The Analysis of NMR data

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The Analysis of NMR data

• David Baird, Robyn Dynes Lester Fletcher
• AgResearch, Lincoln
• David.Baird_at_AgResearch.CO.NZ

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Nuclear Magnetic Resonance

• Electrons protons spin on their axes
• In many atoms these spins are paired against each
  other, but in some there is an overall spin due
  to unpaired particles
• 1H 13C 15N and 19F are such atoms
• Under a magnetic field the 2 spin directions
  represent different energy levels

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Energy Transitions

• If energy is absorbed by the nucleus, then the
  angle of precession, q, will change. For a
  nucleus of spin 1/2, absorption of radiation
  "flips" the magnetic moment so that it opposes
  the applied field (the higher energy state).

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Energy Gap depends on Field Strength

• The stronger the magnetic field the larger the
  energy gap
• Thus large superconducting electromagnets used

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Absorbing EM radiation causes Transition

• EM radiation absorption depends on the wavelength
• Wavelength corresponding to transition energy is
  most strongly absorbed
• When the spin swaps back the radiation is emitted

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Boltzmann Distribution
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Probing the Sample

• The chemical sample may be tested by probing with
  constant frequency under a varying magnetic field

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Probing the Sample

• OR The chemical sample may be tested by probing
  with varying frequency/energy under a constant
  magnetic field

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Shielding

• Hydrogen (Protons) main atom used
• Electronegative atoms shield the protons
• Example

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Shielding

• Height proportional to no of atoms in the state

Spectra

• Shift controlled by surrounding electronegative
  atoms

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Spin-Spin Coupling

• Neighbouring protons feel each others spin
  interact, splitting the signal

Doublet
Triplet
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Energy Gap depend on other protons spins
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Spin-Spin Coupling

• Number of sub-signals no of neighbouring
  protons 1

Triplet
Quartet
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Signal Splitting

• Oxygen double bond very electronegative signal
  far to the right
• 6 protons in methyl groups causes 7 splits, each
  further split into 2 signals by methine proton
• Peak ratios follow Pascals Triangle

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Shielding Effects
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Pulse NMR

• Varying Frequency/Magnetic field too slow
• Introduce a very short (2 micro second) pulse of
  RF
• Equivalent to radiating over a large range of
  frequencies
• Record the time relaxation to Boltzmann
  equilibrium of all bonds over time
• Do a Fast Fourier transform in time domain to
  recover intensity of different frequencies

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Fourier Transform
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Phase Selection

• Signal recorded in X Y axes in NMR (Real and
  Imaginary inputs to FFT)
• Real Imaginary signals may be rotated
• Intensity read as real part of FFT

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Phase selection
Real
Imaginary
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Actual Time Domain Signal
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Frequency Domain Signal (after FT)
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Frequency Domain Signal (bad Phasing)
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Water Peak

• Water is main component of urine
• This peak dominates the spectra
• This peak is reduced in the sample by saturating
  the sample with RF of the corresponding
  wavelength (quenching)
• The water molecules stay in an excited state,
  reducing their signal

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NMR Machines
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Large NMR Machine
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NMR Schematic
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Inside NMR machine
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Loading Sample
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Ryegrass Endophyte
Endophyte hyphae growing through ryegrass cells

• Fungi with symbiotic relationship with grasses
• Passed on in the seed
• Gives resistance to insects
• Produces a range of Alkaloid metabolites
• Ergovalines - raise animals body temperature
  kills insects
• Lolitrems - muscle tremagens
• Peramines Feeding inhibitors
• Concentrates in reproductive tissues

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Effect of Endophyte on Pasture
Low
High
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Effect of Endophyte on Animals

• Ryegrass staggers

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Endophyte Toxicity Experiment

• Aim to create a discriminant function that
  indicates sheep have levels of endophyte that
  impair their productivity (sub-clinical effects)
• Can we detect endophyte in pasture from urine or
  blood samples from sheep?
• Test urine from sheep in NMR machine to detect
  endophyte metabolites
• Data NMR spectra from each urine sample
• Complex chemical sample not interested in
  identifying differing chemicals, but looking for
  consistent differences between spectra

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Trial Design

• Feed sheep control diet, and then switch to
  treated diet
• Endophyte fed as contaminated seeds (strongest
  concentration)
• Alkaloid Ergotamine added to feed
• Sporidesmin another fungal alkaloid which
  damages the liver (Facial Eczema) added to feed
  known liver metabolites can be detected.

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Trial Design
Treatment Added to feed
1. Endophytic Seed 2. Ergotamine 3. Sporidesmin
Control Nil
1
5
4
6
3
2
Day

• Some core animals used multiple times at all time
  points
• Other animals just a pre and post measurement

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Sources of Variation

• Temperature affects the spectra
• Room kept at constant temperature by may be
  variation with time first samples brought to
  room may not have equilibrated
• Different operators
• Day day variation
• Biological variation
• Fourier Transform Phase selection

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Data Acquisition

• NMR machine produces
• Paper output of spectra
• HPG graphics file
• Binary file in Mac Format
• Students used a routine that read the curve from
  the HPG file (2048 points resolution)
• Developed an extension to GenStat IMPORT that
  read the binary data in (by disassembling the
  binary file!)
• Now have full precision 8192 points per sample
• 710 Samples in experiment 50MB of data

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Randomization of samples

• Animals randomized to added treatments in each
  period all have control period.
• Samples not randomized in order presented to NMR
  machine (oversight due to being processed outside
  our control).
• Samples done in batches by different operators
• New improved water quenching technique developed
  during the analysis period
• Did not change to the new technique to avoid
  added variation

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Resulting Spectra
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Range of peak intensities - Scaling
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Phase problems with Water peak
Scaled Spectra
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Baseline Drift Problems
Base line not flat
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Base Line Adjustment

• Remove linear trend
• Smooth bottom p of points remove from curve to
  leave peaks

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Peak Location
Are the peaks of the three spectra at the same
locations or has the curve shifted?
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Standardization

• Different levels of intensity across samples
  (particularly for water peak) Adjustment to
  common scale (90 percentile or median set to
  same location)
• Phase change differences (base line going below
  zero) base line estimation and adjustment
• Possible location of peaks at different
  locations Single translation or warping

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Registration

• Small jitter in X for peaks gives
• increase in standard deviation,
• decrease in means ? large decrease in
  significance

µ 1 s 0.3
µ 0.3 s 0.5
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Optimal Translation between 2 spectra

• Can calculate cross-correlations and take maximal
  shift

Optimal shift -2
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Dynamic Warping

• When moving through two series we can at any
  point move on 1 in both series or not take a step
  in either series
• Find the path through both series that minimizes
  the mismatch between the 2 series
• Can enforce that both series start and finish at
  the end if wanted
• Algorithm exists to find optimal path in a single
  pass

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Optimal Path Algorithm
Mismatch
Minimum to cell
Path Memory
Backtrack through path memory
Calculate minimum mismatch from 1 stage to next
stage for each cell
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Warping Penalty

• Add ?(change in row number) to sums of squares
• Minimize penalized sums of squares
• Larger ? induces smoother path (more likely to
  move horizontally)
• Can scale ? to make penalized sums of squares
  more consistent between data sets

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Optimal For Series Matching
Mismatch

• Movement along 1 1 axis.
• Can enforce starting and ending in a corner
• Need only path memory and final mismatch column
• Penalty for not moving in 1-1 direction

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Application to NMR data

• GenStat procedure developed for matching
  curvesUses DLL for speed and minimizing memory
  usage
• Path memory requires lots of memory (8192 x 8192
  matrix but 2 bytes per unit)
• Algorithm still very quick
• What standard to warp to?
• Use any curve first time
• Take average of warped curves and warp to this
• Iterate

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Warp Path (Deviations from 1-1)

• Three typical paths
• Black Little adjustment
• Red- Pushed right
• Green - Pushed left

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Endophyte Effect (No adjustment)
Intensity
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Endophyte Difference
Change in Intensity
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Endophyte Probabilities
log(Probability)
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Endophyte Effect (Warped Baseline)
Intensity
Water Peak excluded
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Endophyte Difference
Change in Intensity
Cleaner/Tighter Spikes
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Ergotamine Effect
Intensity
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Ergotamine Effect
Change in Intensity
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Ergotamine Effect
log(Probability)
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Sporidesmin Effect (unadjusted)
Intensity
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Sporidesmin Effect
Change in Intensity
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Sporidesmin Effect
log(Probability)
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Sporidesmin Effect (adjusted)
Intensity
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Sporidesmin Effect
Change in Intensity
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Sporidesmin Effect
log(Probability)
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To do

• Integrate peaks to improve precision(Need limits
  of peak)

• Discriminant analysis to use multiple peaks in
  classification
• Look at components of variation
• REML analysis to allow for experimental structure

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Thanks to conference organizers