Many applications require accurate determination of the molecular masses and relative intensities of metabolites, peptides and intact proteins in complex mixtures. Time-of-flight (TOF) with reflecting analyzers provides excellent resolving power, mass accuracy, and sensitivity at lower masses (up to 5-10 kda), but performance is poor at higher masses primarily because of substantial fragmentation of ions in flight. At higher masses, simple linear TOF analyzers provide satisfactory sensitivity, but resolving power and mass accuracy are low. A TOF mass analyzer combining the best features of reflecting and linear analyzers is required for these applications.
An important advantage of TOF mass spectrometry (MS) is that essentially all of the ions produced are detected, unlike scanning MS instruments. This advantage is lost in conventional MS-MS instruments where each precursor is selected sequentially and all non-selected ions are lost. This limitation can be overcome by selecting multiple precursors following each laser shot and recording fragment spectra from each can partially overcome this loss and dramatically improve speed and sample utilization without requiring the acquisition of raw spectra at a higher rate.
All of these improvements will have limited impact unless the instruments are reliable, cost-effective, and very easy to use. Improvements in instrumentation which affect each of these issues are found in the present invention.
Several approaches to matrix assisted laser desorption/ionization (MALDI)-TOF MS-MS are described in the prior art. All of these are based on the observation that at least a portion of the ions produced in the MALDI ion source may fragment as they travel through a field-free region. Ions may be energized and caused to fragment as the result of excess energy acquired during the initial laser desorption process, or by energetic collisions with neutral molecules in the plume produced by the laser, or by collisions with neutral gas molecules in the field-free drift region. These fragment ions travel through the drift region with approximately the same velocity as the precursor, but their kinetic energy is reduced in proportion to the mass of the neutral fragment that is lost. A timed-ion-selector may be placed in the drift space to transmits a small range of selected ions and reject all others. In a TOF analyzer employing a reflector, the lower energy fragment ions penetrate less deeply into the reflector and arrive at the detector earlier in time than the corresponding precursors. Conventional reflectors focus ions in time over a relatively narrow range of kinetic energies; thus only a small mass range of fragments are focused for given potentials applied to the reflector.
In the pioneering work by Spengler and Kaufmann this limitation was overcome by taking a series of spectra at different mirror voltages and piecing them together to produce the complete fragment spectrum. An alternate approach is to use a “curved field reflector” that focuses the ions in time over a broader energy range. The TOF-TOF approach employs a pulsed accelerator to re-accelerate a selected range of precursor ions and their fragments so that the energy spread of the fragments is sufficiently small that the complete spectrum can be adequately focused using a single set of reflector potentials. All of these approaches have been used to successfully produce MS-MS spectra following MALDI ionization, but each suffers from serious limitations that have stalled widespread acceptance. For example, each involves relatively low-resolution selection of a single precursor, and generation of the MS-MS spectrum for that precursor, while ions generated from other precursors present in the sample are discarded. Furthermore, the sensitivity, speed, resolution, and mass accuracy for the first two techniques are inadequate for many applications.
The invention comprises apparatus and methods for rapidly and accurately determining mass-to-charge ratios of molecular ions produced by a pulsed ionization source, and for fragmenting the molecular ions produced and rapidly and accurately determining the intensities and mass-to-charge ratios of the fragments produced from each molecular ion.
The apparatus comprises a pulsed ion source, a field-free drift space, a two-stage ion reflector, a baffle in the field-free drift space adjacent to the mirror with an aperture for admitting ions to the mirror and a second aperture for allowing ions to exit the mirror, a deflection means for directing ions from the source to the entrance aperture in the baffle and an ion detector located to detect ions passing through the exit aperture.
In contrast to the prior art, a timed-ion-selector is not required for selecting precursor ions, although in some embodiments one may be provided. The distances and voltages employed in the apparatus are selected so that ions produced in the ion source are focused in time at the detector so that the time-of-flight is independent of kinetic energy to second order. Furthermore, the entrance aperture positions and sizes are chosen so that only ions with sufficient kinetic energy to reach the second stage of the reflector are detected.
In the present invention multiple segments of fragment spectra are required, each segment corresponding to a particular range of the ratio of fragment mass to precursor mass; but unlike the prior art, accurate fragment ion masses are determined simultaneously for fragments present due to all of the precursor ions in the spectrum. Thus although 10-15 segments may be required to generate a complete fragment spectrum, 100 or more precursors can be fragmented without sacrificing sensitivity or mass accuracy.
In one embodiment a pulse rate of 5 khz is employed, allowing data to be acquired much faster than in existing TOF instruments typically limited to rates of 200 hz or less. Any combination of the key elements of the TOF analyzer can be employed in this invention but in a preferred embodiment these elements are combined to optimize the sensitivity, dynamic range, and mass accuracy for both precursors and fragments.
In addition to the key elements of the TOF analyzer, a computer algorithm is used to process the measured TOF spectra to first determine abundance, centroid, and standard deviation of all significant peaks in the spectrum and then to assign these peaks to the correct monoisotopic precursor and fragment masses.
In one embodiment the pulsed ion source is a matrix assisted laser desorption/ionization source (MALDI) employing time lag focusing. In one embodiment the MALDI source employs a laser operating at 5 khz. In one embodiment the electrical field adjacent to the sample plate in the MALDI source is approximately equal to the maximum value that can be sustained without initiating an electrical discharge.
In one embodiment this electrical field is approximately 30 kV/cm.
In one embodiment the ion reflector comprises a two-stage gridded ion mirror.
In one embodiment the length of each stage of the mirror is substantially equal to 1/16 of the length of the field-free region less the focal length of the ion source.
In one embodiment the electric field strength in the first stage of the ion mirror is substantially equal to three times the field strength in the second stage.
The foregoing and other objects, features and advantages of the invention will be apparent from the following more particular description of preferred embodiments of the invention, as illustrated in the accompanying drawings in which like reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention.
A description of preferred embodiments of the invention follows. Referring now to
At a certain or selected time following the laser pulse, a high-voltage pulse 12 (shown in
Deflection electrodes 28A and 28B are energized to direct ion beam 85 through the field-free space or region 80 located within the analyzer vacuum housing toward baffle aperture 302 in baffle 300. Ions with a predetermined kinetic energy V are reflected by a two-stage gridded ion mirror 200 (comprising electrodes 202, 210 and 220 in the Figure) and exit the mirror near the center of a second baffle aperture 304 and travel through the field-free space 80 along a first ion trajectory 85A then pass through a grid 112 built into the detector unit and strike the input surface 92 of the detector 90 which is housed in housing 110. In one embodiment the detector comprises a dual channel plate electron multiplier having an input surface 92 and an output surface 94. Each ion impinging on the input surface 92 produces a large number of electrons (ca. 1 million) in a narrow pulse at the output surface 94. The gain of the electron multiplier is determined by the bias voltage Vd applied across the dual channel plate. The electrons are accelerated by the electric field between the output surface 94 and the anode 100 at ground potential, and strike the anode producing an electrical pulse that is coupled through an electrical feedthrough 104 in the wall of the analyzer vacuum housing 25 and connected to the input of a digitizer (not shown).
Ions with substantially lower kinetic energy than the predetermined value V penetrate a shorter distance into the ion mirror and strike the baffle plate 300 as indicated by the fourth ion trajectory 85D.
Ions with substantially higher kinetic energy than V pass through gridded aperture 306 in mirror electrode 220, and are not reflected. Electrode 220 receives voltage via feedthrough 222 in aperture 224. Likewise, mirror electrode 210 receives voltage via feedthrough 212 in aperture 214.
Ions within a predetermined kinetic energy range closer to V pass through aperture 304 along second and third ion trajectories 85B and 85C and are detected by detector 90.
The overall length of the analyzer is the sum of these distances plus any additional required for the ion source and analyzer vacuum housings.
In one embodiment the length D of the field free drift space (i.e., drift tube) 80 is large compared to the sum of the other distances, and d1 is small as practical without initiating electrical discharge within the vacuum system.
In one embodiment the mirror dimensions and operating voltages are chosen so that the time required for ions to travel from a predetermined focal point 81 in the field-free region 80, be reflected by the mirror, and reach the detector is independent of the energy of the ions to both first and second order. First and second order focusing in a reflector requires satisfying the following equations:
4d3/Dm=1−3/w (1)
4d4/Dm=w−3/2+(4d3/Dm)/(w+w1/2) (2)
where Dm is the total length of the ion path from the focal point 81 to the entrance of mirror 200 plus the path from the mirror exit to the detector input surface 92, d3 is the length of the first region of the mirror, d4 is the distance than an ion with initial energy V penetrates into the second region of the mirror and w=V/(V−V1) is the ratio of the ion energy at the entrance to the mirror to that at the entrance to the second region with the intermediate electrode at potential V1. Thus, first and second order focusing can be achieved for any value of w>3, and the corresponding distance ratios are uniquely determined by equations (1) and (2). For predetermined values of d3 and Dm, voltage V1 212 applied to mirror electrode 210 is adjusted to satisfy equation (1) and voltage V2 222 applied to mirror electrode 220 is adjusted to satisfy equation (2), where
d4=d40(V−V1)/(V2−V1) (3)
Voltage may be applied to one or more of the electrodes, 27A, 27B, 28A, and 28B to deflect ions in the ion beam 85 produced by the pulsed laser beam 60 striking sample 29 deposited on the surface of the MALDI plate 10. A voltage difference between 27A and 27B deflects the ions in a direction perpendicular to the plane of the drawing, and a voltage difference between 28A and 28B deflects ions in the plane of the drawing to direct the ion beam 85 toward aperture 302 in baffle 300.
Voltages can be applied as necessary to correct for misalignments in the ion optics and to direct ions along a preferred path. Also, a time dependent voltage can be applied to one or more of the deflection electrodes to deflect ions within predetermined mass ranges so that they cannot reach aperture 302 and to allow ions in other predetermined mass ranges to pass through aperture. Electrodes 50 and 51 together with the extraction electrode 20 comprise an einzel lens that may be energized by applying voltage VL 52 to electrode 50 to focus the ion beam 85 so that substantially all of the ions pass through aperture 302.
A potential diagram for this embodiment is shown in
Ion Source
The focal lengths for first order velocity and space focusing, respectively, for the embodiment employing two-stage acceleration in the ion source as depicted in
Ds=2d0y3/2[1−(d1/d0)/(y1/2+y)] (4)
Dv=Ds+(2d0y)2/(vn*Δt) (5)
where d0 is the length of the first acceleration region d1 is the length of the second acceleration region, Δt is the time lag between ion production and application of the accelerating field, y=V/(V−Vg), and vn* is the nominal final velocity of the ion of mass m* focused at Dv. vn* is given by
vn*=C1(V/m*)1/2 (6)
The numerical constant C1 is given by
C1=(2z0/m0)1/2=2×1.60219×10−19 coul/1.66056×10−27 kg=1.38914×104 (7)
For V in volts and m in Da (or m/z) the velocity of an ion is given by
v=C1(V/m)1/2 m/sec (8)
It is numerically more convenient in many cases to express distances in mm and times in nanoseconds. In these cases C1=1.38914×10−2, and v is in units of mm/nsec. The focal lengths of a single-field pulsed ion source as depicted in
Second order focusing for a two-stage source occurs at
Ds2=2d1(1−3/y)−1 (9)
And for a single-stage source
Ds2=6d0 (10)
The relative contribution to peak width due to variation δx in the initial position of the ions is given by
Rs1=[(Dv−Ds)/De](δx/d0y) (11)
and De is the total effective flight length of the ions. With delayed extraction the focal length of the source is mass dependent, and the contribution to peak width for ions other than the focused mass is given by
Rm=Rv1[1−(m/m*)1/2] (12)
Where
Rv1=(4d0y/De)(δv0/v) (13)
Where δv0 is the width of the initial velocity distribution.
If Dv=Ds2 then the focus at Dv is independent of initial velocity to both first and second order, and the contribution to peak width at the focused mass due to the initial velocity distribution is given by
Rv3=2[2d0y/(Dv−Ds)]3(δv0/v)3 (14)
Clearly the best resolving power is obtained by making De as large as possible within the overall geometric constraints imposed by the overall size of the instrument. Addition of a reflector allows the effective length to be increased without increasing the other contributions to peak width.
Ion Reflector
First and second order velocity focusing in a reflector requires satisfying equations (1)-(3) as discussed above.
The time of flight through a two-stage reflecting analyzer with dissociation of the precursor ion mp to fragment mf in the first field-free drift space is given by
t=(D/v){1+(4d3/D)(mf/mp)(V/V1){1+[(d4/d3)(V1/[V−V1])−1][1−(mp/mf)(V1/V)]1/2} (15)
t1(mp)=D/v (16)
is the time spent in the field-free region between the focal point and the detector. The velocity of the ions in the field-free region, v, is given by
v=(2zV/mp)1/2 (17)
and is essentially unchanged even though fragmentation occurs. After fragmentation the kinetic energy of the fragment ions is V(mf/mp). If the potentials applied to the reflector are adjusted by an amount R so that
R=V1/V10=mf/mp=V2/V20 (18)
where V10 and V20 are the potentials applied for focusing unfragmented ions, then the flight time of a fragment ion mf is identical to that for the precursor ion mp with R=1.
The total flight time for a fragment ion mf formed by fragmentation of mp in the field-free region is
t(mf,mp)=t1(mp)+tm(mf/Rmp) (19)
Where
tm(mf/Rmp)=(4d3/v)(mf/mp)(V/RV10){1+[(d40/d3)(V1/[V2−V1])−1][1−(mp/mf)(RV10/V)]1/2}} (20)
Define
x=tm(mf/Rmp)/(4d3/V),z=(mp/mf)(RV10/V),ε=(d40/d3)(V1/[V2−V1])−2 (21)
Then equation (20) may be written as
x=(1/z)[1+(1+ε)(1−z)1/2] (22)
This is a quadratic equation that can be inverted by the following procedure
(xz−1)2=(1+ε)2(1−z) (23)
x2z2−2xz+1=(1+ε)2−z(1+ε)2 (24)
x2z2−z[2x−(1+ε)2]−[2ε+ε2]=0 (25)
Equation (25) can be inverted using the quadratic formula to give z as a function of x. The general solution is
z=[2x−(1+ε)2]{1+/−[1+4x2(2ε+ε2)/(2x−(1+ε)2))]1/2}/2x2 (26)
An important practical case corresponds to that where the field strength in the first stage of the mirror is three times that in the second stage and the effective length of the second stage d4 is ⅔ that of the first stage d3. In this case
ε=0, and (V10/V) is ¾. The non-zero root of (22) is then
z=(1/x2)[2x−1] (27)
1/z=x2/[2x−1]
mf=(mp/z)R(V10/V)=mp(3R/4)x2/[2x−1] (28)
If ε is not zero but small compared to unity, then to first order in ε the solution is
z=(1/x2)[2x−1+ε(x−1)/2] (29)
The value of x can be determined from the measurements of flight times as follows. When mf/Rmp=1, the time in the mirror is equal to the time for the precursor ion. Thus
t(mp)=t1(mp)+tm(1) (30)
and substituting into (12) with ε=0, V10/V=¾
tm(1)=2(4d1/v) (31)
thus x can be expressed in terms of measurable quantities as
x=2[t(mf,mp)−t1(mp)]/[t(mp)−t1(mp)] (32)
Thus the fragment mass mf produced from any precursor mass mp can be determined using equation (29) using the value of x determined by the measurements of flight times for fragment and precursor masses. The ratio of flight time in the field-free region t1(mp) to the total flight time t(mp) is independent of mass and can be determined by measuring flight times for precursor ions as a function of R. Alternatively, we can set
q=x/2=[t(mf,mp)−t1(mp)]/[t(mp)−t1(mp)] (33)
and
mf=(mp/z)R(V10/V)=mp(3Rq2)/[4q−1] (34)
Design of the Analyzer
One embodiment of the invention is illustrated in
This geometry satisfies the conditions required for the simpler calibration equation (34) to apply. The nominal flight time through the field free region relative to the total is given by
t1(mp)/t(mp)=1224/1824=0.671=C (35)
q=[t(mf)/t(mp)−0.671]/0.329=3.040[t(mf)/t(mp)]−2.040 (36)
The calibration is not very sensitive to the value of the constant C; thus the default value may be adequate. The important parameter determining calibration accuracy is the mirror ratio R. If 16-bit DAC's are used for setting the voltages, then the accuracy is not better than about 15 ppm. Data from fragmentation of a known peptide, e.g. Glu 1-Fib, can be used to construct a calibration curve for actual value Ra relative to set value Rs. If the actual value of R is equal to mf/mp, then t(mf)/t(mp)=1, and any observed deviation can be used to determine the true value of R. This can then be used to construct a calibration curve
Ra=aRs+b (37)
By a least-squares fit between the actual and observed values.
Ra=[3.040t(mf)/t(mp)−2.040]Rs (38)
where Rs is nominally set equal to mf/mp.
With the proposed geometry, ions with ratios mf/mp between 0.85 and 1.12 R are focused and transmitted to the detector. Those with higher ratios exit through the back of the mirror. Ions corresponding to lower ratios are rejected by a baffle adjacent to the mirror exit. The displacement of ions as a function of mf/mpR is shown in
Depending on the coverage of the low mass portion of the fragment spectra required by the application, approximately 10 or fewer segments corresponding to different values of R are required to generate a complete spectrum, and at least 5 fold multiplexing can be done in most cases. Thus, the speed of this system operating at 5 khz is at least an order of magnitude faster than a conventional TOF-TOF operating at 200 hz. Furthermore, the sensitivity may be much higher, particularly for high-mass precursors, since there are no critical apertures or focusing required. The manufacturing cost is less than half that of commercial TOF-TOF instruments and it fits in a small bench-top cabinet less than 1500 mm in height.
Calibration
The precursor mass calibration employs the same algorithms used previously for calibrating reflector spectra, and the scale for R can be corrected and calibrated using known fragment spectra. Default values of the other parameters may be sufficiently accurate, but these can be independently determined using known precursor masses and observing the shifts in flight time produced by varying R about the nominal value of R=1. The flight time of a precursor ion for a given value of R can be expressed as
t(m,R)=C1[1+( 4/3R)C2{1+(1−3R/4)1/2}]=C1[1+C2f(R)] (39)
t(m,1)=C1[1+2C2] (40)
f(R)=( 4/3R){1+(1−3R/4)1/2} (41)
Solving for C1 and C2 gives
C2=[1−t(m,R)/t(m,1)]/{[(2t(m,R)/t(m,1)]−f(R)} (42)
C1=t(m,1)/[1+2C2] (43)
These should be independent of the mass used for determination as well as the value of R, and may be compared with the default values for the geometry described above where
C1=(D/v)=t1(m) and C2=(4d1/D)=0.245 (44)
The coefficient C required in the calibration is given by
C=t1(m)/t(m,1)=1/(1+2C2)=0.671 for the default value of C2 (45)
Deviations in the apparent value of C2 determined at different values of R may indicate either that the value of V1/V is not exactly 0.75 or that the ratio of the field in the first region of the mirror is not exactly equal to twice that in the second region. In this case the data may be fit to equation (30) to determine the actual value of ε. Calibration of the voltages V1 and V2 may be required to remove any apparent dependence on R.
Calculation of Resolving Power and Mass Accuracy for MS and MS-MS
The contribution to peak width due to the uncertainty δt in the time measurement is given by
Rt=2vδt/De (46)
The other important contributions to peak width for precursor ions are given in equations (11) to (14) above. For fragment ions the resolving power is somewhat lower for ions detected where Rmp/mf is not equal to one. These ions travel a longer or shorter time in the mirror that that required for the optimum time focus, so their focus occurs at a distance from the detector. The additional peak width due to this effect is given by
RR=Δm/m=2Δdf/De=2ΔtR(Δv)/De (47)
where De is the effective total flight distance, Δv is the velocity spread introduced by time lag focusing, and ΔtR is the difference in time for a fragment ion for a particular value of mf/mp compared to one where mf/mpR=1. Thus
Δv=(v0Δt/2ds)v=[(2ds/(Ds−2da)]δv0=(½)δv0 (48)
ΔtR=t(mf/mpR)−t(1) (49)
De=t(1)v (50)
Thus
RR=Δm/m={[t(mf/mpR)/t(1)]−1}(δv0/v) (51)
The quantity in the { } brackets is plotted as a function of mv/mpR in
For any geometry such as that depicted in
δv0=400 m/s=4×10−4 mm/nsec,δx=0.01 mm. (52)
The ratio δv0/v for 8.8 kV ions is approximately 0.01 m1/2 for m in kDa. Thus for the geometry illustrated in
Rs1=4(0.01)/1824=2.2×10−5 Rs1−1=45,600
Rv1=[4(3)/1824](0.01 m1/2)=6.56×10−5 m1/2 Rv1−1=15,200 m−1/2
Rv3=(0.01 m1/2)3=10−6 m3/2 Rv3−1=1,000,000 m−3/2
Rt=m−1/2/[2(1.5)(0.041)]/1824=6.78×10−5 m−1/2 Rt−1=14,700 m1/2
RR(max)=(0.07)(0.01 m1/2)=7×10−4 m1/2 RR−1(min)=1,430 m−1/2
In all cases the mass is that of the precursor. The time resolution Rt is calculated using a minimum peak width of 1.5 nsec; this is consistent with experimental results employing 0.5 nsec digitizer bins and 5 um channel plates. This clearly is the major limitation of resolving power for the precursor spectra at low mass, and could be improved by using a faster detector and narrower bin widths.
Since each of these contributions to peak width are essentially independent, the overall peak width can be estimated by taking the square root of the sum of the squares of the individual concentration. The contribution to peak width due to energy imparted in the fragmentation process has not been taken into account in this analysis. This may make a significant contribution to peak widths for low mass fragments.
Calculated resolving powers are summarized below in Table 1 for the source delay optimized for m/z 3 kda.
Source delay is focused for 3 kda. Calculated resolving power as function of precursor mass is shown in
Operating Protocol
The system operates in both MS and MS-MS modes. In MS mode the laser is set at a relatively low level appropriate for obtaining high-resolution spectra. The mirror voltages are set to the nominal values as shown in
Normally each sample spot will include a known component used to internally calibrate the spectrum, providing routine mass errors less than 1 ppm RMS. The raw time-of-flight spectra are processed to produce mono-isotopic peak tables including integrated intensity (expressed as ions/laser shot integrated over the isotopic envelope), centroid mass, and peak width as Δm/m (FWHM) for each spot. These peak tables are then analyzed to produce as set of mono-isotopic masses that require MS-MS spectra to be measured. Some may be excluded by criteria established in a peak exclusion list. Some examples of peaks that might be excluded are listed below:
In many cases MS-MS spectra for all of the peaks can be acquired in a single acquisition. In others, particularly those containing a large number of peaks of varying intensity in a particular region of the spectrum, may require two or more acquisitions to obtain satisfactory MS-MS spectra on all of the peaks.
Two examples of peptides from tryptic digests of relatively pure proteins are shown in
Acquisition of MS-MS Spectra
A file of switching times for the timed-ion-selector is generated for each sample spot based on the above automated analysis of the MS spectra for each spot. Since the time required for downloading switching times is expected to be fast compared to settling times for voltages changes to the mirror, normally spectra from all of the sample spots in a set will be acquired for each value of R corresponding to mirror voltages. The first segment acquired, with the timed-ion-selector on, is with R=1 and with the laser at the intensity used for MS-MS and the multiplier gain adjusted so that precursor peaks are not in saturation. The flight time for all mono-isotopic precursor masses detected are recorded for use in the subsequent analysis of fragment spectra. These times are expected to be accurate for subsequent since they are recorded using the same laser intensity as the fragment spectra. The precursor masses determined in the original MS run will be to internally calibrate the mass scale.
The multiplier voltage is increased as required and mirror voltages are then set to the first value of R. The TOF spectrum is acquired and the data converted to peak tables consisting of ion intensity (ions/laser shot), centroid (in time) and peak width. The peak tables for each spot are added to that generated from the previous value of R for that spot and the raw data discarded. The mirror is then set to the next value of R and the process repeated until the complete set of spectra has been generated. Processing of the time spectra to produce fragment masses corresponding to each of the precursor will be carried out on acquired spectra at the same time that new spectra are being acquired. An example of a set of R values and maximum and minimum relative fragment masses are summarized below in Table 3. Except in cases where the low mass fragment are of particular interest, the first 10 segments are sufficient. In many cases, only 3 or 4 segments may be required to unambiguously identify the peptides.
If the masses selected differ by less than a factor of about 1.3, then the fragments from multiple precursors may occur within the same time range in the fragment TOF spectrum. This is illustrated schematically in
The equation for the flight time of a fragment mass mf from a precursor mp can be written as
t(mf,mp)=A(1+α)1/2{(Ds/De)+(D/De)[1+(⅓)(1+β)/(1+α)][1+[1−(1+α)/(1+β)(¾)]1/2]}A=De(mp0/2zV)1/2 (53)
where mp=mp0(1+α) and mf/mp0R=1+β, and the constants are for the geometry defined in
The apparent error in fragment mass due to an error in precursor mass can be magnified by increasing the focal length of the source.
An embodiment using a 2-field source is illustrated in
Determination of Fragment Peaks for Each Precursor
For each precursor a flight time t(mp) is uniquely determined for each mp included in the set of peaks transmitted by the timed ion selector. All fragment peaks with flight times between 0.85 and 1.125 times t(mp) are possible fragments of that precursor for each value of R. The variable q is computed for each fragment via equation (34) for the geometry with the 24 mm source focal length
q=[t(mf)/t(mp)−0.671]/0.329=3.400[t(mf)/t(mp)]−2.400 (54)
with the constants determined by the calibration procedures described above. For the alternative geometry with 200 mm source focal length
q=[t(mf)/t(mp)−0.7059]/0.2941=3.400[t(mf)/t(mp)]−2.400 (55)
The apparent fragment mass is then given by
mf=mp(3Ry2)/[4y−1] (56)
If the apparent fragment mass is within the accepted range of possible mass defects and if the peak satisfies the peak width and intensity criteria, then it is added to the fragment peak table for that precursor. In cases where there are closely spaced precursors, a peak may be tentatively included in more than one precursor fragment peak table. In each case the exact mass determined corresponding to that precursor is the value included in that table.
Performance of the Analyzer with 200 mm Source Focus
By increasing the relative length of the source the ability to discriminate between potential precursor masses for a given fragment is improved, but the basic resolving power of the MS instrument is somewhat reduced; however, for most applications it is still adequate.
The important parameters determining resolving power in this case are as follows:
Rs1=(158/1700)(0.01/13.2)=7.0×10−5 Rs1−1=14,200
Rv1=[4(13.2)/1700](0.01 m1/2)=3.11×10−4 m1/2 Rv1−1=3,220 m−1/2
Rv3=(26.2/158)3(0.01 m1/2)3=4.7×10−9 m3/2 Rv3=2×108 m−3/2
Rt=m1/2/[2(1.5)(0.041)]/1700]=7.2×10−5 m−1/2 Rt−1=13,700 m1/2
RR=Δm/m=2{[t(mf/mpR)/t(1)]−1}[(2dsy/(Dv−Ds)]δv0
RR(max)=(0.07)(0.304)(0.01 m1/2)=2.12×10−4 m1/2 RR−1(min)=4,700 m−1/2
Calculated resolving power as a function of m/z is shown in
Analyzer Geometry Design
Increasing the source focal length improves the ability to discriminate between precursors for a particular fragment, but reduces the overall resolving power for an instrument of the same overall dimensions as discussed above. However, the resolving power can be at least partially restored by placing the detector near the source and increasing the length of the mirror. This geometry is illustrated in
For this geometry, C=(Des+D)/1.5 D+Des)=0.6875
q=[t(mf)/t(mp)−0.6875]/0.3125=3.200[t(mf)/t(mp)]−2.200 (57)
The apparent fragment mass is then given by
mf=mp(3Rq2)/[4q−1] (58)
Performance of the Instrument
By increasing the relative length of the source the ability to discriminate between potential precursor masses for a given fragment is improved, and by also increasing the effective length of the reflecting analyzer the basic resolving power of the MS instrument is maintained. The important parameters determining resolving power in this case are as follows:
R
s1=(158/3200)(0.01/12)=4.1×10−5 Rs1−1=24,300
Rv1=[4(12)/3200](0.01 m1/2)=1.5×10−4 m1/2 Rv11=6,670 m−1/2
Rv3=(24/158)3(0.01 m1/2)3=3.5×10−9 m3/2 Rv3−1=2.85×108 m3/2
Rt=m−1/2/[2(1.5)(0.041)]/3200]=3.84×10−5 m−1/2 Rt−1=26,000 m1/2
RR(max)=(0.07)(0.304)(0.01 m1/2)=2.12×10−4 m1/2 RR−1(min)=4,700 m−1/2
Calculated resolving power for precursor ions as a function of m/z is summarized as curve C in
Precursor Scanning
The configuration illustrated in
R=mf0/mp0 (59)
And the shift in flight time for fragment ion mf0 from any other precursor mp relative to that for mp0 is given by
Δt(mp,mf0)/t(mp0)=(Des/2De)(mp−mp0)/mp0 (60)
For the embodiment illustrated in
Δt(mf,mp0)/t(mp0)=(0.75D/De)(mf−mf0)/mf0 (61)
The range of precursor ions that can be monitored simultaneously without overlap between adjacent fragment ions can be estimated setting (60) equal to (61) with
mf−mf0=0.5 (62)
This gives
Δmp/mp0=1.5D/(Desmf0)=7.5/mf0 (63)
In one example, mf0=184, mp0=736, and R=0.25. Then Δmp=736(7.5/184)=30. Thus the 184 fragment from all precursors in the range from 721 to 751 can be measured in a single acquisition with no interference from fragments at 185 or 183. In cases where the fragment of interest is expected to be very intense relative to adjacent peaks the range of precursor ions selected can be expanded to at least +/−5% of the nominal precursor selected. Thus, in this case a range of m/z 700-770 can be acquired in a single acquisition.
At lower fragment mass a broader range of precursor masses can be scanned simultaneous, but when multiple fragment ions are measured, as in the case with ITRAQ the precursor range must be limited to avoid overlap between adjacent fragment ions. For example with ITRAQ the relative range of precursors is approximately 7.5/117=0.064. Thus all precursors in the range between m/z 1000 and 2000 can be quantified in 11 acquisitions, and the range between 2000 and 4000 using an additional 11 acquisitions. (1.06411=2). Since each acquisition requires at most 0.4 seconds (2000 laser shots) a complete precursor scan from m/z 1000 to 4000 can be completed in about 8.8 seconds, corresponding to a scanning rate of 340 Da/sec.
Neutral Loss
The major difference between precursor scanning and neutral loss scanning is that in the latter the ratio of fragment mass to precursor mass is generally higher, thus requiring higher values of the mirror ratio R. The range of precursor masses that can be sampled without overlapping fragment ions can be calculated from equation (63) with R=mf0/mp0 to give
Δmp/mp0=1.5D/(Desmf0)=7.5/Rmp0 or Δmp=7.5/R (64)
Thus a maximum precursor window only 7 or 8 mass units wide can be employed at high value of R without spectral overlap. However the width of the total mass window that can be focused at a given value of R is proportional to the nominal focus mass. Thus at ca. m/z 1000 a fragment mass range more than 200 Da wide can be simultaneously focused. If the timed ion selector is set to transmit multiple mass windows ca. 8 mass units wide with spaces of ca. 8 mass units separating these, then all of the fragments from all of the precursors corresponding to a given value of R can be acquired in at most 2 or 3 acquisitions, and there is no ambiguity in assigning fragments to the correct precursors.
Multiple Reaction Monitoring
In multiple reaction monitoring one or more fragment ions from each of several predetermined precursor ions are monitored. In conventional MS-MS systems, a precursor ion is selected by a first MS, the precursor ion is caused to fragment, a predetermined fragment ion is selected by a second MS and the intensity of the fragment ion recorded. A second pair of precursor and fragment ions is selected and the measurement is repeated until all of the predetermined precursor and fragment pairs have been measured. This method is generally employed with chromatographic separation; thus it is essential that the complete set of measurements is accomplished in a time less than that of the peak width in the chromatogram.
The present invention allows a number of precursor and fragments ions to be monitored simultaneously. Each set of precursor and fragment ions can be measured simultaneously that satisfy the condition
0.88R<mf/mp<1.12R (65)
In some cases it may be necessary to limit the range of precursor ions measured, as described above, to limit the possibility of overlapping fragment ions. In many applications the range of precursor and fragment masses required is rather small so that a single value of R and a single acquisition can be employed to monitor the complete set. In other cases covering wider mass ranges it may be necessary to employ multiple acquisitions using several different R values.
While this invention has been particularly shown and described with references to preferred embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the invention encompassed by the appended claims.
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