NMR Analysis of Protein Dynamics

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NMR Analysis of Protein Dynamics
Despite the Typical Graphical Display of Protein
Structures, Proteins are Highly Flexible and
Undergo Multiple Modes Of Motion Over a Range of
Time-Frames
DSMM - Database of Simulated Molecular
Motions http//projects.villa-bosch.de/dbase/dsmm/

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NMR Analysis of Protein Dynamics
Typical Time Regions For Molecular Motion
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NMR Analysis of Protein Dynamics

• Multiple Signals for Slow Exchange Between
  Conformational States
• Two or more chemical shifts associated with a
  single atom/nucleus

Populations relative stability
Rex lt w (A) - w (B)
Exchange Rate (NMR time-scale)

• Factors Affecting Exchange
• Addition of a ligand
• Temperature
• Solvent

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NMR Analysis of Protein Dynamics
k p Dno2 /2(he - ho)
k p Dno / 21/2
k p (Dno2 -  Dne2)1/2/21/2
k p (he-ho)
k exchange rate n peak frequency h
peak-width at half-height e with exchange o
no exchange
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NMR Analysis of Protein Dynamics

• For Protein Samples, Typically Monitor Exchange
  Using 2D NMR Experiments
• Need resolution and chemical shift dispersion to
  identify exchange peaks
• presence of slow exchange effectively increases
  the number of expected peaks based on the
  sequence
• typically in the range of milusecond to second
  time range

Expanded Region of 2D 1H-15N HSQC Showing Major
and Minor Conformational Exchange Peaks
Biochem. J. (2002) 364, 725737
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NMR Analysis of Protein Dynamics

• As We Have Seen Before, Line-Widths Are
  Indicative of Overall Tumbling Times of the
  Molecule
• Rotational Correlation Time (tc)
• related to MW
• time it takes a molecule to rotate one radian
  (360o/2p)
• typically in the nanosecond time range

where r radius k Boltzman constant h
viscosity coefficient
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NMR Analysis of Protein Dynamics

• The MW of the Protein Would Imply an Expected NMR
  Line-Widths
• Broader than expected line-widths in the 2D
  1H-15N HSQC may imply
• multimer formation (dimer, tetramer, etc)
• aggregation
• unfolded/denatured

Can estimate tc for a spherical protein tc
MW/2400 (ns)
Barstar pH 6.8
Barstar pH 2.7
Biochemistry, Vol. 41, No. 31, 2002
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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), 4983-993.
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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

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NMR Analysis of Protein Dynamics

• Hydrogen-Deuterium Exchange
• Can measure exchange rates for NHs with fast
• exchange using using inversion/exchange
• fast exchanging NHs do not exhibit a
• crosspeak in the first 1H-15N HSQC after
• exchange into D2O

Exchange between H2O and NHs were observed by
selective inversion of H2O signal followed by
exchange build-up (t) and monitored by a 2D
1H-15N HSQC
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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

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NMR Analysis of Protein Dynamics

• Quantifying Protein Dynamics From NMR Data
• T1 and T2 relaxation and the NOE are related to
  dynamics
• correlated to the rotational correlation time of
  the protein

Biochemistry, Vol. 28, No. 23, 1989
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NMR Analysis of Protein Dynamics

• Quantifying Protein Dynamics From NMR Data
• T1, T2 and the NOE defined in terms of spectral
  density function
• total power available for relaxation is the
  total area under the spectral density function

where
rAX 1H-15N bond distance Ho magnetic field
strength - 15N chemical shift
tensors
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NMR Analysis of Protein Dynamics

• Quantifying Protein Dynamics From NMR Data
• For a Protein in Solution, J(wi) depends on
• overall motion of the protein as a whole
• internal motion of the 1H-15N bond vector

Lipari-Szabo Model-Free Formulism
t-1 te-1 tm-1
where tm is the overall motion of the protein
te is the 1H-15N internal motion S2 is the
spatial restriction of internal motion (order
parameter)
If the internal motion is very rapid, te
approaches zero. If the internal motion is not
present, S2 approaches one.
Sometimes it is necessary to add an exchange
contribution (Rex) to the predicted R2 (T2) to
account for the experimentally observed R2
Journal of Biomolecular NMR, 18 83100, 2000.
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NMR Analysis of Protein Dynamics

• Quantifying Protein Dynamics From NMR Data
• For a Protein in Solution, J(wi) depends on
• overall motion of the protein as a whole
• internal motion of the 1H-15N bond vector

Extended Model-Free Approach
t-1 te-1 tm-1
where tm is the overall motion of the protein
te is effective correlation time for the slow
motion Sf2 is the order parameter for fast
internal motion Ss2 is the order parameter for
slow internal motion
The effective correlation time for the fast
motion is assumed to be zero.
Sometimes it is necessary to invoke internal
motions on two widely different time scales
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NMR Analysis of Protein Dynamics

• Quantifying Protein Dynamics From NMR Data
• T1, T2 and NOE can then be described in terms
  of
• order parameters (S2, Ss2, Sf2)
• correlation time (tm,te)

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NMR Analysis of Protein Dynamics

• Quantifying Protein Dynamics From NMR Data
• If you assume the only motion present in the
  protein is the overall molecular tumbling then
• spectral density function is only dependent on
  S2 and tm
• correlation time can then be determined from the
  ratio of experimental T1/T2 ratios
• determined by minimizing the difference between
  the left and right side of the following
• equation for each T1/T2 pair for each residue
  in the protein.
• ModelFree software program generally used to
  analyze NMR T1,T2 and NOE data to
• extract dynamic parameters (tm,te,S2,Sf2,Ss2)

Mandel, A. M.,Akke, M. Palmer, A. G. (1995) J.
Mol. Bio 246, 144-163. Palmer, A. G.,Rance, M.
Wright, P. E. (1991) J. Am. Chem. Soc. 113,
4371-4380.
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NMR Analysis of Protein Dynamics

• Quantifying Protein Dynamics From NMR Data
• Given the overall rotational correlation time tm
  for the protein, can determine how well each
• residues T1,T2 and NOE data can be explained
  by only this motion
• Does the data fit better by adding
• exchange (Rex)
• single internal motion (te)
• fast (Sf2) and slow (Ss2,te) internal motion
• Using ModelFree, tm and the individual T1,T2 and
  NOE data calculate dynamic parameters
• for each residue in the protein.

Relationship between S2 and the angle (q) between
the bond vector (m) and the cone the bond vector
traces. Smaller q angle ? smaller motion ?
larger S2 Larger q angle ? larger motion ?
smaller S2
nature structural biology volume 7 number 9
september 2000
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NMR Analysis of Protein Dynamics

• Quantifying Protein Dynamics From NMR Data
• Model for system with two distinct internal
  motions
• motions on time scale of lt20-50 ps and 0.5-4 ns
• slower motion is represented by a jump between
  two states (i and j)
• faster motion is represented as free diffusion
  within two axially symmetric cones centered
• about the two I and j states
• qof is the semiangle of the cone
• f is the angle between the NH vectors in the two
  states (i and j)

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NMR Analysis of Protein Dynamics

• How Do We Measure T1, T2 and NOE data For a
  Protein?
• Modified 2D 1H-15N HSQC Spectra
• Standard 1D T1, T2, and NOE experiments are
  incorporated into the HSQC experiment

T1 experiment generate Z magnetization that
relaxes as exp(-T/T1)
T2 experiment generate XY magnetization that
relaxes as exp(-T/T2) with re-focusing of field
inhomogeniety (CPMG)
NOE experiment data sets are collected
with/without 1H presaturation. NOE is measured
from the ratio of the peak intensity in the two
experiments.
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NMR Analysis of Protein Dynamics
Typical T1 and T2 data For a Protein
Biochemistry 1990, 29, 7387-7401
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NMR Analysis of Protein Dynamics
Typical Quality of Fits for T1 and T2 2D 1H-15N
HSQC Data
Positive (A) and Negative (B) contours for NOE
data - negative NOEs indicate highly mobile
residues
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NMR Analysis of Protein Dynamics
Experimental parameters plotted as a function of
sequence
Calculated order parameters (S2) as a function of
sequence. Regions of high mobility are inferred
from low S2 values
Residues with exchange contribution (Rex) to T2 ?
slow conformational exchange (msec to sec)
Residues that exhibit fast internal motions (te)
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NMR Analysis of Protein Dynamics
Difference in calculated NOEs between models with
one and two internal motions
Calculated fast (Sf2) and slow (Ss2) order
parameters for residues exhibiting both a fast
(ps) and slow (ns) internal motion
Slow internal motions (ts) for residues
exhibiting both fast and slow internal motion (te
0)
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NMR Analysis of Protein Dynamics
In general, regions of secondary structure show
low mobility while turns, loops and N-,C-terminus
exhibit high mobility
PNAS 2002 vol. 99 no. 21 13560-13565
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NMR Analysis of Protein Dynamics

• Quantifying Protein Dynamics From NMR Data
• Using Residual Dipolar Coupling (RDC) Constants
  to Measure Protein Dynamics
• RDCs are conformationally averaged
• uses 11 different alignment media combined with
  molecular dynamics simulation

J. AM. CHEM. SOC. 9 VOL. 124, NO. 20, 2002