Automatic Peak Picking Using Wavelet De-noised Spectra in Automated Struture Determination.

Transcription

1 Automatic Peak Picking Using Wavelet De-noised Spectra in Automated Struture Determination

2 Automatic peak picking in automatic structure determination Wavelet de-noising Peak Integration Network anchoring, symmetry mapping Other applications of wavelets in NMR WaveWat: water signal suppression WavePCA: PCA of screening data in wavelet space

3 Automatic peak picking in automatic structure determination Wavelet de-noising Peak Integration Network anchoring, symmetry mapping Other applications of wavelets in NMR WaveWat: : water signal suppression WavePCA: : PCA of screening data in wavelet space

4 Wavelets Wavelet waving above and below zero integrate to zero Wavelets chop up data into frequency components, and analyze each frequency component with a resolution matched to its scale. 1980: Jean Morlet, French seismologist Collaborated with the theoretical physicist Alex Grossmann 1985: Stephane Mallat: MRA Yves Meyer, Grossmann and Ingrid Daubechies: wavelet frames Daubechies: Orthogonal wavelets with compact support Donoho: thresholding for noise suppression

5 Wavelet Applications Data approximation Noise reduction Data compression (jpeg, mpeg) Time-frequency analysis Image analysis Two basic types of wavelet transforms: Continuos wavelet transform CWT Discrete wavelet transform DWT

6 Discrete Wavelet Transform Ψ j j / 2 j, k ( x) = 2 Ψ(2 x k ) k translation j dilatation Wavelets derived from The Haar mother wavelet

7 Properties of the Haar Wavelet Compact support: [ ] j Ψ ) = k2,( k + 1) 2 j sup(, j k i.e. they are zero outside this interval. For each Haar wavelet: ( x) dx 0 L 2 2 = f ( x) Ψ j, k = i.e. the area above the x -axis is equal to the area below the x -axis. constitutes a complete orthonormal basis in L 2 { Ψ, j, k Z} j, k i.e. any square integrable function can be represented by a linear combination of wavelet functions Ψ jk

8 Signal Approximation in the Haar System f ( x) = c j n φ( x) c jkψ jk ( x) j= 0 k = 0 c jk = wavelet coefficients Ψ jk = wavelets derived from a mother wavelet Ψ φ = scaling function (father wavelet)

9 Scaling functions and Wavelets

10 Wavelet Basis Scale Direction Time

11 The Mallat WT Algorithm φ Lowpass x(n) Highpass Ψ φ Lowpass x(n-1) Highpass Ψ w(n-1) x(n-2) w(n-2) φ Lowpass Highpass Ψ x(n-3) w(n-3) Computational efficiency: WT: O(N) FFT: O(N log(n))

12 The Mallat DWT Algorithm Level 0 Original signal L H Level 1 L H Level 2 Wavelet coefficients

13 Wavelet De-nosing DWT thresholding IWT

14 Thresholding methods keep-or-kill shrink-or-kill Threshold estimation is based on the wavelet coefficient values

15 Translation-Invariant De-noising Gibbs artefacts

16 Translation-invariant De-noising Suppression of wavelet coefficients may cause Gibbs artefacts =associated with the lack of translation-invariance Cycle-spinning: Average out Gibbs artefacts Shift data WT & De-noise Shift back Average all Computational effiiency of TI-WT: O(n log 2 (n))

17 De-noising: natural abundance HSQC

18 De-noising: natural abundance HSQC

19 De-noising schemes scoring Statistical Assessment σ noise dfactor = = min( std( I k )), k 1,int(dim 1/16 dim2/16) σ σ noise noise ( raw) ( wav) Peak list oriented scores Fine structure score (fscore) fscore =1 V ref V V ref wav Peak picking score (pscore) De-noising score (dscore) pscore= N wav N raw dscore=1 noise N wav noise N raw

20 384 different de-noising protocols Order (1-8): S5-8-10, D4-10, C1-5, Haar red = 1D DWT (1/2), blue = 1D DWT (2/1), green = 2D DWT L = 2 (+), 3 (o), 4 (x) and 5(*)

21 General Results: 1. Best wavelets: Daubechies and Symmlets 2. Translation-Invariant transform 3. Hard thresholding - preserve the fine structure Soft thresholding + better S/N gain, - suppression of some peaks

22 Analysis on a full 15 N-edited NOESY of the Sud protein from Wolinella succinogenes

23 Automated peak picking and peak integration Peak picking: grid search over a sparse data matrix bnoise( P) n = F σ dim= 1 2 dim, i dim 2 + ( n 1) min( σ dim, i dim, i dim ) Peak integration: object related growing algorithm

24 Automated peak picking and peak integration

25 Consistency check of the NOESY spectra NOECHECK => dfactor = 0.9

26 Outside NMRLaB: plugin for ARIA1.2

27 Automated protein structure determination Test case: monomer unit of the Sud dimer Incremental peak lists for ARIA: stage 1: de-noising + NOEcheck: 75% complete, 90% de-noised NOEcheck: Validation + AssignFilter stage 2: de-noising + NOEcheck: 90% complete, 75% de-noised NOEcheck: Validation stage 3: complete peak lists (raw spectra)

28 Stage 1 1D TI-DWT D4 Soft NOEcheck + ARIA (5 iterations) Precision : 4.68±1.08 Å Accuracy : 2.64 Å

29 Stage 2 1D TI-DWT S5 Hard NOEcheck + ARIA (4 iterations) Precision : 2.00±0.36 Å Accuracy : 1.72 Å

30 Stage 3 Original (raw) spectra NOEcheck + ARIA (4 iterations) Precision : 0.85+/-0.20 Å Accuracy : 1.06 Å

31 Automatic peak picking in automatic structure determination Wavelet de-noising Peak Integration Network anchoring, symmetry mapping Other applications of wavelets in NMR WaveWat: water signal suppression WavePCA: : PCA of screening data in wavelet space

32 MRA - WAVEWAT

33 MRA WAVEWAT -Zero-filling: Increase number of dyadic levels -Mirror image reflection: reduce edge artefacts

34 WAVEWAT

35 WAVEWAT convolution WAVEWAT CCPN 2004

36 MRA applied to the diagonal signal

37 original wwdiag Cadzow

38 Automatic peak picking in automatic structure determination Wavelet de-noising Peak Integration Network anchoring, symmetry mapping Other applications of wavelets in NMR WaveWat: : water signal suppression WavePCA: PCA of screening data in wavelet space

39 PCA for NMR screening Series of [ 15 N, 1 H]-HSQC spectra Binding Ligand Non-binding ligand

40 PCA with bucketing vs. PCA in wavelet space NMR spectra NMR spectra Scaling Scaling Bucketing PCA WT + thresholding PCA

41 PCA with bucketing

42 PCA on wavelet coefficients

43 Spectrum 42 - False Hit

44 Bucketing artefacts

45 BMRZ Frankfurt Felician Dancea Christian Ludwig Nicola Trbovic Wavelets, peak picking NMRLaB,, wavelet application WavePCA