Transcript No Slide Title

Heteronuclear Relaxation and
Macromolecular Structure and Dynamics
Outline:
Note: refer to lecture on “Relaxation & nOe”
•
Information Available from Relaxation Measurements
•
Relaxation Mechanisms
•
Relaxation Rates
•
Experimental Methods
•
Data Analysis
•
Case Studies
•
1.
Fushman, D., R. Xu, et al. (1999). "Direct determination of
changes of interdomain orientation on ligation: Use of the
orientational dependence of N-15 NMR relaxation in Abl
SH(32)." Biochemistry 38(32): 10225-10230.
1.
Eisenmesser, E. Z., D. A. Bosco, et al. (2002). "Enzyme
dynamics during catalysis." Science 295(5559): 1520-1523.
1.
Lee, A. L., S. A. Kinnear, et al. (2000). "Redistribution and
loss of side chain entropy upon formation of a calmodulinpeptide complex." Nature Structural Biology 7(1): 72-77.
1.
Ishima, R., D. I. Freedberg, et al. (1999). "Flap opening and
dimer-interface flexibility in the free and inhibitor-bound
HIV protease, and their implications for function." Structure
with Folding & Design 7(9): 1047-55.
References
NMR Relaxation and Dynamics
NMR relaxation measurements provide information on structure and
dynamics at a wide range of time scales that is site specific:
S2
ti
Rex
D
kon
koff
tc
Biomolecules are not static:
• rotational diffusion (tc)
• translational diffusion (D)
• internal dynamics of backbone and sidechains (ti)
• 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)
Structure/Dynamics
Function
• Dynamics on Different Time Scales
time scale
example
experiment type
ns – ps
bond librations
reorientation of protein
motions of protein main chain
side chain rotations
(case study #2)
rapid conformational exchange
(case study #4)
lab frame relaxation
T1, T2
us – ms
ms – s
interconversion of discrete
conformations
>s
protein folding
opening of 2o structures
lineshape analysis
rotating frame relax.
T1r
magnetization exch.
exchange rates
(H/D exchange)
• Structural Information from Relaxation
• anisotropy of overall shape (case study #1)
• distance information from cross-correlation relaxation
• Thermodynamics from Relaxation
• relationship to entropy (case study #3)
Relaxation
Bloch equations – introduce relaxation to account for return of
magnetization to equilibrium state:
relax
excite
treat relaxation as a first order process:
dM/dt = gM x B – R(M-Mo)
where
1/T2 0
R=
0
0 1/T2 0
0
0 1/T1
T1 (longitudinal or spin-lattice relaxation time) is the time constant used 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.
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:
RF
photon
transition probability a 1/l3 = 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, 679712 (1948)) found that relaxation is related to molecular motion (NMR
relaxation time varied as a function of viscosity or temperature). They
postulated that relaxation is caused by fluctuating fields caused by
molecular motion.
• relaxation is dependent on motion of molecule
• Zeeman interaction is independent of molecular motion therefore “local
fields” exist that are orientation dependent and couple the magnetic
moment with the external environment (the “lattice”)
• time dependence of interaction determines how efficiently the moment
couples to the lattice
• it is the fluctuating “local fields” that induce transitions between energy
levels of spins:
source of local fields?
RF
timescale of fluctuation?
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 and
chemical shift anisotropy:
• Magnetic Dipole-Dipole Interaction - the dipolar interaction is a
through-space coupling between two nuclear spins:
q
S
rIS
I
The local field experienced by spin I is:
Hloc = gSh/r3IS ((3cos2q – 1)/2)
• Chemical Shift Anisotropy - the CSA interaction is due to the distribution of
electrons surrounding the nucleus, and the local magnetic field generated by
these electrons as they precess under the influence of the applied magnetic
field. The effective field at the nucleus is:
Hloc = Ho(1-s)
where Ho is the strength of the applied static magnetic field and s is the
orientationally dependent component of the CSA tensor.
Expressions for Relaxation Rates
The relaxation rate constants for dipolar, CSA and quadrupolar
interactions are linear combinations of spectral density functions, J(w).
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(wH-wN) + 3J(wN) + 6J(wH+wN)]
R2,N = 1/T2,N = (d2/8)[4J(0) + J(wH-wN) + 3J(wN) + 6J(wH) + 6J(wH+wN)]
NOE15N{1H} = 1 + (d2/4)(gH/gN) [6J(wH+wN) - J(wH-wN)] x T1,N
where d = (gHgN(h/8p)/rHN3)
The J(w) terms are “spectral density” terms that tell us what frequency of
motions are going to contribute to relaxation. They have the form
J(w) = tc/(1+w2tc2)
and allow the motional characteristics of the system (the correlation time
tc) to be expressed in terms of the “power” available for relaxation at
frequency w:
tc =10-7
J(w)
tc =10-8
tc =10-9
106
107
108
109
1010
w
Measurement of Relaxation Rates
• spin lattice relaxation is measured using an inversion recovery
sequence:
180
t
I
It = Io(1-2exp(-t/T1))
t
• spin-spin relaxation is measured using a “spin echo” sequence
(removes effect of field inhomogeneity):
90
t
180
t
I
It = Ioexp(-t/T2)
t
Measurement of Relaxation Rates
The inversion-recovery sequence and spin-echo sequence can be
incorporated into a 2D 1H-15N HSQC pulse sequence in order to measure
15N T and T for each crosspeak in the HSQC:
1
2
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.
Data Analysis
Analysis of the relaxation data provides dynamical parameters (amplitude
and timescale of motion) for each bond vector under study and parameters
related to the overall shape of the molecule (rotational diffusion tensor):
Dynamical parameters in proteins.
(a) Overall rotational diffusion of the molecule is represented using an axially
symmetric diffusion tensor for an ellipsoid of revolution. The diffusion
constants are D|| for diffusion around the symmetry axis of the tensor and
Dperp. for diffusion around the two orthogonal axes. For isotropic rotational
diffusion, D|| = Dperp.. The equilibrium position of the ith N-H bond vector is
located at an angle qi with respect to the symmetry axis of the diffusion tensor.
Picosecond-nanosecond dynamics of the bond vector are depicted as
stochastic motions within a cone with amplitude characterized by S 2 and time
scale characterized by te.
(b) The value of S2 is graphed as a function of (-) qo calculated using Equation
22 for diffusion within a cone or (- - -) sf calculated using Equation 23 with
q= 70.5° for the GAF (Gaussian Axial Fluctuation) model.
from: Palmer, A. G. (2001). “NMR probes of molecular dynamics: Overview
and comparison with other techniques.” Annual Review of Biophysics and
Biomolecular Structure 30: 129.
Data Analysis
“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:
• internal correlation time, te
• spatial restriction of motion of bond vector, S 2
S2 = 1 highly restricted
S2 = 0 no restriction
• Rex, exchange contribution to T2
tc
Rex,S2,te
15N
1H
The spectral density terms in the relaxation equations are modified with
terms representing internal dynamics and spatial restriction of bond
vector:
J(w) ~ { S2tc/(1+w2tc2) + (1-S2)t/(1+w2t2) }
where t = tetc/(te + tc).
Analysis of relaxation data using software package (eg. Model-Free or
DASHA) allows the dynamical parameters to be calculated:
measure:
15N T
1
15N T
2
15N{1H} NOE
calculate
relaxation
data for a
given tc
recalculate
by varying
values of S2,
te and Rex
Compare
measured
vs. calc.
value
Defining Regions of Structure using NMR Relaxation Measurements
Case study #1
Red indicates chemical shift
changes observed upon ligand
binding
Case study #2
Case study #3
Case study #4
goal: measure effects of inhibitor
binding on conformational fluctuations
of HIV protease on ms-ms timescale.
sample: 0.3mM protease dimer +
DMP323 inhibitor
experiments: 1H and 15N T2 and T1r
at 500MHz
result: inhibitor binding enhances
dyanamics on the ms timescale of
the b-sheet interface, a region that
stabilizes the dimeric structure of
the protease (residues 95-98).
Relaxation behavior of the flap
(residues 48-55) indicates a
transition from a slow dynamic
equilibrium between semi-open
conformations on the 100ms
timescale to a closed conformation
upon inhibitor binding.
References
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.
Brutscher, B. (2000). “Principles and applications of cross-correlated relaxation in
biomolecules.” Concepts in Magnetic Resonance 12(4): 207.
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.
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.
Cavanagh, J., W. J. Fairbrother, A. G. Palmer and N. J. Skelton (1996). Protein
NMR Spectroscopy: Principles and Practice, Academic Press.
Chapter 5 “Relaxation and Dynamic Processes”
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: 220257.
Mini Reviews:
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.
Case Studies:
Fushman, D., R. Xu, et al. (1999). "Direct determination of changes of interdomain
orientation on ligation: Use of the orientational dependence of N-15 NMR
relaxation in Abl SH(32)." Biochemistry 38(32): 10225-10230.
Eisenmesser, E. Z., D. A. Bosco, et al. (2002). "Enzyme dynamics during
catalysis." Science 295(5559): 1520-1523.
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.
Ishima, R., D. I. Freedberg, et al. (1999). "Flap opening and dimer-interface
flexibility in the free and inhibitor-bound HIV protease, and their implications for
function." Structure with Folding & Design 7(9): 1047-55.