NMR Spectral Assignment and Structural Calculations Lucia Banci CERM – University of Florence

Structure determination through NMR Protein Sample NMR spectroscopy Sequential resonance assignment Collection of conformational constraints 3D structure calculations Structure refinement and Analysis

The protein in the NMR tube! • Protein overexpression • Purification • 15 N/ 13 C labelling < 25 KDa 13 C, 15 N labeling about 240 AA 13 C, 15 N labeling > 25 kDa + 2 H labeling necessary!! about 240 AA Which experiments should I run to assess sample quality?

Is my sample OK for NMR? 1 H- 15 N HSQC spectra give the protein fingerprint folded unfolded 15 N 15 N NH 2 groups of ASN, GLN sidechains 1 H 1 H Folded proteins have larger dispersion Signals of unfolded proteins have little 1 H dispersion, that Can I see all the peaks I expect? means the 1 H frequencies of all residues are very similar. Count the peaks! Backbone NH (excluding prolines!)

Making resonance assignment What does it mean to make sequence specific resonance assignment ? HN(Asp2) HN i HN j HN(Leu50) N i N(Asp2) N j N(Leu50) C a i , C b i C a , C b (Asp2)..etc H a i , H b i H a , H b (Asp2) H a j , H b j H a , H b (Leu50) C a j , C b j , C g j ..etc C a , C b , C g 1 (Leu50)..etc To associate each resonance frequency to each atom of the individual residues of the protein

Assignment Strategy The strategy for assignment is based on scalar couplings

Experiments for backbone assignment 1 H i - 15 N i - 13 C a 13 C b i-1 i-1 CBCA(CO)NH and Res i-1 Res i CBCANH correlate amide groups (H and 15 N) with C a and C b resonances. 1 H i - 15 N i - 13 C a 13 C b i i 1 H i - 15 N i - 13 C a 13 C b i-1 i-1 Res i-1 Res i 1 H (i) - 15 N (i) - 13 C a (i) 1 H (i) - 15 N (i) - 13 CO (i-1) HNCO HNCA { 1 H (i) - 15 N (i) - 13 C a (i-1) 1 H (i) - 15 N (i) - 13 CO (i-1) HN(CA)CO { 1 H (i) - 15 N (i) - 13 C a (i-1) HN(CO)CA 1 H (i) - 15 N (i) - 13 CO (i)

Experiments for backbone assignment CBCA(CO)NH CBCANH The chemical shifts of C a and C b atoms can be used for a preliminary identification of the amino acid type.

Sequential Assignment The 'domino pattern' is used for the sequential assignment with triple resonance spectra CB CANH CBCA(CO)NH Green boxes indicate sequential connectivities from each amino acid to the preceeding one

Experiment for side-chain assignment 1 H i a , 1 H i b , 1 H i g 1 ……. Res i-1 Res i In H(C)CH-TOCSY, magnetization coherence is transferred, through 1 J couplings, from a proton to its carbon atom, to the neighboring carbon atoms and finally to their protons.

H(C)CH-TOCSY experiment F2 (ppm) 13 C F1 (ppm) 1 H C d C g 2 C g 1 C b C a Isoleucine 1 H F3 (ppm)

Conformational restraints NMR experimental data Structural restraints NOEs Proton-proton distances Coupling constants Torsion angles Torsion angles Chemical shifts H -bonds Proton-proton distances RDCs Bond orientations Relaxation times Metal-nucleus distances Metal-nucleus distances { PCSs Orientation in the metal frame Torsion angles Contact shifts

Distance constraints NOE is based on a relaxation process due to dipolar coupling between two nuclear spins. NOESY volumes are proportional to the inverse of the sixth power of the interproton distance (upon vector reorientational averaging)

The NOESY experiment: 1 H Any 1 H within 5-6 Å from a given 1 H can give rise to a cross-peak in NOESY spectra whose volume provides 1 H- 1 H distance restraints 15 N 1 H 1 H

How are the distance constraints obtained from NOEs intensities? CYANA 2.x NOEs calibration The intensity of the NOESY cross-peak between atoms I and j is converted into upper distance limit (d) through a simple function: Isolated spin approximation NOE IJ C cal x d IJ -6 Calibration constant C cal can be derived from reference distances C cal = NOE ref / d ref 6 Reference distances can be relative to a covalent bond with fixed distance Distances are given as value range, i.e. as lower and upper distance limits Wuthrich, K. (1986) "NMR of Proteins and Nucleic Acids"

Dihedral angles Backbone dihedral angles Sidechain dihedral angles

Dihedral angle restraints 3 J coupling constants are related to dihedral angles through the Karplus equation H a C a ψ H N 3 2 a J ( HN H ) A cos ( 60 ) B cos( 60 ) C Karplus equation – 155 ° < < – 85 ° b strand conformation J HNH a > 8Hz – 70 ° < < – 30 ° a helix J HNH a < 4.5Hz 4.5Hz < J HNH a < 8Hz coil ,y are also determining the J HNC values

Chemical Shift Index As chemical shifts depend on the nucleus environment, they contain structural information. Correlations between chemical shifts of C a , C b ,CO, H a and secondary structures have been identified. Chemical Shift Index CSI’s are assigned as: C a and carbonil atoms chemical shift difference with respect to reference random coil values: -0.7 ppm < Dd < 0.7 ppm 0 Dd < - 0.7 ppm -1 Dd > +0.7 ppm +1 For C b the protocol is the same but with opposite sign than C a Any “dense” grouping of four or more “ -1 ’s”, uninterrupted by “ 1 ’s” is assigned as a helix, while any “dense” grouping of three or more “ 1 ’s”, uninterrupted by “ - 1 ’s”, is assigned as a b -strand. Other regions are assigned as “coil” . A “dense” grouping means at least 70% nonzero CSI’s .

H-bonds as Structural restraints HNCO direct method Experimental Determination of H-Bonds: H/D exchange indirect method Upper distance limit Distance and angle restraints Lower distance limit Distance between the donor and the a -Helix b Sheet acceptor atoms is in the range 2.7- 3.2 Å 140 ° < N-H···O < 180 °

Residual dipolar couplings Z B 0 Y X Proteins dissolved in liquid, orienting medium Some media (e.g. bicelles, filamentous phage, cellulose crystallites) induce some orientational order to the solute in a magnetic field A small “residual dipolar coupling” results

Residual dipolar couplings D RDC f , IS i i i where is the molecular H alignment tensor with respect to the magnetic field N i , and are the angles i between the bond vector and the tensor axes Relative orientation of RDCs provide information on the secondary structural orientation of (in principle each) elements can also be bond-vector with respect to the determined molecular frame and its alignment in the magnetic field

A General Consideration How complete are the NMR structural restraints? NMR mainly determines short range structural restraints but provides a complete network over the entire molecule

3D structure calculations Most Common Algorithms • MD in cartesian coordinates/Simulated annealing X PLOR-NIH • MD in torsion angle space/Simulated annealing X PLOR-NIH and CYANA A random coil polypeptide chain is generated, which is folded through MD/SA calculations and applying experimental constraints

Molecular Dynamics (MD) How the algorithms work: • MD calculations numerically solve the equation of motion to obtain trajectories for the molecular system • In Cartesian coordinates, the Newton‘s equation of motion is: E hybrid = w i • E i • In torsion angle space the equations of motion (Lagrange equations) are = w bond •E bond + w angle •E angle + w dihedral • E dihedral + solved in a system with N torsion angles as the only degrees of freedom. w improper •E improper + w vdW •E vdW + Conformation of the molecule is uniquely specified by the values of all w NOE •E NOE + w torsion •E torsion + ... torsion angles. About 10 times less degrees of freedom than in Cartesian space L = E kin – E pot d L L 0 q = generalized dt coordinate q q k k

Hybrid energy function NMR experimental conformational restraints 2 k d ( d d ) 0 distance restraints + y y 2 k ( ) ... y 0 torsional restraints A hybrid energy function is defined, that incorporates a priori information and NMR structural restraints as potential and pseudopotential energy terms, respectively

Knowledge about the topology of the system is needed: • Experimental data are supplemented with information on the covalent structure of the protein (bond lengths, bond angles, planar groups...) and E hybrid = w i • E i the atomic radii (i.e. each atom pair cannot be = w bond •E bond + w angle •E angle + w dihedral • E dihedral + closer than the sum of their atomic radii) w improper •E improper + w vdW •E vdW + w NOE •E NOE + w torsion •E torsion + ...

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