NMR Structure Determination
With The NMR Assignments and Molecular Modeling Tools in Hand:
• All we need are the experimental constraints
Distance constraints between atoms is the primary structure determination factor.
 Dihedral angles are also an important structural constraint

What Structural Information is available
from an NMR spectra?
How is it Obtained?
How is it Interpreted?
NMR Structure Determination
NOE
NOE
- a through space correlation (<5Å)
4.1Å
- distance constraint
2.9Å
Coupling Constant (J)
- through bond correlation
J
NH
CaH
- dihedral angle constraint
Chemical Shift
- very sensitive to local changes
in environment
- dihedral angle constraint
Dipolar coupling constants (D)
- bond vector orientation relative
to magnetic field
- alignment with bicelles or viruses
CaH
D
NH
Nuclear Overhauser Effect (NOE)
Nuclear Overhauser Effect (NOE, h) – the change in intensity of an NMR
resonance when the transition of another are perturbed, usually by saturation.
hi = (I-Io)/Io
where Io is thermal equilibrium intensity
Saturation – elimination of a population difference between transitions
(irradiating one transition with a weak RF field)
irradiate
bb
ab
N
N-d
X
A
ba
X
aa
N+d
N
A
Populations and energy levels of a homonuclear
AX system (large chemical shift difference)
Observed signals only occur
from single-quantum transitions
Nuclear Overhauser Effect (NOE)
Saturated
(equal population)
ab
N-½d
saturate
bb N-½d
I
S
ba
I
aa
N+½d
N+½d
S
Saturated
(equal population)
Observed signals only occur
from single-quantum transitions
Populations and energy levels immediately
following saturation of the S transitions
bb
ab
W1A
N-½d
W1X
N-½d
W2
W0
aa
W1X
N+½d
ba
W1A
N+½d
Relaxation back to equilibrium can occur through:
Zero-quantum transitions (W0)
Single quantum transitions (W1)
Double quantum transitions (W2)
Nuclear Overhauser Effect (NOE)
Intensity of NOE “builds-up” as a
function of the mixing time (tm)
bb
ab
W1A
N-½d
X
W1
N-½d
W2
W0
aa
W1X
N+½d
ba
W1A
N+½d
Solomon Equation:
W2  W0
X
hi 
 A 2W1A  W2  W0
Steady-state NOE enhancement at spin A is
a function of all the relaxation pathways
If only W1, no NOE effect at HA
If W0 is dominant, decrease in intensity at HA  negative NOE
If W2 is dominate, increase in intensity at HA  positive NOE
For homonuclear (X=A), maximum enhancement is ~ 50%
For heteronuclear (X=A), maximum enhancement is ~50%(X/A)
Nuclear Overhauser Effect (NOE)
Mechanism for Relaxation
• Dipolar coupling between nuclei
interaction between nuclear magnetic dipoles
– local field at one nucleus is due to the presence of the other
– depends on orientation of the whole molecule
 in solution, rapid motion averages the dipolar interaction
 in crystals, positions are fixed for single molecule, but vary between molecules
leading range of frequencies and broad lines.
• Dipolar coupling, T1 and NOE are related through rotational correlation time (tc)
o
 recall: rotational correlation is the time it takes a molecule to rotate one radian (360 /2p)

tc ~ 10ns (macromolecule)
Relaxation or energy transfers
only occurs if some frequencies
of motion match the frequency
of the energy transition.
tc ~ 10ps (small molecule)
1/tc
The available frequencies for a
molecule undergoing Brownian
tumbling depends on tc.
The total “power” available for
relaxation is the total area under
the spectral density function.
Nuclear Overhauser Effect (NOE)
Mechanism for Relaxation
• Spectral density is constant for w << 1/tc
tc decreases, wo also decreases and T1 increases
 at 1/tc ≈ wo there is a point inflection
– W2 falls off first since it it the sum of two transitions
 relaxation rates via dipolar coupling are:

3t c
3t c
W1  6
 6
2 2
r (1  w At c )
r
A
3t c
2t c
W0  6
 6
2 2
r (w A  w X ) t c )
r
W2 
12t c
12t c

r 6 (1  (w A  w X ) 2t c2 )
r6
NOE is dependent on the
distance (1/r6) separating the
two dipole coupled nuclei
Important: the effect is time-averaged!
Extreme narrowing limit: 1/tc >>wo then wo2tc2 <<1)
2D NOESY (Nuclear Overhauser Effect)
Relative magnitude of the cross-peak is related to
the distance (1/r6) between the protons (≥ 5Ǻ).
NOE is a relaxation factor that builds-up during
The “mixing-time (tm)
NMR Structure Determination
How DO We Go From the NOESY Data to A Structure?
2D NOESY Spectra at 900 MHz
Lysozyme Ribbon Diagram
NMR Structure Determination
We Need to Assign Each NOE Cross-Peak to A Specific
1H-1H Pair from Assignment Table.
Assignment Table
Resi due
D1
E2
D3
E4
R5
W6
T7
N8
N9
F10
R11
E12
Y13
N14
L15
N
120.1
128.9
116.1
113.3
123.8
127.8
109.9
115.2
116.7
110.1
121.2
119.0
122.1
121.5
127.7
(8.08)
(9.93)
(8.90)
(7.45)
(7.97)
(9.27)
(9.32)
(8.42)
(7.88)
(7.57)
(8.03)
(8.56)
(8.28)
(8.45)
(9.02)
CO
179.1
176.6
176.5
175.6
173.1
177.1
174.8
174.5
173.3
177.2
175.0
177.9
173.2
175.7
176.9
Ca
53.8
56.0
56.2
52.9
54.3
55.4
59.6
50.9
52.1
58.2
55.8
52.3
61.9
54.7
58.0
(4.37)
(4.55)
(4.73)
(4.71)
(4.43)
(5.50)
(4.85)
(5.06)
(4.94)
(4.46)
(4.06)
(3.79)
(3.80)
(4.89)
(4.48)
Cb
39.9
30.9
38.9
27.2
28.9
30.8
71.3
38.7
38.0
38.5
29.7
27.4
41.2
39.2
41.2
(3.00,0.58)
(2.11,1.78)
(2.70,2.34)
(1.23,0.63)
(1.84,1.47)
(3.11)
(4.34)
(3.13,2.70)
(3.33,3.01)
(2.63,2.67)
(1.83,1.67)
(1.16,-0.05)
(2.99,2.52)
(2.26)
(1.96,1.64)
Ot her s
Cg 36.2(2.75,2.41)
Cg 34.8(2.57,1.79)
Cg 26.2(1.59,1.16);Cd 42.6(3.09,3.02)
Cg 20.2(0.73)
Cg 27.4(1.45,1.35);Cd 43.1(3.13)
Cg 36.6(2.19,1.97)
Cg 27.2(1.20);Cd 27.8(0.87);Cd 27.8(0.78)
.
.
.
What H assignments
for the protein are
consistent with 10.5
ppm & 7.65 ppm?
10.5 ppm to 7.65 ppm
In some cases, the chemical shifts associated with the NOE cross-peak are unique and an assignment
is straight-forward. More likely is the occurrence that the assignment is ambiguous  multiple
possible assignments to one or both of the chemical shifts.
NMR Structure Determination
We Need to Assign Each NOE Cross-Peak to A Specific
1H-1H Pair from Assignment Table.
Assignment Table
Resi due
D1
E2
D3
E4
R5
W6
T7
N8
N9
F10
R11
E12
Y13
N14
L15
.
.
.
N
120.1
128.9
116.1
113.3
123.8
127.8
109.9
115.2
116.7
110.1
121.2
119.0
122.1
121.5
127.7
(8.08)
(9.93)
(8.90)
(7.45)
(7.97)
(9.27)
(9.32)
(8.42)
(7.88)
(7.57)
(8.03)
(8.56)
(8.28)
(8.45)
(9.02)
CO
179.1
176.6
176.5
175.6
173.1
177.1
174.8
174.5
173.3
177.2
175.0
177.9
173.2
175.7
176.9
Ca
53.8
56.0
56.2
52.9
54.3
55.4
59.6
50.9
52.1
58.2
55.8
52.3
61.9
54.7
58.0
(4.37)
(4.55)
(4.73)
(4.71)
(4.43)
(5.50)
(4.85)
(5.06)
(4.94)
(4.46)
(4.06)
(3.79)
(3.80)
(4.89)
(4.48)
Cb
39.9
30.9
38.9
27.2
28.9
30.8
71.3
38.7
38.0
38.5
29.7
27.4
41.2
39.2
41.2
(3.00,0.58)
(2.11,1.78)
(2.70,2.34)
(1.23,0.63)
(1.84,1.47)
(3.11)
(4.34)
(3.13,2.70)
(3.33,3.01)
(2.63,2.67)
(1.83,1.67)
(1.16,-0.05)
(2.99,2.52)
(2.26)
(1.96,1.64)
Ot her s
Cg 36.2(2.75,2.41)
Cg 34.8(2.57,1.79)
Cg 26.2(1.59,1.16);Cd 42.6(3.09,3.02)
Cg 20.2(0.73)
Cg 27.4(1.45,1.35);Cd 43.1(3.13)
Cg 36.6(2.19,1.97)
Cg 27.2(1.20);Cd 27.8(0.87);Cd 27.8(0.78)
To determine the structure, an
assignment has to be made for each of
the thousands of observed NOE cross
peaks  A lot of manual effort!
Ambiguity in assignments also arises from errors in peak position and correlation to assignment table.
Need to “match” assignments with an error range that is dependent on the resolution associated with
each axis. Typically, 1H errors may range from 0.02 to 0.06 ppm and 13C, 15N from 0.25 to 1.0 ppm.
An NOE cross-peak of 4.25 ± 0.02 ppm to 2.21 ± 0.02 ppm may be consistent with a dozen or more
possible combinations!
NMR Structure Determination
Peak-Picking is Very Challenging in A Protein
NOESY Spectra
• Spectra Can be very crowded with a number of
overlapping peaks
• Automatic peak-picking fails in these crowded regions
• the quality of the structure is inherently dependent on
the quality of the peak-picking
 assignments are made from the peak lists
 wrong peak position or picked noise peaks results
in a mis-assignment that results in an incorrect
structure distance constraints that results in a local
distortion in the structure
How Many Peaks?
What is each Peak’s Position?
Which are Noise Peaks?
NMR Structure Determination
How Do We Resolve These Peak-Picking and Ambiguity Issues?
• Spread out the data into 3D and 4D
symmetry can help remove ambiguities
• Use 1H-15N and 1H-13C connections
• Iterative analysis of the NOE data
 use structure and distance filter to remove ambiguities

NMR Structure Determination
Iterative Analysis of NOESY Data, How Does It Work?
• Assign All unique or unambiguous NOEs
• Calculate Initial Structure with All the Data possible
• Use the Structure to Filter Ambiguous Assignments
possible assignment has to be ≤ 6 Ǻ
 removes all possible assignments with distances ≥ 6Ǻ
• Calculate New Structure With New constraints
 identify & correct violated constraints
 repeat NOE analysis
 repeat process until all NOEs correctly assigned and a
quality structure is obtained

NMR Structure Determination
Using PIPP to Analyze NOESY Data
• read in your initial structure(s)
• read in your NMR assignment list
• click on a peak and PIPP tells you:
the possible assignments
 chemical shift errors relative to assignment table
 minimum, average and standard deviation distances

NMR Structure Determination
After Assigning an NOE Peak to 1H-1H pair, Need to Assign a Distance Constraint
• There are Two Generally Accepted Approaches:
“Two-Spin” Approximation
 Relaxation Matrix Approach

“Two-Spin” Approximation – the observed volume or intensity of a NOE cross-peak is directly
related to the distance between the 1H-1H pair
V (I ) 
1
r6
This approximation only holds true for the linear part
of the NOE build-up curve (short-mixing times)
when spin diffusion is not a significant component of
the observed volume (intensity)
NMR Structure Determination
Spin Diffusion – in the limit of wtc >> 1 (biomolecules), the rate of transfer of the spin energy
between nuclei becomes much larger than the rate of transfer of energy to the lattice.
The observed NOE cross-peak
volume between Hi & Hj is
potentially increased by a
HiHkHj & HiHlHj
energy transfer.
Effectively, the spin energy diffuses through all possible paths between all possible
spin systems. Spin diffusion is always present, the magnitude depends on the mixing
time and the efficiency of any particular pathway. The longer the path, the smaller the
energy that is transferred
NMR Structure Determination
As We Discussed Before, One Common Approach Uses a Qualitative Binning of
NOE Intensities
• generally cluster NOE volumes into strong, medium, weak and very weak
• The following rules apply:
Strong
2.5 0.7 0.2  for NH-NH constraints use: 2.5 0.7 0.6
Medium
3.0 1.2 0.3  for NOEs with NH use:
3.0 1.2 0.5
Weak
4.0 2.2 1.0
Very Weak 5.0 2.0 1.0
the lower limit is always set to slightly less than twice the hydrogen
van der Waals radius (1.8Å)
• NOEs for methyls are scaled down by 1/3
• Uses reasonably short mixing-time (100-150msec) and allows quantity of distance constraints to
correct for spin-diffusion effects
 remove or move to lower bin violated constraint that may arise from spin-diffusion
 alternative is to leave all constraints as observed with corresponding contribution to
violation energy and potential structure distortion  point of debate in NMR community
NOEs are observed between the Ala methyl
and both Leu methyls. Structure indicates a
violation to one methyl-methyl pair  NOE
probably a result of spin diffusion
Violated constraint
NMR Structure Determination
Two-Spin Approximation
• Instead of binning into strong, medium, weak and very weak, can assign a relative distance
• Use a reference volume with a known fixed distance to calibrate all volumes
2.52 Å for Leu Ha-Hb
 2.52 Å for Phe or Tyr Hd-He

Serious Problems: obtain a highly precise distance that ignores all the inherent errors associated
with the accuracy of measuring volumes, spin-diffusion and dynamics.
Short, inaccurate distance constraints cause severe local structure distortions
What would happen to the
structure if both Leu d had to
be 3Å to the Ala b?
Violated constraint
NMR Structure Determination
Relaxation Matrix Approach Takes Into Account Spin-Diffusion
• removes manual and potentially biased approach to identify spin-diffusion issues
From the structure, calculates a spin relaxation matrix to correct for spin-diffusion
contributions to observed volumes
 There are a number of programs that perform this analysis (CORMA, FIRM, MardiGras,
MORASS, etc)

Calculate from
structure
Experimental
Volumes from
NOESY spectra
J. Am. Chem. Soc. 1990, 112, 6803-6809
NMR Structure Determination
Relaxation Matrix Approach Takes Into Account Spin-Diffusion
• Merge the cross-relaxation rates calculated from the structure with experimental volumes
obtain distance matrix to calculate new structure
 iterate process

Can relate cross-relaxation rates(G) with experimental NOE volumes (V)
NMR Structure Determination
Problems with Relaxation Matrix Approach
• Errors and Failures with Matrix Calculations
Do not obtain complete experimental NOESY volume matrix
Very difficult to accurately measure diagonal peaks
 Significant errors in measuring experimental volumes
 Peak overlaps and degenerate assignments
 Missing peaks, limits of S/N
 Noise
• Assume Uniform Dynamics (tc)
Poor Assumption
 Different regions of protein structure have very different local dynamics
 Contributions to relaxation rates by dynamics can be much more significant than
spin-diffusion
• Output of calculation is a very specific distance constraint
 But, may have high errors (volume, dynamics)
 Large structure distortion that is propagated through iteration

NMR Structure Determination
Two Very Important Facts to Remember
• NOEs Reflect the Average Distance
• Protein Structures Are Dynamic
In reality, protein undergoes wide-ranges
of motions (snapshots of 100 BPTI
conformations)
We visualize protein
structures as a static image
J. Mol. Biol. (1999) 285, 727±740
NMR Structure Determination
2D, 13C, 15N
We have already
discussed labeling the
protein, data
collection and the
resonance assignment
Labeled Protein
NMR Data Collection
Next Step, is to identify which residues
adopt which secondary structure present
Resonance Assignments
Secondary Structure
X-ray or Homology Model
Low Resolution Structure
C.S
NOE
High Resolution Structure
Dock Ligands
NMR Structure Determination
Protein Secondary Structure and NOE Patterns
• a-Helix
Sequential NOEs observed in 3D 15N-edited NOESY are indicative of a-helix

NMR Structure Determination
Protein Secondary Structure and NOE Patterns
• a-Helix
Sequential NOEs observed in 3D 15N-edited NOESY are indicative of a-helix

NMR Structure Determination
Protein Secondary Structure and NOE Patterns
• a-Helix
Sequential NOEs observed in 3D 15N-edited NOESY are indicative of a-helix

NMR Structure Determination
Protein Secondary Structure and NOE Patterns
• a-Helix
Sequential NOEs observed in 3D 15N-edited NOESY are indicative of a-helix

NMR Structure Determination
Protein Secondary Structure and NOE Patterns
• a-Helix
Sequential NOEs observed in 3D 15N-edited NOESY are indicative of a-helix

NMR Structure Determination
Protein Secondary Structure and NOE Patterns
• b-Sheet
Across strand NOEs observed in 3D 15N-edited NOESY and 3D 13C-edited NOESY are
indicative of b-sheet

NMR Structure Determination
Protein Secondary Structure and NOE Patterns
• b-Sheet
Across strand NOEs observed in 3D 15N-edited NOESY and 3D 13C-edited NOESY are
indicative of b-sheet

NMR Structure Determination
Protein Secondary Structure and NOE Patterns
• b-Sheet
Across strand NOEs observed in 3D 15N-edited NOESY and 3D 13C-edited NOESY are
indicative of b-sheet

NMR Structure Determination
Protein Secondary Structure and NOE Patterns
• Turns
Sequential NOEs observed in 3D 15N-edited NOESY are indicative of turns
 Similar to a-helix, shorter amino acid stretches connect b-strands

NMR Structure Determination
Protein Secondary Structure and NOE Patterns
• Turns
Sequential NOEs observed in 3D 15N-edited NOESY are indicative of turns
 Similar to a-helix, shorter amino acid stretches connect b-strands

NMR Structure Determination
Protein Secondary Structure and Carbon Chemical Shifts
Chemical shift differences
between Ca,Cb random-coil
values and experimentally
observed values yields
secondary structure chemical
shift.
Helix:
b-strand:
DCa ~ 3 ppm
DCb ~ -1 ppm
DCa ~ -2 ppm
DCb ~ 3 ppm
NMR Structure Determination
Protein Secondary Structure and Carbon Chemical Shifts
a1
bIV
a2
bIII
a3 bI
bII
a4
NMR Structure Determination
Protein Secondary Structure and Carbon Chemical Shifts
• TALOS +
Shen et al. (2009) J. Biomol NMR 44:213
NMR Structure Determination
Protein Secondary Structure and Carbon Chemical Shifts
• TALOS+
Given the Ca, Cb Chemical shift assignments and primary sequence
 Compares the secondary chemical shifts against database of chemical shifts and associated
high-resolution structure
 comparison based on “triplet” of amino acid sequences present in database structures
with similar chemical shifts and secondary structure
 Provides potential f , y backbone torsion constraints

Issues: May not provide a unique solution, two or more sets of f , y are possible. Can not
initially use TALOS results if ambiguous. Can add constraint latter if consistent with
structure.

NMR Structure Determination
Protein Secondary Structure and Carbon Chemical Shifts
• TALOS+
TALOS may provide relatively tight
error bounds associated with the
predicted f,y.
It is better being more conservative by
using minimal errors of:
f ± 30
y ± 50
c ± 20
NMR Structure Determination
Protein Secondary Structure and 3JHNa
• Karplus relationship between f and 3JHNa
f =180o  3JHNa  ~8-10 Hz  b-strand
o
3
 f = -60  JHNa = ~3-4 Hz  a-helix

Vuister & Bax (1993) J. Am.Chem. Soc. 115:7772
NMR Structure Determination
Protein Secondary Structure and 3JHNa
• Karplus relationship between f and 3JHNa


Measure 3JHNa for a protein using HNHA
Ratio of cross-peak to diagonal intensity
yields coupling constant
 Common approach to measure coupling
constants in complex protein NMR spectra
J. Am. Chem. Soc. 1993,115, 7772-7777
NMR Structure Determination
Protein Secondary Structure and NH Exchange Rates
• Relatively Slower Exchanging NHs are involved in Hydrogen Bonds or Buried

Hydrogen Bonds are an important component of secondary structures
NH Exchange Rate
NMR Structure Determination
Protein Secondary Structure and NH Exchange
Rates
• Measure Relatively Slow Exchanging NHs
Exchange NMR sample into 100% D2O and
measure series of 1H-15N HSQC as a function of
time.

• Observed slowly exchanging NHs are
correlated with secondary structure.
Secondary structures identified from NOEs,
chemical shifts and 3JHNa
 Assign hydrogen-bond distance constraint

J. Mol. Biol. (1997) 271, 472-487
NMR Structure Determination
Protein Secondary Structure and NH Exchange Rates
• Measure Fast Exchanging NHs
CLEANEX-PM experiment
 amount of exchange depends on mixing time
 Missing Peaks are slowly exchanging NHs

selects H2O
NH exchange with H2O
during spin-lock
• Observed slowly exchanging NHs are
correlated with secondary structure.
Secondary structures identified from NOEs,
chemical shifts and 3JHNa
 Assign hydrogen-bond distance constraint

2D 1H-15N HSQC
CLEANEX-PM
J. Am. Chem. Soc. (1997) 119, 6203
J. Biomol. NMR (1998) 11:221
NMR Structure Determination
Protein Secondary Structure and NH Exchange Rates
• Measure Fast Exchanging NHs
CLEANEX-PM experiment
 amount of exchange depends on mixing time

–

Can measure exchange rates by varying mixing time
Missing Peaks are slowly exchanging NHs
NMR Structure Determination
Protein Secondary Structure and NH Exchange Rates
• Assign Hydrogen-Bond Distance Constraints for Slowly Exchanging NHs
For a –helix hydrogen bond constraints:
constraint between Oi & Ni+4
2.8 0.4 0.5
constraint between Oi & HNi+4 1.8 0.3 0.5
For b –sheet hydrogen bond constraints are
Across strands:
constraint between Oi & Nj
2.8 0.4 0.5
constraint between Oi & HNj
1.8 0.3 0.5
NMR Structure Determination
Protein Secondary Structure Summary
• Secondary Structure NOEs, slowly exchanging NHs, 3JNHa and secondary
structure chemical shifts provide the foundation for detemining a protein NMR
structure
NMR Structure Determination
Protein Tertiary Structure Determination
• Include all the various structural information, disulphide bonds, hydrogen
bonds, dihedral angles, chemical shifts, coupling constants, and NOES (distance
constraints) to calculate (FOLD) the structure using simulated annealing
Depiction of short-range and long range NOEs
Anal. Chem. 1990, 62, 2-15
Simply Need to Complete the Assignment of All the Remaining NOEs in an
Iterative Process to Obtain the Structure
NMR Structure Determination
Automated Protein Structure Determination
• A number of efforts are on-going to automate the process (ARIA,
AutoStructure, CYANA, Rosetta, etc)
From assignment tables, NOE peak lists, coupling constants and slowly
exchanging NHs.

NMR Structure Determination
Improving the Quality of NMR Structures
• Stereospecific Assignments
Assign Hb1 and Hb2 chemical shifts and determine c1 dihedral angle

NMR Structure Determination
Improving the Quality of NMR Structures
• Stereospecific Assignments
Assign Hb1 and Hb2 chemical shifts and
determine c1 dihedral angle.
 Assign Val H1 and H2 chemical shifts and
determine c1 dihedral angle.
 HNHB and HN(CO)HB experiments
 Relative intensities of Hb cross-peaks
determines c1 and stereospecific assignment

Can include c1 dihedral
constraints and replace HB#
pseudoatoms with specific
distance constraints.
Pseudoatoms require weaker
upper bound constraints that
can be tighten with specific
assignment
HNHB
HN(CO)HB
NMR Structure Determination
Improving the Quality of NMR
Structures
• Stereospecific Assignments
Assign Leu Hd1 and Hd2 chemical
shifts and determine c2 dihedral
angle.
 based on c1 assignments
 Assign Ile c2 dihedral angle.

NMR Structure Determination
Improving the Quality of NMR Structures
• Stereospecific Assignments
Assign Leu Hd1 and Hd2 chemical shifts and
determine c2 dihedral angle.
 Assign Ile c2 dihedral angle.
13C-13C Correlation
 Long Range
 Relative intensities of Hd cross-peaks
compared to diagonal determines 3JCaCd

NMR Structure Determination
Improving the Quality of NMR Structures
• Stereospecific Assignments
Assign Hd1, Hd2 and He1,He2 chemical shifts and determine c2
dihedral angle for Phe and Tyr.
 Inferred assignment from structure.
 Phe and Tyr undergo rapid ring flip so Hd1, Hd2 and He1,He2
are equivalent  degenerate chemical shifts
o
o
 c2 should be 90 or -90 , which are symmetrically equivalent

Hd1
He1
Based on which (90,-90) c2 is closer
to the observed structure, add that c2
constraint and replace Hd#, He#
pseudoatoms with stereoassignments
that are consistent with the structure.
NMR Structure Determination
Improving the Quality of NMR Structures
• Stereospecific Assignments
Making stereospecific assignments increase the relative number of distance
constraints while also tightening the upper bounds of the constraints
 There is a direct correlation between the quality of the NMR structure and the
number of distance constraints
 more constraints  higher the precision of the structure

Increasing Number of NOE Based Constraints
NMR Structure Determination
Improving the Quality of NMR Structures
• Dipolar Coupling Constants
Solid state NMR yields a powder pattern or a ensemble of
chemical shifts due to different orientations relative to the
magnetic field.
 CSA –chemical shift anisotropy
 In liquids, isotropic tumbling averages the various
orientations to zero
 Simulated in a solid by spinning the sample

w  ½(3cos2q-1)
Magic Angle (54.7o)  averages to zero
NMR Structure Determination
Improving the Quality of NMR Structures
• Residual Dipolar Coupling Constants (RDC)
In liquids, dipolar coupling can become non-zero if isotropic tumbling is removed.
 proteins can be aligned by using bicelles, virus particles or polyacrylamide gels.
 mechanically impede the random tumbling of protein
 do not want and interaction between the protein and alignment media

NMR Structure Determination
Improving the Quality of NMR Structures
• Residual Dipolar Coupling Constants (RDC)

RDC can be measured for each bond vector in the protein
 RDCs are measured from a difference in the coupling constants between
aligned and unaligned media.
 Different RDCs can be normalized based on ratios of bond lengths
3
3
D AB ( NH )  D AB ( N  H  rNH
 /  A B  rAB
A )
unaligned
aligned
DAB(NH) = 93.3 Hz – 100.2 Hz = - 6.9 Hz
The magnitude of RDC depends on the extent of the
alignment of the protein and the orientation of the bond
vector to BO
NMR Structure Determination
Improving the Quality of NMR Structures
• Residual Dipolar Coupling Constants (RDC)
Alignment frame
of the protein
Orientation of
bond-vector in
protein alignment
DAB(q,f) = Da(3cos2q- 1) + 3/2 Dr(sin2q cos2f)]
where Da and Dr are the axial (**) and rhombic (2) components of the traceless diagonal
tensor D given by 1/3[DZZ - (Dxx+ Dyy)/2] and 1/3(Dxx- Dyy), with Dzz > Dyy  Dxx
Da and Dr measure the magnitude (intensity) of the alignment.
q is the angle between the bond and the z-axis of the principal alignment frame (x, y, z)
f is the angle between the bond's projection in the x-y plane and the x-axis
To use DAB in a structure calculation, need to know Da and Dr
NMR Structure Determination
Improving the Quality of NMR Structures
• Residual Dipolar Coupling Constants (RDC)
Dxx most populated
value in histogram
Recreate “Powder
Pattern” by histogram plot
of all normalized RDCs
Dyy average of the
low extreme values
of RDC
Dzz average of the
high extreme values
of RDC
Extremes of the histogram correspond to the alignment tensor components D xx, Dyy, and Dzz
Dxx+Dyy+Dzz =0
Dzz = 2Da
R is the rhombicity given by Dr/Da
Dyy = - Da(1 + 3/2 R)
Dxx = - Da(1 - 3/2R)
- use different normalized sets of RDCs (CH, NH, CaC’, NC , NC’, etc) to create one histogram , etc)
- exclude residues with substantially lower order parameter than average
NMR Structure Determination
Improving the Quality of NMR Structures
• Residual Dipolar Coupling Constants (RDC)
RDC provide long-range (> 5 Å) interaction
 RDCs identify angular orientation of bond vector to alignment axis
 No translational orientation of bond vector.
 RDC alone can not define a protein structure
 NOEs are necessary to define translational orientation of bond vectors
 Absolute alignment axis is unknown
 RDC are all relative to an alignment axis
 Allow the structure and RDC to be refined against a coordinate position that
“floats” or changes during the simulation

Refine RDCs against coordinate vector
position that is free to move during
Observed RDC only limits bond vector
to taco shaped curve on sphere
NMR Structure Determination
Without RDCs
Improving the Quality of NMR Structures
• Residual Dipolar Coupling Constants (RDC)
Addition of RDCs do not induce dramatic
changes in structure
 improves relative orientation/packing
 very valuable for proper alignment of complexes

Without RDCs
With RDCs
Consistency of Structures with Experimental RDCs
Protein Science (2004), 13:549-554
With RDCs
NMR Structure Determination
Improving the Quality of NMR Structures
• Water Refinement
protein structures generally calculated in vacuum.
 water has a significant effect on protein structures
 explicit solvent model

MD simulation in box of water
– box > 10 Å, keep solvent from edge
– 1000 to 10,000s water molecule
– Computationally expensive not usually done
–

implicit solvent model
treat solvent as a high dielectric continuous
medium (e) around protein
– significantly faster
– different solvation models  generalized Born model (GB)
–
where :
where q – point charge , r is the distance between the
charges and a is the radius of ion, eo dielectric constant
for a vacuum, e of solvent
http://cmm.cit.nih.gov/intro_simulation/node8.html
NMR Structure Determination
Improving the Quality of NMR Structures
• Water Refinement

generalized Born model (GB) has been implemented in Xplor
 compare structures in vacuum to water
–
no visible difference
Xia et al. (1996) J. Biomol. NMR 22:317
NMR Structure Determination
Improving the Quality of NMR Structures
• Water Refinement

generalized Born model (GB) has been implemented in Xplor
 subtle, but significant improvements
 compare structures in vacuum to water
improves NH to CO hydrogen bonds
– improves f and y angle distributions
–
NMR Structure Determination
Improving the Quality of NMR Structures
• Water Refinement
generalized Born model (GB) has been implemented in Xplor
 sample Xplor script

.
.
.
Read in the GB parameter and
topology files (partial charges)
Set N- and C-terminal
charges for protein
topology
@TOPPAR:topamber.inp
@TOPPAR:amberpatches.pro
end
parameter @TOPPAR:paramber.gb.inp end
segment
name="ASN1"
molecule name=ASN number=1 end
end
patch NASN refe=nil=(resid 1) end
patch CASN refe=nil=(resid 1) end
vector do (charge = charge + .2306) (name ht%)
vector show sum (charge) (all)
segment
name="ASN1"
molecule name=ASN number=1 end
end
patch NTER refe="+"=(resid 1) end
patch CTER refe="-"=(resid 1) end
vector
show sum (charge) (all)
.
.
.
NMR Structure Determination
Improving the Quality of NMR Structures
• Water Refinement
generalized Born model (GB) has been implemented in Xplor
 sample Xplor script (continued)

.
.
.
Set standard electrostatic
parameters
Set GB parameters
Read in volumens and
tell Xplor to use GB in
calculation
parameter
nbonds
atom cdie trunc
e14fac=0.8333333
! use this to reproduce amber elec
cutnb 500. ctonnb 480. ctofnb 490. ! essentially no cutoff
tolerance=100.
! only build the nonbonded list once
nbxmod 5 vswitch
wmin=1.0
end
end
parameters nbonds
EPS=1. WEPS=80. offset=0.09 GBHCT ! GB parameters
end
End
@TOPPAR:volumes.amber
vector do (rmsd = rmsd * 0.9) (all) ! reduce volumes by 10%
flags include gbse gbin end
parameter reduce selection=(all) overwrite=true mode=average end end
energy end
.
.
.
NMR Structure Determination
Improving the Quality of NMR Structures
• Water Refinement
generalized Born model (GB) has been implemented in Xplor
 sample Xplor script (continued)

.
.
.
Weakly restrain Ca
position during dynamics
Don’t allow large structural
changes. Just make local
changes to fix problems
! weakly restrain Calpha position
vector do (harmonic = 0.5) (name ca)
coor disp=reference @asn.-80.10.pdb
constraints harmonic end
flags include harmonic end
.
.
.