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COURSE#1022: Biochemical Applications of NMR Spectroscopy
http://www.bioc.aecom.yu.edu/labs/girvlab/nmr/course/
Heteronuclear Relaxation and
Macromolecular Structure and Dynamics
LAST UPDATE: 4/16/2010
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References
Cavanagh, J., W. J. Fairbrother, A. G. Palmer and N. J. Skelton (2007).
Protein NMR Spectroscopy: Principles and Practice, Academic Press.
Chapter 5 Relaxation and Dynamic Processes
Chapter 8 Experimental NMR Relaxation Measurements
Palmer, A. G. and F. Massi (2006). "Characterization of the dynamics
of biomacromolecules using rotating-frame spin relaxation NMR
spectroscopy." Chemical Reviews 106(5): 1700-1719.
Igumenova, T. I., K. K. Frederick and A. J. Wand (2006).
"Characterization of the fast dynamics of protein amino acid side chainsusing NMR relaxation in solution." Chemical Reviews 106(5): 1672-
1699.
Jarymowycz, V. A. and M. J. Stone (2006). "Fast time scale dynamics
of protein backbones: NMR relaxation methods, applications, and
functional consequences." Chemical Reviews 106(5): 1624-1671.
Palmer, A. G. (2001). NMR probes of molecular dynamics: Overview
and comparison with other techniques. Annual Review of Biophysics
and Biomolecular Structure 30: 129.
Palmer, A. G., C. D. Kroenke and J. P. Loria (2001). Nuclear magnetic
resonance methods for quantifying microsecond-to-millisecond motions
in biological macromolecules. Nuclear Magnetic Resonance of
Biological Macromolecules, Pt B 339: 204.
Engelke, J. and H. Ruterjans (1999). Recent Developments in Studying
the Dynamics of Protein Structures from 15N and 13C Relaxation Time
Measurements. Biological Magnetic Resonance. N. R. Krishna and L. J.
Berliner. New York, Kluwer Academic/ Plenum Publishers. 17: 357-
418.
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Fischer, M. W. F., A. Majumdar and E. R. P. Zuiderweg (1998).
Protein NMR relaxation: theory, applications and outlook. Progress in
Nuclear Magnetic Resonance Spectroscopy 33(4): 207-272.
Daragan, V. A. and K. H. Mayo (1997). Motional Model Analyses of
Protein and Peptide Dynamics Using 13C and 15N NMR Relaxation.
Progress in Nuclear Magnetic Resonance Spectroscopy 31: 63-105.
Nicholson, L. K., L. E. Kay and D. A. Torchia (1996). Protein
Dynamics as Studied by Solution NMR Techniques. NMR
Spectroscopy and Its Application to Biomedical Research. S. K. Sarkar.
Peng, J. W. and G. Wagner (1994). Investigation of protein motions
via relaxation measurements. Methods in Enzymology 239: 563-96.
Wagner, G., S. Hyberts and J. W. Peng (1993). Study of Protein
Dynamics by NMR. NMR of Proteins. G. M. Clore and A. M.
Gronenborn, CRC Press: 220-257.
Mini Reviews:
Akke, M. (2002). "NMR methods for characterizing microsecond to
millisecond dynamics in recognition and catalysis." Current Opinion in
Structural Biology 12(5): 642-647.
Ishima, R. and D. A. Torchia (2000). Protein dynamics from NMR.
Nature Structural Biology 7(9): 740-743.
Kay, L. E. (1998). Protein dynamics from NMR. Nature Structural
Biology 5: 513-7.
Palmer, A. G., 3rd (1997). Probing molecular motion by NMR.
Current Opinion in Structural Biology 7(5): 732-7.
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Biomolecules are not static it is often Structure AND
Dynamics that determine Function:
rotational diffusion (c) translational diffusion (D)
internal dynamics of backbone and sidechains (i) degree of order for backbone and sidechains (S2)
conformational exchange (Rex)
interactions with other molecules (kon,koff)
Biomolecules are often not globular spheres:
anisotropy (Dxx,Dyy,Dzz)
All of these parameters are accessible through NMR
measurements
c
S2iRex
D
kon
koff
Types of Motion Involved in Dynamics
NMR relaxation measurementsprovide information on dynamics at a
wide range of time scales that issite specific:
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time scale example experiment type
ns ps bond librations lab frame relaxation
reorientation of protein T1, T2motions of protein backbonefast side chain rotations
us ms rapid conformational exchange lineshape analysis
rotating frame relax. (T1)
ms s interconversion of discrete magnetization exch.
conformations lineshape analysis
> s slow protein folding exchange rates
opening of 2o structures (H/D exchange)
Nuclei used to Report Protein/Nucleic Acid Dynamics Site
Specifically1H 15N 13C 2H 31P
Dynamics on Different Time Scales can be
Probed by Various NMR Experiments and Parameters
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Structural Information from Relaxation
anisotropy of overall shape
distance information from cross-correlation relaxation
Thermodynamics from Relaxation
relationship to entropy and binding events
Function from Relaxation
binding sites for protein ligand interactions
binding interfaces for protein protein interactions
Importance of NMR relaxation measurements is underscored by
number of publications:
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NMR Relaxation
Bloch equations introduce relaxation to account for return of
magnetization to equilibrium state:
excite
relax
treat relaxation as a first order process:
dM/dt = M x BR(M-Mo)
where
T1 (longitudinal or spin-lattice relaxation time) is the time constantused to describe rate at which Mz component of magnetization returns to
equilibrium (the Boltzman distribution) after perturbation.
T2 (transverse or spin-spin relaxation time) is the time constant used
to describe rate at which Mxy component of magnetization returns to
equilibrium (completely dephased, no coherence) after perturbation.
R =
1/T2 0 0
0 1/T2 0
0 0 1/T1
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so far, all we have is a time constant; is it possible to get a picture of
what is causing relaxation?
consider spontaneous emission of photon:
transition probability 1/3 = 10-20 s-1 for NMR
consider stimulated emission:
the excited state couples to the EMF inducing transitions this
phenomenon is observed in optical spectroscopy (eg. lasers) but
its effect is negligible in RF fields.
in a historic paper, Bloembergen, Purcell and Pound (Phys. Rev. 73,
679-712 (1948)) found that relaxation is related to molecular motion
they found that the NMR relaxation time varied as a function of
viscosity or temperature
they postulated that relaxation is caused by fluctuating fields
caused by molecular motion.
RF photon
NMR Relaxation, cont.
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In other words, relaxation is dependent on motion of
molecule
Zeeman interaction is independent of molecular motion
therefore local fields must exist that are orientation
dependent and can causes relaxation:
fluctuating local fields create an oscillating field that inducetransitions between energy levels of spins
time dependence of interaction determines how efficiently
relaxation occurs
RF
source of local fields?
timescale of fluctuation?
NMR Relaxation, cont.
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Some Relaxation Mechanisms
The relaxation of a nuclear spin is governed by the fluctuations of
local fields that result when molecules reorient in a strong external
magnetic field. Although a variety of interactions exist that can give rise
to a fluctuating local field, the dominant sources of local fields
experienced by 15N and 13C nuclei in biomolecules are dipole-dipole
interactions andchemical shift anisotropy:
Magnetic Dipole-Dipole Interaction - the dipolar interaction is a
through-space coupling between two nuclear spins:
I
S
rIS
The local field experienced by spin I is:
Hloc = Sh/r3IS ((3cos2 1)/2)
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Some Relaxation Mechanisms, cont.
Chemical Shift Anisotropy (CSA) - the chemical shift is due, in part,
to the distribution of electrons surrounding the nucleus and the local
magnetic field generated by these electrons as they precess under theinfluence of the applied magnetic field. The effective field at the
nucleus is:
Hloc = Ho(1-)where Ho is the strength of the applied static magnetic field and is the
orientationally dependent component of the CSA tensor . The CSA
tensor determines how much the chemical shift varies with respect to
the orientation of the nucleus within the magnetic field the larger
the CSA, the larger the CSA relaxation.
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Some Relaxation Mechanisms, cont.
In contrast to the case of the dipole-dipole interactions, the CSA
interaction constant depends on the strength of the static magnetic
fieldB0. As a consequence, the contribution of the CSA to the relaxation
rates increases with the increase of the static magnetic field strength.
Some CSA values of nuclei found in proteins:
13C_CSA PROTEIN Cb ~32ppm
13C_CSA PROTEIN Ca 46.5ppm
13C_CSA PROTEIN CO 130ppm
15N_CSA PROTEIN N -163ppm
1H_CSA PROTEIN HN -8.9ppm
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The additional broadening seen
in signals characterized by
exchange is given by the Rexterm
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Expressions for Relaxation Rates
The relaxation rate constants for dipolar, CSA and quadrupolar
interactions are linear combinations of spectral density functions, J().
For example, one can derive the following equations for dipolar
relaxation of a heteronucleus (i.e. 15N or 13C) by a proton
R1,N = 1/T1,N = (d2/4)[J(H-N) + 3J(N) + 6J(H+N)]
R2,N = 1/T2,N = (d2/8)[4J(0) + J(H-N) + 3J(N) + 6J(H) +
6J(H+N)]NOE15N{1H} = 1 + (d
2
/4)(H/N) [6J(H+N) - J(H-N)] x T1,Nwhere d = (HN(h/8)/rHN
3)
The J() terms are spectral density terms that tell us what frequency of
motions are going to contribute to relaxation. They have the form
J() = c/(1+2c2)and allow the motional characteristics of the system (the correlation
time c) to be expressed in terms of the power available for relaxationat a given frequency :
J()
107 108 109 1010
c=10 7
c=10 8c=10 9
NOTE: maximum at J(=108) term occurs
when c=10-8; motions most efficient for
inducing relaxation are c = 1/
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15N Dipolar Relaxation Time as a Function of
Correlation Time
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The Heteronuclear nOe as a
Function of Correlation Time
e.g. 15N {1H}
Without NOE
S = AS = A00 =1=1
S =S =AA00+NOE=+NOE= --44
NOENOEmaxmax2 5
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Measurement of Relaxation Rates
spin lattice relaxation (T1) is measured using an inversion recovery
sequence:
180
I
I = Io(1-2exp(-/T1))
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Measurement of Relaxation Rates
spin-spin relaxation (T2) is measured using a spin echo sequence
(removes effect of field inhomogeneity):
90 180
I = Ioexp(-/T2)
I
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Measurement of Relaxation Rates, cont.
The inversion-recovery sequence and spin-echo sequence
can be incorporated into a 2D1
H-15
N HSQC pulse sequencein order to measure 15N T1 and T2 for each crosspeak in the
HSQC:
Experimental techniques for 15N (a) R1, (b) R2, and (c) {1H}15N NOE
spin relaxation measurements using two-dimensional, proton-detected
pulse sequences. R1 and R2 intensity decay curves are recorded by
varying the relaxation period T in a series of two dimensional
experiments. The NOE is measured by recording one spectrum with
saturation of 1H magnetization and one spectrum without saturation.
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Measurement of Relaxation Rates, cont.
Example 2D 1H-15N spectra recorded with the pulse sequence used to
measure 15N T1 and corresponding decay curves:
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Sample Output from 15N Relaxation
Meaurements
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Model Free analysis of relaxation based on Lipari, G. and A. Szabo
Model-Free Approach to the Interpretation of Nuclear Magnetic
Resonance Relaxation in Macromolecules. 1. Theory and Range of
Validity. Journal of the American Chemical Society 104: 4546 (1982).
Internal dynamics characterized by:
spatial restriction of motion of bond vector, S2
S2 = 1 highly restricted
S2 = 0 no restriction
internal correlation time, e Rex, exchange contribution to T2
Data Analysis
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The spectral density terms in the relaxation equations are modified
with terms representing internal dynamics and spatial restriction of
bond vector:
The T1, T2 and NOE can then be described in terms of the order
parameter (S2) and the correlation times (m,e). Analysis of relaxation
data using software package (eg. Model-Free or DASHA) allows the
dynamical parameters to be calculated:
measure:15N T115N T215N{1H} NOE
calculate
relaxation
data for a
given m
recalculate
by varying
values of S2,e and Rex
Compare
measured
vs. calc.
value
Data Analysis, cont.
Lipari-Szabo Model-Free Formulism
where: m is the overall motion of the protein
e is the1H-15N internal motion
S2 is the spatial restriction of internal motion (order parameter)
-1 = e-1 + m
-1
If the internal motion is very rapid, e approaches zero.
If the internal motion is not present, S2 approaches one.
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Sample Output from 15N Relaxation Analysis
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Example: Using Dynamics to Probe the
Origin of Structural Uncertainty
15N relaxation measurements
show if high RMSD is due to
high flexibility (low S2) or lack
of structural restraints (few
nOes)
Strong correlation
Weak correlation
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Ribbon diagram of calbindin D9k (PDB file 2BCA).
The N-terminal (left) and C-terminal (right) EF
hand motifs are orange and green, respectively,
with the calcium-binding loops within these motifs
red and blue, respectively. Atoms involved in
calcium coordination are shown in stick
representation.
- Calbindin D9k is a small protein that contains a pair of calcium-binding
EF-hand motifs and is involved in the intracellular buffering of calcium
ions.
- observed that Ca2+-binding to site I reduces the mobility of both Ca2+-
binding motifs (i.e. site I and II) compared with the apo state
- Hypothesized that the long-range structural and dynamic changes
induced by binding of the first Ca2+
ion lowers the free energy cost forsubsequent structural reorganization during the second binding step
consistent with observed cooperativity of calcium binding.
Akke, M., N. J. Skelton, J. Kordel, A. G. Palmer and W. J. Chazin (1993). "Effects of Ion Binding on
the Backbone Dynamics of Calbindin D9k Studied determined by 15N NMR Relaxation."
Biochemistry 32: 9832-9844.
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Example: Determining Domain Orientation in
Macromolecules Using 15N Relaxation
Dependence of the observed 15N T1/T2ratio on the anglebetween the NH
bond vectors and the unique axis of the
diffusion tensor
Tjandra, N., D. S. Garrett, et al. (1997). "Defining long range order in NMR structure
determination from the dependence of heteronuclear relaxation times on rotational diffusion
anisotropy." Nature Structural Biology 4(6): 443-9.
The observed 15N T1/T2 can be used as a
restraint during structure refinement:
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Variation in the experimentally determined backbone 15NR2/R1 ratio
versus protein sequence. Vertical bars represent the data for the unligated(white) and ligated (black) SH(32) and for the free SH3 and SH2 domains
(hatching). Horizontal bars on the top indicate the location of the
individual domains in the Abl SH(32) dual domain sequence
Differences in the average levels ofR2/R1 ratio in the SH3 and SH2 parts
of the free dual domain construct, although small, indicate some degree of
interdomain flexibility in SH(32). No significant difference was observed
for the two domains in the SH(32)/ligand complex, consistent withrestriction in the interdomain flexibility expected upon binding of the
consolidated ligand.
Fushman, D., R. Xu, et al. (1999). "Direct determination of changes of interdomain orientation on
ligation: Use of the orientational dependence of 15N NMR relaxation in Abl SH(32)." Biochemistry
38(32): 10225-10230.
Using a SH3SH2 (SH32) segment from the human Abelson tyrosine
kinase, the relative orientation of the domains could be defined using 15N
T1/T2 for an unbound form and a form bound to a consolidated ligand.
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Red indicates chemical shift changes
observed upon ligand binding
Orientation dependence of relaxation data allows
positioning of domains with respect to each other.
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Example: NMR Relaxation for Characterizing
Microsecond to Millisecond Dynamics in Catalysis
Eisenmesser, E. Z., D. A. Bosco, et al. (2002). "Enzyme dynamics during catalysis."
Science 295(5559): 1520-1523.
Standard15
N T2 measurements were made for each residue in a peptidyl-prolyl cis/trans isomerase, cyclophilin A, as a function of substrate
concentration (a prolyl-containing peptide) which allows characterization
of enzyme dynamics during catalysis.
Three-state model used for this study, cyclophilin A free (E), cyclophilin
A bound to substrate (EScis) and cyclophilin A bound to product (EStrans):
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Chemical shift changes of the amide signals in CypA upon titration with
the substrate Suc-Ala-Phe-Pro-Phe-4-NA. (A) At a constant CypA
concentration of 0.43 mM, spectra were recorded at 0 mM (blue), 0.38 mM
(orange), 1.01 mM (green), and 2.86 mM (red) substrate. The signal of
R55 is progressively shifting upon addition of increasing amounts of
substrate, indicating fast conformational exchange during catalysis. The
observed chemical shifts are population-weighted averages of E and ES,
and thus shift towards the position of the ES complex with increasingamounts of substrate. In contrast, the signal of V139 is not affected by
catalysis. (B) The chemical shift differences between free CypA and in the
presence of 2.86 mM substrate were mapped onto the structure (1RMH)
with the use of a continuous color scale.
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Differential build-up of backbone 15N R2 relaxation rates allows the
behavior of residues to be associated solely with binding (for example
K82) or with binding and isomerization (for example R55):
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The catalytically essential arginine, R55, undergoes
conformational exchange on a timescale that corresponds well to
that of the catalyzed isomerization reaction, strongly suggesting
that the processes are correlated.
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Example: Changes in Side Chain Dynamics Upon
Formation of a ProteinPeptide Complex Using 2H
Relaxation of Methyl Groups
Lee, A. L., S. A. Kinnear, et al. (2000). "Redistribution and loss of side chain entropy
upon formation of a calmodulin-peptide complex." Nature Structural Biology 7(1):
72-77.
A detailed study of the complex between calcium saturated calmodulinand a peptide model of the calmodulin-binding domain of smooth muscle
myosin light chain kinase described the role of conformational entropy
changes involving side-chain motions. The backbone of calmodulin was
found to be nearly unaffected by binding, whereas the dynamics of side
chains are significantly perturbed with an overall loss of psns time scale
mobility.
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Using 2H spin relaxation methods, the degree of spatial restriction of a
given methyl group was assessed via the the model-free generalized
order parameter, S2. Values of the order parameter can range from 0 to
1, corresponding to isotropic disorder and a fixed orientation in the
molecular frame, respectively. For each generalized order parameter, acorresponding effective internal correlation time (te) was obtained.
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Comparison of the total entropic cost of binding (estimated at 146 kJ
mol-1 using relation between order parameter, S2, and entropy ) with the
total free energy change of complex formation (250 kJ mol-1) implies
considerable entropy/enthalpy compensation. The favorable enthalpic
contributions are provided by the extensive buried hydrophobic surface
that characterizes the calmodulinpeptide complex. Interestingly, despite
this global rigidification, some conserved methionine side-chains,
important for peptide recognition, exhibit significant increases in psns
time-scale motion upon binding, reflecting a re-distribution of
conformational entropy at the protein surface.
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Example: Characterizing Exchange Between the
Ground State and Excited State of a Protein Using
Rotating Frame 15N and 13C Relaxation Measurements
Mulder, F. A. A., A. Mittermaier, et al. (2001). "Studying excited states of
proteins by NMR spectroscopy." Nature Structural Biology 8(11): 932-
935.
X-ray studies of a cavity mutant of T4 lysozyme, L99A, show that thecavity is sterically inaccessible to ligand, yet the protein is able to bind
substituted benzenes rapidly. Mulder et al. used relaxation dispersion
(rotating frame relaxation) NMR techniques to kinetically and
thermodynamically characterize a transition between a highly
populated (97%, 25 C) ground state conformation and an excited state
that is 2.0 kcal mol1 higher in free energy. The residues involved
cluster about the cavity, providing evidence that the excited state
facilitates ligand entry.
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Other Topics
- Field dependence
- protein unfolding
- pressure dependence
- temperature dependence