Introduction to Biomolecular NMR

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Introduction to Biomolecular NMR
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Nuclear Magnetic Resonance Spectroscopy

• Certain isotopes (1H, 13C, 15N, 31P ) have
  intrinsic magnetic moment
• Precess like tops in magnetic field B0
• In a 600 MHz spectrometer
• protons precess at 600 MHz
• 15N nuclei precess at 60 MHz
• 13C nuclei precess at 125 MHz

w g Bo
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Creating coherence

• Unless the spins are aligned (coherent), their
  nett effect will be zero
• B0 field aligns spins M0
• B1 field rotates M0 into x-y plane
• M0 rotates at speed n in x-y plane
• Coils in x-y plane record fluctuating magnetic
  field
• B1 field must rotate about z-axis at precession
  frequency n

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1D NMR experiment
z
90y
x
pulse
Mxy
y
Free Induction Decay (FID)
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Free Induction Decay
FT ?
M
M(t) cos(w t) exp(- t/T)
w
t
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Fourier transform spectroscopy

• System resonates at many different frequencies
  (c.f. church bell)
• Excite all frequencies simultaneously using a
  hard pulse
• Frequency analyse (Fourier transform) to yield
  component frequencies

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Two major causes of decay of signal

• Spin-lattice relaxation (T1 decay)
• loss of energy by spins leads to return of M to z
  axis
• happens with time constant T1
• Loss of coherence due to dephasing (T2 decay)
• T1 gtgt T2
• T2 inversely related to homogeneity of B0
• No energy is lost during dephasing ? signal may
  be refocused

M(t) M(0) e-t / T1
M(t) M(0) e-t / T2
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NMR of proteins

• A sample of protein contains many protons
• HN proton attached to N on backbone
• Ha proton attached to Ca on backbone
• Hb proton attached to Cb on backbone (typically
  2)
• Hg proton attached to Cg on backbone
• Protons in H2O molecules (concentration 110 M as
  compared to 1mM for protein)
• Different protons precess at different
  frequencies, depending on their chemical
  environment
• s depends on the chemical shielding e.g. how
  exposed the nucleus is to the solvent or how
  close it is to a heavy atom such as C or N
• protons in water correspond to s0 (no chemical
  shielding)
• protons in the protein may have sgt0 (to the right
  of the water peak) or slt0 (to the left)
• Define a B0-independent scale
• known as ppms

w - g (1-s) B0

• wH2O - w ) / ( 106 wH2O ) s / 106

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1D NMR spectrum of a protein

• In terms of ppm scale, peaks appear at same place
  irrespective of the strength of B0
• ? larger proteins have more overlapping peaks
• But line width is independent of B0
• roughly ? T2-1
• increases with size of protein
• ? less overlap at higher field
• Also strength of signal increases with B0
• Conclusion going to higher field increases
  sensitivity and resolution

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Interactions between nuclei (couplings)

• Coupled springs
• transfer of energy back and forth
• Scalar coupling
• mediated through overlap of electronic orbitals
• through bond coupling
• useful for assigning particular peaks to
  particular protons
• determine covalent structure of the protein
  molecule
• Dipolar coupling
• results from interaction of dipolar fields of
  nuclei
• through space coupling
• useful for determining non-covalent structure
  (folded shape) of molecule

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Simplest 2D experimentCorrelation spectrOScopY
experiment
COSY pulse sequence

• Pair of coupled nuclei s1 and s2
• Record whole series of 1D experiments, each with
  a different value of t1
• Second 90 pulse transfers magnetization from s1
  to s2
• Data acquired during t2 tells us the precession
  frequency (w2) of s2
• During t1 magnetization is on s1 and therefore
  precesses at frequency w1
• initial magnitude at beginning of t2 depends on
  t1 and w1

S(t2) cos(w2t2)
S(t1,t2) cos(w1t1) cos(w2t2)
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The amplitiude of the 1D spectrum acquired during
t2 varies sinusoidally with a different frequency
as a function of the interval t1, indicating that
during t1 the magnetization is on a spin with the
corresponding frequency
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2D NMR spectrum

• Fourier transform in both t1and t2 gives S(w1,
  w2), which when plotted as contour function gives
  a peak at coordinates w1 and w2

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2D COSY spectrum

• Magnetization which stays on same nucleus during
  t1and t2 has the same frequency in both
  dimensions
• ? along the diagonal
• Magnetisation which jumps from a nucleus with
  frequency w1 during t1 to one with frequency w2
  during t2 is represented by a cross-peak at
  cooordinates (w1,w2)
• The furthest that magnetisation is able to jump
  is the distance of 3 bonds i.e
• HN - Ha
• Ha - Hb
• Hb - Hg

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COSY spectrum of a small molecule

• COSY spectrum directly confirms covalent
  structure of molecules

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TOCSYTOtal Correlation SpectroscopY

• TOCSY is an relayed extension of COSY
• uses scalar coupling
• Cross-peaks appear between all spins which can be
  connected by relaying
• Magnetisation still cant be transferred across
  peptide bond (3-bond limit still applies)
• ? amino acids still form isolated spin systems
• Useful for recognising particular amino acids

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Heteronuclear NMR

• 3-bond limit means that cross-peaks are never
  observed between protons in different amino
  acids i.e. there is no magnetization transfer
  across the peptide bond
• Magnetization can be transferred if the
  intervening nuclei are magnetic i.e. 13C and
  15N.
• This is achieved by producing the protein
  recombinantly in bacteria grown with 15N-ammonium
  chloride and 13C-glucose as the sole nitrogen and
  carbon sources respectively

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3D experiments

• The previous experiments can be extended to two
  indirect dimensions, t1 and t2
• The real time interval during which all the FIDs
  are recorded is called t3, or the direct
  dimension.
• S is a function of t1, t2, and t3 to get the
  spectrum it must be Fourier transformed inall
  three time dimensions.
• If the magnetization is on a nucleus with
  frequency w1 in t1, w2 in t2 and w3 in t3, the
  spectrum will have a peak centred at
  coordinates (w1, w2, w3)
• In 3D a peak is more like a ball

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Heteronuclear assignment experiments

• 3D HNCA experiment
• protein must be isotopically enriched with 1H,
  13C and 15N
• Peaks represented as balls in 3D space at
  coordinates corresponding to
• 1H shift of an amide proton (HN)
• 15N shift of attached N
• 13C shift of attached Ca
• At same 1H and 15N values, another peak
  corresponding to 13C shift of Ca of preceding
  residue
• makes it possible to walk along sequence to
  assign entire backbone

residue i
residue i-1
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wC
wN
wHN
Assignment of all HN, N and Ca resonances of a
pentapeptide in a HNCA spectrum by walking
along the backbone. In each case the black sphere
represents the in-residue Ca , the grey sphere
the Ca of the preceding residue
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NOE effect provides structural information

• Nuclear Overhauser Effect produces coupling
  between protons which are close in space (though
  not necessarily covalently bonded)
• NOE cross-peaks ? R-6
• ? only observed for R lt 5 Å
• NOESY is 2D experiment in which cross peak
  intensities are proportional to NOE between
  corresponding protons

NOESY spectrum of lysozyme
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Basic method for protein structure determination
by NMR

• ASSIGN all peaks using COSY-type spectra
• Identify all cross peaks between assigned
  diagonal peaks on NOESY spectra
• Convert NOESY cross-peaks to distance constraints
  between corresponding protons
• Find 3D structure which optimally satisfies
  distance constraints as well as protein
  stereochemistry

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Structure determination

• Molecular modelling with energy function
• Etotal Ecovalent geometry ENOE restraints
• Use optimisation algorithm to find molecular
  structure with lowest value of Etotal which still
  satisfies all NMR-derived distance constraints
• Generate family of structures
• Resolution generally not as good as X-ray, but
  may be better reflection of molecules in-vivo