Mathematical tools in analytical mass spectrometry

AbstractOver the last few decades, mass spectrometry has become a powerful tool for exploring various aspects of molecular processes occurring in biological systems. Such exploration is leading to a greater understanding of various complex life processes; unraveling these processes poses the greatest challenge to contemporary bioscience. With due respect to sample preparation, data analysis is rapidly becoming a major obstacle to the conversion of experimental knowledge into valid conclusions. It is interesting to note that many problems related to mass spectrometry can be solved using techniques from computer science, graph theory and discrete mathematics. The aim of this manuscript is to recollect several essays that demonstrate the power and the need to apply such skills to mass spectrometry data interpretation. Special attention is paid to situations where traditional chemical analysis reaches its limits but mathematical reasoning can still allow us to reach valid conclusions.

[1]  T. Yen,et al.  Analysis of phytochelatin-cadmium complexes from plant tissue culture using nano-electrospray ionization tandem mass spectrometry and capillary liquid chromatography/electrospray ionization tandem mass spectrometry. , 1999, Journal of mass spectrometry : JMS.

[2]  J. Rappsilber,et al.  Peptide identification using vectors of small fragment ions. , 2005, Journal of proteome research.

[3]  D. Manolopoulos,et al.  An Atlas of Fullerenes , 1995 .

[4]  C. S. Hsu.  Diophantine approach to isotopic abundance calculations , 1984 .

[5]  Valmir F. Juliano,et al.  Eliminating the interference of M-nH ions in isotope patterns from low-resolution mass spectra , 1998 .

[6]  Richard D. Smith,et al.  Rapid Calculation of Isotope Distributions , 1995 .

[7]  J. Meija,et al.  Selenium and sulfur trichalcogenides from the chalcogenide exchange reaction. , 2004, Inorganic chemistry.

[8]  Graham R. Ball,et al.  Classification of bacterial species from proteomic data using combinatorial approaches incorporating artificial neural networks, cluster analysis and principal components analysis , 2005, Bioinform..

[9]  K. Resing,et al.  Modeling deuterium exchange behavior of ERK2 using pepsin mapping to probe secondary structure , 1999, Journal of the American Society for Mass Spectrometry.

[10]  F. McLafferty.  Interpretation of Mass Spectra , 1966 .

[11]  K. Varmuza,et al.  Spectral similarity versus structural similarity: mass spectrometry , 2004 .

[12]  B. Blum,et al.  History of Medical Informatics , 1990, Yearbook of Medical Informatics.

[13]  I. Vidavsky,et al.  Comparing similar spectra: From similarity index to spectral contrast angle , 2002, Journal of the American Society for Mass Spectrometry.

[14]  A. Sanz-Medel,et al.  Isotope dilution analysis for elemental speciation: a tutorial review , 2005 .

[15]  S. Guan,et al.  Enhancement of the effective resolution of mass spectra of high-mass biomolecules by maximum entropy-based deconvolution to eliminate the isotopic natural abundance distribution , 1997 .

[16]  Marc Garland,et al.  Weighted two-band target entropy minimization for the reconstruction of pure component mass spectra: Simulation studies and the application to real systems , 2003, Journal of the American Society for Mass Spectrometry.

[17]  Z. Mester,et al.  Analytical Applications of Volatile Metal Derivatives , 2002 .

[18]  J. B. Justice,et al.  Factor analysis of mass spectra , 1975 .

[19]  Robert Petesch,et al.  "Mass defect" tags for biomolecular mass spectrometry. , 2003, Journal of mass spectrometry : JMS.

[20]  Diophantine mass spectrometric structure analysis , 1999 .

[21]  Alain Hertz,et al.  On some Properties of DNA Graphs , 1999, Discret. Appl. Math..

[22]  Daniel L Sweeney,et al.  Small molecules as mathematical partitions. , 2003, Analytical chemistry.

[23]  T. Sakurai,et al.  PAAS 3: A computer program to determine probable sequence of peptides from mass spectrometric data , 1984 .

[24]  Roman A. Zubarev,et al.  Accuracy Requirements for Peptide Characterization by Monoisotopic Molecular Mass Measurements , 1996 .

[25]  Ming-Yang Kao,et al.  A dynamic programming approach to de novo peptide sequencing via tandem mass spectrometry , 2000, SODA '00.

[26]  J. F. Burke,et al.  Determination of the isotope enrichment of one or a mixture of two stable labelled tracers of the same compound using the complete isotopomer distribution of an ion fragment; theory and application to in vivo human tracer studies. , 1993, Biological mass spectrometry.

[27]  Morton E. Munk,et al.  A Novel Formalism To Characterize the Degree of Unsaturation of Organic Molecules , 2001, J. Chem. Inf. Comput. Sci..

[28]  D. V. Krevelen.  Organic geochemistry—old and new , 1984 .

[29]  M. Senko,et al.  Determination of monoisotopic masses and ion populations for large biomolecules from resolved isotopic distributions , 1995, Journal of the American Society for Mass Spectrometry.

[30]  Valerie Daggett,et al.  Protein folding from a highly disordered denatured state: The folding pathway of chymotrypsin inhibitor 2 at atomic resolution , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[31]  S. Mjøs.  Quantification of linolenic acid isomers by gas chromatography-mass spectrometry and deconvolution of overlapping chromatographic peaks , 2004 .

[32]  D. Matthews,et al.  Determination of complex isotopomer patterns in isotopically labeled compounds by mass spectrometry. , 2005, Analytical chemistry.

[33]  Renato Bruni,et al.  On peptide de novo sequencing: a new approach , 2005, Journal of peptide science : an official publication of the European Peptide Society.

[34]  Kwanyoung Lee,et al.  Molecular Weight Distribution of Branched Polystyrene: Propagation of Poisson Distribution , 2004 .

[35]  Joshua Lederberg.  How DENDRAL was conceived and born , 1990 .

[36]  E. Kendrick.  A Mass Scale Based on CH2 = 14.0000 for High Resolution Mass Spectrometry of Organic Compounds. , 1963 .

[37]  Sunghwan Kim,et al.  Graphical method for analysis of ultrahigh-resolution broadband mass spectra of natural organic matter, the van Krevelen diagram. , 2003, Analytical chemistry.

[38]  T. Beck,et al.  Interpretation of alkyl diselenide and selenosulfenate mass spectra , 2004, Journal of the American Society for Mass Spectrometry.

[39]  Sebastian Böcker,et al.  Novel Mass Spectrometry-Based Tool for Genotypic Identification of Mycobacteria , 2004, Journal of Clinical Microbiology.

[40]  K. Standing,et al.  A Selenoprotein in the Plant Kingdom , 2002, The Journal of Biological Chemistry.

[41]  W. Lee,et al.  Mass isotopomer analysis: theoretical and practical considerations. , 1991, Biological mass spectrometry.

[42]  A. Marshall,et al.  Two- and three-dimensional van krevelen diagrams: a graphical analysis complementary to the kendrick mass plot for sorting elemental compositions of complex organic mixtures based on ultrahigh-resolution broadband fourier transform ion cyclotron resonance mass measurements. , 2004, Analytical chemistry.

[43]  I. Mills,et al.  Quantities, Units and Symbols in Physical Chemistry , 1993 .

[44]  A. Sanz-Medel,et al.  Strategies to study human serum transferrin isoforms using integrated liquid chromatography ICPMS, MALDI-TOF, and ESI-Q-TOF detection: application to chronic alcohol abuse. , 2005, Analytical chemistry.

[45]  Alan Willse,et al.  Identification of major histocompatibility complex-regulated body odorants by statistical analysis of a comparative gas chromatography/mass spectrometry experiment. , 2005, Analytical chemistry.

[46]  L. M. Schwartz.  Random error propagation by Monte Carlo simulation , 1975 .

[47]  R. Appel,et al.  Popitam: Towards new heuristic strategies to improve protein identification from tandem mass spectrometry data , 2003, Proteomics.

[48]  Keith Richardson,et al.  Noise filtering techniques for electrospray quadrupole time of flight mass spectra , 2003, Journal of the American Society for Mass Spectrometry.

[49]  S. Eyles,et al.  Methods to study protein dynamics and folding by mass spectrometry. , 2004, Methods.

[50]  Determination of atomic isotope patterns from mass spectra of molecular ions containing multiple polyisotopic elements , 2002 .

[51]  A. Rockwood,et al.  Simultaneous quantitative analysis of isobars by tandem mass spectrometry from unresolved chromatographic peaks. , 2004, Journal of mass spectrometry : JMS.

[52]  J. Yates,et al.  Statistical models for protein validation using tandem mass spectral data and protein amino acid sequence databases. , 2004, Analytical chemistry.

[53]  V. Pellegrin.  Molecular formulas of organic compounds: the nitrogen rule and degree of unsaturation , 1983 .

[54]  Jacek A Szymura,et al.  Band composition analysis: a new procedure for deconvolution of the mass spectra of organometallic compounds. , 2003, Journal of mass spectrometry : JMS.

[55]  John Skilling,et al.  Maximum entropy deconvolution in electrospray mass spectrometry , 1991 .

[56]  Sebastian Böcker,et al.  Sequencing from Compomers: Using Mass Spectrometry for DNA de novo Sequencing of 200+ nt , 2004, J. Comput. Biol..

[57]  Igor A Kaltashov,et al.  Estimates of protein surface areas in solution by electrospray ionization mass spectrometry. , 2005, Analytical chemistry.

[58]  F. Regnier,et al.  An automated method for the analysis of stable isotope labeling data in proteomics , 2005, Journal of the American Society for Mass Spectrometry.

[59]  Z. Zhang,et al.  De novo peptide sequencing by two-dimensional fragment correlation mass spectrometry. , 2000, Analytical chemistry.

[60]  A. Dobó,et al.  A chemometric approach to detection and characterization of multiple protein conformers in solution using electrospray ionization mass spectrometry. , 2003, Analytical chemistry.

[61]  Edmund R. Malinowski,et al.  Qualitative and quantitative determination of suspected components in mixtures by target transformation factor analysis of their mass spectra , 1977 .

[62]  A. Proctor,et al.  Automation of data collection for matrix-assisted laser desorption/ionization mass spectrometry using a correlative analysis algorithm. , 1998, Analytical chemistry.

[63]  J. Margrave,et al.  Relative abundance calculations for isotopic molecular species , 1962 .

[64]  A. Marshall,et al.  Exact masses and chemical formulas of individual Suwannee River fulvic acids from ultrahigh resolution electrospray ionization Fourier transform ion cyclotron resonance mass spectra. , 2003, Analytical chemistry.

[65]  A. Rockwood,et al.  Dissociation of individual isotopic peaks: predicting isotopic distributions of product ions in MSn , 2003, Journal of the American Society for Mass Spectrometry.

[66]  K. Heumann.  Isotope dilution mass spectrometry (IDMS) of the elements , 1992 .

[67]  Flavio Monigatti,et al.  Algorithm for accurate similarity measurements of peptide mass fingerprints and its application , 2005, Journal of the American Society for Mass Spectrometry.

[68]  Bo Yan,et al.  A graph-theoretic approach for the separation of b and y ions in tandem mass spectra , 2005, Bioinform..

[69]  A. Marshall,et al.  Petroleomics: the next grand challenge for chemical analysis. , 2004, Accounts of chemical research.

[70]  Van Krevelen,et al.  Graphical-statistical method for the study of structure and reaction processes of coal , 1950 .

[71]  A. Sanz-Medel,et al.  Interpretation of butyltin mass spectra using isotope pattern reconstruction for the accurate measurement of isotope ratios from molecular clusters. , 2005, Journal of mass spectrometry : JMS.

[72]  DNA Sequencing Challenge , 2006, Analytical and bioanalytical chemistry.

[73]  J. Yergey.  A GENERAL APPROACH TO CALCULATING ISOTOPIC DISTRIBUTIONS FOR MASS SPECTROMETRY. , 1983, Journal of mass spectrometry : JMS.

[74]  S. Roussis,et al.  Reduction of chemical formulas from the isotopic peak distributions of high-resolution mass spectra. , 2003, Analytical chemistry.

[75]  A. Sanz-Medel,et al.  Species-specific isotope dilution analysis and isotope pattern deconvolution for butyltin compounds metabolism investigations. , 2005, Analytical chemistry.

[76]  Peter B O'Connor,et al.  Use of statistical methods for estimation of total number of charges in a mass spectrometry experiment. , 2004, Analytical chemistry.

[77]  M. Mann,et al.  Interpreting mass spectra of multiply charged ions , 1989 .

[78]  A. Dobó,et al.  Detection of multiple protein conformational ensembles in solution via deconvolution of charge-state distributions in ESI MS. , 2001, Analytical chemistry.

[79]  A. Savitzky,et al.  Smoothing and Differentiation of Data by Simplified Least Squares Procedures. , 1964 .

[80]  T. Schaub,et al.  Petroleomics: MS Returns to Its Roots. , 2005 .

[81]  Sunghwan Kim,et al.  Hydrogen Deficient Molecules in Natural Riverine Water Samples - Evidence for the Existence of Black Carbon in DOM , 2004 .

[82]  M. Wehofsky,et al.  Automated deconvolution and deisotoping of electrospray mass spectra. , 2002, Journal of mass spectrometry : JMS.

[83]  Z. Alfassi.  On the normalization of a mass spectrum for comparison of two spectra , 2004, Journal of the American Society for Mass Spectrometry.

[84]  R. W. Rozett,et al.  Classification of compounds by the factor analysis of their mass spectra , 1976 .

[85]  Bin Ma,et al.  An effective algorithm for peptide de novo sequencing from MS/MS spectra , 2005, J. Comput. Syst. Sci..

[86]  A G Marshall,et al.  Kendrick mass defect spectrum: a compact visual analysis for ultrahigh-resolution broadband mass spectra. , 2001, Analytical chemistry.

[87]  Zhongqi Zhang.  Prediction of low-energy collision-induced dissociation spectra of peptides. , 2004, Analytical chemistry.

[88]  David C Schriemer,et al.  Quantitating the statistical distribution of deuterium incorporation to extend the utility of H/D exchange MS data. , 2006, Analytical chemistry.

[89]  Juris Meija,et al.  Deconvolution of isobaric interferences in mass spectra , 2004, Journal of the American Society for Mass Spectrometry.

[90]  J. Lederberg.  Rapid calculation of molecular formulas from mass values , 1972 .

[91]  Alan L. Rockwood,et al.  Relationship of Fourier transforms to isotope distribution calculations , 1995 .

[92]  Jürgen W Einax,et al.  Chemometrics in analytical chemistry , 2004, Analytical and bioanalytical chemistry.

[93]  F. McLafferty,et al.  Fourier-transform mass spectrometry of large molecules by electrospray ionization. , 1989, Proceedings of the National Academy of Sciences of the United States of America.

[94]  Z. Mester,et al.  The mechanism of formation of volatile hydrides by tetrahydroborate(III) derivatization: A mass spectrometric study performed with deuterium labeled reagents , 2005 .

[95]  M. T. Fernandez,et al.  Iron and copper chelation by flavonoids: an electrospray mass spectrometry study. , 2002, Journal of inorganic biochemistry.

[96]  Sebastian Böcker,et al.  Sequencing from Compomers: The Puzzle , 2006, Theory of Computing Systems.

[97]  Mohammad Hossein Fatemi,et al.  Simulation of mass spectra of noncyclic alkanes and alkenes using artificial neural network , 2000 .

[98]  Sebastian Böcker,et al.  High-throughput MALDI-TOF discovery of genomic sequence polymorphisms. , 2003, Genome research.

[99]  T. O'Haver,et al.  Error Propagation in Isotope Dilution Analysis As Determined by Monte Carlo Simulation , 1994 .

[100]  Pavel A. Pevzner,et al.  De Novo Peptide Sequencing via Tandem Mass Spectrometry , 1999, J. Comput. Biol..

[101]  N. Everall,et al.  High energy collision-induced dissociation (CID) product ion spectra of isomeric polyhydroxy sugars , 2003 .

[102]  H. Kipphardt,et al.  New mathematical models with associated equations for isotope dilution mass spectrometry (IDMS) , 2004, Analytical and bioanalytical chemistry.

[103]  Edmond J. Breen,et al.  Automatic Poisson peak harvesting for high throughput protein identification , 2000, Electrophoresis.

[104]  J. G. Hughes,et al.  Heuristic charge assignment for deconvolution of electrospray ionization mass spectra. , 2003, Rapid communications in mass spectrometry : RCM.

[105]  Tetsuo Iwata,et al.  New Method to Eliminate the Background Noise from a Line Spectrum , 1994 .