Anal. Chem. 1990, 62, 1809-1818
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Systematic Delineation of Scan Modes in Multidimensional Mass Spectrometry J a e C. Schwartz,lJ Adrian P. Wade,b5 Christie G. Enke? a n d R. Graham Cooks*J
T h e Chemistry Department, Purdue University, West Lafayette, Indiana 47907-3699, T h e Chemistry Department, Michigan State University, East Lansing, Michigan 48824, and British Petroleum Research Centre, Chertsey Road, Sunbury-on-Thames, Middlesex TW16 7LN, United Kingdom
A logical analysts of mass spectrometrlc scan modes is performed that reveals the full set of experiments avallabie in muitidhenslonal mass spectrometry. The analysts utlllzes a symbokm that helps provlde an organizatbnai scheme for the representation and classlflcatlon of the wide variety of experiments that exist. I n general, for an n-stage experlment, there is a closed set of experimental modes producing spectral types that vary In mass dimensionality from 0 to n . There Is a total of 2” experlments that have 1 or 0 mass dimensions, along with an Increasing number of experiments of hlgher mass dimensionality. There also exists a set of 2” fundamental scan modes, viz., experiments in whlch only massto-charge ratlos of individual ions, but not their interrelatlonships, are specifled. Scans In whlch functlonal reiationshlps between ion masses are deflned (e.g., neutral loss scans) introduce complexity into the total number of scan types available in an MS” experlment, giving a total of 1, 2, 5, 15, 52, and 203 experlments of 0 through 5th order, respectlvely. It is shown that combinations of data from lower order experiments can be used to construct higher order spectra. Extraction of data of lower mass dimensionality from data of hlgher dlmenslonalHy Is also demonstrated. A different method of reduclng dimensionality, projection of dlspersed data back Into a smaller number of mass dimensions, is also introduced and characterized. The analysis reveals several new types of scan modes including an MS/MS/MS scan havlng unit mass dhensionality, referred to as the selective neutral-loss scan, and several new MS/MS/MS scans that are two-dimenslonai In mass. Examples of these new experiments are provlded, and their potential value is discussed.
INTRODUCTION Experiments that utilize multiple stages of separation or that combine chromatography and spectroscopy have become well-known (I). They have helped stimulate consideration of the data available from particular instruments in terms of discrete data dimensions (2). For example, the full data domain yielded by the combined GC/MS instrument (3) is usefully considered as three dimensional-one dimension in time, one in mass-to-charge ratio, and one in ion abundance. It is not only desirable but often necessary to conduct economical searches of the data domain. In other words, constraints in sample availability and in instrument time force attention to be focused on those regions of the entire data domain that are most rich in information bearing on the Purdue Universit *Present address: hnnigan Corp., 355 River Oaks Parkway, San Jose, CA 95134. Michi an State University. Britisi Petroleum Research Centre. sPresent address: Department of Chemistry, University of British Columbia, Vancouver, British Columbia V6T 1Y6,Canada.
problem in hand. The question of just what experiments are available to achieve this objective and what their characteristics are therefore takes on significance. Experiments in which information from a single spectroscopic technique is dispersed into multiple dimensions are exemplified by two-dimensional NMR (4)and tandem mass spectrometry (MS/MS) (5). Distinct experiments are used to sample particular regions of the total data domain, and in mass spectrometry the situation is further complicated by the fact that a wide variety of different types of mass analyzers are available to perform analogous tasks and by the fact that a variety of different methods can often be used to acquire the same type of information. For example, the set of fragment ions arising by collision-induceddissociation of a selected molecular ion can be recorded by using either an electric sector scan or a linked scan of the magnetic and electric sectors in a double-focusing mass spectrometer (6). This paper examines the general question of the information content of multistage mass spectrometry. It seeks to provide a logical framework for all possible experiments, independently of considerations of instrumentation, and to characterize their properties. It also deals with the interconnections between these subsets of the entire data domain. In the course of the work, new types of experiments are described and demonstrated. Tandem mass spectrometry (MS/MS) is an increasingly widely used technique that has value in studies of ion chemistry and in qualitative and quantitative chemical analysis (7, 8). Four types of MS/MS experiments have been recognized and widely utilized. They are the reaction monitoring, parent, product, and neutral loss (gain) scan modes (9). (The term “scan mode” is used here in the general sense as a method of acquisition of data of a certain type. The term does not necessarily imply that any “scanning” is actually occurring; nor does it constrain the types of analyzers or instrumental procedures used to obtain the data. Note also that the established term, daughter spectrum, is considered undesirable by some. We have therefore used the term product spectrum for daughter spectrum whenever possible.) Recently, the neutral loss (gain) scan has been recognized as a special case of a more general scan type, the functional relationship scan (10). Each of these four MS/MS experiments represents a subset of the complete MS/MS data domain ( I l ) , and each has its own particular utility when applied in solving particular problems. The addition of further stages of mass analysis introduces more possible scan types. As many as seven stages of mass analysis (MS’) have been performed in sequence using a FTMS instrument (12),and an even larger number has been performed in a quadrupole ion trap mass spectrometer (13). Three- and four-sector instruments have proven useful for experiments that require more than two stages of mass analysis, although relatively little use has been made of this latter capability (14). Pentaquadrupole instruments utilize three quadrupole mass filters and two additional quadrupoles in which reactions or dissociations occur (15). They are
0003-2700/90/0382-1809$02.50/0 0 1990 American Chemical Society
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well-suited for multiple-stage experiments but have seen limited application, even for MS/MS experiments. Hybrid mass spectrometers incorporate several different types of analyzers in a single versatile instrument (16),and these devices have been the principal tool used in experiments aimed at extending the scope of MS/MS and MS" experiments. With the construction of a BEQQ hybrid mass spectrometer (B, magnetic sector; E, electric sector; Q, quadrupole), an attempt was made to implement and investigate the MS3 (MS/MS/MS) scan modes (17). A number of three-stage experiments were demonstrated, and a first attempt was made to provide a rational framework to accommodate the increasing number of multistage (MS") mass spectral scan types (18). Nevertheless, a more complete and rigorous methodology for representing, categorizing, and understanding all mass spectral scan modes was desirable, and this study attempts to provide such a methodology and to begin to characterize the new scan modes it yields. EXPERIMENTAL SECTION Two different triple-analyzer mass spectrometers were used to obtain the data reported here. The first is a Finnigan MAT HSQ30, a hybrid instrument that has both magnetic (B) and electric (E) sectors combined with an rf-only quadrupole collision cell (Q) and a mass analyzing quadrupole (Q). This BEQQ instrument is described in detail elsewhere (17). Two stages of collision-activateddissociation were used in this instrument; 3-keV collisions occurred in the collision cell in the f i t field-free region, before the magnetic sector, and approximately 30-eV collisions in the rf-only collision quadrupole. Both collision regions utilized Torr. Sample argon collision gas at approximately 2.0 x pressures were typically 5.0 X lod TOR.The sectors were scanned in the B/E or B2/E linked scan modes (6) to perform product and parent scans, respectively. These linked scans were used in conjunction with scans of the quadrupole maSS analyzer to perform MS3 experiments. The second instrument is a pentaquadrupole instrument (19) that utilizes three mass analyzing quadrupoles and two rf-only collision quadrupoles. Low-energy collisions, usually 20 eV, were employed in both collision regions. All experiments employed Torr as read argon as collision gas at approximately 4.0 X by ionization gauges situated in the vacuum cradle system outside the collision cells. Total operating pressure in the ion source, including sample and collision gas pressure, was approximately 8.0 x Torr. The ease of computer control of quadrupoles allowed experiments in which more than one quadrupole was scanned simultaneously to be implemented readily. A full description of this new instrument, along with the data system used to control the mass spectrometer and to acquire and manipulate MS3 data (five-termboxcar smoothing and base-line subtraction), is given elsewhere (20). RESULTS AND DISCUSSION Symbolism and Terminology. A systematic analysis of all possible scan modes for multistage mass spectrometry is achieved by utilizing a particular symbolism for their representation. Table I gives an essential glossary of the terms and symbols used throughout the analysis. To describe a particular experiment explicitly, all fixed masses and defined mass transitions must be stipulated; this is done by using a succinct notation that is employed with the scan symbol as shown in the spectra reproduced below. The term order will be used to specify the number of stages of mass analysis, i.e., the term n in the expression MS". For simplicity, it may be easiest to envision quadrupole analyzers as providing the stages of mass analysis since these devices are true mass-to-charge analyzers, but sectors, time-of-flight instruments, and ion-trapping devices can be substituted with no effect on the following presentation. The symbolic representations of the different types of experiments discussed can be viewed equally well as referring to the scan modes themselves or to the types of spectra produced by particular
Table I. Glossary of Terms and Symbols fixed mass variable mass + fixed or defined mass transition variable mass transition order number of stages of mass analysis; the term n in the expression MS" mass dimensionality number of mass axes required to display the data produced by a particular scan type fundamental scan modes set of scans for a given order experiment for which no mass transitions have been defined by the user extraction process of generating data having the same order but a lower mass dimensionality from a given spectrum projection process of generating data having a lower order and a lower mass dimensionality from a given spectrum intersection process of generating data having a higher order from data of lower order and the same mass dimensionality 0
0
-
MS3
I
e21
Figure 1. Summary of the scar node analysis delineating all possible scan modes for MSO. MS'. MS2 MS3. The number under the svmbol is the mass dimensionalityof the scan, and the number in parenkses is the number of the scan referred to in the text.
scans. A useful classification of scan modes is in terms of mass dimensionality. For example, an ion-monitoring experiment requires no mass axis for the display of the data produced, whereas a mass spectrum requires one. We define the muss dimensionality of the experiment (or scan mode) as the number of mass axes required to display the data produced by a particular scan type. A full analysis of the MSO, MS', MS2, and MS3 cases is performed with extrapolation to higher orders. Throughout the following analysis refer to Figure 1, which is a summary of the representations of all possible MSo-MS3 experiments. Note that scans are referred to by the numbers that appear in parentheses in Figure 1. Analysis of Scan Modes. MSO: This is an experiment that has no mass analysis step and therefore has no repre-
ANALYTICAL CHEMISTRY, VOL. 62. NO. 17, SEPTEMBER 1. 1990
sentation as a mass spectrometric scan mode. However, an interpretation that fits nicely into the analysis and therefore warrants mentioning is that it represents the "total ion current" (TIC) mode, a frequently used procedure for nonselective mass spectrometric detection in chromatography. MS1 (MS): The single mass analysis step in this experiment analyzes for ions on the basis of mass-to-charge ratio m, (referred to hereinafter for brevity as analysis for mass m,). The analyzer can either be fixed, to transmit ions of a single mass m,, or allowed to scan to record the abundances of all m, ions over a specified mass range. We shall let a fixed mass be represented by a single filled circle (e),while a single unfilled circle (0) represents a scanned or variable mass. These symbols depict the only two possibilities for MS1 experiments, viz., the single-ion-monitoringexperiment (1)and a simple mass spectrum (Z), respectively (Figure 1). Note that a multiple ion monitoring experiment, in which a limited number of ions is interrogated, is viewed as an abbreviated form of mass scan and classified accordingly. The two MS' scans are zero and one dimensional in mass, respectively. Of course, the overall dimensionality of the experiment will be greater than the mass dimensionality since measurements of ion abundance must be made. In some cases additional variables, for example, collision energy in energyresolved mass spectrometry (211, collision angle in angle-resolved mass spectrometry (22).or other parameters related to ion internal energy are also studied and add to the overall dimensionality of the data. The open circle can be envisioned as a complete set of filled circles in a mass range of interest; viz., the mass spectrum is simply the complete set of ion-monitoring experiments. In general all higher dimensional scan modes are complete sets or maps of experiments having lower mass dimensionality. Just as the zero- and one-dimensional experiments of ion monitoring and mass spectra are both useful modes of operation, so experiments with still higher mass dimensionality are also useful, as will he demonstrated below. MS* (MS/MS): Two stages of mass analysis are used in MS/MS experiments to select the parent and product ion masses, m, and m, respectively. Each stage of mass analysis can be made to define either a fixed or a variable mass and each can he represented by a filled or unfilled circle. The result is Z2, or 4, possible combinations that form the basis for representing different types of experiments. The first combiition (3, Figure l), repreaentd by two fded circles, specifies that both masses m, and m2 are fixed a t particular values. In general, some reaction (dissociative, associative, etc.) is taking place that causes a change from one state, m, to another, m2 (charge changes and simple ion-removal processes are not excluded). Thus, the transition is the (mathematical) relationship between m, and m2. An arrow between the two filled circles is used to represent this transition. The thick arrow (analogous to the filled circle) used in this case, denotes that the mass transition (mas8 loss, gain, etc.) between m, and m, is fixed by the two fixed masses it connects. This experiment (3) is known as the reaction monitoring experiment and is zero dimensional in mass. Varying m2 while fixing m, (4) and varying m, while fixing m2(5), describe product and parent scans, respectively. Since one mass is varying in each case, the mass transition between ml and m2also varies. Therefore the transition in these two cases is represented hy a thin m w (by analogy to the unfilled circle) signifying a freely ranging mass transition. Both of these scans require one mass axis to represent their spectra and as such are one-dimensional in mass. The last possible combination of analyzer states, when utilizing two mass analyzers, is represented by two unfilled circles, a symbol that allows the masses of both ions to vary
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Flgure 2. Dispersive analyzer used with an imaging detector to Produce a spectrum having two mass dimensions. This is achieved with a si@ scan of the s e k i k analyzer usiw a OnedimsDnaI delecta (upper) M Hithoul scanning provided a two dimensbml detector is used (lower).
MS/MS DATA DOMAIN FOR "-DECANE ( m r = 142)
I
' 4 o ' B o ' S o
do' 820 ' Ib
DAUGHTER
w s
Flgure 3. MSlMS data &main for n&cane obtained by using a hybrid BEQQ instrument.
This Combination requires more consideration,since up to this point the nature of the transition between the masses, represented by the arrows, has been determined by the selection criteria applied directly to the ion masses themselves. However, in the case of this Combination of symbols, two options exist. One option is to have the masses vary independently. This implies that the transition between the masses is not fixed and the experiment is designated by using a thin m o w to connect the open-circle symbols (6). All masses in a mass range of interest for both masses m, and m2 are included. Instrumentally, this scan can be accomplished by stepping one analyzer one mass a t a time or scanning i t very slowly, while the second analyzer scans an entire mass range of interest quickly at each setting of the first. Alternatively a multidimensionaldetector system and dispersive analyzer may be utilized (Figure 2). This type of experiment requires two mass axes in its representation and so has a mass dimensionality of two. The entire MS/MS data domain represents the data for scan (61,and such experiments have been carried out ( I I , 23). Figure 3 shows an example of such a two-dimensional spectrum for n-decane. The alternative option for the case of two varying masses is that they be dependent variables, viz., that the transition between them be specified (7). This defined transition (as
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ANALYTICAL CHEMISTRY, VOL. 62, NO. 17, SEPTEMBER 1, 1990
I MS/MS SCAN LINES j
Table 11. Number and Mass Dimensionality of the Fundamental Scan Modes mass dimensionality n
0
0
1
1 2 3
1 1 1
4
1
5 6
1 1
2
1
3
4
5
6
total no. 1
2
1 2 3
4 5
1 6
1 3 6 0
15
4 8
1
4 1 1 0 5 20 15
16 1
6
32 1
64
opposed to being determined by the prior selection of the masses involved) is depicted by a thick arrow just as is done in designating the reaction monitoring experiment. This specification allows both masses, ml and m2,to vary but only in some controlled fashion where the value of one is dependent on the value of the other. One example of this experiment is the well-known constant neutral loss scan (24))in which both analyzers are scanned such that a constant difference between m, and m2 is maintained. The mass difference corresponds to the mass of a specified neutral fragment, Le., m2 = m, k , where k = mass of neutral fragment. More generally (IO), any prescribed relationship between the masses, Le., m2 = f ( m J , may be chosen as the defined transition; hence, the constant neutral loss (gain) scan is just one particular member of the more general class of scans referred to as "functional relationship" scans and represented by symbol 7 in Figure 1. The functional relationship scan is a new experiment, first recognized in the course of this analysis of scan modes. It has been demonstrated, and examples of its utility are reported in a separate publication (25). Defining a relationship between two variable masses is analogous to having two variables and one equation. The number of independent variables is reduced to one, and this specifies the mass dimensionality of the resulting spectrum. For example, one and only one mass axis, either parent or product mass, is required to represent a constant neutral loss spectrum, since the mass of the other ion is implicitly known. Scan 7 therefore represents a third MS/MS scan which has one mass dimension. Fundamental Scan Modes. At this point, the concept of a set of fundamental scan modes is introduced. For the 2n combinations of circles representing n stages of mass analysis in an experiment of given order, we define as fundamental scans that subset of scans for which no mass transitions have been defined by the user. The reaction monitoring, parent, product, and the MS/MS data domain experiments (scan 3-6) therefore represent the set of fundamental scan modes for an MS2 experiment, while the neutral loss (generally functional relationship) scan (7) is not a member. The number of fundamental scans, when arranged in terms of mass dimensionality, follows a binomial expansion for each MS order. Table I1 demonstrates this in the form of a Pascal triangle by showing the number of fundamental scans for orders up to 6 in terms of their mass dimensionality. All scans other than the fundamental scans in a given order experiment incorporate defined transitions, and these can be considered as "reduced forms" of members in the fundamental set. In particular, the functional relationship scan (7) is derived from the corresponding two-dimensional scan (6),by defining a relationship between the two variable masses. This reduces the mass dimensionality from two to one. A total of five scan modes exists for a second-order experiment. These include one experiment of zero mass dimensions (3))three with one mass dimension ( 4 , 5 , 7 ) ,and one with two mass dimensions (6).
3-( 0 DOMAIN
Flgwe 4. Scans of lower mass dimensionality can be extracted from those of higher dimension. The figure represents all five MS2 experiments.
9',u"-'" JJUlrw
I42
Figure 5. Results, for the case of ndecane, of extraction and projection operations on the MSlMS data domain (the data domain Is that shown in Figure 3).
As observed in Figure 1, the analysis of MS2 experiments gives the first indication of the asymmetry introduced into the complete set of scan modes of a given order by the existence of scans that utilize defined mass relationships. This asymmetry will multiply as the order of the MS experiment increases as is discussed later. Of course, as already indicated in Table 11, a high degree of symmetry is obtained if attention is confined to fundamental scan modes. Similarly, as will also be detailed later, a high degree of symmetry is obtained if one restricts attention to scans of zero and one mass dimension. Extraction and Projection. Again, we emphasize that the data produced by scans of lower mass dimensionality are included in one or more scans of higher dimension, that is, they are subsets of the data of higher dimensionality. For example, reaction monitoring data (3) is embedded in both product (4) and parent (5) scans. All product (4), parent (51, and functional relationship (neutral loss) (7) data are included in the experiment having two mass dimensions (6). Extraction of data of lower dimensionality is straightforward and involves simply including only data that are encompassed in a particular point, line, plane, or, in general, an ( n- 1)-dimensional subspace. This operation is depicted in Figure 4, and an example is given in Figure 5. Another operation, here termed projection, can also be performed on the n-dimensional data. This operation involves
ANALYTICAL CHEMISTRY, VOL. 62. NO. 17. SEPTEMBER 1. 1990
4 1fi 1 uuLl
0
Readion Monitoring
1
Daughter. Parent and Neutral Lws (Funnional Relationship)
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/'1
Anlerior and Posterior Mass
Spectra
Pro$ction
fi
o
Total ton Current
npure E. Sumnary of Um extradim and p m m operatbns lor an MS' experiment. The number to the right of the symbol is the mass dimensionaihy.
Figure 7. Familial scan of mlz 57 fromndecane. recorded by a BEQQ instrument.
forcing the entire data set into one of lower order. Conceptually, the process is the oppoaite of the generation of MS/MS spectra from MS spectra. Information is lost by compaction into a smaller data array. Projection has not previously been utilized in mass spectrometry and is a potentially useful operation in certain cases. For example, the entire MS/MS data array, scan 6, can be projected onto the parent mass or the product mass axis. Both procedures remove a variable rather than fix it, as occurs in parent and product spectra, and hence they reduce the order of the data, not simply its dimensionality. Note that the two methods of projection applicable to a given MS2 data domain (6) both yield mass spectra hut that these are nonidentical. Projection onto the parent ion axis gives the anterior mass spectrum, which represents a form of the initial mass spectrum before it is distorted hy reaction. I t is often very similar to the original maw spectrum but with subtle differences in ion ahundances due to the occurrence of ion removal by collision processes other than dissociation (e.g., neutralization). Projection onto the product ion axis gives the posterior (or residual) mass spectrum. This mass spectrum explicitly represents the effects of the reaction, including dissociation and any other processes, and as such it may he quite different from the original mass spectrum. Both of these types of spectra can be obtained directly, hut only on certain types of instruments. For example, with a triple-quadrupole instrument, the anterior mass spectrum can he recorded by using the first quadrupole to scan the mass spectrum, with the second quadrupole as the reaction region and the third quadrupole set in the rf-only mode. Conversely, the p t e r i o r spectrum can be obtained by using the first quadrupole in the rf-only mode, the second for reaction, and the third for mass analysis. A summary of the extraction and projection processes is given in Figure 6. MS3 (MS/MS/MS): Three analyzers, each capable of being fixed to transmit a particular mass or varied through a mass range, give Z3, or 8, combinations of mass settings. These are shown as experiments S l 8 in Figure 1. Transitions between m a w s are shown as heavy m w s when they are fixed by mass settings and as light arrows otherwise. However, just as both 6 and 7 represent valid but different MS/MS experiments, so scans 15 and 16 are alternatives to 12 and 13 while 19, 20, and 22 are all alternatives to 18. Two additional experiments must also he considered for the following reason. In general, given n variables, there exist n(n - 1)/2 different binary relationships between these variables. In a three-stage mass spectrometric experiment, therefore, there exist three relationships between three masses
to consider. In most cases, the status of the third relationship is implied by the status of the other two, and so specification of the third is not necessary. In other cases specification is necessary, and it requires explicit inclusion in the symbolism. Experiments 17 and 21 in Figure 1are examples of this type. Having briefly delineated the complete set of MS3 scan modes, we can systematically develop the set while briefly considering the individual experiments. A g d starting point is the most constrained scan (8) where the status of all three mass analyzers is specified and two mass transitions are explicitly defined while the third is implied. This combination of symbols represents the known ( 1 7) hut as yet little-used experiment called consecutive reaction monitoring. It has zero mass dimensions. The next three combinations of symbols ('311)each include just one variable mass (one unfilled circle) and therefore describe experiments that have one mass dimension. All mass transitions are implied by the nature of the mass selections themselves. These scans have previously (17) been referred to as the sequential daughter or granddaughter (9),sequential parent or grandparent (lo),and reaction intermediate (11) scans. The sequential daughter (product) experiment was the first MS3 experiment to he described (ZS),and it has been quite widely used. The reaction intermediate scan has proven to he a useful new experiment in higher order mass spectrometry (27). Continuing the logical development of the full set of experiments via the symbology,the next three comhinationseach have two variable masses and one fixed mass. If the two variable masses are allowed to he independent variables, signified by using thin arrows between them, each of the resulting scans (12-14) has two mass dimensions. One of these experiments (14), was referred to as the familial scan in ref 17. This scan has now been implemented, and some examples of the data it produces are given below. The name is chosen to describe the experiment since the relationship of all products (daughters) and all parents to a particular intermediate is obtained. The data display requires both product and parent mass axes, viz., this is a two-dimensional experiment. An example of this new scan is given in Figure 7 for the ion m / z 57 from decane. The other two scans having two mass dimensions (12 and 13), neither of which has been delineated previously, should also produce unique and useful data. Scan 12 is the full MS/MS data domain arising from reactions of just one parent ion of particular mass, and scan 13 is the MS/MS data domain of all parent/product mass Combinations that can produce a final product ion of selected mass. Figure 8 provides a first example of the intermediate product domain in the case of the decane molecular ion.
wing
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ANALYTICAL CHEMISTRY. VOL. 62. NO. 17. SEPTEMBER 1, 1990 INTERMEDIATE-DAUGHTER DOMAIN
I
.
I
o
I
o
II
Figure 10. Symbols and names given to the complete set of MS/ MSIMS experiments having 2 mass dimensions.
Figure 8. Intermediatedaughter (woduct)domain for mlz 142 generated from n-decane.
i 0
(
r
0 0
Flgure 11. Example of the relationships of scans of lower mass dimensbnaiity to ihose of a higher mass dimensionality faihe familial scan, an MSSexperiment.
Figure 8. Symbols and names given to the cmplete set of MSI MS/MS experiments havlng 0 and 1 mass dimensions. Following previous arguments, at this point the option exists of defining the nature of the mass transition between any two varying masses in the MS3 experiments 12-14. Systematic substitution of thick for thin arrows generates three additional symbols, shown as scans 15-17 in Figure 1. This increases the number of MS3 experiments beyond the eight so far recognized. Scans with defined relationship between m2and m3 (15) and between m, and m2,(16) have been referred to as selective daughter (product) and selective parent scans and examples have been published (17). The case (17) where a relationship is defined between the first variable mass m, and the last variable mass m3 (while the intermediate is fixed) has not previously been described, although an example is reproduced in a recent conference proceedings (28). Its pattern of fixed and variable masses is the same as the familial scan (14). but the experiment is reduced to one mass dimension by the defined relationship between the two variable masses. This scan is appropriately referred to as the selective neutral-loss scan or, in the general cnse,as the selective functional relationship m,and it should have been included in place of the familial scan in the set of scans listed in ref 17c. If this is done, the resulting set includes only (and all) the zero and one mass dimensional scans for an MS3 experiment. This set of Z3 scans is given in Figure 9. In summary, it is clear that by defining mass transitions, each one of the scan modes that has a mass dimensionality of two in the fundamental set of scans (12-14) has been reduced to produce a corresponding scan having a mass dimensionality of one 05-11). The last method of combining fixed and variable masses in an MS3 experiment is that in which all three masses are
variable.' When allowing each variable mass to change independently from the others, and therefore representing each transition with thin arrows (18), an experiment results that requires three mass axes for the display of its data. This three-dimensional experiment represents the entire data domain for a third-order (MS3) experiment. By defining any single m a s transition, of which there are three to choose from, the mass dimensionality of the experiment can be reduced to two. This adds three new experiments each having mass dimensionality equal to two (19-21). Last, two transitions between masses can be defined, which implies a definition for the third, and consequently this reduces the experiment to one scan having just one mass dimension (22). This last scan, using constant neutral loss relationships between variable masses, has been called a consecutive neutral loss scan, and examples have been reported (17). The other scans (19,20, or 21) have not been considered, named, or demonstrated previously. The symbols and names of these, together with the other two-dimensional MS3 scans, are summarized in Figure 10. Relationship between Scans of Different Dimensions. All data produced by MS3 scans of lower mass dimension are contained in one or more of the scans having higher mass dimensionality. Consecutive reaction monitoring data (8)is included as a particular element in any MS3 scan having one mass dimension, assuming the specified masses and mass ranges are appropriately chosen. Data produced by each scan having one mass dimension are contained in the data produced by some (but not all) of the scans having two m a s dimensions. For example, Figure 11 shows how scans having mass dimensionality of zero or one are contained in and can be extracted from the familial scan (14) which has two mass dimensions. Figure 12 displays data resulting from extraction and projection operations performed on the familial scan spectrum of mJz 57 in n-decane. The projected spectra are similar to but not identical with the parent and product spectra of mJz 57. Note that extraction along the diagonal
ANALYTICAL CHEMISTRY, VOL. 62, NO. 17, SEPTEMBER 1, 1990
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.nt=.
142
0
0
4
4
I
0
0
bnr,
0
C,I
0
4
=0
0
I
0
0
0
1
0
I
0
Figure 15. Construction of MS3 scan data from MS2 scan data.
Table 111. Classification of 0 and 1 Mass Dimensional Scans Flgure 12. Results of extraction and projection operations upon the famillal scan spectrum of m l z 57 generated from ndecane (the familial scan is shown in Figure 7). EXTRACTEDSELECTIVE NEUTRAL LOSS DATA
Figure 13. Selective neutral loss spectrum extracted from the familial scan of m l z 57 generated from ndecane.
[ Parent Intermediate M a r Doughtor
Maw
MS/MS/MS DATA DOMAIN
[ 0
0
0
Figure 14. MS3data domain, abundance axis not included. The familial scan, having mass dlmensionaiity of two, falls in the hatched plane.
gives a selective neutral loss spectrum as shown in Figure 13. Direct recording of the selective neutral loss spectrum using a pentaquadrupole (19)shows the same two peaks (see below). Figure 14 shows conceptually how familial scan data are extracted from the MS/MS/MS data domain. Note, however, that the one-dimensional experiments 11,15, and 16, in which m2+ varies, are not encompassed in this particular two-dimensional experiment in which m2+is fixed. Of course, all the data produced by scans having two mass dimensions must be included in the single scan mode having three mass dimensions (18). It is noted again that projections can be used to reduce the mass dimensionality as well as the order in MS3 experiments, to produce parent, product, and other forms of MS/MS spectra. At this point, the general relationship between scan modes of lower order (MSn-l) and higher order (MS") can be discussed. In a tandem mass spectrometer only ions that emerge
no. of defined transitions
n
zero
0 1 2 3 4 5 6
0 1 1 1 1 1 1 1
one 0 1 2 3 4
5 6
1 1 3 6 10 15
2
total no. 3
4
5 1 2 4
1 4 10
20
8 1 5 15
1 6
1
16 32 64
from the first mass analysis stage can pass into the second, and so on. This is true since experiments are performed sequentially, whether in time or in space. This fact implies a logical "and" relationship between two stages of analysis. When so considered, it is clear that the data produced by certain nth-order scans may be constructed from several (n - 1)th order spectra. To make this point clearer, consider the data produced by the MS3 reaction intermediate (11) scan. Theoretically, given that all reaction region conditions are identical and that the fixed masses are chosen appropriately, the same data resulting from this scan can be produced by intersecting ("and"ing) the data produced by a product (4) and a parent (5) scan, which are both MS2 experiments. This type of operation, of course, holds only when intersecting the variable mass intensities for sets of data having the same mass dimensionality and not for data with differing mass dimensionality. Figure 15 shows possible methods of constructing MS3 data from MS2 data. MS": In general there are 2" experiments in the set of fundamental scan modes for an MS" system. Each of the scans in this set with a mass dimensionality greater than one can be reduced in dimensionality to yield additional MS" experiments by defining relationships between variable masses. At most, each scan of mass dimensionality greater than one can be reduced to a corresponding scan having no more than one mass dimension, and thus there are 2" scans having mass dimensionality of zero or one (i.e., 2" - 1 with mass dimension one and one with dimension zero). Table I11 classifies the 2" zero- and one-dimensional scan modes in terms of the number of relationships that have to be defined to produce them from a fundamental scan for experiments of up to sixth order. Note the high degree of symmetry that exists in this set of scans as it follows a binomial expansion. Similar symmetry was found in the set of fundamental scans when broken down in terms of mass dimensionality as presented earlier (Table 11). The relationship of these two sets of scans relative to the entire set of scans and how they intersect is evident in Figure 1.
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ANALYTICAL CHEMISTRY, VOL. 62, NO. 17. SEPTEMBER 1, 1990
Table IV. Total Number of MS" Experiments mass dimensionality n
0
1
0 1 2 3 4 5
1 1 1 1 1 1
1 3 7 15 31
3
2
4
totalno.
5
1 2 .
5 15 52 203
1
6 25 90
1
10 65
1
15
1
i
65
2:
FAMILIAL SCAN of M E 109 ME
Figure 17. Sequential daughter (product)spectra extracted from the familial scan data of Figure 16. 124
ENl
ss
Figure 18. Familial scan of mlz 109 generated from a mixture of phosphorus compounds by using the BEQQ instrument.
I
0 27
IR
150
T o obtain the total number of scans for a given order experiment, a double summation is required. First, to obtain the number of scans of a certain mass dimensionality, one must sum the number of scans in the fundamental set with greater or equal mass dimensions multiplied by the number of scans that can be produced by defining mass transitions (found in Table 111). Then, one sums the number of scans of each dimensionality to get the total number of scans of a given order. The general form of this summation is (n = order, r = mass dimensionality) n-r
MS(n,r) = E i-dr
n!
+ l)
