Structure Calculations Using NMR Data• Development began in the middle of the 1980s.

• Most of the early structures were of very small

proteins or peptides.

• You do not determine a single structure as in

crystallography, but rather an ensemble of

structures that satisfy a group of restraints.

• In general, the more experimental restraints

that are used, the better the precision of the

structures calculated.

• Advancements (new experiments, bigger

magnets, faster computers) have not only

increased the size of the molecule that can be

studied, but they have improved the quality of

the structures calculated

Principles of NMR-based Structure Calculations

• The goal of all NMR structure calculation

protocols is to find the global minimum region

of a target function Etot.

Etot = Ecov + Evdw + ENMR

Ecov = covalent geometry terms for: bonds, angles

planarity and chirality.

Evdw = nonbonded contacts.

ENMR = experimental NMR restraints.

Algorithms used in NMR structure calculations

• Simulated annealing (SA) in both cartesian and

torsion angle space.

• Metric matrix distance geometry (DG).

• Minimization with a variable target function in

torsion angle space.

Ecov

• Depending on the algorithm used systematic

biasing may arise when calculating the

structure.

• Deviations from ideal geometry must be kept to

a minimum since the value of bond lengths,

angles, planes and chirality are known to very

high accuracy.

Evdw

• This term is associated with more uncertainty.

• It may be represented as a simple van der Waalsrepulsion term.

• It may also be a complete energy function thatincludes an electrostatic and a hydrogenbonding potential.

• All structures must display good non-bondedcontacts.

• Uncertainties associated with Ecov and Evdw canintroduce errors in the range of 0.3 Å.

Steps in NMR-based Structure Calculations

1) Data Input

2) Structure Determination Protocol

3) Acceptance Tests

4) Analysis of NMR structure.

Types of NMR Experimental Restraints

1) Noe-derived distance restraints.

2) Torsion angle restraints.

3) Chemical shift restraints.

4) Hydrogen bond restraints.

5) Residual Dipolar Coupling Angular restraints.

Outline of structure calculation protocol

Nuclear Overhauser Effect (NOE)

NOEs in solution structure determinations• NOEs provide the main source of geometric

information from the experimental data.

• NOEs are short in distance (~ 5Å) but they areconformationally very restrictive when they arefar apart in the primary sequence.

• At short mixing times, NOE signal isproportional to the inverse sixth power of thedistance between two protons.

• NOE intensities are converted to approximateinterproton distant restraints with lower andupper bounds.

Strong: 1.8 – 2.7 ÅMedium: 1.8 – 3.3 ÅWeak: 1.8 – 5.0 ÅVery Weak: 3.0 – 6.0 Å

Types of Helices

3.10- φ= -74.0° and ϕ= --4.0°pi- φ= -57.1° and ϕ= -69.7°

Short range NOEs in α-helix

Anti-parallel β-sheet

Parallel β-sheet

Parallel vs. anti-parallel β-sheets

* Parallel sheets tend to be more regular if one examinesthe φ and ϕ angles.

* Anti-parallel sheets have H-bonds perpendicular to thestrands and alternate narrow and widely spaced pairs.

* Parallel sheets have equally spaced H-bonds that angleacross the strands.

NOE patterns is β-sheet

NOE patterns is β-sheet

Overview of tight(β) turns* They have a succession of different φ and ϕ values for

each residue.

* They have a H-bond between the >C=0 of residue iand the >N-H of residue i+3.

* Backbone at either end of Type I or II turn is in theright position to continue an anti-parallel β-ribbon.

Type I : φ2= -60°, ϕ2= -30°, φ3= -90°, ϕ3= 0°

Type II: φ2= -60°, ϕ2= 120°, φ3= 90°, ϕ3= 0°

Type I turn

Type II turn

Short range NOEs in β turns

NOE patterns associated with 2°structure

Examples of 3D NOESY Experiments

3D 15N-NOESY 3D 13C-NOESY

3D 15N/ 13C -NOESY

Pictorial of NOEs in a structure

Coupling constants and torsion angles

• It is possible to directly refine structures against

a HN-C!H three-bond coupling constants as

well as conformational data bases.

• There is a very good experiment to accurately

measure 3JHN! (3DHNHA)

• Although Karplus curve is symmetric about " =

-120°, other experimental data allows us to

resolve the ambiguity.

Correlation between 3Jhnα and 2°Structure

Pardi et al, J. Mol. Biol 180, 741-751 1984

3D- HNHA experiment for 3Jhnα

TALOS* Database system for empirical prediction of phi and psi

backbone angles.

* Uses a combinations of five kinds (HA, CA, CB, CO ,N) of chemical shifts.

* Like CSI relies on fact that many secondary chemicalshifts are highly correlated with aspects to proteinsecondary structure.

* It uses triplets of amino acids to make predictions.

Reference: Cornilescu, Delaglio and Bax, J. Biomol. NMR 13, 289-302 (1999).

Talos Random Coil Table

RES HA C CA CB N

A 4.32 177.8 52.3 19.0 123.8

C 4.55 174.6 56.9 28.9 118.8

C 4.71 174.6 55.4 43.7 118.6

D 4.64 176.3 54.0 40.8 120.4

E 4.35 176.6 56.4 29.7 120.2

F 4.62 175.8 58.0 39.0 120.3

G 3.96 174.9 45.1 9999. 108.8

H 4.73 173.3 54.5 27.9 118.2

I 4.17 176.4 61.3 38.0 119.9

K 4.32 176.6 56.5 32.5 120.4

L 4.34 177.6 55.1 42.3 121.8

M 4.48 176.3 55.3 32.6 119.6

N 4.74 175.2 52.8 37.9 118.7

P 4.42 177.3 63.1 31.7 135.8

Q 4.34 176.0 56.1 28.4 119.8

R 4.34 176.3 56.1 30.3 120.5

S 4.47 174.6 58.2 63.2 115.7

T 4.35 174.7 62.1 69.2 113.6

V 4.12 176.3 62.3 32.1 119.2

W 4.66 176.1 57.7 30.3 121.3

Y 4.55 175.9 58.1 38.8 120.3

The TALOS triplet system

TALOS searches database for the ten best matches to agiven triplet in the target protein (Data base uses 20proteins representing 3,000 triplets).

Reliability of TALOS

* makes no prediction on 20-45% of the residues in proteins.

* makes predictions for about 65% of the residues onaverage.

* in 5 of 20 proteins studied the results included no badpredictions.

* about 3% of the predictions were bad!!!

* the uncertainty for good predictions was 14 degrees for phiand 13 degrees for psi.

Web Site: http://spin.niddk.nih.gov/bax/software/TALOS/info.html

Example of TALOS output

Chemical shifts and 2°structure

* One can often quickly determine the 1H, 15N and 13Cchemical shifts with triple resonance experiments.

* There is a correlation between chemical shift deviations andsecondary structure elements.

* These deviations are from random coil values

* Most important ones are CO, HA and CA.

For a good recent reference on measuring chemical shift of amino acids in randomcoils see: Schwarzinger et al, J. Am. Chem. Soc 121, 2970-2978 (2001)

Pattern between 2°Structure and 13C Shifts

Reference: Spera and Bax, J. Am. Chem. Soc. 113, 5490-5492 (1991)

Deviations from random coil values

Chemical shift index (CSI)

* Fast, simple and reliable method to assign secondarystructure.

* It is based on a statistical analysis of chemical shifts inproteins of known structure.

* CSI=0: δ in range of random coil values* CSI= +1 or -1: δ is greater or less than random coil

chemical shift values.* Must consider at least four residues to define an element

of secondary structure.

Reference: Wishart and Yip, Biochem. and Cell Biol. 76, 153-176 (1998)

CSI RANDOM COIL VALUES

RES HA C CA CB N HN

A 4.32 177.8 52.5 19.1 123.8

C 4.55 174.6 58.2 28.0 118.8

C 4.71 174.6 55.4 41.1 118.6

D 4.64 176.3 54.2 41.1 120.4

E 4.35 176.6 56.6 29.9 120.2

F 4.62 175.8 57.7 39.6 120.3

G 3.96 174.9 45.1 9999. 108.8

H 4.73 174.1 55.0 29.0 118.2

I 4.17 176.4 61.1 38.8 119.9

K 4.32 176.6 56.3 33.1 120.4

L 4.34 177.6 55.1 42.4 121.8

M 4.48 176.3 55.4 32.9 119.6

N 4.74 175.2 53.1 38.9 118.7

P 4.42 177.3 63.3 32.1 135.8

Q 4.34 176.0 55.7 29.4 119.8

R 4.34 176.3 56.0 30.9 120.5

S 4.47 174.6 58.3 63.8 115.7

T 4.35 174.7 61.8 69.8 113.6

V 4.12 176.3 62.2 32.9 119.2

W 4.66 176.1 57.5 29.6 121.3

Y 4.55 175.9 57.9 37.8 120.3

CSI Scoring and 2°Structure

!-helix "-sheet

CSI (CO) +1 -1

CSI (C!) +1 -1

CSI (H!) -1 +1

CSI (C") n.a. +1

Example of CSI analysisCα

CO

Residue # 10 20 30 40 50 60 70 80

Secondary structure: α1 α 2 α3 β1 β2

Hα

Cons

ensu

s

Residue # 10 20 30 40 50 60 70 80

• Currently, there is no experiment to directly

measure hydrogen bonds present in proteins.

• Hydrogen bonds can be modeled base on known

secondary structure elements and by measuring

slowly exchanging amide protons in deuterium

oxide.

Hydrogen bond restraints

• Direct measurement of hydrogen bonds inproteins is rare but new sequence are beingdeveloped that should be more common in thenext couple of years.

Detection of slowly exchanging amide protons

Hydrogen bonds is β-sheet

Residual dipolar couplings

• Provide long range angular constraints

• They are not redundant with NOE constraints

• They can be used to validate structures.

• They can help provide relative orientations of

subunits within a complex.

Pictorial view of RDCs � �

Prestegard, Nat. Struct. Biol. 5, 517, 1998

Weak alignment media (bicelle)

DHPC/DMPC

Prestegard, Nat. Struct. Biol. 5, 517, 1998.

Weak alignment media (bicelle)

DHPC/DMPCBax, Prot. Sci. 12, 1, 2003.

Isotropic 4.5% w/v 85 w/v

Tunable alignment media (Phage)

Hansen et al., Nature Struct. Biol. 5, 1065, 1998.

Tunable alignment media (Phage)

de Alba et al., Prog. Nucl. Mag. Res. Spec. 40, 175, 2002.

Tunable alignment media (Phage)

Hansen et al., Nature Struct. Biol. 5, 1065, 1998.

-Phage + Phage

Determining alignment tensor

Bax, Prot. Sci. 12, 1, 2003

Measurement in multiple alignment media

Bax, Prot. Sci. 12, 1, 2003.

RDCs and structure validation

Bax, Prot. Sci. 12, 1, 2003.

An ensemble of structures