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Solution structures by NMR. Structural Biology. • Structure • Mobility. }. • Protein-protein • Protein-ligand. interactions. NMR is a powerful method to address these problems. year. NMR structures per year. • 1984 1 (first structure!) • 1990 25

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Structural Biology

• Structure

• Mobility


• Protein-protein

• Protein-ligand


NMR is a powerful method to address these problems


NMR structures per year

• 1984 1 (first structure!)

• 1990 25

• 1994 80 (first paramagnetic structure!)

• 1998 125

• 2000 200

Structure determination through NMR

Resonance assignment


NOE intensities and J couplings

(plus other structural constraints)

Conversion of NMR data in distances and angles

Structural constraints

Structure calculations

3D structure

Structure refinement:


  • Total Correlation Spectroscopy

Esperimento 2D analogo al COSY, utile per misurare gli accoppiamenti scalari “consecutivi”

Multifrequency NMR experiments

To make full use of multidimensional NMR, isotope labeled samples are needed

Multifrequency NMR experiments

For each frequency dimension a different type of coupling can be detected

triple resonance
Triple Resonance

J couplings

Relaxation rates


H – N - CO

Trasferisco da Hn ad N

Osservo N prima dimensione

Trasferisco da N a CO

Osservo CO Seconda dimensione

Trasferisco da CO a N, da N ad Hn

Osservo Hn Terza dimensione

sequential assignment in triple resonance experiments hnca
Sequential assignment in triple resonance experiments. HNCA



Backbone assignment of 6 residues using 13Ca

nmr structural characterization of the target protein
NMR structural characterization of the target protein
  • Approaches to the Structure Determination of Proteins
  • For proteins of up to 30 kDa, use 13C/15N-labelling
  • For proteins of higher molecular weight, use fractional deuteration and 13C/15N-labelling
  • For proteins of 100 kDa and above, use selective protonation and 13C/15N-labelling
Classical constraints for structure determination






3J couplings

Chemical shifts





Residual dipolar couplings

Cross Correlation effects


Side chain

Torsion angles.

Protein structure and dihedral angles

Contraints for Structure Calculation

So far, the emphasis has been on identification of the observed signals in the spectra and their correlation with the amino acid protons giving rise to the signals. Afterwards, one has to extract the data which are relevant for the structure. Of special importance in this respect are proton-proton distances, which can be estimated from the signal intensities in the 2D NOESY, 3D 15N-NOESY-HSQC and 3D 13C-NOESY-HSQC spectra .

Signal intensity depends on the distance r between two nuclei i and j, according to:

NOEij ~ 1/rij6

Distances are derived from the spectra after calibration against NOE signals for known distances (such as distances in elements of secondary structure) and grouped into a few classes. An upper and a lower bound of distance is assigned to each class. The lower bound is often set to the sum of the van der Waals radii of the two protons.

NOE class

distance [Å]

upper bound [Å]

very strong












very weak



In this procedure, all non-sequential signals which are visible in the NOESY spectra have to be assigned, the number of which easily exceeds 1000 in a medium-sized protein (ca. 120 amino acids). It is distinguished between cross peaks of protons no more than five amino acids apart in the protein sequence (medium range NOE's) and those which are more than five amino acids apart (long range NOE's). The former are mainly indicative of the protein backbone conformation and are used for secondary structure determination, whereas the latter are an expression of the global structure of the protein and therefore contain the main information used for tertiary structure calculation.

In addition to interproton distances the phi-dihedral angles of the protein backbone can be determined from a COSY spectrum or a HNCA-J spectrum (a variant of the HNCA spectrum, from which the coupling constants of the N-Calpha bonds can be determined). Dihedral angles are connected with the coupling constants via the Karplus equation .


Side chain

Torsion angles.

Protein structure and dihedral angles

Calculation of 3D protein and nucleic acid structures

The program DYANA

Simulated annealingcombined withmolecular dynamics

in torsion angle space

Numerical solution of the classical mechanical Lagrange equations of motion with torsion angles as generalized internal coordinates

The NMR constraints are used

as pseudopotential to calculate the velocity

A temperature bath to cross barriers between local minima is cooled down slowly from its initial high temperature

The target function represents the potential energy of the system

+ other constraint contributions

Güntert P., Mumenthaler C., Wüthrich K., J.Mol. Biol., 1997

Structure quality through PROCHECK
  • Covalent geometry
  • Torsion angles
  • Chirality
  • Planarity
  • Precision
  • Restraint violations

Results are presented as plots suitable for publication

Laskowski R A, MacArthur M W, Moss D S & Thornton J M (1993). J. Appl. Cryst., 26, 283-291.

Classical constraints for structure determination






3J couplings

Chemical shifts





Residual dipolar couplings

Cross Correlation effects

Strategies for Sequential Assignment

Using this cyclic procedure of alternatively connecting intraresidual TOCSY

with interresidual NOESY cross peaks one can walk - ideally - along the

entire length of the protein.

Problem: there are a few proline residues in most proteins.

Problem: there are a number of additional short proton proton distances

which can occur as a result of certain elements of secondary structure.

The general work of

Wuthrich and co-workers

identified a whole range

of secondary specific

short proton proton

distances that are

summarized here:

Strategies for Sequential Assignment

Here are a number of characteristic

distances that connect the two strands

of a b-sheet; short enough to appear

as cross peaks in a NOESY spectrum.

These are a- a, amide- a and

amide-amide distances

  • b-sheet specific NOEs in red and simple sequential NOEs in green.
  • Other regular elements of secondary structure, e.g. different types of
  • -turns, 3-10 helices and parallel b-strands, are characterized by similar

patterns of short distances involving backbone protons.

calculation of tertiary structure
Calculation of Tertiary Structure

Results - The Structure Family

After the structural calculations a family of structures is obtained instead of an exactly defined structure. This family spans out a relatively narrow conformational space. Therefore, the quality of a NMR structure can be defined by the mean deviation of each structure from this family (RMSD) from an energy minimized mean structure which has to be calculated previously. The smaller the deviation from this mean structure the narrower the conformational space. Another definition of RMSD is to compare pairwise the structures of a family and calculate the mean of these deviations.

The RMSD is different for different parts of the protein structure: Regions with flexible structure or without secondary structure (loops) show a larger deviation than those with rigid and well defined secondary structure. This higher RMSD in loops results in first instance from the smaller number of distance constraints for these parts of the protein structure. Additionally it can originate from real flexibility, but this diagnosis can only be confirmed by measuring the relaxation times for the protein.

A result of a structure calculation is shown here:

calculation of tertiary structure2
Calculation of Tertiary Structure

The idea of computer-aided structure calculation is to convert distance- and torsion-angle-data (constraints) into a visible structure. However, the experimentally determined distances and torsion angles by themselves are not sufficient to fully characterize a protein structure, as they are based on a limited number of proton-proton distances. Only the knowledge of empirical input data, such as bond lengths of all covalently attached atoms and bond angles, enables a reasonably exact structure determination.

calculation of tertiary structure3
Calculation of Tertiary Structure

For this purpose, a randomly folded starting structure is calculated from the empirical data and the known amino acid sequence. The computer program then tries to fold the starting structure in such a way, that the experimentally determined interproton distances are satisfied by the calculated structures. In order to achieve this, each known parameter is assigned an energy potential, which will give minimal energy if the calculated distance or angle coincides with its input value. The computer program tries to calculate a structure with a possibly small overall energy.

calculation of tertiary structure4
Calculation of Tertiary Structure

Without the experimentally determined distance- and torsion angle-constraints from the NMR spectra, the protein molecule can adopt a huge number of conformations due to the free rotation around its chemical bonds (except for the peptide bond, of course). the N-Calpha bond and the Calpha-CO bond. All these possible conformations are summed up in the so-called conformational space. Therefore, it is important to identify as many constraints as possible from the NMR spectra to restrict the conformational space as much as possible, thus getting close to the true structure of the protein. In fact, the number of constraints employed is more important than the accuracy of proton-proton distances, so that the classification above is sufficiently precise.

calculation of tertiary structure5
Calculation of Tertiary Structure

Energy Potentials

A starting structure is needed for a molecular dynamics calculation, which is generated from all constraints for the molecular structure, such as bond-lengths and bond-angles. This starting structure may be any conformation such as an extended strand or an already folded protein. During the simulation, it develops in a potential field under the influence of various forces, in which all information about the protein is summarized. Two classes of energy terms are distinguished: Eempirical and Eeffective:

V = Eempirical + Eeffective


Eeffective = ENOE + Etorsion,


Eempirical = Ebond + Eangle + Edihedral + Evdw + Eelectr

Eempirical contains all information about the primary structure of the protein and also data about topology and bonds in proteins in general.                                   The contributions of covalent bonds, bond-angles and dihedral angles towards Eempirical are approximated by a harmonic function. In contrast, non-covalent van-der-Waals forces and electrostatic interactions are simulated by an inharmonic Lennard-Jones potential or Coulomb potential, respectively. Eeffective takes the experimentally determined constraints into account. Angle constraints are introduced by a harmonic function analogous to that for the dihedral angles. For distance constraints, the energy potential will be set to zero, if the corresponding distance is within the given limits. If it is outside these limits, a harmonic energy potential is used, which tries to push the value of the distance into the limits.


Ogni aminoacido ha valori precisi di

Distanze tra atomi.


Sequenza primaria

Libreria di aminoacidi

Legame peptidico 180°

Distanze tra protoni intraresiduo

Distanze tra protoni di residui consecutivi

Distanze tra protoni di residui a breve distanza (i,i+4)

Angoli diedri y j

Distanze tra prootni a madio e lungo raggio

target penalty function
Target (penalty) Function

Ripeto il calcolo n volte

Per Ogni struttura calcolo il valore della funzione penalità

Seleziono le strutture che hanno il piu’ basso valore della funzione penalità

target penalty function1
Target (penalty) Function

La somma delle violazioni dei vincoli sperimentali

E’ di fatto, impossibile ottenere una struttura che sia in grado di rispettare perfettamente l’insieme di tutti i vincoli sperimentali che noi imponiamo

Non ci sono solo I vincoli sperimentali, ma quelli derivanti dalla struttura di un polipeptide, (es: le violazioni di Van der Walls, gli angoli non permessi, etc..)

target penalty function2
Target (penalty) Function

La somma delle violazioni dei vincoli sperimentali

Considero “buone” tutte quelle strutture che hanno il più basso valore della funzione penalità

famiglia di strutture
Famiglia di strutture

Perché ne considero 20 e non una sola?

In principio, esistono infiniti modi (conformazioni) che permettono di ottenere una bassa funzione penalità.

Non vi é nessun motivo per sceglierne una piuttosto che un altra

In linea di principio, la conformazione a piu’ bassa funzione penalità é considerabile “la migliore”, ma tutte le altre che hanno valore molto simile sono ugualmente valide

Quindi, preferisco prendere in considerazione un numero fisso di conformazioni (20, o 30) che hanno la piu’ bassa penalità e vedere quanto esse sono simili tra loro

famiglia di strutture1
Famiglia di strutture


Se le strutture sono molto simili tra loro significa che tutte le conformazioni che ho considerato sono molto simili. Avro’ una struttura accurata

famiglia di strutture2
Famiglia di strutture


Se le strutture sono molto diverse tra loro significa che devo considerare come ugualmente “buone” conformazioni molto diverse.

Avro’ una struttura molto poco accurata

Solution structure of oxidized and reduced Cytochrome c

Cyt c oxidized

Cyt c reduced

Banci, Bertini, Bren, Gray, Sompornpisut, Turano, Biochemistry, 1997

Baistrocchi, Banci, Bertini, Turano, Bren, Gray, Biochemistry, 1996

Active site channel of Reduced Monomeric Q133 Copper Zinc Superoxide dismutase

 Reduced Q133M2SOD

Oxidized human SOD



Paramagnetic structure


Diamagnetic structure





RMSD backbone













Residue Number

Structure of Ce3+ substituted Calbindin D9k

Bertini, Donaire, Jiménez, Luchinat, Parigi, Piccioli, Poggi, J.Biomol. NMR, 2001,21,85-98

Stucture Calculation
  • Structure Validation
  • Structure Visualisation

How to overlay structures



- bb & all heavy atoms

Average pairwise rmsd values calculated for backbone heavy atoms N, Ca, and C' ("Backbone"), all heavy atoms ("All heavy"), and backbone heavy atoms N, Ca, and C' together with heavy atoms of the best defined side-chains. The values for the DYANA structures are represented by red bars, and values for molecular dynamics refined (MDR) and energy-minimization refined (EMR) structures are displayed in green and gray, respectively. Standard deviations are indicated by vertical error bars.
target function analysis
Target function analysis

Violations < threshold

Energy terms


The PROCHECK suite of programs provides a detailed check on the stereochemistry of a protein structure. Its outputs comprise a number of plots in PostScript format and a comprehensive residue-by-residue listing. These give an assessment of both the overall quality of the structure, as compared with well-refined structures of the same resolution, and also highlight regions that may need further investigation. The PROCHECK programs are useful for assessing the quality not only of protein structures in the process of being solved, but also of existing structures and those being modelled on known structures.

procheck procheck nmr

The only input required for PROCHECK is the PDB file holding the coordinates of the structure of interest. For NMR structures, each model in the ensemble should be separated by the correct MODEL and ENDMDL records

Plots of PROCHECK G-factor (all dihedrals) vs. MOLPROBITY Z-scores (1) calculated for x-ray crystal structures (circles) deposited in the PDB during 2000-2004 colored according to resolution [green: high-resolution (£ 1.8 Å); gray: medium-resolution (1.8 – 2.5 Å); red: low-resolution (2.5– 3.5 Å)] and NMR structures (yellow triangles) deposited in the PDB during 2000-2004 by other leading NMR groups.