 -70
Inverse -70 60
-70 70
-85 60
-85 70
direct inverse
-turns
Computational modeling of ideal -and -turns according to torsion angles
Classic -turn criteria
-180
-120
-60
0
60
120
180
-180 -120 -60 0 60 120 180
-
-II
-I’
-II’
-VIII
-direct
-inverse
-180
-120
-60
0
60
120
180
-180 -120 -60 0 60 120 180
-
-II
-I’
-II’
-VIII
-direct
-inverse
Chawner & Morikis, in preparation
Nuclear Overhauser effects (NOEs) inter-proton distances
Characteristic -turn distancesH(2)-HN(4): (i, i+2)H(2)-HN(3): (i, i+1)H(3)-HN(4): (i, i+1)HN(2)-HN(3): (i, i+1)HN(3)-HN(4): (i, i+1)
1
2
3
H
HN
N
C
C
OHN
HN
H
H
(1,2)(2,3)
(1,2) (2,3)
(1,3)
J
1
2
3
H
HN
N
C
C
OHN
HN
H
H
(1,2)(2,3)
(1,2) (2,3)
(1,3)
J
Characteristic -turn distancesH(1)-HN(3): (i, i+2)H(1)-HN(2): (i, i+1)H(2)-HN(3): (i, i+1)HN(1)-HN(2): (i, i+1)HN(2)-HN(3): (i, i+1)
J2
J3
H
HN
NC
OC
1
3
2
HN
H
HN
HN
H
H
(2,3)(3,4)
(2,3)
(3,4)(2,4)
4
J2
J3
H
HN
NC
OC
1
3
2
HN
H
HN
HN
H
H
(2,3)(3,4)
(2,3)
(3,4)(2,4)
4
-turn -turn
Torsion angles (o) D < 7 Å H-bond distance (Å) H-bond angle (°)
Type 2 2 3 3 C(1)-C(4) O(1)-N(4) O(1)-HN(4) O(1)-H(4)-N(4)
I -60 -30 -90 0 4.7 2.6 1.6 153.2
II -60 120 80 0 4.7 2.6 1.7 152.2
I' 60 30 90 0 4.7 3.0 2.1 151.1
II' 60 -120 -80 0 4.7 2.9 2.0 153.4
VIII -60 -30 -120 120 6.2 4.3 4.5 69.5
Torsion angles (o) D < 7 Å H-bond distance (Å) H-bond angle (°)
Type 2 2 C(1)-C(3) O(1)-N(3) O(1)-HN(3) O(1)-H(3)-N(3)
Direct 70 -60 5.4 2.7 1.8 142.2
70 -70 5.5 2.7 1.9 135.5
85 -60 5.5 3.1 2.2 137.4
85 -70 5.6 3.1 2.3 134.6
Inverse -70 60 5.4 2.4 1.5 143.6
-70 70 5.5 2.5 1.7 131.3
-85 60 5.5 2.8 1.9 141.9
-85 70 5.6 2.8 2.0 136.0
Marginal H-bonds presentbecause of larger deviations from linearity
Test of compliance of molecular models with ideal turn criteria
Notpresent
H-bond present
Chawner & Morikis, in preparation
Inter-proton distance (Å)
TypeHN(2)-HN(3)
HN(3)-HN(4)
H(2)-HN(3)
H(3)-HN(4)
H(2)-HN(4)
H(2)-H(3)
H(3)-H(4)
HN(2)-H(3)
HN(3)-H(4)
I 2.6 2.4 3.5 3.3 3.7 4.7 4.8 5.3 4.7
II 4.5 2.5 2.1 3.3 3.3 4.4 4.8 6.4 5.2
I' 2.6 2.4 3.0 3.3 4.2 4.8 4.8 5.0 5.0
II' 4.5 2.5 3.3 3.3 4.2 4.5 4.8 5.7 4.9
VIII 2.6 4.3 3.5 2.1 5.8 4.6 4.4 5.3 4.9
Torsion angles (°)
Inter-proton distance (Å)
Type 2 2HN(1)-HN(2)
HN(2)-HN(3)
H(1)-HN(2)
H(2)-HN(3)
H(1)- HN(3)
H(1)- H(2)
H(2)- H(3)
HN(1)- H(2)
HN(2)- H(3)
Direct 70 -60 2.0 3.7 3.6 3.6 4.0 5.3 4.8 3.9 5.7
70 -70 2.0 3.8 3.6 3.6 4.2 5.3 4.7 3.9 5.7
85 -60 2.0 3.6 3.6 3.6 4.2 5.3 4.8 3.8 5.5
85 -70 2.0 3.8 3.6 3.6 4.4 5.3 4.7 3.8 5.6
Inverse -70 60 2.0 3.7 3.6 2.6 3.8 4.8 4.6 4.5 5.1
-70 70 2.0 3.8 3.6 2.5 4.1 4.8 4.6 4.5 5.1
-85 60 2.0 3.6 3.6 2.6 3.9 4.7 4.6 4.4 4.9
-85 70 2.0 3.8 3.6 2.5 4.2 4.7 4.6 4.4 4.9
Ideal -turns
Ideal-turns
Molecular models: measured distances corresponding to characteristic NOEs
We classified the inter-proton distances as corresponding to strong, medium, weak and very weak NOE intensities:
1.8-2.6 Å = strong 2.7-3.5 Å = medium 3.6-4.4 Å = weak 4.5-5.0 Å = very weak
Relative NOE intensities
TypeHN(2)-HN(3)
HN(3)-HN(4)
H(2)-HN(3)
H(3)-HN(4)
H(2)-HN(4)
H(2)-H(3)
H(3)-H(4)
HN(2)-H(3)
HN(3)-H(4)
I S S M M W VW VW N/O VW
II VW S S M M W VW N/O N/O
I' S S M M W VW VW VW VW
II' VW S M M W VW VW N/O VW
VIII S W M S N/O VW W N/O VW
-turns
Relative classification of NOE intensities
Chawner & Morikis, in preparation
1.8 Å: sum of van der Waals radii with some overlap
Torsion angles (°)
Relative NOE intensities
Type 2 2HN(1)-HN(2)
HN(2)-HN(3)
H(1)-HN(2)
H(2)-HN(3)
H(1)- HN(3)
H(1)- H(2)
H(2)- H(3)
HN(1)- H(2)
HN(2)- H(3)
Direct 70 -60 S W W W W N/O VW W N/O
70 -70 S W W W W N/O VW W N/O
85 -60 S W W W W N/O VW W N/O
85 -70 S W W W W N/O VW W N/O
Inverse -70 60 S W W S W VW VW VW N/O
-70 70 S W W S W VW VW VW N/O
-85 60 S W W S W VW VW W VW
-85 70 S W W S W VW VW W VW
-turns
We classified the inter-proton distances: 1.8-2.6 Å = strong 2.7-3.5 Å = medium 3.6-4.4 Å = weak 4.5-5.0 Å = very weak
Relative classification of NOE intensities
2 (°) J2 (Hz) 3 (°) J3 (Hz)
Type I -60 4.2 -90 8.2
Type I’ 60 7.3 90 5.8
Type II -60 4.2 80 6.6
Type II’ 60 7.3 -80 6.9
Type VIII -60 4.2 -120 10.1
Type 2 (°) J2 (Hz)
Direct 70 7.1
Direct 85 6.2
Inverse -70 5.5
Inverse -85 7.5
Solution of Karplus equation:calculations of characteristic 3J(HN-H)-coupling constants
-turns
-turns
Chawner & Morikis, in preparation
2 (°) J2 (Hz) 3 (°) J3 (Hz)
Type I -60 Weaker -90 Stronger
Type I’ 60 Stronger 90 Weaker
Type II -60 Weaker 80 Stronger
Type II’ 60 Stronger -80 Weaker
Type VIII -60 Weaker -120 Stronger
Type 2 (°) J2 (Hz)
Direct 70 S
Direct 85 W
Inverse -70 W
Inverse -85 S
We classified the turn’s 3J(HN-H)-coupling constants as stronger or weaker relative to itself, so that the different types can be differentiated comparatively
-turns
-turns
Caution: small variations in -torsion angles result to very large variations in j-coupling constants. In general, the use of j-coupling constants is not as helpful as NOE intensity patterns and connectivities.
-helix
-sheet
Chawner & Morikis, in preparation
Conclusions
• NOE intensity patterns and connectivities can be used to distinguish turn type without a complete structure determination. We have created small NOE intensity databases that discriminate Type I, I’, II, II’, and VIII -turns, and direct and inverse -turns.
Caution: Classification of strong, medium, weak, and very weak NOEs is relative.
• Small variations of the characteristic -torsion angles introduce very large variations in the 3J(HN-H)-coupling constant values, sometimes spanning the whole range of possible solutions for the Karplus equation and the whole allowed region of the Ramachandran plot.
Why? the small variations in -torsion angles are owed to the dynamic character of turns in proteins and peptides and to conformational averaging.
• Overall, NOEs are more useful than J-coupling constants.
Acknowledgements
• Dr. Dimitrios Morikis• Li Zhang• Coordinators of BRITE Program• Fellow BRITE students
o60
3J(HN-H)
N C
H
3J(HN-H)
H
Cis
N C
H
HTrans
C
N C
C
Cis
C
N C
C
Trans
N C
H
3J(HN-H)
H
Cis
N C
H
HTrans
C
N C
C
Cis
C
N C
C
C
N C
C
Cis
C
N C
C
Trans
C
N C
C
C
N C
C
Trans
Cis=0o
=60o
=90o
=150o
Newman Projection
N
C=OC=O
HHC
N
C=OC=O
HHC
N
C=OC=O
HHC
N
C=OC=O
HHC
N
C=O
C=O H
H
C
N
C=O
C=O H
H
C
=-90o
=-30oN
C=O
C=OC
N
C=O
C=OH
H
C
N
C=O
C=OC
N
C=O
C=OH
H
C
Trans=180o
=-120o