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Power Law Approach as a Convenient Protocol for Improving Peak Shapes and Recovering Areas from Partially Resolved Peaks

  • M. Farooq Wahab
  • Fabrice Gritti
  • Thomas C. O’Haver
  • Garrett Hellinghausen
  • Daniel W. Armstrong
Original
Part of the following topical collections:
  1. 50th Anniversary Commemorative Issue

Abstract

Separation techniques have developed rapidly where sub-second chromatography, ultrahigh resolution recycling chromatography, and two-dimensional liquid chromatography have become potent tools for analytical chemists. Despite the popularity of high-efficiency materials and new selectivity columns, peak overlap is still observed because as the number of analytes increases, Poisson statistics predicts a higher probability of peak overlap. This work shows the application of the properties of exponential functions and Gaussian functions for virtual resolution enhancement. A mathematical protocol is derived to recover areas from overlapping signals and overcomes the previously known limitations of power laws of losing area and height information. This method also reduces noise and makes the peaks more symmetrical while maintaining the retention time and selectivity. Furthermore, it does not require a prior knowledge of the total number of components as needed in curve fitting techniques. Complex examples are shown using chiral chromatography for enantiomers, and twin-column recycling HPLC of IgG aggregates and with tailing or fronting peaks. The strengths and weaknesses of the power law protocol for area recovery are discussed with simulated and real examples.

Keywords

Signal processing Peak area recovery Power laws Exponential functions Peak purity Recycling HPLC 

Notes

Compliance with Ethical Standards

Conflict of interest

The authors declare no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

References

  1. 1.
    Kauppinen JK, Moffatt DJ, Mantsch HH, Cameron DG (1981) Appl Spectrosc 35:271–276.  https://doi.org/10.1366/0003702814732634 CrossRefGoogle Scholar
  2. 2.
    Ferrige A, Lindon J (1978) J Magn Reson (1969) 31:337–340CrossRefGoogle Scholar
  3. 3.
    Sinanian MM, Cook DW, Rutan SC, Wijesinghe DS (2016) Anal Chem 88:11092–11099CrossRefGoogle Scholar
  4. 4.
    The United States Pharmacopeia Convention (2012) “<621> Chromatography”, vol 1, USP35-NF30  Google Scholar
  5. 5.
    Snyder LR (1970) J Chromatogr Sci 8:692–706.  https://doi.org/10.1093/chromsci/8.12.692 CrossRefGoogle Scholar
  6. 6.
    Wahab MF, Anderson JK, Abdelrady M, Lucy CA (2014) Anal Chem 86:559–566.  https://doi.org/10.1021/ac402624a CrossRefPubMedGoogle Scholar
  7. 7.
    Dyson N (1998) Chromatographic Integration Methods, 2nd edn. Royal Society of Chemistry, CornwallGoogle Scholar
  8. 8.
    Patel DC, Wahab MF, O’Haver TC, Armstrong DW (2018) Anal Chem 90:3349–3356.  https://doi.org/10.1021/acs.analchem.7b04944 CrossRefPubMedGoogle Scholar
  9. 9.
    Wahab MF, Wimalasinghe RM, Wang Y, Barhate CL, Patel DC, Armstrong DW (2016) Anal Chem 88:8821–8826.  https://doi.org/10.1021/acs.analchem.6b02260 CrossRefPubMedGoogle Scholar
  10. 10.
    Ciogli A, Ismail OH, Mazzoccanti G, Villani C, Gasparrini F (2018) J Sep Sci 41:1307–1318.  https://doi.org/10.1002/jssc.201701406 CrossRefPubMedGoogle Scholar
  11. 11.
    Barhate CL, Joyce LA, Makarov AA, Zawatzky K, Bernardoni F, Schafer WA, Armstrong DW, Welch CJ, Regalado EL (2017) Chem Commun 53:509–512CrossRefGoogle Scholar
  12. 12.
    Wahab MF, Patel DC, Wimalasinghe RM, Armstrong DW (2017) Anal Chem 89:8177–8191.  https://doi.org/10.1021/acs.analchem.7b00931 CrossRefPubMedGoogle Scholar
  13. 13.
    Godinho JM, Reising AE, Tallarek U, Jorgenson JW (2016) J Chromatogr A 1462:165–169CrossRefGoogle Scholar
  14. 14.
    Gritti F, Besner S, Cormier S, Gilar M (2017) J Chromatogr A 1524:108–120CrossRefGoogle Scholar
  15. 15.
    Daniel E, Nicola L (2016) Chem Commun 52:13253–13256CrossRefGoogle Scholar
  16. 16.
    Porath J, Flodin P (1959) Nature 183:1657–1659CrossRefGoogle Scholar
  17. 17.
    Lim LW, Uzu H, Takeuchi T (2004) J Sep Sci 27:1339–1344CrossRefGoogle Scholar
  18. 18.
    Davis JM, Giddings JC (1983) Anal Chem 55:418–424.  https://doi.org/10.1021/ac00254a003 CrossRefGoogle Scholar
  19. 19.
    Shalliker RA, Stevenson PG, Shock D, Mnatsakanyan M, Dasgupta PK, Guiochon G (2010) J Chromatogr A 1217:5693–5699CrossRefGoogle Scholar
  20. 20.
    Shock D, Dennis GR, Guiochon G, Dasgupta PK, Shalliker RA (2011) Anal Chim Acta 703:245–249CrossRefGoogle Scholar
  21. 21.
    Dasgupta PK, Chen Y, Serrano CA, Guiochon G, Liu H, Fairchild JN, Shalliker RA (2010) Anal Chem 82:10143–10150CrossRefGoogle Scholar
  22. 22.
    de Juan A, Tauler R (2006) Crit Rev Anal Chem 36:163–176CrossRefGoogle Scholar
  23. 23.
    Chesler SN, Cram SP (1973) Anal Chem 45:1354–1359CrossRefGoogle Scholar
  24. 24.
    Wilks DS (2011) Statistical methods in the atmospheric sciences. Academic press, CambridgeGoogle Scholar
  25. 25.
    Gritti F, Wahab MF (2018) LCGC North Am 36(2):82–98Google Scholar
  26. 26.
    Gritti F, Dion M, Felinger A, Savaria M (2018) J Chromatogr A 1567:164–176CrossRefGoogle Scholar
  27. 27.
    Westerberg A (1969) Anal Chem 41:1770–1777CrossRefGoogle Scholar
  28. 28.
    Foley JP (1987) J Chromatogr A 384:301–313CrossRefGoogle Scholar
  29. 29.
    Wahab MF, Patel DC, Armstrong DW (2017) J Chromatogr A 1509:163–170.  https://doi.org/10.1016/j.chroma.2017.06.031 CrossRefPubMedGoogle Scholar
  30. 30.
    Kalambet Y, Kozmin Y, Mikhailova K, Nagaev I, Tikhonov P (2011) J Chemom 25:352–356CrossRefGoogle Scholar
  31. 31.
    Jansson PA (1984) Deconvolution with applications in spectroscopy. Academic Press, New YorkGoogle Scholar
  32. 32.
    Wahab MF, Dasgupta PK, Kadjo AF, Armstrong DW (2016) Anal Chim Acta 907:31–44.  https://doi.org/10.1016/j.aca.2015.11.043 CrossRefPubMedGoogle Scholar
  33. 33.
    Weber HJ, Arfken GB (2003) Essential mathematical methods for physicists, ISE. Elsevier, New YorkGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Chemistry and BiochemistryUniversity of Texas at ArlingtonArlingtonUSA
  2. 2.Waters Corporation, Instrument/Core Research/FundamentalMilfordUSA
  3. 3.Department of Chemistry and BiochemistryUniversity of Maryland at College ParkCollege ParkUSA

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