Lecture RelaxationDynamics 2010

8/21/2019 Lecture RelaxationDynamics 2010

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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

Documents

Lecture RelaxationDynamics 2010