Transcript Refinement of x-ray data - Clayton State University

Protein Structure Determination
Major Methods for Structure Determination
X-ray Crystallography
• Works with larger proteins than can be solved through traditional solution
NMR
• An excellent summary of X-ray Crystallography can be found online at:
http://www.its.caltech.edu/~heathgrp/Courses/Lectures_2014/wiener_50
3_xray.pdf
Nuclear Magnetic Resonance (NMR) spectroscopy
• Has many applications beyond just determining structures
• An excellent summary of NMR can be found online at:
https://www.cis.rit.edu/htbooks/nmr/
X-rays
•
X-rays are higher energy wavelengths of EMR used in crystallography, medical
scanning, and other applications (airport security scanning).
"X-ray applications" by Ulflund - This figure is a compilation of different images from wikimedia commons.The graph at the top I have
made myself, originaly uploaded as .Own workThe crystallography image is from File:Lysozym diffraction.png by user:Del45.The
mammography image is from File:40F MLO DMMG.png by Nevit Dilmen (talk).The CT image is from File:Ct-workstation-neck.jpg
by.The luggage scanner image is from File:Luggage screening at VTBS.JPG by user User:Mattes.. Licensed under CC BY-SA 3.0 via
Wikimedia Commons - http://commons.wikimedia.org/wiki/File:X-ray_applications.svg#mediaviewer/File:X-ray_applications.svg
Nobel History of X-ray Crystallography
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1895 - Wilhelm Röntgen, a German physicist, discovered X-rays and demonstrated
that this type of radiation could pass directly through human tissues leaving
behind images of bones. He won the Nobel Prize in Physics in 1901.
1912 – Max von Laue, another German physicist, proved that crystals could diffract
X-rays. He won the Nobel Prize in Physics in 1914.
1913 – William Henry Bragg and William Lawrence Bragg (father and son) solved
first X-ray structure, using table salt. They shared the 1915 Nobel Prize for their
pioneering efforts.
1946 – James B. Sumner discovered that proteins could be crystallized. Received
the 1946 Nobel Prize in Chemistry.
The first protein structures ever solved were myoglobin and hemoglobin. The work
was carried out by John Kendrew and Max Perutz, and together they shared the
Nobel Prize in 1962 in Chemistry.
1962 - Francis Crick, John Watson, and Maurice Wilkins received the Nobel Prize in
Physiology/Medicine for their pioneering contributions towards the understanding
of DNA, based on X-ray diffraction patterns of the DNA double helix produced by
Rosalind Franklin. Unfortunately Franklin’s contributions to the field were ignored
by the Nobel Prize committee, even though it was her data that Crick, Watson, and
Wilkins used.
http://www.projectcrystal.org/hl-xray-crystallography.html
X-ray crystallography today
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It took Kendrew and Perutz almost 20 years to solve the globin structures (Left).
Today, with a very good crystal, a protein structure can be solved in a day.
Modelling has become much more sophisticated (Right).
http://www.astbury.leeds.ac.uk/history/astbury29.htm;
http://www.bio.davidson.edu/Courses/Molbio/MolStudents/spring2010/Hua/Hemoglobin.html
Growing Protein Crystals – Hanging Drop Method
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1-2 μl of concentrated protein solution are mixed with
a more or less equal amount of reservoir solution
containing the precipitants (previously balanced with a
pH buffer).
Solution then deposited on a cover slip covering the
precipitant reservoir.
Protein/precipitant mixture in the drop is less
concentrated than reservoir solution, so water
evaporates from the drop into the reservoir.
As a result the concentration of both protein and
precipitant in the drop slowly increases
(supersaturation), and crystals may form.
http://www.xtal.iqfr.csic.es/Cristalografia/parte_07_1-en.html;
http://www.cs.cornell.edu/boom/2004sp/projectarch/appofneuralnetworkcrystallography/proteindiffraction.htm;
http://www.scienceinschool.org/2009/issue11/lysozyme;
http://www.projectcrystal.org/hl-xray-crystallography.html
X-ray Diffraction
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In a single-crystal X-ray diffraction measurement, a crystal is mounted, then
positioned at multiple selected orientations. The crystal is bombarded with a finely
focused monochromatic beam of X-rays, producing a diffraction pattern of
regularly spaced spots known as reflections.
Two-dimensional images taken at different rotations are converted into a threedimensional electron density model using Fourier transforms, combined with
chemical data known for the sample.
Poor resolution (fuzziness) or even errors may result if the crystals are too small, or
not uniform enough in their internal makeup.
http://www.cs.cornell.edu/boom/2004sp/projectarch/appofneuralnetworkcrystallography/proteindiffraction.htm
Electron Density Maps – Amino Acid Residues
Amino acid residues can produce distinctive electron density signatures at higher
resolutions (less than 2.0 Å)
Electron Density Map of GFP
Figure 4. Model of the GFP
fluorophore and its environment
superposed on the MAD-phased
electron density map at 2.2 Å
resolution. The clear definition
throughout the map allowed the
chain to be traced and side chains
to be well placed. The density for
Ser65, Tyr66 and Gly67 is quite
consistent with the dehydrotyrosine
- imidazolidone structure proposed
for the fluorophore. Many of the side
chains adjacent to the fluorophore
are labeled.
http://www-bioc.rice.edu/Bioch/Phillips/Papers/gfpbio.html
Quality Parameters Associated with X-ray Structures
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Resolution
Refinement (the R-factor)
The B-factors (temperature factors)
Model geometry (bond distances, bond
angles, Ramachandran plot)
http://www.proteinstructures.com/Experimental/Experimental/electron-density.html
Resolution of X-ray data
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Primary factor determining the accuracy of an experimental protein structure is the
resolution of the X-ray data.
Resolution: The amount of information obtained from a crystal in a protein
crystallography experiment, which for the given crystal lattice dimensions can be
described by the total number of unique diffraction intensities collected.
In the figure below of two diffraction images from two different lysozyme crystals, the left
crystal was small and did not diffract well, so the diffraction spots disappear rather
quickly, while moving from the center of the image towards its edges. On the other
hand, the image on the right comes from a better crystal. In this case the diffraction
spots continue much longer towards the edge of the image (i.e., better resolution).
PDB ID 2H1W
2.6 Å resolution
http://www-bioc.rice.edu/Bioch/Phillips/Papers/gfpbio.html
PDB ID 2H1W
1.2 Å resolution
Refinement of x-ray data: R-value vs. R-free
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Refinement (R-value) is the measure of the quality of atomic model obtained from
crystallographic data.
When solving the structure of a protein, the researcher first builds an atomic model and
then calculates a simulated diffraction pattern based on that model.
The R-value measures how well the simulated diffraction pattern matches the
experimentally-observed diffraction pattern.
A totally random set of atoms will give an R-value of about 0.63, whereas a perfect fit
would have a value of 0. Typical values are about 0.20.
Problem with R-values: The refinement process used to fit structure to the experimental
data and improve the R-value introduces bias into the process, since the atomic model
is used along with the diffraction pattern to calculate the electron density.
The R-free value is a less biased way to look at this.
R-free value: Before refinement begins, about 10% of the experimental observations
are removed from the data set. Then, refinement is performed using the remaining 90%.
The R-free value is then calculated by seeing how well the model predicts the 10% that
were not used in refinement.
For an ideal model that is not over-interpreting the data, the R-free will be similar to the
R-value. Typically, it is a little higher, with a value of about 0.26.
http://www-bioc.rice.edu/Bioch/Phillips/Papers/gfpbio.html
Refinement of x-ray data: B-factor
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The B-factors can be taken as indicating the relative vibrational motion of different parts
of the structure. Atoms with low B-factors belong to a part of the structure that is wellordered. Atoms with large B-factors generally belong to part of the structure that is very
flexible. Each ATOM record (PDB file format) of a crystal structure deposited with the
Protein Data Bank contains a B-factor for that atom.
For a B-factor of 15 Å2, the mean square displacement of an atom from its equilibrium
position is approximately 0.44 Å, and approximately 0.87 Å for a B-factor of 60 Å2.
For structures that may have more flexibility, the atoms may be in slightly different
places in each protein within the crystal, so B-factor would increase.
http://www-bioc.rice.edu/Bioch/Phillips/Papers/gfpbio.html
Refinement of x-ray data: Ramachandran Plots
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Torsion angles can be observed in disallowed regions of plot in cases when protein X-ray
structure was not properly refined.
In Ramachandran plots below, the structure on right was refined using more modern
refinement programs. Red = low-energy regions; brown = allowed regions; yellow =
generously-allowed regions and pale-yellow marks disallowed regions.
Torsion angles on the left plot do not cluster around secondary structure regions and show
wider distribution compared to plot on right. This is often observed for low resolution
structures with bad geometry. On the left plot you may also see many dots in the disallowed
regions, but almost none on the right.
http://www.proteinstructures.com/Structure/Structure/Ramachandran-plot.html
NMR Protein Structures
• Nuclei with an odd mass or odd atomic number have "nuclear spin" (in a
similar fashion to the spin of electrons). This includes 15N, 1H and 13C
(but not 12C). Nuclear spins are sufficiently different that NMR
experiments can be sensitive for only one particular isotope of one
particular element. The NMR behavior of 1H and 13C nuclei has been
exploited by organic chemist since they provide valuable information that
can be used to deduce the structure of organic compounds.
• Isotopes with 0 spin are not visible to NMR.
• 2H and 1H have different spin signals. 2H added to protein samples and
used to stabilize field strength and reduce noise from 1H in aqueous
solvents.
http://www.chem.ucalgary.ca/courses/350/Carey5th/Ch13/ch13-nmr-1.html; http://www.nucleonica.net/wiki/index.php?title=Spin
Application of External Magnetic Field
Isotropic thermal
equilibrium – No external
magnetic field
Anisotropic equilibrium in
applied external magnetic
field
Spinning nuclei produce magnetic fields (like bar magnets). In the absence of a
magnetic field, these are randomly oriented but when a field is applied they line up
parallel or antiparallel to the applied field. The more highly populated state is the lower
energy spin state parallel.
http://www.chem.ucalgary.ca/courses/350/Carey5th/Ch13/ch13-nmr-1.html
β or ENERGY
ΔE = hν
Boltzmann Distribution of Nuclear Spin States
α or +
When a group of spins is placed in a
magnetic field, each spin aligns in one of
the two possible orientations. At room
temperature, the number of spins in the
lower energy level, N+, slightly
outnumbers the number in the upper
level, N-. Boltzmann statistics tells us that
N-/N+ = e-E/kT
= 10,000/10,001
E is the energy difference between the spin states; k is Boltzmann's constant,
1.3805x10-23 J/Kelvin; and T is the temperature in Kelvin.
As T decreases, so does the ratio N- /N+. As T increases, the ratio approaches
one.
The NMR signal results from difference between E absorbed by N+ spins
transitioning to higher energy state, and E emitted by the N- spins which
simultaneously transition to lower energy state. The signal is thus proportional to
the population difference between the states. It is the resonance, or exchange of
energy at a specific frequency between the spins and the spectrometer, which
gives NMR its sensitivity.
https://www.cis.rit.edu/htbooks/nmr/inside.htm
Spin Packets and Net Magnetization
Net Magnetization
Anisotropic equilibrium in
applied external magnetic
field
+
+
+
+
Bo
+
+
+
https://www.cis.rit.edu/htbooks/nmr/inside.htm
+
A spin packet is a group of spins
experiencing the same magnetic field
strength.
Each spin packet is described by a
vector. The strength of each vector is
proportional to N+ - N-.
The sum of these vectors describes the
net magnetization.
At equilibrium, the net magnetization
vector lies along the direction of the
applied magnetic field Bo and is called the
equilibrium magnetization Mo. In this
configuration, the Z component of
magnetization MZ equals Mo. MZ is
referred to as the longitudinal
magnetization. There is no transverse
(MX or MY) magnetization here.
Application of RF field
Bo
Net Magnetization
+
ΔE = hν
+
+
+
RF
+
+
Following RF pulse,
particles precess
around BO
ν = γB = Larmour frequency
γ = gyromagnetic ratio
B = applied magnetic field strength
μ
+
μ = nuclear magnetic
moment
Longitudinal Relaxation – T1
• By exposing the nuclear spin system to energy (RF pulse) of a frequency
equal to the energy difference between the spin states (Larmor
frequency), it is possible to saturate the spin system and make MZ=0.
• Longitudinal relaxation is the time for M0 to return to maximum
equilibrium along Z axis after displacement (e.g., after RF pulse is turned
off).
Mz = Mo ( 1 - e-t/T1 )
90° PW
Mz = Mo ( 1 - 2e-t/T1 )
180° PW
Mo
RF
Mo
90° PW
Bo
X
Y
180° PW
Z
X
Y
Z
Transverse Magnetization and T2 relaxation
• If the net magnetization is placed in the XY plane it will rotate about the Z
axis at a frequency equal to the frequency of the photon which would
cause a transition between the two energy levels of the spin (Larmor
frequency).
• Net magnetization also starts to dephase because each of the spin packets
experience a slightly different magnetic field and rotate at different
Larmor frequencies (out of phase with rotating frame of reference).
RF
Mo
Mo
Bo
Dephasing
X
Y
Z
X
Y
Z
T1 and T2 processes occur simultaneously
Mz = Mo ( 1 - e-t/T1 )
Mo
T1
MXY =MXYo e-t/T2
T2
X
Y
Z
T1 ≥ T2
NMR Chemical Shifts
Chemical Shift
•An NMR spectrum is a plot of the radio frequency applied against absorption.
•A signal in the spectrum is referred to as a resonance.
•The frequency of a signal is known as its chemical shift, d
The chemical shift in absolute terms is defined by the frequency of the resonance
expressed with reference to a standard compound which is defined to be at 0 ppm.
The scale is made more manageable by expressing it in parts per million (ppm) and
is independent of the spectrometer frequency.
http://www.chem.ucalgary.ca/courses/350/Carey5th/Ch13/ch13-nmr-2.html
Chemical Shift Anisotropy (CSA)
• Chemical shifts arise from electronic shielding
of the nucleus
– shielding depends on orientation of the
molecule with respect to B0
– the orientation dependent chemical shift
differences or range is called the CSA
– in solution, rapid reorientation results in
averaging of the chemical shift
• Rapid molecular reorientation results in local,
fluctuating magnetic fields (magnitude and
direction)
– these local fluctuating fields lead to
energy level transitions, just like applied
fields
RF
ee-
+
e-
Shielding
RF
e-
+
ee-
Deshielding
Protein NMR
1D 1H NMR is very useful for organic compounds and other small molecules,
but has limited applications for proteins due to the large number of chemical
shifts that overlap.
1D 1H NMR Spectrum for L-valine
1D 1H NMR Spectrum for Vam7p protein
• Proteins are generally too large for us to determine their structures using 1D
1H and 13C NMR techniques.
• Instead we use a variety of 2D and 3D NMR techniques to determine protein
structure.
2D Protein NMR Techniques
2D NMR spectroscopy is a set of methods which provide data
plotted in a space defined by two frequency axes rather than
one.
Several 2D methods are widely used for the structure
determination of proteins with a mass of up to 10 kD.
Homonuclear through-bond correlation methods:
• 2D COSY
• 2D TOCSY
Heteronuclear through-bond correlation methods:
• HSQC
Through-space correlation methods:
• NOESY
2D COSY Protein NMR Techniques
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2D correlation spectroscopy (COSY) is used to identify coupled spins (e.g., hydrogen
atoms on connected carbon atoms).
It consists of the following sequence: a single RF pulse (p1); evolution time (t1); a
second RF pulse (p2); a measurement period (t2).
The second pulse transfers magnetization between coupled hydrogens.
These show up as cross peaks in spectrum.
Only signals of protons which are
two or three bonds apart are visible
in a COSY spectrum. The cross signals
between HN and Halpha protons are
of special importance because the
phi torsion angle of the protein
backbone can be derived from the 3J
coupling constant between them.
http://www.cryst.bbk.ac.uk/PPS2/projects/schirra/html/2dnmr.htm; http://www.chem.ucalgary.ca/courses/350/Carey5th/Ch13/ch132dnmr-1.html; http://en.wikipedia.org/wiki/Two-dimensional_nuclear_magnetic_resonance_spectroscopy
2D TOCSY Protein NMR Techniques
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2D total correlation spectroscopy (TOCSY) correlates all protons of the spin system,
including those not directly connected via 3 chemical bonds.
This ability is achieved by
inserting a repetitive series
of pulses which
cause isotropic
mixing during the mixing
period. Longer isotropic
mixing times cause the
polarization to spread out
through an increasing
number of bonds.
http://chem.ch.huji.ac.il/nmr/techniques/2d/tocsy/tocsy.html
Analysis of HSQC Data
Comparison of chemical shifts in CaM between binding of Pb2+ and Ca2+ reveals structural changes associated
with metal binding.
6
7
8
9
E82
10
11
11
10
D80
8
9
E82
9
8
4CaCaM-NH
7
11
11
6
T28 D22
S81
10
6PbCaM-N
T26
D80
120
125
9
8
6CaCaM-NH
7
11
11
6
125
120
T28 D22
S81
115
4CaCaM-N
110
105
T26
D80
120
130
130
E82
10
9
8
6Ca2PbCaM-NH
7
6
120
115
6CaCaM-N
115
110
105
T26
D80
120
125
E82
125
T28 D22
110
115
125
E82
9
105
110
115
8
10
105
110
4PbCaM-N
7
10
105
130
130
S81
D80
6PbCaM-NH
S81
D80
6PbCaM-NH
4PbCaM-NH
7
6
6
6PbCaM-N
•
130
130
E82
125
120
115
6Ca2PbCaM-N
110
105
a
Kirberger 2013
0:1, Ca:CaM
G113
G59
G96
G96
G23
c
2:1, Ca:CaM
• Binding events alter the
kinetics of chemical shift
changes (chemical
exchange).
• We can observe changes
at different concentrations
to observe how binding
affects dynamics of the
protein, and these
changes identify where
binding occurs.
1:1, Ca:CaM
Analysis of HSQC
Data
G113
b
DTDSEEE
Fast
Intermediate
Slow
NOE (Nuclear Overhauser Effect)
• The Nuclear Overhauser Effect is the change in intensity for a signal
(resonance) when the equilibrium spin populations of a different spin are
perturbed (cross-relaxation).
• The local field at one nucleus is affected through space by nearby nuclei,
resulting in mutual modulation of resonance frequencies.
• The intensity of the interaction is represented by the following equation:
I = A(1/r6)
where I is the intensity, A is a scaling constant, and r is the distance
between the nuclei. Effect observable where r ≤ 5 Å.
Crossrelaxation
between
protons
chemistry.umeche.maine.edu/CHY431/NMR/NMR-5.html; http://tesla.ccrc.uga.edu/courses/BioNMR2005/lectures/feb2.pdf
2D NOESY Protein NMR Techniques
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In NOESY, the Nuclear Overhauser cross relaxation between nuclear spins during the
mixing period is used to establish the correlations. The spectrum obtained is similar to
COSY, with diagonal peaks and cross peaks, however the cross peaks connect
resonances from nuclei that are spatially close rather than those that are throughbond coupled to each other.
http://www.acornnmr.com/codeine/noesy.htm
3D HNCA Protein NMR Techniques
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HNCA is a 3D triple-resonance NMR experiment.
Magnetization of the amide proton of an amino acid residue is transferred to the amide nitrogen,
and then to the alpha carbons of both the starting residue (i) and the previous residue (i-1) in the
amino acid sequence.
HNCA is used with complementary HNCOCA experiment that transfers magnetization only to the
alpha carbon of the previous residue[1]. This allows for assignment of alpha carbon resonance
signals to specific residues in the protein.
Requires a purified sample of protein prepared with 13C and 15N isotopic labelling, at a
concentration greater than 0.1 mM.
The spectrum produced by this experiment has 3 dimensions: A proton axis, a 15N axis and a 13C
axis. For residue i peaks will appear at {HN(i), N(i), Calpha (i)} and {HN(i), N(i), Calpha(i-1)}, while
for the complementary HNCOCA experiment peaks appear only at {HN(i), N(i), Calpha(i-1)}.
Together, these two experiments provide information linking adjacent residues in the protein's
sequence.
http://en.wikipedia.org/wiki/HNCA_experiment
HNCA and HNCOCA Can Determine Sequence
HNCA
R
H
C
H H
CH
N
N
C
CH
H
O H
C
R
Res i-1
Res i
H
08/19/2009 1 mM apoCaM 37 °C, pH 6.5
D78 T79 D80 S81
HSQC
R
H
C
H H
CH
N
N
C
CH
H
O H
C
H
R
HNCA
R
H
C
H H
CH
N
N
C
CH
H
O H
C
H
R
Res i-1
Res i
ω1 – 1H (ppm)
E82
Why are protein dynamics important?
• Related to protein function
• Contribute to thermodynamic stability
• Dynamics also play important role in:
– Catalysis
– ligand binding
– Molecular recognition
– Allosteric protein responses
• NMR is a good tool to study these processes because
different techniques allow for analysis over a wide
range of timescales (ps to s)
Factors affecting relaxation
General Relaxation
• In general, relaxation times get longer as Bo increases because there are
fewer relaxation-causing frequency components present in the random
motions of the molecules.
• Dipolar interactions between N (or C) and H.
• Chemical Shift Anisotropy.
T1
• Inversely proportional to the density of molecular motions at the Larmor
frequency.
• Varies as a function of field strength, temperature or viscosity.
T2
• Molecular interactions can produce fluctuating fields which perturb the
energy levels of the spin states, causing the transverse magnetization to
dephase.
http://www.cis.rit.edu/htbooks/nmr/
Backbone dynamics of calmodulin by 15N relaxation
Barbato et al. used model-free approach of
Lipari and Szabo to analyze T1, T2 and NOE
relaxation data for engineered fly calmodulin
(1.5 mM CaM, 6.1 mM Ca2+, 100 mM KCl).
Pulse programs were modified to suppress
effects of cross correlation between dipolar
and chemical shift anisotropy.
S2 derived from T1, T2 and NOE data by
minimizing the following function:
f ( S 2 , e )  [(T1,calc  T1,meas ) / T1,calc ]2 
[(T2,calc  T2,meas ) / T2,calc ]2 
[( NOEmeas  NOEcalc ) / 2]2
Results indicated a high-degree of
flexibility in the central helix (residues 7781) and the helix separating EF-III and EFIV.
Barbato, G., et al., Backbone dynamics of calmodulin studied by 15N relaxation using inverse detected two-dimensional NMR spectroscopy: the central helix is
flexible. Biochemistry, 1992. 31(23): p. 5269-78.
Backbone dynamics of apo-calmodulin by 15N relaxation
Tjandra et al. used a similar approach to
analyze apo-calmodulin, but looked at several
models:
Axially symmetric model (e.g., Lipari-Szabo)
for fast internal motions
Spectral density function for internal motions
on an intermediate timescale
Results indicated apo-CaM consists of
stable secondary structure rather than
‘molten globule’.
Also suggests dumbbell model with a
flexible linker which allows two domains
diffuse freely.
Tjandra, N., et al., Rotational dynamics of calcium-free calmodulin studied by 15N-NMR relaxation measurements. Eur J Biochem, 1995. 230(3): p. 1014-24.
Application of Dynamic NMR Data
• Determine whether metals other than calcium alter
the flexibility of the central helix in calmodulin due to
binding in or near this region.
NOE Values indicate 2° structure
t = 4.00 s
RNOE
t4
( )
t0
t = 0.00 s
t4 = Integrated peak volume at 4 s
relaxation time
t0 = Integrated peak volume at 0 s
relaxation time
S2 for Ca-CaM from ModelFree
S2 > 0.8, N-H unit bond vector highlyrestricted
Ca-CaM NOE
Ca-CaM
1.6
1.4
NOE
EF-I
EF-II
Linker
EF-III
Ca-CaM NOE
EF-IV
R4/R0
1.2
1.0
0.8
0.6
0.4
0.2
1.2
1.0
1
4
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148
0.0
S2
S2
0.8
0.6
0.4
0.2
1
4
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0.0
Residue
Palmer, A. G.,Rance, M. & Wright, P. E. (1991) J. Am. Chem. Soc. 113, 4371-4380
References
• http://www.cis.rit.edu/htbooks/nmr/
• http://www.chem.queensu.ca/facilities/nmr/nmr/we
bcourse/
• http://tesla.ccrc.uga.edu/courses/bionmr/lectures/p
dfs/spin_relaxation_in_proteins_10.pdf
• Palmer, A.G., 3rd, Nmr probes of molecular dynamics:
overview and comparison with other techniques.
Annu Rev Biophys Biomol Struct, 2001. 30: p. 129-55.