New Statistical Algorithms for the Analysis of Mass - FU Berlin, FB MI ...

More documents

Recommendations

Info

40 CHAPTER 3. MATHEMATICAL MODELING AND ALGORITHMS Analyzing Candidate Peaks In mass spectra of complex protein mixtures (such as serum) most of the peaks detected are broadened and/or highly convoluted. This results for example from molecular fragments having very similar masses and thus partly overlay, from poor machine resolution, or different isotopic forms of the same molecule. Therefore, a successful peak detection algorithm needs to deconvolute those peaks. A widely accepted method assumes a blurred peak to be a mixture of Gaussians and tries to resolve it back into its original components. A commonly used technique is Maximum Entropy that has been originally developed for clarifying blurred images (see (Guiasu and Shenitzer, 1985)). Based on this idea we have developed an approach to separate and evaluate the assumed mixture of Gaussians. The key steps for each candidate peak found are as follows: 1. Determine number of Gaussian components by density estimation using the Greedy Expectation Maximization algorithm (Verbeek et al., 2003). This algorithm has been shown to have a very good performance even on large mixtures often found in peaks at higher masses (> 3000Da). (For a comparative study see (Paalanen et al., 2005).) 2. To account for isotopic forms a de-isotoping step is carried out by fitting a mass dependent pre-calculated model (see (Zhang et al., 2005) for details) if more than one Gaussian component is found. If successful, the peaks involved are tagged as belonging to the same molecule(-fragment). If the quality of the fit is too poor the peak is split according to the number of Gaussians found and for each of the new parts step 1 is performed again. 3. Determine and store the parameters (height, width, center, area, shape quality 7 ) of this peak. 3.4.4 Computational Complexity Analysis of Peak Picking The complexity of the peak picking is O(n) where n is the number of input points since we loop over all points and determine properties of some areas (candidate peaks) which are performed in constant time. 3.4.5 Comparison to Threshold-driven Algorithms To obtain a first proof-of-principle we spiked a subset of human serum samples 8 (see section 4.1.2) with a peptide mix 9 . We split 16 different samples into five groups each. Before sample pretreatment and measurement each of the groups was spiked with one of the following concentrations: 121.21nMol/L, 0.76nMol/L, 0.30nMol/L, 3.03pMol/L, 0.075pMol/L, resulting in 320 spectra (64 for each concentration group due to 4-fold spotting). 7 This is achieved by geometrical hashing (Wolfson and Rigoutsos, 1997). The hashing algorithm returns a discrete value c ∈ {0, 1 . . . 5}, indicating the class the hashing algorithm has assigned to this shape. c = 0 means noise and c = 1..5 peak, where c = 5 is assigned if the peak looks perfect. The categories are trained a priori. 8 The protocol used for preprocessing and (magnetic bead) fractionation has been described in (Baumann et al., 2005). 9 Protein calibration standard mix (Part No.: 206355 & 206196 purchased from Bruker Daltronics, Leipzig, Germany)
3.4. HIGHLY SENSITIVE PEAK DETECTION 41 Substance Plat- Theor. Center found form 3 Center (Concentration of spiked peptide mix as stated below) 121.21nMol/L 0.76nMol/L 0.30nMol/L 3.03pMol/L 0.075pMol/L Angiotensin II P.NET 1047.20 1047.1 - 1 - 1 - 1 - 1 Angiotensin II CPT 1047.20 1046.9 - 2 - 2 - 2 - 2 Angiotensin I P.NET 1297.51 1297.6 1298.0 1299.3 1299.2 - 1 Angiotensin I CPT 1297.51 1297.2 - 2 - 2 - 2 - 2 Bombesin P.NET 1620.88 1620.9 1618.1 1617.2 1617.2 - 1 Bombesin CPT 1620.88 1620.6 - 2 - 2 - 2 - 2 ACTH clip 18-39 P.NET 2466.73 2466.8 2465.8 2465.8 2466.2 - 1 ACTH clip 18-39 CPT 2466.73 2466.2 - 2 2466.1 2465.9 - 2 Somatostatin 28 P.NET 3149.61 3149.5 - 1 - 1 - 1 - 1 Somatostatin 28 CPT 3149.61 3149.0 - 2 - 2 - 2 - 2 Insulin P.NET 5734.56 5734.3 - 1 - 1 - 1 - 1 Insulin CPT 5734.56 5734.2 - 2 - 2 - 2 - 2 Table 3.4.1: Results of the spiking experiments (see text for explanation). Note that no calibration has been performed for the Proteomics.NET platform. 1 : No significant masterpeak in this range at this concentration found, 2 : No significant peaks in this range at this concentration found, 3 : CPT: Bruker ClinprotTools, P.NET: Our Proposed Platform: Proteomics.NET We then processed each resulting raw spectrum as described above. For each of the five resulting concentration groups we ran the peak detection algorithm of our platform and of the Bruker software. Table 3.4.1 summarizes the findings: The algorithms successfully detect peaks even for very small concentrations at pMol/L level. This is exemplarily shown for the hormones Angiotensin, Bombesin and ACTH clip 18-39 which can be detected in a very low and biologically relevant concentration range ( ∼3 pMol/L). Peaks for Angiotensin and Bombesin are not detected by commercial software 10 . Therefore, in these examples, our algorithm is at least 20000 times more sensitive than a commercial algorithm using a signal-to-noise threshold. 10 ClinProTools 2.0, Bruker Daltronics. Parameters used: Signal-to-Noise Level: 3, Peak Detection Algorithm: Centroid
Page 1 and 2: New Statistical Algorithms for the
Page 3 and 4: Contents Acknowledgments . . . . .
Page 5 and 6: New Statistical Algorithms for the
Page 7 and 8: Extended Abstract English Version M
Page 9 and 10: German Version Das Gebiet der Prote
Page 11 and 12: Chapter 1 Introduction and Survey 1
Page 13 and 14: 1.2. GOALS, OBJECTIVES AND TASKS 7
Page 15 and 16: 1.2. GOALS, OBJECTIVES AND TASKS 9
Page 17 and 18: Chapter 2 Preliminaries 2.1 Topic O
Page 19 and 20: 2.1. TOPIC OVERVIEW 13 Figure 2.1.1
Page 21 and 22: 2.1. TOPIC OVERVIEW 15 completeness
Page 23 and 24: 2.2. AN EXAMPLE 17 (a) Opera A (b)
Page 25 and 26: 2.2. AN EXAMPLE 19 Figure 2.2.6: Tw
Page 27 and 28: 2.2. AN EXAMPLE 21 successes. We ca
Page 29 and 30: Chapter 3 Mathematical Modeling and
Page 31 and 32: 3.2. INTRODUCTION TO MALDI TOF MS 2
Page 37 and 38: 3.3. PREPROCESSING 31 mix (external
Page 39 and 40: 3.3. PREPROCESSING 33 Figure 3.3.5:
Page 41 and 42: 3.3. PREPROCESSING 35 Figure 3.3.7:
Page 43 and 44: 3.4. HIGHLY SENSITIVE PEAK DETECTIO
Page 45: 3.4. HIGHLY SENSITIVE PEAK DETECTIO
Page 49 and 50: 3.5. PEAK DETECTION IN 2D MAPS 43
Page 51 and 52: 3.6. PEAK REGISTRATION (ALIGNMENT)
Page 57 and 58: 3.7. IDENTIFYING POTENTIAL FEATURES
Page 63 and 64: 3.8. EXTRACTING FINGERPRINTS 57 Fig
Page 65 and 66: 3.8. EXTRACTING FINGERPRINTS 59 FID
Page 67 and 68: 3.8. EXTRACTING FINGERPRINTS 61 Dim
Page 69 and 70: 3.9. COMPLEXITY ANALYSIS 63 3.9 Com
Page 71 and 72: Chapter 4 (Bio-)Medical Application
Page 73 and 74: 4.1. DATA USED 67 4.1.2 Serum Data
Page 75 and 76: 4.2. STATISTICAL REMARKS 69 1. Vali
Page 77 and 78: 4.2. STATISTICAL REMARKS 71 Molar v
Page 79 and 80: 4.2. STATISTICAL REMARKS 73 � Fir
Page 81 and 82: 4.2. STATISTICAL REMARKS 75 Let ˆ
Page 83 and 84: 4.2. STATISTICAL REMARKS 77 the boo
Page 85 and 86: 4.3. STUDY RESULTS 79 Figure 4.3.3:
Page 87 and 88: 4.3. STUDY RESULTS 81 Figure 4.3.4:
Page 89 and 90: 4.3. STUDY RESULTS 83 � kNN (gen.
Page 91 and 92: 4.3. STUDY RESULTS 85 d(x, θi) =
Page 93 and 94: 4.3. STUDY RESULTS 87 pairs of obje
Page 95 and 96: 4.3. STUDY RESULTS 89 � “Peptid
Page 97 and 98:
4.4. IDENTIFICATION OF PROTEOMIC FI
Page 99 and 100:
Page 101 and 102:
Page 103 and 104:
Page 105 and 106:
Page 107 and 108:
4.6. BIOLOGICAL APPLICATIONS 101 4.
Page 109 and 110:
Chapter 5 Computer Science Grid Str
Page 111 and 112:
5.1. INTRODUCTION 105 � A node is
Page 113 and 114:
5.1. INTRODUCTION 107 of and config
Page 115 and 116:
5.1. INTRODUCTION 109 particular pr
Page 117 and 118:
5.2. THE QUASI AD-HOC (QAD) GRID 11
Page 119 and 120:
5.2. THE QUASI AD-HOC (QAD) GRID 11
Page 121 and 122:
5.3. QAD GRID PLATFORM SERVER 115 F
Page 123 and 124:
5.3. QAD GRID PLATFORM SERVER 117 j
Page 125 and 126:
5.3. QAD GRID PLATFORM SERVER 119 (
Page 127 and 128:
5.3. QAD GRID PLATFORM SERVER 121 p
Page 129 and 130:
5.3. QAD GRID PLATFORM SERVER 123 D
Page 131 and 132:
5.3. QAD GRID PLATFORM SERVER 125 F
Page 133 and 134:
5.3. QAD GRID PLATFORM SERVER 127 t
Page 135 and 136:
5.4. QAD GRID WORKER 129 field. A w
Page 137 and 138:
5.4. QAD GRID WORKER 131 2. This re
Page 139 and 140:
5.4. QAD GRID WORKER 133 Figure 5.4
Page 141 and 142:
5.4. QAD GRID WORKER 135 Checkpoint
Page 143 and 144:
5.4. QAD GRID WORKER 137 database b
Page 145 and 146:
5.5. QAD GRID PLATFORM SERVICES 139
Page 147 and 148:
5.6. QAD GRID WORKFLOWS 141 � Dat
Page 149 and 150:
5.6. QAD GRID WORKFLOWS 143 Service
Page 151 and 152:
5.6. QAD GRID WORKFLOWS 145 Figure
Page 153 and 154:
5.7. RELATED WORK 147 to set-up sys
Page 155 and 156:
5.7. RELATED WORK 149 Table 5.7.1 -
Page 157 and 158:
Chapter 6 proteomics.net - Product-
Page 159 and 160:
6.2. CASE STUDIES 153 6.2 Case Stud
Page 161 and 162:
6.2. CASE STUDIES 155 Figure 6.2.2:
Page 163 and 164:
6.2. CASE STUDIES 157 MASCOT and SE
Page 165 and 166:
6.2. CASE STUDIES 159 The peak pick
Page 167 and 168:
6.2. CASE STUDIES 161 first entry i
Page 169 and 170:
6.2. CASE STUDIES 163 Approach Base
Page 171 and 172:
6.2. CASE STUDIES 165 Figure 6.2.5:
Page 173 and 174:
Chapter 7 Related Work In this chap
Page 175 and 176:
Chapter 8 Conclusion and Future Dir
Page 177 and 178:
8.3. FROM BIOMARKERS TO BIOPRINTS 1
Page 179 and 180:
Appendix A Implementation Details T
Page 181 and 182:
Appendix B Curriculum Vitae Name Ti
Page 183 and 184:
References Aebersold, R. and Mann,
Page 185 and 186:
REFERENCES 179 Breiman, L. (2001).
Page 187 and 188:
REFERENCES 181 Downard, K. M. and M
Page 189 and 190:
REFERENCES 183 Gillette, M. A., Man
Page 191 and 192:
REFERENCES 185 Huyghe, E., Muller,
Page 193 and 194:
REFERENCES 187 Kuijpens, J. L. P.,
Page 195 and 196:
REFERENCES 189 McLachlan, S. M. and
Page 197 and 198:
REFERENCES 191 Platt, J. C. (1999).
Page 199 and 200:
REFERENCES 193 Stone, M. (1974). Cr
Page 201 and 202:
REFERENCES 195 Washburn, M. P., Wol
show all

New Statistical Algorithms for the Analysis of Mass - FU Berlin, FB MI ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?