Quantification by Matrix-Assisted Laser Desorption Ionization Mass Spectrometry Using An Approach Based On Stochastic Dynamics. Experimental And Theoretical Correspondences

TABLE OF CONTENT

Introduction

1. Experimental
1.1. Synthesis
1.2. Analytical instrumentation and methods
1.2.1. Mass spectrometric measurements
1.2.2. Sample preparation for the MALDI-MS measurements
1.3. Theory/Computations
1.3.1. Stochastic dynamics
1.3.2. Chemometrics
1.3.3. Computational quantum chemistry

2. Results and discussion
2.1. Experimental MALDI mass spectrometric data – qualitative analysis
2.2. Experimental MALDI mass spectrometric data – quantitative analysis
2.3. MALDI mass spectrometric method performances
2.4. Experimental electrospray ionization mass spectrometric data – quantitative analysis
2.5. Correspondence between diffusion parameters obtained on the base on stochastic dynamics and current monitoring method

3. Theoretical data

Conclusion

References

PREFACE

The goal of this work is to describe more recent developments in the quantitative mass spectrometry and to illustrate how our new model equations based on the stochastic dynamics relate to the determining the 3D molecular and electronic structures of analytes. It is aimed at researchers in Chemistry who would like to find out about what is going on in mass spectrometric methodological contributions more recently. The work could also be used to MSc and PhD students in the field of Chemistry, in particular, highlighting the ‘Analytical chemistry’, ‘Physico–chemistry’ and/or ‘Computational and theoretical chemistry’, respectively.

ABSTRACT

In the present work we argue for that the temporal behaviour of the analyte MS intensity under matrix–assisted laser desorption/ionization (MALDI) and electrospray ionization (ESI) mass spectrometric (MS) experimental conditions can be expressed quantitatively by means of stochastic dynamics. We explore the Box–Müller’s method with an implication to an approximation to the Maxwell–Boltzmann distribution of the intensity of analyte MS peaks as a random variable for the thermodynamic equilibrium. The description of the MS intensity as a stochastic variable has led to exact model equations valid to any MS peak intensity of any MS analyte ion within the framework of series of independent measurements and sample techniques for MALDI– or ESI–MS analyses over a random scan time. The model equations are obtained from a representative statistically study. In total, intensities of ninety MS peaks of molecular and fragment ions of (4-diethylamino-benzylidene)-pyridin-4-yl-amine (1) are examined. There are used two sample preparation techniques and two matrix components: (i) an analysis of single crystal; and (ii) an analysis polycrystalline analyte–matrix compositions in presence of matrixes 2,5–dihydroxybenzoic acid (DHB) or 4–hydroxy–a–cyanocynnamic acid (CHCA) within the t Î 0.009–114.51 mins. The employment of the Ornstein–Uhlenbeck’ and Einstein’s approximations to the stochastic variance parameter (s2) as ‘ diffusion parameter ’ leads to a significant statistical correspondence between MALDI–MS and ESI–MS diffusion parameters showing a correlation coefficient r = 0.995. The theoretical quantum chemical modeling of the molecular and electronic structures of the analyte MS ions and the employment of high accuracy ab initio and methods based on the density functional theory (DFT) including both static and molecular dynamic computations as well as adiabatic and diabatic method of the diffusion coefficients result to a correlation between theory and experiment r = 0.7732–1. The capability of MALDI–MS to elicit 3D structural information about the analytes is highlighted explicitly and quantitatively discussing the relations between the temporal behavior of the analyte MS intensity–experimental ‘diffusion’ parameter–theoretical ‘diffusion’ parameter–molecular/electronic structure of analyte MS ion. The theoretical modeling of the diffusion parameters is based on the Arrhenius’ approximation, which becomes valid to both ESI– and MALDI–MS methods. The experimental diffusions are correlated independently with the corresponding data obtained on the base on ’current monitoring method ’. The work therefore is intended as a bridge between theory and experiment drawing upon the mass spectrometric capability of an exact 3D structural determination based on a stochastic dynamic approach. The empirical adequacy of our theoretical concept is tested by chemometrics. The statistical analysis shows that it is really empirically testable. Moreover, it is applicable to atmospheric pressure chemical ionization mass spectrometric data, as well.

Acknowledgments

The authors thank the Deutscher Akademischer Austausch Dienst for a grant within the priority program “Stability Pact South-Eastern Europe” and for an Evolution 300 UV–VIS–NIS spectrometer ; the Deutsche Forschungsgemeinschaft; the Alexander von Humboldt Stiftung (Germany) for the donation, a single crystal X–ray diffractometer; the central instrumental laboratories for structural analysis at Dortmund University (Federal State Nordrhein–Westfalen, Germany) and analytical and computational laboratory clusters at the Institute of Environmental Research at the same University. Conflict of interests: Michael Spiteller has received research grants (Deutsche Forschungsgemeinschaft, 255/22–1 and 255/21–1); Bojidarka Ivanova has received research grants (Deutsche Forschungsgemeinschaft, 255/22–1; Alexander von Humboldt Foundation, research fellowship).

This work was carefully carried out. Nevertheless, authors and publisher do not warrant the information therein to be free of errors. The work is being published in English aiming a widest access to the scientific contributions. English is not native language of the authors. Therefore, stylistic rough edges may occur. The authors hope of the understanding of the reader.

Address correspondence to the authors:

Lehrstuhl für Analytische Chemie, Institut für Umweltforschung, Fakultät für Chemie und Chemische Biologie, Universität Dortmund, Otto–Hahn–Straße 6, 44221 Dortmund, Nordrhein–Westfalen, Deutschland.

KEYWORDS

Stochastic dynamics, mass spectrometry, quantification

Introduction

Mass spectrometry becomes among the most powerful method for qualitative, quantitative and structural analyses. It gains increasing and considerable interest in both fundamental and applied sciences. The MS analytical instrumentation provides highly reliable, accurate, sensitive, precise and selective information. It is irreplaceable and robust approach in the analytical practice encompassing many inter– and multidisciplinary research fields, for instance, analytical chemistry; environmental analysis; food chemistry and agricultural sciences; clinical diagnostics and medicine; forensic chemistry; nuclear forensics; archeology, and more [1]. The MALDI– and ESI–MS are powerful analytical method having superior instrumental characteristics. They consisting of: (a) ultrahigh resolving power and accurate detection of a single analyte in complex multicomponent mixture; (b) low concentration limits of detection and quantization ranging from fmol to attomol levels; (c) rapid, cheap and simple sample pretreatment procedures, including direct assay (MALDI); (d) quantification from low molecular weight analytes (LMW) to (bio)macromolecules (~ 100 kDa); (e) implementation of imaging techniques (MALDI and ESI); (f) analysis of gaseous, liquid, semi–liquid and solid samples in homogeneous and heterogeneous phases (MALDI); and (g) flexible instrumental design allowing different coupling instrumental schemes, improving significantly the method performances, respectively [1–7]. The ultrahigh mass resolving power using Fourier transform ion synchrotron (FTICR) or Orbitrap analyzers has been demonstrated for metabolomics and proteomics [2]. Analysis of pharmaceutics or archaeological artifacts can be found [3]. Studies devoted to food omics [4], peptidomics [5] and clinical diagnostics of pathogens and fungi [6,7f] are known. The environmental analysis of contaminating agents like therapeutics, agricultural and/or industrial chemicals, contaminating food additives or cosmetics in foods, water, soil, air, different animals and/or plants has been shown [7n]. The MALDI–MS has been elaborated as a method for (bio)macromolecular screening, in vivo imaging and assay of living cells, whole organs and bodies by Caprioli [8], with implementation to the clinical research. In spite of these outstanding achievements, which have resulted in a significant impact to the chemical biology, neuroscience, medicinal chemistry, etc., there are many protocols determining LMW analytes [7]. But the most interesting research question is whether MALDI–MS method is a prospective approach having a great capability of quantitative analysis of reaction kinetics, thermodynamics, diffusion and exact 3D structural determination of the analytes? We can distinguish from three different types ‘ quantitative analysis ’ or ‘ quantification ’ based on MALDI–MS: (i) determination based on the standard calibration approach; (ii) quantification via MALDI–MS imaging technique; and (iii) 3D structural determination based on quantitative relations and model equations determining the mutual correspondence between kinetic and thermodynamic parameters as well as diffusion coefficients. As might be seen from the tremendous research contributions devoted to quantification via MALDI–MS only scarce number contributions have been devoted to points (i) and (ii) [9]. So far, there is a lack of quantitative models in context point (iii). Thus, the main goal of this work is to elicit a highly accurate quantitative 3D structural information employing MALDI mass spectrometry. It seems best to mention that the lack of quantitative models in context point (iii) are associated with the still not well understood phenomenology of the desorption–ionization mechanisms of MALDI–method and the factors governing the ion efficiency [1]. There are different sample preparation methods, as well [1]. Furthermore there have been reported conflicting results and disputes associated with the few available theoretical concepts and models of ionization/desorption processes/mechanisms and the experimental evidences for the facts [1,10]. On the other hand, more recent impressive amount of methodological newcomers have been associated with instrumentation itself, rather than focused on phenomenology of MALDI process, including fundamental knowledge about MS reaction kinetics, thermodynamics, etc. In this context, before presenting our contributions in the next sections of the work we would like to underline in this introductory part that we will propose completely different and new view about MALDI–MS phenomena which faces all mentioned above challenges of explaining MALDI–MS processes, including quantification of those processes associated with gas–phase reactions; effect of the matrix component on the analyte ionization efficiency and MS intensity; quantification of processes under direct assay of single crystal of analyte; new model equations determining the intensity of the analyte signals based on nonlinear approximation and it treatment via stochastic dynamics. In particular, problem for any MALDI–MS based quantitative analytical protocol is that it should be able to overcome by a series of experimental factors associated with the type of the sample sample heterogeneity and no uniform distribution of the polycrystalline matrix and analyte components [9]. As has been comprehensively discussed in the latter reference the MALDI–MS sample preparation steps can show poor accuracy and/or precision; poor linearity and dynamic range; and low shot-to-shot, region-to-region and sample-to-sample reproducibility. For this reason it is well to argue for that our experimental design includes a comparative quantification of analyte in presence of different matrixes together with a direct analysis of isolated single crystal. The quantification is carried out using nonlinear model equation in order to account for a stochastic character of the mentioned above random variations. As will be seen our new methodology overcomes by all mentioned above difficulties associated with the sample preparation techniques in MALDI–MS.

1. Experimental

1.1. Synthesis

The synthesis of (4-diethylamino-benzylidene)-pyridin-4-yl-amine (1) has been reported to our common scheme for synthesis of Schiff’s bases [11a]. The experimental optical properties of (1) have been described in the same reference. A crystallographic determination of the structure of a positional isomer of (1), i.e. N,N-diethyl-N'-pyridin-4-ylmethylene-benzene-1,4-diamine, which is used in our comparative analysis can be found as well [11b].

1.2. Analytical instrumentation and methods

1.2.1. Mass spectrometric measurements

Mass spectrometric measurements were carried out by TSQ 7000 instrument (Thermo Fisher Inc., Rockville, MD, USA). A triple quadruple mass spectrometer (TSQ 7000 Thermo Electron, Dreieich, Germany) equipped with an ESI 2 source were used for ESI–MS and APCI–MS measurements. The quantification using the lastly mentioned instrument was carried out via a combination of mass detectors (trap, linear ion trap and orbitrap), accumulating spectra for t = 7–30 mins (420–1800 s). The selected reaction monitoring approach was used, where the data were saved as individual files. The relative intensities of the species studied were obtained using QualBrowser software 2.7. The program package ProteoWizard 3.0.11565.0 (2017) was used as well. The mass resolving power R = 98 101. The ESI, atmospheric pressure chemical ionization (APCI) and collision induced dissociation (CID) resolving powers are R = 55 121, 19 341, 15 700, respectively. A standard LTQ Orbitrap XL (Thermo Fisher Inc.) spectrometer was used for MALDI–MS measurements, using the UV laser source at lmax = 337.2 nm. An overall mass range of m/z 100–1000 was scanned simultaneously in the Orbitrap analyzer in presence of inner standard (Figs. 1 and 2; m/z 283). The ImageQuest 1.0.1 program package was used. The extracted MS spectra (without the MS peaks of the inner standard) and processing of the ion chromatograms was performed using AMDIS 2.71 (2012) and SeeMS 3.0.11.565.0 (2017), respectively. The laser energy values were Î 14.8–15.5 mJ. The numbers of averaged laser shots lies Î 18–80, the MALDI flow rate values were Î 25.01–25.08, the corresponding elapsed scan time range lies Î 18.0–2.50 s, respectively. Additional detail can be found in Table 1. The measurements were carried out using direct analysis of analyte single crystal and of polycrystalline analyte/matrix co–crystals using dried droplet technique described in [1]. The following matrixes were used: 2,5–dihydroxybenzoic acid (DHB) and 4–hydroxy–a–cyanocynnamic acid (CHCA), respectively (Figs. 1 and 3). The processing of the MS isotope shape includes analysis of the MS spectra in the presence of the inner standard (m/z 283, Fig. 2). In parallel, the quantification of the intensities of the MS peaks is carried out using the so–called extracted spectra (Fig. 4). The latter procedure is performed according to the algorithm [12] incorporated in AMDIS 2.71 (2012) consisting on manual deconvolution using the constant peaks of the inner standard extracting m/z values from the ion chromatograms (See the lastly mentioned figures). The corresponding MS peaks of the matrix components DHB or CHCA are almost completely suppressed. The intensity of the analyte signal of CHCA in (1) /CHCA at m/z 189.06 has relative intensity 0.05 %. The corresponding automatized procedure (reference [12a]) is also employed. The chromatographic analysis was carried out by Gynkotek (Germering, Germany) HPLC instrument, equipped with a preparative Kromasil 100 C18 column (250×20 mm, 7 μm; Eka Chemicals, Bohus, Sweden) and a UV detector set at 250 nm. The analytical HPLC was performed on a Phenomenex (Torrance, CA, USA) RP−18 column (Jupiter 300, 150×2 mm, 3 μm) under same chromatographic conditions. The analysis was performed on a Shimadzu UFLC XR (Kyoto, Japan) instrument. The chromatographic and MS measurements were conducted during synthesis in order to determine the chemical purity of the starting substances used; control of their chemical reactivity under the shown experimental conditions in order obtaining of any chemically changed condensation/interaction product/s, as well as isolation of pure component/s system/s.

Abbildung in dieser Leseprobe nicht enthalten

Figure 1. MALDI–MS ion chromatograms of single crystal of (1) and analyte matrix polycrystalline composition (1) /CHCA.

Abbildung in dieser Leseprobe nicht enthalten

Figure 2. MALDI–MS spectrum of single crystal of (1) in presence of inner standard (M/z 283.13599).

Table 1. MALDI–MS experimental parameters/conditions

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Figure 3. 3D imaging of the analyte distribution on the MS holder shown as relation between the coordinates X, Y and the relative abundance (%) (The resolution DX is 100 mm) (A); Optical images of a MALDI polycrystalline sample (B) and single crystal of (1) (inverted) (C); and photograph of single crystals of (1) (D), respectively.

Abbildung in dieser Leseprobe nicht enthalten

Figure 4. Experimental temporal behavior of the analyte MS intensity; Ion currents; Total ion currents (TIC) versus the scan time [mins]; Mass spectra per shot; The different figures depict the experimental MS ion intensities of different analyte peaks during different scan times. The TIC illustrates the sum of all analyte MS ion intensities at the different times; Chemical diagram of the analyte (1).

1.2.2. Sample preparation for the MALDI-MS measurements

The MALDI–MS single crystal measurements were carried out using direct measurements of a single crystal (Fig. 3). The MALDI matrixes and the polycrystalline composites of analyte/matrix samples were prepared, using the dried droplet technique [1]. The obtained matrix-analyte embedded solid-samples were measured as well by XDR methods (both single crystal as well as the powder one) in order to exclude from unwanted chemical modifications of both the analytes and/or the matrix components, which would influenced the precise assignment of the observed MS peaks. As standard solvent mixture of methanol/water (1:1, v/v) was used. The dried droplet preparations were performed, using the 1 mol/L concentration of matrix solution and analyte solutions (10-4-10-3 M). The obtained solutions were mixed on MALDI target and dried by a gentle flow of air. The same analyte solutions were used for the independent ESI–MS measurements, using however acetonirile:methanol solvent mixtures 1:1. Under these conditions the powder X-ray diffraction method shows the formation of the polycrystalline sample in large amounts of crystals (Fig. 5). The aggregations of the crystals (crystal sizes > 3 mm), were observed around the edge of the drop, thus leading to the inhomogeneous and irregular (random) distribution of crystals on MALDI target.

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