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