Abstract
Over 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.
Similar content being viewed by others
References
Laurent AM (1846) Ann Chim Phys 18:266
Morikawa T, Newbold BT (2003) Chemistry (Russian) 12:445
Pellegrin V (1983) J Chem Educ 60:626
McLafferty FW, Turecek F (1993) Interpretation of mass spectra. University Science Books, Sausalito, CA
Meija J, Bisenieks J (2004) J Chem Educ 81:995
Lederberg J (1972) J Chem Educ 49:613
Crocker R (1968) J Chem Educ 45:731
Frevel LK, Lee W-L, Tecklenburg RE (1999) J Am Soc Mass Spectrom 10:231
Hsu CS (1984) Anal Chem 56:1356
Castillo Busto EM, Montes-Bayon M, Blanco-Gonzalez E, Meija J, Sanz-Medel A (2005) Anal Chem 77:5615
Badertscher M, Bischofberger K, Munk ME, Pretsch E (2001) J Chem Inf Comp Sci 41:889
Fowler PW, Manolopoulos DE (1995) An atlas of fullerenes. Clarendon, Oxford
Henry KD, Williams ER, Wang BH, McLafferty FW, Shabanowitz J, Hunt DF (1989) Proc Natl Acad Sci USA 86:9075
Mann M, Meng CK, Fenn JB (1989) Anal Chem 61:1702
Maleknia SD, Downard KM (2005) Anal Chem 77:111
Mohimen A, Dobo A, Hoerner JK, Kaltashov IA (2003) Anal Chem 75: 4139
Kaltashov IA, Mohimen A (2005) Anal Chem 77:5370
Dobo A, Kaltashov IA (2001) Anal Chem 73:4763
Eylesa SJ, Kaltashov IA (2004) Methods 34:88
Kazmirski SL, Wong K-B, Freund SMV, Tan Y-J, Fersht AR, Daggett V (2001) Proc Natl Acad Sci USA 98:4349
Margrave JL, Polansky RB (1962) J Chem Educ 39:335
Rockwood AL (1997) Rapid Commun Mass Sp 11:241
Yergey JA (1983) Int J Mass Spectrom 52:337
Wolfram S (2002) A new kind of science. Wolfram Media, Inc., Champaign, IL
Rockwood AL, Van Orden SL, Smith RD (1995) Anal Chem 67:2699
Kaur P, O’Connor PB (2004) Anal Chem 76:2756
Meija J (2005) PhD thesis. Department of Chemistry, University of Cincinnati, Cincinnati, OH
Rockwood AL, Kushnir MM, Nelson GJ (2003) J Am Soc Mass Spectrom 14:311
Heumann KG (1992) Mass Spectrom Rev 11:41
Rodriguez-Gonzalez P, Marchante-Gayón JM, Garcia Alonso JI, Sanz-Medel A (2005) Spectrochim Acta B 60:151
Senko MW, Beu SC, McLafferty FW (1995) J Am Soc Mass Spectrom 6:229
Meija J, Centineo G, Garcia Alonso JI, Sanz-Medel A, Caruso JA (2005) J Mass Spectrom 40:807
Lee PW-N, Byerley LO, Bergner AE (1991) Biol Mass Spectrom 20:451
Vogt JA, Chapman TE, Wagner DA, Young VR, Burke JF (1993) Biol Mass Spectrom 22:600
Chik JK, Vande Graaf JL, Schriemer DC (2006) Anal Chem 78:207
Meija J, Caruso JA (2004) Inorg Chem 43:7486
Sakurai T, Matsuo T, Matsuda H, Katakuse I (1984) Biomed Mass Spectrom 11:396
Bruni R, Gianfranceschi G, Koch G (2005) J Peptide Sci 11:225
Lu B, Chen T (2004) BioSilico 2:85
Ma B, Zhang K, Liang C (2005) J Comput Syst Sci 70:418
Chen T, Kao MJ, Tepel M, Rush J, Church GM (2001) J Comput Biol 8:325
Blazewicz J, Hertz A, Kobler D, de Werra D (1999) Discrete Appl Math 98:1
Böcker S (2006) Theory Comput Systems DOI: 10.1007/s00224-005-1238-y
Meija J, Caruso JA (2004) J Am Soc Mass Spectrom 15:654
Szymura JA, Lamkiewicz J (2003) J Mass Spectrom 38:817
Fu L-H, Wang X-F, Eyal Y, She Y-M, Donald LJ, Standing KG, Ben-Hayyim G (2002) J Biol Chem 277:25983
Yen T-Y, Villa JA, DeWitt JG (1999) J Mass Spectrom 34:930
Tereza Fernandez M, Lurdes Mira M, Helena Florencio M, Jennings KR (2002) J Inorg Biochem 92:105
Meija J, Beck TL, Caruso JA (2004) J Am Soc Mass Spectrom 15:1325
Moraes MCB, Brito Neto JGA, Juliano VF, do Lago CL (1998) Int J Mass Spectrom 178:129
Rodríguez-González P, Rodríguez-Cea A, García Alonso JI, Sanz-Medel A (2005) Anal Chem 77:7724
Kushnir MM, Rockwood AL, Nelson GJ (2004) J Mass Spectrom 39:532
Mjos SA (2004) Eur J Lipid Sci Technol 106:307
Sturgeon RE, Mester Z (2002) Appl Spectrosc 56:202A
D’Ulivo A, Mester Z, Sturgeon RE (2005) Spectrochim Acta B 60:423
Zhang H, Garland M, Zeng Y, Wu P (2003) J Am Soc Mass Spectrom 14:1295
IUPAC (1993) Quantities, units and symbols in physical chemistry. Blackwell, Oxford
Meija J (2005) Anal Bioanal Chem 381:11
Hall MP, Ashrafi S, Obegi I, Petresch R, Petersson JN, Schneider LV (2003) J Mass Spectrom 38:809
Hughey CA, Hendrickson CL, Rodgers RP, Marshall AG, Qian K (2001) Anal Chem 73:4676
Zubarev RA, Hakansson P, Sundqvist B (1996) Anal Chem 68:4060
Zhang X, Hines W, Adamec J, Asara JM, Naylor S, Regnier FE (2005) J Am Soc Mass Spectrom 16:1181
Rodgers RP, Schaub TM, Marshall AG (2005) Anal Chem 77:21A
Kendrick E (1963) Anal Chem 35:2146
Marshall AG, Rodgers RP (2004) Acc Chem Res 37:53
Stenson AC, Marshall AG, Cooper WT (2003) Anal Chem 75:1275
Kim S, Kramer RW, Hatcher PG (2003) Anal Chem 75:5336
Kim S, Kaplan LA, Benner R, Hatcher PG (2004) Mar Chem 92:225
van Krevelen DW (1950) Fuel 29:269
van Krevelen DW (1984) Org Geochem 6:1
Wu Z, Rodgers RP, Marshall AG (2004) Anal Chem 76:2511
Fragminder bvba (2006) Company website (see http://www.fragmind.com, last accessed 19th January 2006). Fragminder bvba, Antwerpen, Belgium
Meija J (2006) Anal Bioanal Chem 384:11
Böcker S (2004) J Comp Biol 11:1110
Lefmann M, Honisch C, Böcker S, Storm N, von Wintzingerode F, Schlötelburg C, Moter A, van den Boom D, Göbel UB (2004) J Clin Microbiol 42:339
Stanssens P, Zabeau M, Meersseman G, Remes G, Gansemans Y, Storm N, Hartmer R, Honisch C, Rodi CP, Böcker S, van den Boom D (2004) Genome Res 14:126
Sweeney DL (2003) Anal Chem 75:5362
Einax JW (2004) Anal Bioanal Chem 380:368
Zhang Z (2004) Anal Chem 76:3908
Zhang Z, McElvain JS (2000) Anal Chem 72:2337
Lederberg J (1990) In: Blum BI, Duncan K (eds) A history of medical informatics. ACM Press, New York, pp 14–44
Dancik V, Addona TA, Clauser KR, Vath JE, Pevzner PA (1999) J Comput Biol 6:327
Hernandez P, Gras R, Frey J, Appel RD (2003) Proteomics 3:870
Yan B, Pan C, Olman VN, Hettich RL, Xu Y (2005) Bioinformatics 21:563
Kipphardt H, De Bièvre P, Taylor PDP (2004) Anal Bioanal Chem 378:330
Wan KX, Vidavsky I, Gross ML (2002) J Am Soc Mass Spectrom 13:85
Alfassi ZB (2004) J Am Soc Mass Spectrom 15:385
Cittaro D, Borsotti D, Maiolica A, Argenzio E, Rappsilber J (2005) J Proteome Res 4:1006
Meija J, Mounicou S, Caruso JA (2004) J AOAC Int 87:205
Patterson KY, Veillon C, O’Haver TC (1994) Anal Chem 66:2829
Brito Neto JGA, Do Lago CL (2002) Int J Mass Spectrom 216:95
Savitzky A, Golay MJE (1964) Anal Chem 36:1627
Wehofsky M, Hoffmann R (2002) J Mass Spectrom 37:223
Jennings MEI, Matthews DE (2005) Anal Chem 77:6435
Roussis SG, Proulx R (2003) Anal Chem 75:1470
Iwata T, Koshoubu J (1994) Appl Spectrosc 48:1453
Scrivens JH, Jackson AT, Jennings KR, Jennings RCK, Everall NJ (2003) Int J Mass Spectrom 230:201
Justice JB, Isenhour TL (1975) Anal Chem 47:2286
Willse A, Belcher AM, Preti G, Wahl JH, Thresher M, Yang P, Yamazaki K, Beauchamp GK (2005) Anal Chem 77:2348
Malinowski ERM, McCue M (1977) Anal Chem 49:284
Rozett RW, Peterson ME (1960) Anal Chem 48:817
Demuth W, Karlovits M, Varmuza K (2004) Anal Chim Acta 516:75
Monigatti F, Berndt P (2005) J Am Soc Mass Spectrom 16:13
Nicola AJ, Gusev AI, Proctor A, Hercules DM (1998) Anal Chem 70:3213
Sadygov RG, Liu H, Yates JR (2004) Anal Chem 76:1664
Hoelzl R, Hoelzl C, Kotz L, Fabry L (1998) Accredit Qual Assur 3:185
Breen EJ, Hopwood FG, Williams KL, Wilkins MR (2000) Electrophoresis 21:2243
Ryu J, Im K, Yu W, Park J, Chang T, Lee K, Choi N (2004) Macromolecules 37:8805
Rockwood AL (1995) Rapid Commun Mass Sp 9:103
Kast J, Gentzel M, Wilm M, Richardson K (2003) J Am Soc Mass Spectrom 14:766
Schwartz LM (1975) Anal Chem 47:963
Ferrige AG, Seddon MJ, Jarvis S, Skilling J, Aplin R (1991) Rapid Commun Mass Spectrom 5:374
Zheng H, Ojha PC, McClean S, Black ND, Hughes JG, Shaw C (2003) Rapid Commun Mass Sp 17:429
Resing KA, Hoofnagle AN, Ahn NG (1999) J Am Soc Mass Spectrom 10:685
Zhang Z, Guan S, Marshall AG (1997) J Am Soc Mass Spectrom 8:659
Jalali-Heravi M, Fatemi MH (2000) Anal Chim Acta 415:95
Lancashire L, Schmid O, Shah H, Ball G (2005) Bioinformatics 21:2191
Trinajstic N, Gutman I (2002) Croat Chem Acta 75:329
Author information
Authors and Affiliations
Corresponding author
Additional information
Dedicated to my mentor, Professor Joseph A. Caruso
Rights and permissions
About this article
Cite this article
Meija, J. Mathematical tools in analytical mass spectrometry. Anal Bioanal Chem 385, 486–499 (2006). https://doi.org/10.1007/s00216-006-0298-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00216-006-0298-4