Analysis of Mass Spectrometry Data: Problems and Tools

Transcription

1 Analysis of Mass Spectrometry Data: Problems and Tools Johan Carlson Div. of Systems and Interaction Dept. of Computer Science, Electrical and Space Engineering Luleå University of Technology SE Luleå Sweden

2 Today s menu Background Mass spectrometry Traditional multivariate data analysis Problems Tools Pre-processing Traditional analysis, re-visited Problems? Alternative analysis strategy Future challenges 2

3 Mass spectrometry (MS) Analytical technique that measures the mass-to-charge ratio of charged particles. Used for: Determining masses of particles, Determining the elemental composition of a sample or molecule Revealing chemical structures of molecules and compounds. Works by ionizing chemical compounds to generate charged molecules or molecule fragments and measuring their mass-to-charge ratios 3

4 Mass spectrometry (MS) A sample is loaded onto the MS instrument and undergoes vaporization. The components of the sample are ionized by one of a variety of methods (e.g., by impacting them with an electron beam), which results in the formation of charged particles (ions). The ions are separated according to their mass-to-charge ratio in an analyzer by electromagnetic fields. The ions are detected, usually by a quantitative method The ion signal is processed into mass spectra. 4

5 Mass spectrometry (MS) 5 (Source: wikipedia.org)

6 Mass spectrometry (MS) The output: A vector of mass-to-charge values, i.e. the location of the peaks in the mass spectrum. Abundance values, i.e. the peaks themselves, representing the relative abundance ("amount") of each ion in the sample. This has some implications (causing problems!), but let s leave these for now. The location of the peaks (i.e. the corresponding mass value) give information of what type of molecules are present. The magnitude of the peaks give information of the relative amount of each molecule. 6 The next slide shows an example of a mass spectrum for a reasonably simple peptide.

7 Mass spectrometry (MS) 7 (Source: wikipedia.org)

8 Mass spectrometry (MS) For more complex mixtures, the mass spectra become more difficult to interpret. The following example of a mass spectrum of a crude oil sample is taken from: J. E. Carlson, J. R. Gasson, T. Barth, and I. Eide, "Extracting Homologous Series from Mass Spectrometry Data by Projection on Predefined Vectors", Chemom. Intell. Lab. Syst., Vol. 114, pp ,

9 Mass spectrometry (MS) normalised abundance m/z [Da]

10 Traditional multivariate analysis Purpose: Reveal underlying patterns in large data sets. Example: Look at a set of mass spectra from 10 different oil samples. How are these different? Tool of choice (among chemists): Principal Component Analysis (PCA). So, let s first look at what PCA is! 10

11 Principal component analysis (PCA) Assume we make an observation x m, where x m = [ x 1 x 2 x N ] T, where x 1,x 2,...,x M are measured quantities for different variables. If we have M such multivariate observations, we can store these in a matrix X as x T 1 x T 2 X =... x T M 11

12 Principal component analysis (PCA) Now let s factor X, as X = TP T, where the columns of P are now the normalized eigenvectors of XX T, i.e. a new basis for the column space of X constructed from the eigenvectors of the sample covariance matrix of our M observations (in N variables). The rows of T are then the coordinates in this new basis. Furthermore, let the eigenvectors be sorted so that the first column of P is the eigenvector corresponding to the largest eigenvalue, the second column corresponds to the second largest eigenvalue, and so on. WHY IS THIS GOOD? 12

13 Principal component analysis (PCA) Example Let s look at a two-dimensional case, where x 1 and x 2 are observations from a two-dimensional Gaussian random variable with covariance matrix R = [ ] 13

14 Principal component analysis (PCA) 2 1 x x 1 14

15 Principal component analysis (PCA) 2 1 x x 1 15

16 Principal component analysis (PCA) In essence, PCA is a rotation of the coordinate system. The axes of the new system describe directions in which we have large experimental variation. If there are strong correlations in the original data, we can therefore reduce the dimensionality by discarding PC s, with minimum loss of information (actually optimal, in the least-squares sense). 16

17 Principal component analysis (PCA) 1 p p 1 17

18 Problems with mass spectrometry data Example Assume we have mass spectra of 10 different crude oils (five replicates of each). A PCA should be able to reveal differences between these. So, let s store mass spectra from the samples as rows of our matrix X (columns then represent mass/charge values). Large variations between oil samples should show up, and similar oils should group together. Let s try it! 18

19 Problems with mass spectrometry data p p 1

20 20 Problems with mass spectrometry data It doesn t work! Why? Problem no. 1: In PCA, we assume all columns represent different variables, but that these variables are the same for all rows. The MS data are non-uniformly sampled, meaning that we obtain pairs of mass/charge values and abundance values, only where there are peaks. So, storing all data in one matrix, each column does not represent the same thing for the different spectra. Problem no. 2 Uncertainties in the instrument causes peak locations to shift slightly. So, even for replicate experiments, the mass/charge values will not be the same. Is PCA doomed?

21 Pre-processing of MS data It appears as if we need to do some pre-processing of the spectra before PCA can be applied. 1. Re-sampling of mass spectra so that they share one common mass/charge vector. 2. Taking the uncertainty of the instrument into account, i.e. aligning peaks from different spectra that can be assumed to have the same mass/charge value. So, if we do this (takes a bit of programming...), what do we get? 21

22 Traditional PCA, re-visited p p 1

23 Traditional PCA, re-visited So, it appears we have overcome the main problems. Now: Replicate experiments on the same oils group together. Oils with different chemical compositions are separated. Oils with different, but somewhat similar properties, appear closer to each other in the plot. Remaining problem: The underlying chemical properties are hard to find. The new representation reveals patterns, but these are hard to interpret. 23

24 Alternative analysis strategy Let s go back to the example mass spectrum: 50 normalised abundance m/z [Da]

25 Alternative analysis strategy Observation It appears there are series of peaks, separated by a fixed mass/charge value. A separation of n 14 would mean the molecule has n extra CH 2 groups. Idea Could we analyze the spectra in terms of series like these instead of eigenvectors of the covariance matrix (PCA)? How would we take uncertainties of the instrument into account when doing this? 25

26 Alternative analysis strategy Let s construct a new orthonormal basis for the spectra basis vectors, u i peak width, u 1 u 2 u 3 m-4 m m+4 m+8 m+14 m/z [Da] 26

27 Alternative analysis strategy We can now project our spectra onto this new basis, by T = U T X, where U are the vectors from the previous slides and T are the scores obtained by the projection, i.e. "how much of each basis function is present in each of the spectra" 27

28 Alternative analysis strategy (a) (b) 6 t 3 4 t t t t 1 (d) (c) t 3 t t t 2 28 F01o F02t F03t F04t F05t F06o F07o F08t F09t F10t

29 Alternative analysis strategy Observations Replicates of the same oil group nicely. Oils with similar chemical composition appear close to each other. Chemically different oils will be separated. So far we can see the same things as with PCA. So, what else? Let s look at the corresponding basis vectors. 29

30 30 Alternative analysis strategy ± ± ± basis vector, u m/z [Da] ± ± ± basis vector, u m/z [Da] ± ± ± basis vector, u m/z [Da]

31 Alternative analysis strategy Observations Looking at the mass/charge values of the peaks, a trained chemist can determine what chemical compound class these sequences correspond to. In other words, in addition to the ability to discriminate chemically different oils samples, we can also interpret what type of chemical compounds that causes this difference. 31

32 Future challenges How can we model the original spectra based on this new analysis method? How to model how changing a process variable (in the preparation of the oil) will affect the composition? We still need to develop various diagnostic and visualization tools to aid the chemist in the analysis of the results. 32

33 Thank you!