Protein NMR: Assignment Structure Dynamics

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Protein NMRAssignment Structure Dynamics
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• Cross peak proof of J coupling, i.e. of a bond

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Double Fourier Transformation
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Fourier Transformation
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The J doublet

• Each member of the doublet is treated as a
  separate magnetization vector, with its own
  precession rate.
• Note that the passive spin is in a discrete
  quantum state up or down, but never in between.
  (Stern Gerlach).

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Transfer of magnetization in the J doublet

• Initial state proton polarization or population
  difference follows its Boltzmann factor for its
  energy difference, and nitrogen follows its
  population difference follows its Boltzmann
  factor for its energy difference
• Final State nitrogen polarization or population
  difference follows the Boltzmann factor for its
  energy difference for protons 10z stronger mag
  vector!

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Selective Inversions

• Selective Inversion of one line in the doublet
  without touching the other can be accomplished
  in two very different ways.
• 1) 90 - precession until antiphase -90
• 2) weak irradiation on resonance for one line
• 1) Can be accomplished for many frequencies
  (chemica shift values) simultaneously

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HSQC

• Standard fingerprint
• Folded proteins give nicely dispersed spectra
  (each a.a. is shifted to a unique frequency)
  BOTTOM 2D 15N 1H. Empirical rules distinguish
  sheet and helix and coil (somewhat)
• Unfolded proteins in solution give non-dispersed
  lines TOP
• Data from Dr. Cheryl Arrowsmith, U. Toronto

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3D spectroscopy
Ni Cai COi,/ Cbi
Ni CO i-1 Ca i-1
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Protein Spectra Multinuclear and Site Specific

• Slice the cube at a particular 15N frequency
• Strip along a particular 1H frequency
• The 1H-15N pair of frequencies is already
  identified from the HSQC fingerprint
• Learn the 13C frequencies for Ca and Cb

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Relaxation
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How we measure relaxation
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Simple Sequence for T1 Inversion Recovery
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Simple Sequence for T2 Echo
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Case 1 Neigboring Nucleus is high energy
Splittings are due to Quantized Neighbors
S
Field due to neighbor
Applied Field
Case 2 Neigboring Nucleus is low energy
N
Field due to neighbor
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Relaxation NMR

• Molecular Motion (Tumbling or Conformation
  Change) --gt
• Change in Neighbors Dipolar Field (even if rigid
  internal structure relating the pair)--gt
• Transitions/Relaxation if Tumbling is on
  resonance with transition

U-(m0/4p)m1. m2-3(m1.R)(R. m2) (m0/2p)m1.
m23/2ltcos2qgt-1/2
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Transition Probability

• If transition is due to the field F from
  neighboring dipole (fluctuating angular relation
  between the dipoles described by unit vector R),
  then the correlation function of interest is
• Ensemble Averaged, Assumption of random motion
  with a single correlation time

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??c 3?mol.
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Saturation Recovery SQ vs DQ vs ZQ

• T1 SQ, DQ, ZQ relieve sat.
• NOE Perturbation of neighbor S Only ZQ and DQ
  are effective

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Spin-Lattice Relaxation

• Note for 500 MHz, 13C-1H pair at 1.1 A,
  correlation time of 1nsec
• R1 4 s-1

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NOE Relaxation

• ?ij K (r-6) F(?c )
• Where K (?02/2?2)(1/10) (?H4h2/4?2)
• And F(?c ) ( -?c 6?c/(14?2?c2) )
• Note for two protons at 1A, with F(?c ) 1nsec
• 57.0 sec-1.

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NOE Molecular Weight, and Relaxation

• Spectral Density is provided at all frequencies
  below the tumbling time
• Medium sized or small protein tumbling time 5ns
  (1ns/2.4 kDa)
• DQ timescale is sub-nanosecond (inactive)
• ZQ is millisecond (active) negative NOE (peak
  shrinks
• For small molecules DQ more active positive NOE
• For peptides, equally active cancellation
  condition no NOE

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• Tertiary Contacts

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Typical Correlation Times and Relaxation Mobility

• Large protein DQ timescale is sub-nanosecond
  (inactive), ZQ is millisecond (active)
• If a region (loop, terminus) has independent
  mobility it may exhibit cancellation condition.
  This is strong evidence for a rapidly moving
  segment (not necc. unstructured though)

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NOE Distance Interpretation

• Use a calibration peak (rigid proton pair)
• Assume Vk/r6 to estimate other distances
• Highly inaccurate
• Distances up to about 5A can be detected, several
  tertiary contacts per residue generally obtained