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NMR in biology: Structure, dynamics and energetics Gaya Amarasinghe, Ph.D. Department of Pathology and Immunology [email protected] CSRB 7752

NMR in biology: Structure, dynamics and energetics

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NMR in biology: Structure, dynamics and energetics. Gaya Amarasinghe, Ph.D. Department of Pathology and Immunology [email protected] CSRB 7752. NMR? Nuclear Magnetic Resonance Spectroscopy. - PowerPoint PPT Presentation

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Page 1: NMR in biology: Structure, dynamics and energetics

NMR in biology: Structure, dynamics and energetics

Gaya Amarasinghe, Ph.D.Department of Pathology and Immunology

[email protected] 7752

Page 2: NMR in biology: Structure, dynamics and energetics

NMR?Nuclear Magnetic Resonance

Spectroscopy

Today, we will look at how NMR can provide insight in to biological macromolecules. This information often compliment those obtained from other structural methods.

Page 3: NMR in biology: Structure, dynamics and energetics

http://www.cryst.bbk.ac.uk/PPS2/projects/schirra/html/1dnmr.htm

NMR Spectra contains a lot of useful information: from small molecule to macromolecule.

http://www.nature.com/nature/journal/v418/n6894/fig_tab/nature00860_F1.html

• Few peaks• Sharper lines• Overall very easy to interpret

• Many peaks• Broader lines• Overall NOT very easy to interpret

Page 4: NMR in biology: Structure, dynamics and energetics

• Structure determination by NMR

• NMR relaxation– how to look at molecular motion (dynamics by NMR)

• Ligand binding by NMR – Energetics

Page 5: NMR in biology: Structure, dynamics and energetics

Outline for Bio 5068

December 11• Why study NMR (general discussion)

1. What is the NMR signal (some theory)2. What information can you get from NMR (structure, dynamics, and energetic

from chemical shifts, coupling (spin and dipolar), relaxation—next class)3. What are the differences between signal from NMR vs x-ray crystallography

(we will come back to this after going through how to determine structures by NMR)

• Practical aspects of NMR1. instrumentation2. Sample signal vs water signal3. Sample preparation (very basic aspects & deal with specific labeling during the

description of experiments)

• Assignments and structure determination1. 2-D experiments2. 3/4-D experiments3. Restraints and structure calculations

• Assessing quality of structures1. NMR structure quality assessment2. Comparison with x-ray

Page 6: NMR in biology: Structure, dynamics and energetics
Page 7: NMR in biology: Structure, dynamics and energetics
Page 8: NMR in biology: Structure, dynamics and energetics

Nuclear transitions

Rotational transitions

Translational transitions

Electronic transitions

Diffractions

NMR works in the rf range- after absorption of energy by nuclei, dissipation of energy and the time it takesReveals information about the conformation and structure.

For diffraction, the limit of resolution is ½ wavelength!!

Page 9: NMR in biology: Structure, dynamics and energetics

Protein Structures from an NMR PerspectiveBackground

– We are using NMR Information to “FOLD” the Protein.

– We need to know how this NMR data relates to a protein structure.

– We need to know the specific details of properly folded protein structures to verify the accuracy of our own structures.

– We need to know how to determine what NMR experiments are required.

– We need to know how to use the NMR data to calculate a protein structure.

– We need to know how to use the protein structure to understand biological function

Page 10: NMR in biology: Structure, dynamics and energetics

Protein Structures from an NMR Perspective

Dist

ance

from

Cor

rect

Str

uctu

re

NMR Data Analysis

Correct structure

XNot A Direct Path!

Interpreting NMR Data Requires Making Informed “Guesses” to Move Toward the “Correct” Fold

Initial rapid convergence to approximate correct fold

Iterative “guesses” allow “correct” fold to emerge

Analyzing NMR Data is a Non-Trivial Task!there is an abundance of data that needs to be interpreted

Page 11: NMR in biology: Structure, dynamics and energetics
Page 12: NMR in biology: Structure, dynamics and energetics

Current PDB statistics (as of 3/27/2012)

Exp.Method Proteins Nucleic

AcidsProtein/Nucleic Acid Complexes Total

X-RAY 65828 1346 3260 70436NMR 8167 975 186 9335

ratio 8.06 1.38 17.53

Page 13: NMR in biology: Structure, dynamics and energetics
Page 14: NMR in biology: Structure, dynamics and energetics

Nuclei are positively chargedmany have a spin associated with them.

Moving charge—produces a magnetic field that has a magnetic moment

Spin angular moment

Page 15: NMR in biology: Structure, dynamics and energetics

Mass Charge I

Even Even I=0

Even Odd I= integer

Odd I=half integer

Page 16: NMR in biology: Structure, dynamics and energetics
Page 17: NMR in biology: Structure, dynamics and energetics
Page 18: NMR in biology: Structure, dynamics and energetics

How do we detect the NMR signal?

Page 19: NMR in biology: Structure, dynamics and energetics
Page 20: NMR in biology: Structure, dynamics and energetics
Page 21: NMR in biology: Structure, dynamics and energetics

Next time—pick up on chemical shifts

Page 22: NMR in biology: Structure, dynamics and energetics

• Practical aspects of NMR1. instrumentation2. Sample signal vs water signal3. Sample preparation (very basic aspects & deal with specific

labeling during the description of experiments)

http://chem4823.usask.ca/nmr/magnet.html

http://en.wikipedia.org/wiki/Nuclear_magnetic_resonance

Page 23: NMR in biology: Structure, dynamics and energetics

• Practical aspects of NMR1. instrumentation2. Sample signal vs water signal3. Sample preparation (very basic aspects & deal with specific

labeling during the description of experiments)

http://www.chemistry.nmsu.edu/Instrumentation/NMSU_NMR300_J.html

Page 24: NMR in biology: Structure, dynamics and energetics

Sample preparation using recombinant methods

Page 25: NMR in biology: Structure, dynamics and energetics

Vinarov et al., Nature Methods - 1, 149 - 153 (2004)

Cell-free protein production and labeling protocol for NMR-based structural proteomics

Page 26: NMR in biology: Structure, dynamics and energetics

Segment labeling can simplify NMR spectra

Native chemical ligation Expressed protein ligation

Muir et al. Curr Opin Biotechnol. 2002 Aug;13(4):297-303.

Page 27: NMR in biology: Structure, dynamics and energetics

Sample requirements and sensitivity

Methyl groups are more sensitive than isolated Ha spins

Source : www.chem.wisc.edu/~cic/nmr/Guides/Other/sensitivity-NMR.pdf

Page 28: NMR in biology: Structure, dynamics and energetics

Sample requirements and sensitivity

Cryoprobes are 3-4 times better S/N than standard probes (2x in high salt)

Source : www.chem.wisc.edu/~cic/nmr/Guides/Other/sensitivity-NMR.pdf

mM not mM!!

Page 29: NMR in biology: Structure, dynamics and energetics

Why use NMR ?

Some proteins do not crystallize (unstructured, multidomain) crystals do not diffract well can not solve the phase problem

Functional differences in crystal vs in solution

can get information about dynamics

Page 30: NMR in biology: Structure, dynamics and energetics

Protein Structures from an NMR Perspective

Overview of Some Basic Structural Principals:

a) Primary Structure: the amino acid sequence arranged from the amino (N) terminus to the carboxyl (C) terminus polypeptide chain

b) Secondary Structure: regular arrangements of the backbone of the polypeptide chain without reference to the side chain types or conformation

c) Tertiary Structure: the three-dimensional folding of the polypeptide chain to assemble the different secondary structure elements in a particular arrangement in space.

d) Quaternary Structure: Complexes of 2 or more polypeptide chains held together by noncovalent forces but in precise ratios and with a precise three-dimensional configuration.

Page 31: NMR in biology: Structure, dynamics and energetics
Page 32: NMR in biology: Structure, dynamics and energetics
Page 33: NMR in biology: Structure, dynamics and energetics

Protein Structure Determination by NMR

•Stage I—Sequence specific resonance assignment

•State II – Conformational restraints

•Stage III – Calculate and refine structure

Page 34: NMR in biology: Structure, dynamics and energetics

Resonance assignment strategies by NMR

Page 35: NMR in biology: Structure, dynamics and energetics

Illustrations of the Relationship Between MW, tc and T2

Page 36: NMR in biology: Structure, dynamics and energetics
Page 37: NMR in biology: Structure, dynamics and energetics
Page 38: NMR in biology: Structure, dynamics and energetics
Page 39: NMR in biology: Structure, dynamics and energetics
Page 40: NMR in biology: Structure, dynamics and energetics
Page 41: NMR in biology: Structure, dynamics and energetics
Page 42: NMR in biology: Structure, dynamics and energetics
Page 43: NMR in biology: Structure, dynamics and energetics

NMR Assignments 3D NMR Experiments

• 2D 1H-15N HSQC experiment• correlates backbone amide 15N through one-bond coupling to amide 1H• in principal, each amino acid in the protein sequence will exhibit one peak in the 1H-15N

HSQC spectra also contains side-chain NH2s (ASN,GLN) and NeH (Trp) position in HSQC depends on local structure and sequence no peaks for proline (no NH)

Side-chain NH2

Page 44: NMR in biology: Structure, dynamics and energetics

3D NMR Experiments• Consider a 3D experiment as a collection of 2D experiments

z-dimension is the 15N chemical shift• 1H-15N HSQC spectra is modulated to include correlation through coupling

to a another backbone atom

• All the 3D triple resonance experiments are then related by the common 1H,15N chemical shifts of the HSQC spectra

• The backbone assignments are then obtained by piecing together all the “jigsaw” puzzles pieces from the various NMR experiments to reassemble the backbone

NMR Assignments

Ni-1

H

Cαi-1

H

Ci-1

O

Ni

H

Cαi

Cβi-1

H

Cβi

Ci

O

Page 45: NMR in biology: Structure, dynamics and energetics

NMR Assignments

3D NMR Experiments• Amide Strip

3D cube 2D plane amide strip

Strips can then be arranged in backbone sequential order to visual confirm assignments

Page 46: NMR in biology: Structure, dynamics and energetics

NMR Assignments

3D NMR Experiments• 3D HNCO Experiment

common nomenclature letters indicate the coupled backbone atoms correlates NHi to Ci-1 (carbonyl carbon, CO or C’) no peaks for proline (no NH)

• Like the 2D 1H-15N HSQC spectra, each amino acid should display a single peak in the 3D HNCO experiment

identifies potential overlap in 2D 1H-15N HSQC spectra, especially for larger MW proteins

most sensitive 3D triple resonsnce experiment may observe side-chain correlations

1JNC’

1JNH

Ni-1

H

Cαi-1

H

Ci-1

O

Ni

H

Cαi

Cβi-1

H

Cβi

Ci

O

Page 47: NMR in biology: Structure, dynamics and energetics

NMR Assignments 3D NMR Experiments

• 3D HN(CA)CO Experiment correlates NHi to COi

relays the transfer through Cαi without chemical shift evolution

uses stronger one-bond coupling contains only intra correlation provides a means to sequential connect NH and CO chemical shifts

match NHi-COi (HN(CA)CO with NHi-COi-1 (HNCO) not sufficient to complete backbone assignments because of overlap and

missing information every possible correlation is not observed need 2-3 connecting inter and intra correlations for unambiguous

assignments no peaks for proline (no NH) breaks assignment chain

but can identify residues i-1to prolines

1JCαC’

1JNH

1JNCα

Ni-1

H

Cαi-1

H

Ci-1

O

Ni

H

Cαi

Cβi-1

H

Cβi

Ci

O

Page 48: NMR in biology: Structure, dynamics and energetics

NMR Assignments

3D NMR Experiments• 3D HN(CA)CO Experiment

Amide “Strips” from the 3D HNCO and HN(CA)CO experiments arranged in sequential order

HNCO and HN(CA)CO pair for one residues NH

Connects HNi-COi with HNi-COi-1

Journal of Biomolecular NMR, 9 (1997) 11–24

Page 49: NMR in biology: Structure, dynamics and energetics

NMR Assignments 4D NMR Experiments

• Consider a 4D NMR experiment as a collection of 3D NMR experiments

still some ambiguities present when correlating multiple 3D triple-resonance experiments

4D NMR experiments make definitive sequential correlations

increase in spectral resolution– Overlap is unlikely

loss of digital resolution– need to collect less data points for

the 3D experiment– If 3D experiment took 2.5 days,

then each 4D time point would be a multiple of 2.5 days i.e. 32 complex points in A-dimension would require an 80 day experiment

loss of sensitivity– an additional transfer step is

required– relaxation takes place during each

transfer

Get less data that is less ambiguous?

Page 50: NMR in biology: Structure, dynamics and energetics

NMR Assignments

Page 51: NMR in biology: Structure, dynamics and energetics

NMR Assignments

Page 52: NMR in biology: Structure, dynamics and energetics

Why use deuteration?

• What are the advantages?

• What are the disadvantages?

Page 53: NMR in biology: Structure, dynamics and energetics

2D 15N-NH HSQC spectrum of the 30 kDa N-terminal domain of Enzyme I from the E. coli

Effects of Deuterium Labeling

only 15N labeled 15N, 2H labeled

Current Opinion in Structural Biology 1999, 9:594–601

Page 54: NMR in biology: Structure, dynamics and energetics

Protein Structure Determination by NMR

•Stage I—Sequence specific resonance assignment

•State II – Conformational restraints

•Stage III – Calculate and refine structure

Page 55: NMR in biology: Structure, dynamics and energetics

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?

Page 56: NMR in biology: Structure, dynamics and energetics

4.1Å

2.9Å

NOE

CαH

NH

NH

CαHJ

NOE- a through space correlation (<5Å)- distance constraint

Coupling Constant (J)- through bond correlation- 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

D

NMR Structure Determination

Page 57: NMR in biology: Structure, dynamics and energetics
Page 58: NMR in biology: Structure, dynamics and energetics
Page 59: NMR in biology: Structure, dynamics and energetics
Page 60: NMR in biology: Structure, dynamics and energetics

NMR Structure Determination Protein Secondary Structure and Carbon Chemical Shifts

α1

α2 α3

α4

βI

βII

βIIIβIV

Page 61: NMR in biology: Structure, dynamics and energetics

NMR Structure Determination Protein Secondary Structure and Carbon Chemical Shifts• TALOS +

Shen et al. (2009) J. Biomol NMR 44:213

Page 62: NMR in biology: Structure, dynamics and energetics

NMR Structure Determination Protein Secondary Structure and Carbon Chemical Shifts• TALOS+

Given the Cα, Cβ 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.

Page 63: NMR in biology: Structure, dynamics and energetics

NMR Structure Determination Protein Secondary Structure and 3JHNα

• Karplus relationship between f and 3JHNα

f =180o 3JHNα = ~8-10 Hz β-strand f = -60o 3JHNα = ~3-4 Hz α-helix

Vuister & Bax (1993) J. Am.Chem. Soc. 115:7772

Page 64: NMR in biology: Structure, dynamics and energetics

NMR Structure Determination Protein Secondary Structure and 3JHNα

• Karplus relationship between f and 3JHNα

Measure 3JHNα 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

Page 65: NMR in biology: Structure, dynamics and energetics

Protein Structure Determination by NMR

•Stage I—Sequence specific resonance assignment

•State II – Conformational restraints

•Stage III – Calculate and refine structure

Page 66: NMR in biology: Structure, dynamics and energetics
Page 67: NMR in biology: Structure, dynamics and energetics

Protein Structures from an NMR Perspective

What Information Do We Know at the Start of Determining A Protein Structure By NMR?

Effectively Everything We have Discussed to this Point!

The primary amino acid sequence of the protein of interest.► All the known properties and geometry associated with each

amino acid and peptide bond within the protein.► General NMR data and trends for the unstructured (random

coiled) amino acids in the protein. The number and location of disulphide bonds.

► Not Necessary can be deduced from structure.

Page 68: NMR in biology: Structure, dynamics and energetics
Page 69: NMR in biology: Structure, dynamics and energetics
Page 70: NMR in biology: Structure, dynamics and energetics
Page 71: NMR in biology: Structure, dynamics and energetics
Page 72: NMR in biology: Structure, dynamics and energetics
Page 73: NMR in biology: Structure, dynamics and energetics

Double the nOe restraintsFrom above

Page 74: NMR in biology: Structure, dynamics and energetics

7 restraints/residue

10 restraints/residue

13 restraints/residue

16 restraints/residue

Page 75: NMR in biology: Structure, dynamics and energetics
Page 76: NMR in biology: Structure, dynamics and energetics

Wüthrich et al. , J. Virol. February 15, 2009; 83:1823-1836

Page 77: NMR in biology: Structure, dynamics and energetics

Analysis of the Quality of NMR Protein Structures With A Structure Calculated From Your NMR Data, How Do You Determine the Accuracy and Quality of the Structure?

• Consistency with Known Protein Structural Parameters bond lengths, bond angles, dihedral angles, VDW interactions, etc

all the structural details discussed at length in the beginning• Consistency with the Experimental DATA

distance constraints, dihedral constraints, RDCs, chemical shifts, coupling constants all the data used to calculate the structure

• Consistency Between Multiple Structures Calculated with the Same Experimental DATA

Overlay of 30 NMR Structures

Page 78: NMR in biology: Structure, dynamics and energetics

Analysis of the Quality of NMR Protein Structures

As We have seen before, the Quality of X-ray Structures can be monitored by an R-factor

• No comparable function for NMR • Requires a more exhaustive analysis of NMR

structures

Page 79: NMR in biology: Structure, dynamics and energetics

Analysis of the Quality of NMR Protein Structures Root-Mean Square Distance (RMSD) Analysis of Protein Structures

• A very common approach to asses the quality of NMR structures and to determine the relative difference between structures is to calculate an rmsd

an rmsd is a measure of the distance separation between equivalent atoms

two identical structures will have an rmsd of 0Å the larger the rmsd the more dissimilar the structures

0.43 ± 0.06 Å for the backbone atoms 0.81 ± 0.09 Å for all atoms

Page 80: NMR in biology: Structure, dynamics and energetics

Analysis of the Quality of NMR Protein Structures Root-Mean Square Distance (RMSD) Analysis of Protein Structures

• A variety of approaches can be used to measure an RMSD only backbone atoms exclude disordered regions only regions with defined secondary structure only the protein’s active-site region on a per-atom or per-residue basis

rmsd difference between NMR and X-ray structure

Page 81: NMR in biology: Structure, dynamics and energetics

Analysis of the Quality of NMR Protein Structures Is the “Average” NMR Structure a Real Structure?

• No-it is a distorted structure level of distortions depends on the similarity between the structures in the

ensemble provides a means to measure the variability in atom positions between an

ensemble of structures Expanded View of an “Average” Structure

Some very long, stretched bonds

Position of atoms are so scrambled the graphics program does not know which atoms to draw bonds between Some regions of the structure

can appear relatively normal

Page 82: NMR in biology: Structure, dynamics and energetics

Analysis of the Quality of NMR Protein Structures

As We Discussed Before, PROCHECK is a Very Valuable Tool For Accessing The Quality of a Protein Structure

► Correct f, y, c1, c2 distribution► Comparison of main chain and side-chain

parameters to standard values

Page 83: NMR in biology: Structure, dynamics and energetics

Analysis of the Quality of NMR Protein Structures NMR R-factor

• difference between expected and observed NOEs expected NOEs structure observed NOEs NMR spectra also includes unassigned NOEs perfect fit would yield R = 0

• R-factors have not been readily adapted in NMR community

affected by completeness of assignments, peak overlap, sensitivity, noise, extent of data (RDCs, coupling constants, etc

trends with rmsd without complicationsJournal of Biomolecular NMR, 17: 137–151, 2000.

Page 84: NMR in biology: Structure, dynamics and energetics
Page 85: NMR in biology: Structure, dynamics and energetics

Protein Structures from an NMR Perspective

Dist

ance

from

Cor

rect

Str

uctu

re

NMR Data Analysis

Correct structure

XNot A Direct Path!

Interpreting NMR Data Requires Making Informed “Guesses” to Move Toward the “Correct” Fold

Initial rapid convergence to approximate correct fold

Iterative “guesses” allow “correct” fold to emerge

Analyzing NMR Data is a Non-Trivial Task!there is an abundance of data that needs to be interpreted

Page 86: NMR in biology: Structure, dynamics and energetics

Timescales of Protein Motion

N

HEnergy landscape and dynamicshigh energy barriers = slow ratelow energy barriers = fast rate

Page 87: NMR in biology: Structure, dynamics and energetics

Why do proteins move?• Broad, shallow energy potential

– Thermal energy is sufficient for the protein to sample many different conformations• Change in conditions

– Interaction with a small molecule or binding partner, change in temperature, ion concentration, etc.

– Now a different conformation is lower in energy• Sequence encodes both protein structure and protein flexibility

– Non-bonded interactions determine the lowest energy conformation(s)

Sequence

StabilityFlexibility

Function Function requires•Stability: the right chemical and spatial features in the right place to bind ligand, catalyze a chemical reaction, etc.•Flexibility: the ability to move in order to control access in and out of the active site and to provide energy for chemical reactions

Page 88: NMR in biology: Structure, dynamics and energetics

NMR Analysis of Protein Dynamics

Hydrogen-Deuterium Exchange • As we saw before, slow exchanging NHs

allowed us to identify NHs involved in hydrogen-bonds.

• Similarly, slow exchanging NHs are protected from the solvent and imply low dynamic regions.

• Fast exchanging NHs are accesible to the solvent and imply dynamic residues, especially if not solvent exposed.

Protein sample is exchanged into D2O and the disappearance of NHs peaks in a 2D 1H-15NH spectra is monitored.

Protein Science (1995), 4:983-993.

Page 89: NMR in biology: Structure, dynamics and energetics

tktk

tk

exex

ex

eeI

oreI

2121

−−

++=

+=

ααγ

αγ

NMR Analysis of Protein Dynamics Hydrogen-Deuterium Exchange

• The observed NH intensity loss can be fit to a simple exponential to measure an exchange rate (kex)

• These exchange rates may range from minutes to months! NHs with long exchange rates indicate stable or low mobility regions of the

protein NHs with short exchange rates indicate regions of high mobility in the protein

Page 90: NMR in biology: Structure, dynamics and energetics

NMR Analysis of Protein Dynamics

Hydrogen-Deuterium Exchange • As expected, majority of NHs that exhibit slow exchange rates are located in secondary

structures• fast exchanging NHs are located in loops, N- and C-terminal regions

Page 91: NMR in biology: Structure, dynamics and energetics

NMR Parameters for Protein Dynamics

• Number of signals per atom• Line-widths• Hydrogen Exchange (H-D)• Hetero-nuclear {15N, 13C}

Relaxation measurements– T1 (spin-lattice relaxation time)

– T2 (spin-spin relaxation time)– Hetero-nuclear NOE

Page 92: NMR in biology: Structure, dynamics and energetics

NMR Relaxation After an RF pulse system needs to relax back to equilibrium condition

Related to molecular dynamics of system may take seconds to minutes to fully recovery usually occurs exponentially:

– (n-ne)t displacement from equilibrium value ne at time t– (n-ne)0 at time zero

Relaxation can be characterized by a time T– relaxation rate (R): 1/T

No spontaneous reemission of photons to relax down to ground state Two types of NMR relaxation processes

spin-lattice or longitudinal relaxation (T1) spin-spin or transverse relaxation (T2)

B1 off…

(or off-resonance)

Mo

z

B1

z

x

Mxy

y y w1

Mo

y

z

xT1 & T2

relaxation

)/exp()()( 0 Ttnnnn ete −−=−

Page 93: NMR in biology: Structure, dynamics and energetics

Spin-lattices or longitudinal relaxation Relaxation process occurs along z-axis transfer of energy to the lattice or solvent material coupling of nuclei magnetic field with magnetic fields created by the ensemble of vibrational

and rotational motion of the lattice or solvent. results in a minimal temperature increase in sample Relaxation time (T1) exponential decay

NMR Relaxation

Mz = M0(1-exp(-t/T1))

Page 94: NMR in biology: Structure, dynamics and energetics

T2 relaxation

NMR Relaxation Spin-Spin or Transverse relaxation

Relaxation process in the x,y plane Related to peak line-width

– Inhomogeneity of magnet also contributes to peak width T2 may be equal to T1, or differ by orders of magnitude

– T2 can not be longer than T1 No energy change

(derived from Heisenberg uncertainty principal)

Page 95: NMR in biology: Structure, dynamics and energetics

NMR RelaxationMechanism for Spin-lattices and Spin-Spin relaxation

• Illustration of the Relationship Between MW, tc and T2

Page 96: NMR in biology: Structure, dynamics and energetics

Conformational Exchange Increasesthe Rate of Transverse Relaxation (R2)

in NMR Spectra

R2 = R20 + Rex

Rex depends on:

Kinetics: kex = kA + kB

Thermodynamics:pA*pB

Structure:Dw

Page 97: NMR in biology: Structure, dynamics and energetics

NMR Analysis of Protein Dynamics

k – exchange raten – peak frequencyh – peak-width at half-height

e – with exchangeo – no exchange

k = p (he-ho)

k = p (Dno2 -  Dne

2)1/2/21/2

k = p Dno / 21/2

k = p Dno2 /2(he - ho)

Page 98: NMR in biology: Structure, dynamics and energetics

Preparation Relaxation Frequency Labeling Acquisition

In the Absence of Chemical Exchange Magnetization Refocuses Following a 180° Pulse

Preparation Frequency Labeling Acquisition

Page 99: NMR in biology: Structure, dynamics and energetics

Preparation Relaxation Frequency Labeling Acquisition

Relaxation Due to Chemical Exchange Leads to Loss of Transverse Magnetization

No Chemical Exchange

With Chemical Exchange

Page 100: NMR in biology: Structure, dynamics and energetics

Preparation Relaxation Frequency Labeling Acquisition

Increasing the Number of CPMG Pulses Can Recover Magnetization Due to Rex

pulse rate (1/s)

R2 (1/s) Rex

R20

For 2-state exchange in the ms-µs regime,quantitative analysis can in principle yield:

pA, pB, kA, kB, Dw

···

Page 101: NMR in biology: Structure, dynamics and energetics

Summary --- NMR relaxation/dynamics

• High sensitivity and site specific information

• may need isotopic labeling

• May require assignment of resonances

• Can help narrow construct space and identify interfaces

• regions that interact with solvent or binding partners

Page 102: NMR in biology: Structure, dynamics and energetics

NMR Analysis of Protein-Ligand Interactions

NMR Monitors the Different Physical Properties That Exist Between a Protein and a Ligand

Page 103: NMR in biology: Structure, dynamics and energetics

NMR Analysis of Protein-Ligand Interactions Ligand Line-Width (T2) Changes Upon Protein Binding

• As we have seen before, line-width is directly related to apparent MW a small-molecule (~100-1,000Da) is orders of magnitude lighter than a typical protein

(10s of KDa) a small molecule has sharp NMR line-widths (few Hz at most)) protein has broad line-widths (10s of Hz)

if a small molecule binds a protein, its line-width will resemble the larger MW protein

+

Small molecule: Sharp NMR lines Broad NMR lines

tc » MW/2400 (ns)

Page 104: NMR in biology: Structure, dynamics and energetics

• Slow isomerization of dimethyl amino group at low temperature produces distinct signals for each methyl

• At increasing temperatures (faster exchange rates) peaks broaden and eventually coalesce into one average signal

Chemical exchange NMR timescales

• For binding reactions, slow exchange (higher affinity) produces distinct signals for free and bound states at intermediate titration points - follow binding reaction by watching bound/free peak intensities grow/diminish

• Fast exchange - only one set of peaks throughout titration, shifting in proportion to changing ratio of free:bound

Page 105: NMR in biology: Structure, dynamics and energetics

Summary --- NMR ligand binding• High sensitivity and site specific information

• may need isotopic labeling

• May require assignment of resonances

• Affinity measurements are only valid for low affinity interactions

• Complex structures can be determined for high affinity interactions

Page 106: NMR in biology: Structure, dynamics and energetics

Comparison of NMR and X-ray Structures

Page 107: NMR in biology: Structure, dynamics and energetics

NMR and X-ray Structures Comparison of NMR and X-ray Structures

Science (2000) 289, 905-920

large ribosomal subunit X-ray structure

There is no theoretical limit to the size of the structure that can be determined by X-ray crystallography.

Requires a crystal that diffracts!- requires highly pure samples- requires high solubility (~mM)- requires high stability (crystal may take weeks to months to form)- requires absence of aggregation/ppt- may requires seleno-Met labeling for phase determination- usually need to test 100s to 1,000s of

crystal conditions- requires a protein that will form a crystal

(may require site-directed mutant, N-,C- terminal truncation or using sequences from different species)

Page 108: NMR in biology: Structure, dynamics and energetics

NMR and X-ray Structures Comparison of NMR and X-ray Structures

kTr

c 34 3pηt =

where: r = radiusk = Boltzman constantη = viscosity coefficient

Conversely, there is a molecular-weight upper limit for NMR structures.

molecular-weight of a protein is related to its radius which in turn is related to the protein’s rotational correlation time (tc) :

rotational correlation time (tc) is the time it takes a molecule to rotate one radian (360o/2p).

the larger the molecule the slower it moves tc is related to the efficiency of T2 relaxation

Page 109: NMR in biology: Structure, dynamics and energetics

NMR and X-ray Structures Comparison of NMR and X-ray Structures

As we have seen to this point, that an NMR structure is determined indirectly by combining NMR experimental data as target functions with traditional geometrical potential energy functions.

Conversely, an X-ray structure is determined by directly fitting the structure against the electron density maps. This approach still uses XPLOR to refine the structure and maintain proper geometry (bond lengths, bond angles)

Page 110: NMR in biology: Structure, dynamics and energetics

NMR and X-ray Structures Comparison of NMR and X-ray Structures

As a result, a single optimal structure can be determined to represent the experimental X-ray data where the r-factor indicates the quality of the fit and the data indicates the resolution of the structure

Conversely, the NMR data can be equally represented by an ensemble of structures and there currently is no corresponding equivalent to the r-factor or resolution

The EMBO Journal (2000) 19(13) 3179

Biochemistry (2000) 39(31), 9146-9156

Page 111: NMR in biology: Structure, dynamics and energetics

The resolution of the structure is the minimum separation of two groups in the electron-density plot that can be distinguished from one another.

NMR and X-ray Structures Comparison of NMR and X-ray Structures

Resolution increases (d) as you move out concentric circles in the X-ray diffraction pattern

Acta Cryst. (2000). D56, 1015–1016

Example of Ultra-High Resolution X-ray Diffraction Pattern

Bragg equation: 2dsinf =nlX f d X

Note: diffraction intensity decreases as you move to outer circle

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NMR and X-ray Structures Comparison of NMR and X-ray Structures

Protein Science (1996). 5:2391-2398.

NMR and X-ray structures generally exhibit the same fold

Local differences may be attributed to:1) dynamics2) crystal-packing interactions3) solid vs. solution state

- solvent is present in crystals- lowest energy conformer in crystal?

4) Resolution/experimental error

Nevertheless, there are some examples where distinct functional differences are observed between the NMR and X-ray structures

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NMR and X-ray Structures Comparison of NMR and X-ray Structures

Illustration of the large differences between the NMR (blue) and X-ray (red) structures of the Ca2+–calmodulin complex

“The difference between the crystal and solution structures of Ca2+–calmodulin indicates considerable backbone plasticity within the domains of calmodulin, which is key to their ability to bind a wide range of targets.” Nature Structural Biology (2001), 8(11), 990-997.

X-ray structure suggested a “dumb-bell” structure with an extended α-helixNMR structure indicated the central helix was unstructured and dynamic.

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NMR and X-ray Structures Comparison of NMR and X-ray Structures

Protein Dynamics Is Routinely Measured From NMR Data

Dynamic Data Is Also Implied From the X-ray B-Factor (temperature factor in the PDB).

Overall Poor Correlation Between NMR Dynamic Data and B-factors

1) dynamic regions may have low B-factors if stabilized by an interaction not present in solution2) low dynamic regions may have high B-factors due to resolution issues not related to dynamics – various crystal contacts, lack of uniformity in crystals, etc.

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Final thoughts?

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“NMR of Proteins and Nucleic Acids” Kurt Wuthrich

“Protein NMR Spectroscopy: Principals and Practice” John Cavanagh, Arthur Palmer, Nicholas J. Skelton, Wayne Fairbrother

“Principles of Protein Structure” G. E. Schulz & R. H. Schirmer

“Introduction to Protein Structure” C. Branden & J. Tooze

“Enzymes: A Practical Introduction to Structure, Mechanism, and Data Analysis” R. Copeland

“Biophysical Chemistry” Parts I to III, C. Cantor & P. Schimmel

“Principles of Nuclei Acid Structure” W. Saenger

Some Other Recommended Resources

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Some Important Web Sites:RCSB Protein Data Bank (PDB) Database of NMR & X-ray Structureshttp://www.rcsb.org/pdb/

BMRB (BioMagResBank) Database of NMR resonance assignmentshttp://www.bmrb.wisc.edu/

CATH Protein Structure Classification Classification of All Proteins in PDBhttp://www.biochem.ucl.ac.uk/bsm/cath/

SCOP: Structural Classification of Proteins Classification of All Structures into http://scop.berkeley.edu Families, Super Families etc.

DALI Compares 3D-Stuctures of Proteins to http://www.ebi.ac.uk/dali/ Determine Structural Similarities of New

Structures

NMR Information Server NMR Groups, News, Links, Conferences, Jobshttp://www.spincore.com/nmrinfo/

NMR Knowledge Base A lot of useful NMR linkshttp://www.spectroscopynow.com/

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Many slides have been either taken directly or adapted from the following sources:

http://www.bionmr.com/forum/educational-web-pages-16/lectures-nmr-spectroscopy-protein-structures-university-nebraska-lincoln-324/

David Cistola (Wash U)

Kevin Gardner/Carlos Amzcua (UTSW)

Or as cited