Anal. Chem. 1996, 68, 1419-1428
Space-Velocity Correlation Focusing Steven M. Colby† and James P. Reilly*
Department of Chemistry, Indiana University, Bloomington, Indiana 47405
An algorithm is developed for identifying optimal focusing conditions in time-of-flight mass spectrometers with certain ionization source geometries. Ions are extracted from the source using time-dependent electric fields. Calculations and experiments demonstrate that use of these optimum conditions can significantly improve mass spectrometer resolution. Matrix-assisted laser desorption/ ionization (MALDI) represents an application that is of considerable interest. Because the identification of optimum conditions depends on a correlation between the spatial and velocity distributions of ions in the source region of the instrument, we call this approach spacevelocity correlation focusing. Since the development of the first “ion velocitron” by Cameron and Eggers1 in 1948, a major disadvantage of the time-of-flight mass spectrometer has been its limited mass resolution. A number of factors contribute to this problem, principally the initial temporal, velocity, and spatial distributions of the ions. The situation can also be exacerbated by other factors such as insufficiently fast electronics or the occurrence of collisions.2,3 Fortunately, a number of techniques have been developed to reduce the impact of the three ion distributions. The most successful improvements were the introduction of space and timelag focusing by Wiley and McLaren4 in 1955 and the reflectron by Mamyrin et al.5,6 in 1973. Space focusing is the reduction of the effect of the initial spatial distribution on the measured flight times of analyte ions. It is accomplished through the introduction of a second acceleration region in the source of the instrument. This permits the selection of electric fields that minimize the dependence of flight time on initial ion position. As an alternative to space focusing, it has been shown that the contribution of the initial spatial distribution to peak broadening can be minimized by ionizing a sample adsorbed on a surface.7-9 Unfortunately, while this narrows the spatial distribution it may also increase the initial velocity distribution as a consequence of the desorption process. Time-lag focusing, as conceptualized by Wiley and McLaren, employs time-dependent acceleration fields to reduce the effect of the initial velocity distribution and to compensate for gas phase † Current address: Scientific Instrument Services, Ringoes, NJ 08551. (1) Cameron, A. E.; Eggers, D. F., Jr. Rev. Sci. Instrum. 1948, 19 (9), 605607. (2) Opsal, R. B.; Owens, K. G.; Reilly, J. P. Anal. Chem. 1985, 57, 1884-1889. (3) Weinberger, S. R.; Kenny, J.; Kornfeld, R. Pittsburgh Conference, New Orleans, 1995, 459. (4) Wiley, W. C.; McLaren, I. H. Rev. Sci. Instrum. 1955, 26, 1150-1157. (5) Karataev, V. I.; Mamyrin, B. A.; Shmikk, D. V. Sov. Phys.-Tech. Phys. 1972, 16, 1177. (6) Mamyrin, B. A.; Karateav, V. I.; Shmikk, D. V.; Zagulin, V. A. Sov. Phys. JETP 1973, 37, 45-48. (7) Yang, M.; Reilly, J. P. Int. J. Mass Spectrom. Ion Processes 1987, 75, 1884. (8) Yang, M.; Reilly, J. P. Anal. Instrum. 1987, 16, 133-150. (9) Yang, M.; Millard, J. R.; Reilly, J. P. Opt. Commun. 1985, 55, 41-44.
0003-2700/96/0368-1419$12.00/0
© 1996 American Chemical Society
ion turn-around times. A delay is introduced between the production of ions and their extraction from the source. During this period, ions disperse according to their nascent kinetic energy. When the extraction field is applied, those ions whose direction of travel is toward the detector find themselves in a region of lower electrostatic potential than those whose direction is away from the detector. Following ion acceleration, these differences help to compensate for the effect of the initial velocity distribution on the flight times of the ions. Wiley and McLaren pointed out, however, that the ideal conditions for time-lag focusing and space focusing place opposite requirements on system parameters and a compromise between the two must be sought. Because space focusing is mass independent, and is more easily implemented, it has been more commonly used. Reflectron instruments reduce the effect of initial energy distributions by directing ions into a region of retarding electric fields. Ions with greater initial energy will penetrate this region to a greater extent and therefore travel a greater distance. Proper choice of field strengths enables the additional path length to compensate for the excess energy. This approach is restricted by limitations of ion optics10 and, as often noted, leads to the separation of metastable fragments from parent ions. While this can provide wanted structural information, the concomitant loss in parent ion sensitivity is sometimes undesirable.11 An alternative approach to limiting the effect of the initial velocity distribution is to ionize a sample that has been introduced through a supersonic expansion. This reduces the width of the initial velocity distribution because of the geometric relationship between the source and ionization point2 or through the physical processes of the expansion.12 A number of groups have observed how the application of timedependent fields in various regions of the instrument can lead to improvements in mass resolution.3,13-38 In some cases, enhancement of resolution was attributed to the elimination of metastable (10) Bergmann, T.; Martin, T. P.; Schaber, H. Rev. Sci. Instrum. 1989, 60 (3), 347-349. (11) Wu, K. J.; Shaler, T. A.; Becker, C. H. Anal. Chem. 1994, 66, 1637-1645. (12) Boesl, U.; Weinkauf, R.; Weickhardt, C.; Schlag, E. W. Int. J. Mass Spectrom. Ion Processes 1994, 131, 87-124. (13) Hwang, H. J.; Griffiths J.; El-Sayed, M. A. Int. J. Mass Spectrom. Ion Processes 1994, 131, 265-282. (14) Pan, Y.; Cotter, R. J. Org. Mass Spectrom. 1992, 27, 3-8. (15) Spengler, B.; Bo ¨kelmann, V. Nucl. Instrum. Methods Phys. Res., Sect. B 1993, 82, 379-385. (16) Cotter, R. J. In Time-of-Flight Mass Spectrometry; Cotter, R. J., Ed.; ACS Symposium Series 549; American Chemical Society: Washington, DC, 1994; pp 16-48. (17) Yefchak, G. E.; Enke, G. G.; Holland, J. F. Int. J. Mass Spectrom. Ion Processes 1989, 87, 313-330. (18) Kinsel, G. R.; Johnston, M. V. Int. J. Mass Spectrom. Ion Processes 1989, 91, 157-176. (19) Kinsel, G. R.; Mowray, C. D.; McKeown, P. J.; Johnston, M. V. Int. J. Mass Spectrom. Ion Processes 1991, 104, 35-44. (20) Kinsel, G. R.; Grundwu ¨rmer, J. M.; Grotemeyer, J. J. Am. Soc. Mass Spectrom. 1993, 4, 2-10.
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peak broadening.16 It appears that in many experiments, instrument operating conditions are found by trial and error. We have developed an algorithm that identifies optimal conditions for the time-dependent extraction of ions from the source of a TOF mass spectrometer. It is based on correlations that can be found between the initial spatial and velocity distributions in certain ion source geometries. The approach is primarily intended to simultaneously reduce the effects of both distributions. A mathematical model is critical to the identification of ideal conditions. Its use distinguishes the present method from previous work. As we will show, properly identified and optimized experimental conditions can greatly enhance the resolution of TOFMS. These conditions can be identified for several source geometries, as noted below. We will use matrix-assisted laser desorption/ionization (MALDI) as our principal example to illustrate the utility of the new algorithm. In MALDI/TOF MS, mass resolution is primarily limited by the velocity distribution of ions desorbed from the sample. This distribution is the most difficult to compensate for in a linear instrument.12,16 The use of a reflectron in this application has a number of disadvantages, including a reduction in sensitivity and the separation of metastable fragments.11 The conventional solution to this problem has been to use a linear instrument with as high a drift velocity as possible. Typically, tens of kiloelectronvolts are used. This minimizes the fraction of ion drift energy that is due to the initial velocity. However, the strong acceleration fields also increase the effect of the initial spatial distribution to the point where it may become the dominant factor limiting resolution. The use of high drift energies also reduces the overall flight time and therefore only improves the resolution to a limited extent. In addition to the broad initial velocity distribution, a number of other factors may affect the resolution of MALDI/TOF mass spectrometers. These include the existence of metastable fragmentation, adducts, counterions, imperfect electronics, the spread (21) Grundwu ¨ rmer, J. M.; Bo ¨nisch, M.; Kinsel, G. R.; Grotemeyer, J.; Schlag, E. W. Int. J. Mass Spectrom. Ion Processes 1994, 131, 139-148. (22) Marable, N. L.; Sanzone, G. Int. J. Mass Spectrom. Ion Phys. 1974, 13, 185194. (23) Browder, J. A.; Miller, R. L.; Thomas, W. A.; Sanzone, G. Int. J. Mass Spectrom. Ion Phys. 1981, 37, 99-108. (24) Nose, N. Mass Spectrom. 1983, 31 (3), 165-172. (25) Muga, M. L. Anal. Instrum. 1987, 16 (1), 31-50. (26) Spengler, B.; Pan, Y.; Cotter, R. J.; Kan, L.-S. Rapid Commun. Mass Spectrom. 1990, 4 (4), 99-102. (27) Chien, B. M.; Michael, S. M.; Lubman, D. M. Int. J. Mass Spectrom. Ion Processes 1994, 131, 149-179. (28) Neusser, H. J.; Krause, H. Int. J. Mass Spectrom. Ion Processes 1994, 131, 211-232. (29) Brown, R. S.; Lennon, J. J.; Christie, D. Desorption ‘94, Sunriver Lodge, OR, March 27-31, 1994, p 63. (30) Lennon, J. J.; Brown, R. S. 42nd ASMS Conf. on Mass Spectrom. 1994, 501. Brown, R. S.; Reiber, D. Lennon, J. J. 43nd ASMS Conf. on Mass Spectrom. 1995. (31) Brown, R. S.; Lennon, J. J. Anal. Chem. 1995, 67, 1998-2003. (32) Whittal, R. M.; Li, L. Anal. Chem. 1995, 67, 1950-1954; 43nd ASMS Conf. on Mass Spectrom. 1995. (33) Vestal, M. L.; Juhasz, P.; Martin, S. A. Rapid Commun. Mass Spectrom. 1995, 9, 1044-1050. (34) Ens, W.; Dworschak, R. G.; Spicer, V.; Standing, K. G. 43nd ASMS Conf. on Mass Spectrom. 1995. (35) Colby, S. M.; King, T. B.; Reilly, J. P. Rapid Commun. Mass Spectrom. 1994, 8, 865-868. (36) King, T. B.; Colby, S. M.; Reilly, J. P. Int. J. Mass Spectrom. Ion Processes 1995, 5, L1-L7. (37) Colby, S. M.; King, T. B.; Reilly, J. P. Pittsburgh Conference, New Orleans, 1995; 465. (38) Colby, S. M.; Reilly, J. P. 43nd ASMS Conf. on Mass Spectrom. 1995.
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Figure 1. Cross section of TOF/MALDI instrument. Acceleration fields are established by plate G0, grids G1 through G4, and the front of the microchannel plate detector D. Samples are deposited on the sliding probe (P) inserted into G0. The sample is located at point S. G2 and G3 are connected by an aluminum liner establishing a fieldfree drift region.
of ion formation positions and times, and the occurrence of gasphase collisions. It is necessary to dramatically reduce the effect of the initial ion velocity distribution before these other factors can be observed with a resolution sufficient for their careful study. Evidence supporting this contention is presented in this paper. In the context of MALDI, several groups have used timedependent electric fields in the first acceleration region of their time-of-flight instruments.13-15,29-39 Independently, three of these recently introduced the use of time-dependent fields in the first acceleration region for the specific purpose of improving mass resolution.29-32,35-38 Brown and Lennon pointed out that pulsed ion extraction reduces the number and effect of collisions in the desorption plume.30 They examined the effect of delayed extraction on rapid fragmentation and suggested that collisions were a major contributor to peak broadening. Establishing correlations between initial distributions may, but does not necessarily have to, involve the use of time-dependent fields.40 In the case of MALDI, we will be discussing pulsed extraction of desorbed ions. In this case, the start of the pulse determines the beginning of the time-of-flight measurement. However, the same correlations between velocity and position can be identified when neutral molecules are introduced and then ionized in the gas phase. In this case, the acceleration fields may be time independent and the ionization event determines the start of the ion time of flight. THEORY As with space focusing, the process of finding space-velocity correlation focusing conditions begins with a flight time equation. An ion’s flight time is a function of its mass to charge ratio (m/ z), the distances (dx and x0), potentials (Vx) within the instrument, and its initial velocity (v0).
TOF ) f(m/z,dx,x0,Vx,ν0)
(1)
As illustrated in Figure 1, we refer to the fixed distances as d1, d2, etc. Voltages V0, V1, etc., are applied to plates G0, G1, etc. (39) Wang, B. H.; Dreisewerd, K.; Bahr, U.; Karas, M.; Hillenkamp, F. Am. J. Mass Spectrom. 1993, 4, 393-398. (40) Payne, M. G.; Thonnard, N.; Hurst, G. S. U.S. Patent 4,694,167, 1987.
When employing pulsed ion extraction the flight time measurement begins at the instant the drawout is initiated.4 The distance between plate G0 and the ion’s position at the time of extraction is defined as x0. Before the drawout pulse, both G0 and G1 are held at the same potential. At the time of extraction, an additional voltage, Vpulse, is applied to one of the grids, producing an accelerating electric field between them. For Wiley-McLaren space focusing, the derivative ∂TOF/∂x0 is set equal to zero and an appropriate ratio of electric fields is found that satisfy the equation. This minimizes the dependence of time of flight on the initial ion position. An equivalent approach to minimize the effect of the velocity distribution is not practical because the corresponding derivative (∂TOF/∂v0) can only be made to equal zero when the electric fields are infinite. In space-velocity correlation focusing, one of the variables, v0 or x0, in the TOF equation (eq 1) is replaced by a function defining a correlation between the two variables. For example, x0 may be eliminated by substituting x0 ) f(v0). After the elimination of the variable x0, both spatial and velocity distributions are expressed in terms of the single variable v0. This is only possible when x0 and v0 are directly correlated by a mathematical relationship. We have identified at least three ion source geometries where a correlation can be found. These include conditions in which (1) samples are desorbed from a surface in a direction parallel to the ions’ final direction of flight, (2) samples are desorbed from a surface in a direction perpendicular to the final direction of flight, and (3) samples flow continuously from a point source perpendicular to the direction of flight. Orthogonal sample injection cases have recently been discussed by Laiko and Dodonov41 and they will not be treated in this paper. The geometry most likely to occur in MALDI, LD/I, FAB, or SIMS applications is that of parallel desorption. In this case, the relationship between initial position and velocity is very simple:
x0 ) ν0τ
(2)
Again x0 is the ion’s distance above plate G0 at the instant of extraction, v0 is the initial velocity in the direction of ion flight, and τ is the time delay between ion desorption and the application of the extraction field that begins the time-of-flight measurement. (Implicit in eq 2 is the assumption that v0 does not change between the time of desorption and the time of ion extraction. In principle, the equation could be modified to take collisions into account. In this case, x0 and v0 would be related by an alternative expression.) Equation 2 can be used to eliminate either v0 or x0 from the time-of-flight equation. For example, combining eqs 1 and 2 gives
TOF ) f(m/z,dx,τ,Vx,ν0)
(3)
By eliminating the variable representing initial position, we can now treat the focusing process as one in which the effect of a velocity distribution must be controlled. The advantage gained is that we have replaced the difficult problem of focusing both a spatial and a velocity distribution with the more tractable one of focusing a single distribution. Note that in the process, we have introduced a new parameter τ. However, any experimental aberr(41) Laiko, V. V.; Dodonov, A. F. Rapid. Commun. Mass Spectrom. 1994, 8, 720726.
Table 1. Instrument Conditions grid distances, mm d1 ) 12.04 d2 ) 13.03 d3 )210.74 d4 ) 23.30 d5 ) 5.2 a
conditions lysozyme trypsinogen
insulin Vpulse,a V V1, kV V2, V3, kV V4, V V5, V τ, µs
1793 15.0 12.06 0 -1900 2.323
2950 20.0 14.0 0 -1900 3.88
2000 15.0 10.5 0 -1900 7.37
Applied to grid G0 after delay τ so that V0 ) V1 + Vpulse.
Table 2. Instrumental Conditions Used To Calculate Curves Shown in Figure 5
Vpulse, V V1, kV V2, V3, kV τ, µs
A
B
C
D
E
2000 15.0 11.5 5.04
6000 15.0 0.0 4.715
5000 15.0 4.0 4.126
2000 15.0 10.5 7.37
2900 15.0 8.65 5.649
ration in its value can be made inconsequentially small.42 The new time-of-flight equation can be used for both identifying optimal space-velocity correlation conditions and modeling the effect that these conditions will have on mass spectral resolution. In practice, we have found optimal conditions by examining the range of expected ion flight times as v0 is varied. By minimizing this range as the variables dx, Vx, Vpulse, and τ are varied, satisfactory conditions can easily be identified. An example of this process is shown below. THEORETICAL RESULTS As an example of the effect of space-velocity correlation focusing we have used eq 3 to model the flight of ions in our MALDI instrument under conditions that could be experimentally tested. Calculations were made assuming that the initial spatial and velocity distributions are the sole factors limiting resolution; other factors, such as isotope distributions and electronics, are ignored, even though they do affect experiments. Consequently, calculated results are not always expected to match those experimentally measured. We assume a parallel desorption geometry typical of most MALDI instruments. On the basis of previous experimental measurements,43-46 we assume that MALDI ions are desorbed with a broad range of velocities (0-1200 m/s). Unless noted, the experimental conditions used for calculations are listed in Tables 1 and 2. Figure 2 illustrates the flight times expected for bovine insulin (m/z 5733) as a function of initial velocity for several different instrument operating conditions. Part A shows the expected flight times when (Wiley-McLaren) dc space focusing potentials are applied to instrument grids. For initial velocities ranging from 0 to 1200 m/s, flight times are calculated to be between 22.9 and 23.8 µs. This very poor result is a consequence of the broad (42) Cowen, K. A.; Coe, J. V. Rev. Sci. Instrum. 1990, 61 (10), 2601-2604. (43) Beavis, R. C.; Chait, B. T. Chem. Phys. Lett. 1991, 181 (5), 479-484. (44) Huth-Fehre, T.; Becker, C. H. Rapid Commun. Mass Spectrom. 1991, 5, 378-382. (45) Chan, T.-W. D.; Thomas, I.; Colburn, A. W.; Derrick, P. J. Chem. Phys. Lett. 1994, 222, 579-585. (46) Zhou, J.; Ens, W.; Standing, K. G.; Verentchikov, A. Rapid Commun. Mass Spectrom. 1992, 6, 671-678.
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Figure 3. Expected insulin mass spectral peak width as a function of delay time (τ) between ion formation and extraction. Calculated “peak width” is the range in flight times predicted assuming a linear initial velocity distribution from 0 to 1200 m/s.
Figure 2. Calculated time of flight as a function of initial velocity for insulin under different conditions: (A) using Wiley and McLaren space focusing, (B) with the conventional MALDI approach of accelerating ions to 30 keV in the first acceleration region, and (C) using the space-velocity correlation focusing conditions of Table 1.
velocity spread. In most MALDI experiments, the effect of the initial velocity distribution is reduced by employing a high drift energy. Figure 2B shows the significantly improved result that is predicted for ions accelerated to 30 keV between G0 and G1. The calculated time dispersion is only 35 ns. Unfortunately, the flight time is also much shorter in this case. In contrast, Figure 2C demonstrates the expected flight times for ions with the same initial velocities but under space-velocity correlation focusing conditions. In this case, the field in the first acceleration region is created by the application of an optimized voltage pulse at a time τ following the desorption pulse. The resulting times of flight vary by only 6 ns and the overall flight time is comparable to the space-focusing case (Figure 2A). Note that the abscissa of Figure 2C is labeled in both position and velocity units. This is possible because once a value of τ has been specified, x0 and v0 are related by eq 2. Since Figure 2C demonstrates that the variation of ion flight time with initial ion position and with initial ion velocity have both been significantly reduced relative to the results displayed in parts A and B of Figure 2, we say that both spatial and velocity focusing have been accomplished. The instrument operating parameters are critical for spacevelocity correlation focusing. Figure 3 shows how peak widths for the protein insulin are predicted to vary as a function of τ. “Peak width” in this context is the full range of calculated flight times determined using an initial velocity range of 0-1200 m/s. For example, in parts A through C of Figure 2, the peak widths are 900, 35, and 6 ns, respectively. These represent the maximum contributions to peak broadening expected from any initial velocity distribution within the range of 0-1200 m/s. Figure 3 shows that there is clearly an optimum delay time to apply the ion extraction pulse. Longer or shorter times sharply reduce the focusing effect. Nevertheless, the peak width is predicted to be better than that calculated for space-focused conditions (Figure 2A) over a wide range of τ values. Away from the optimum, the data are slightly nonlinear. While Figure 3 was calculated for the particular case of insulin, similar curves can be derived for ions of other masses. 1422 Analytical Chemistry, Vol. 68, No. 8, April 15, 1996
Figure 4. Calculated flight times as a function of initial velocity for trypsinogen using various conditions. Differences in the shapes of the curves reflect the degree to which experimental conditions are optimized. The parameters used in these calculations are found in Table 2.
The optimal value of τ varies with analyte mass and other instrument operating parameters. Figure 4 displays the dependence of predicted ion flight time on initial velocity for a larger protein trypsinogen (m/z 23981). The inverted parabolic dependence of Figure 4A is qualitatively similar to that in Figure 2C and is likewise reminiscent of a Wiley-
Figure 5. Calculated trypsinogen flight times as a function of initial velocity when delay times ( 500 ns from the optimum τ are used.
McLaren space-focusing curve.4 Indeed, this curve represents the best possible time-of-flight focusing for the set of grid voltages listed in Table 2, part A. Nevertheless, flight time dispersion is seen to be on the order of 40 ns. Although ∂TOF/∂x0 and ∂TOF/ ∂v0 are both 0 at the center of the curves, time-of-flight focusing is not very good. By using another set of grid voltages (Table 2, part B), the curve displayed in Figure 4B was calculated. Here, the time-of-flight spread is only about 4 ns, although the overall flight time is about half of that in the first case. Parts C-E of Figure 4 display more interesting, higher order functional dependencies of flight time on initial ion velocity. Each shows good time-of-flight focusing; the highest resolution is predicted for case C, for which ∂TOF/∂v0 is not zero at the center of the velocity range considered, but is zero at approximately v0 ) 300 and 900 m/s. Figure 4 demonstrates that there are multiple solutions to the problem of how to minimize the effect that initial ion velocity has on flight time spread. However, some solutions are better than others and all instrument parameters must be varied in order to find the best solutions. The use of nonoptimal pulsed ion drawout delay times results in substantial broadening of predicted peaks. For example, Figure 5 displays the dependence of trypsinogen flight time on initial ion velocity for τ delays that deviate (500 ns from their optimal values. All other conditions are the same as those used for the calculation of Figure 4D. Ion peak widths are predicted to be about 170 ns in either case. Space-velocity correlation focusing conditions are also mass dependent. To demonstrate this, we derived the optimal instrument operating conditions for chicken egg lysozyme (m/z 14306) that are listed in Table 1. Then, using these conditions, we calculated peak widths for masses ranging from 500 to 30 000 Da. The result is displayed in Figure 6. As shown, calculated peak widths can be much wider for masses other than those for which conditions were optimized. Curves with similar shapes are observed when conditions are optimized for other masses. To demonstrate the effectiveness of space-velocity correlation focusing for both small and large proteins, optimizations were performed for bradykinin (m/z 1060) and bovine serum albumin (m/z 66430). Rather spectacular peak narrowing is predicted for the former, as reflected in Figure 7A. It was not possible to achieve calculated peak widths narrower than 8 ns (with a TOF of 37.89 µs) for bovine albumin without changing source region distances d1 and d2 from the values listed in Table 1. However, reducing d1 to 7 mm and increasing d2 to 49 mm enabled us to compute the flight time curve displayed in Figure 7B. The timeof-flight spread in this case is only about 2 ns.
Figure 6. An illustration of the calculated mass dependence of space-velocity correlation focusing. Peak width is defined as in the text. The experimental conditions are optimized for chicken egg lysozyme.
Figure 7. Calculated flight times for two proteins as a function of initial ion velocity. The following optimized conditions were used (A) bradykinin, Vpulse ) 1875 V, V1 ) 15 kV, V2 ) 11.3 kV, τ ) 1.2695 µs and (B) bovine albumin, Vpulse ) 2000 V, V1 ) 15 kV, V2 ) 1.5 kV, τ ) 5.654 µs, d1 ) 7 mm, and d2 ) 49 mm.
Figure 8. Calculated optimal values of τ as a function of mass. Three drawout voltages (Vpulse) are examined: 2000, 5000, and 8000 V. Grid voltage V1 was held at 15 kV while V2 was optimized for each mass.
Figure 8 displays the dependence of optimal τ delay on mass for three different ion drawout voltages, 2000, 5000, and 8000 V. Instrument distances listed in Table 1 were employed. Voltage V1 was fixed at 15 kV while V2 was varied to obtain optimal ion focusing. It is quite apparent that the lowest drawout fields require the longest delay times. For the lowest extraction voltage, the Analytical Chemistry, Vol. 68, No. 8, April 15, 1996
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Figure 9. Optimal extraction voltage (Vpulse) as a function of mass. (V0 ) V1 + Vpulse during extraction.) Each line represents a set of instrumental parameters in which only Vpulse was varied. The other parameters were optimized for different analyte masses as follows: (A) bradykinin (1060 Da), conditions of Figure 8A; (B) lysozyme (14306 Da); conditions listed in Table 1; (C and D) trypsinogen (23981 Da) conditions of Table 2, columns C and D, respectively.
optimal value of τ is limited by the residence time of the ions in the source. This corresponds to approximately 10 µs and reduces the focusing possible for ions with mass above 40 kDa. It is also evident that τ increases with ion mass. It has previously been reported that the optimal extraction voltage increases linearly with mass.29-31 This conclusion was based on empirical observations. To test this, we calculated optimal space-velocity correlation focusing conditions for a few protein masses. Then for each of these conditions, we varied the ion mass from 500 to 100 000 Da and computed the optimal Vpulse. The result is displayed in Figure 9. The relationship between Vpulse and mass is evidently not linear, although the curvature occurs mainly at low masses and it might not be observed in experiments. EXPERIMENTAL METHODS The achievement of space-velocity correlation focusing has been experimentally demonstrated using a variety of molecules.35-38 This was accomplished using the time-of-flight mass spectrometer illustrated in Figure 1. It includes a source with two acceleration regions, a field-free region surrounded by an aluminum liner and two postacceleration regions preceding a tandem microchannel plate detector. Unless otherwise noted, experimental conditions are listed in Table 1. Note the relatively short overall length of the instrument (25 cm). This design was chosen in part to improve sensitivity. Initially both of the plates defining the first acceleration region (G0 and G1) are held at the same potential. At a time τ following the desorption light pulse the potential on G0 is incremented by voltage Vpulse, producing the ion drawout field and defining the start of the time-of-flight measurement. Ions were detected with a pair of tandem microchannel plates (Galileo). The signal was amplified 10× and digitized by a Biomation 6500 waveform recorder with 2 ns/channel resolution and (1 channel jitter. Samples were ionized using the frequencytripled output of a Quanta-Ray DCR-2 Nd:YAG laser. Ferulic acid was used as a matrix for the protein samples. Approximately 100 pmol of protein were typically contained in a 2 µL sample volume. The matrix to analyte molar ratio was 1000:1. Voltage pulsers were designed and built in house. Further details of the experimental apparatus have been provided elsewhere.35,36 1424 Analytical Chemistry, Vol. 68, No. 8, April 15, 1996
EXPERIMENTAL RESULTS Mass spectra of a number of molecules have been recorded with our TOF instrument using a variety of operating conditions. Mass spectra of insulin, for example, are shown in Figure 10. Parts A and B of Figure 10 show data recorded using instrument conditions identical to those employed in the calculation that produced Figure 2A. Both plots include the same data, but the time axis is expanded in the latter case. As predicted by our calculation, the peak width is hundreds of nanoseconds wide. Figure 10C shows data recorded under space-velocity correlation focusing conditions defined in Table 1. The peak has been reduced from 300 to 12 ns fwhm. The resolution obtained is approximately 1100, which is remarkable for such a small linear instrument. The width of this peak is limited by the resolution of the digitizer and the isotope distribution of the analyte molecule. For further comparison, Figure 10D shows data recorded with the conventional MALDI approach of applying 30 kV to grid G0 and grounding the other grids. This approach reduces the effect of the initial velocity distribution. Unfortunately, as noted earlier, it also reduces the overall flight time so that resolution is not significantly improved. The experimental peak is, in fact, significantly broader than that predicted by calculation (Figure 2B). This will be discussed further in the next section. A critical dependence of insulin mass spectral peak width on ion drawout delay time (τ) was predicted by the calculation that produced Figure 3. To verify this experimentally, we recorded a series of bovine insulin mass spectra with different values of τ. As shown in Figure 11, the optimum delay time is ∼2.38 µs. Clearly, both smaller and larger values of τ result in a rather symmetric increase in peak width that is comparable to that predicted in Figure 3. A negative τ is equivalent to dc ion drawout conditions because in this case, the electric field is applied before the laser pulse. Figure 12 shows mass spectra of another protein, trypsinogen. The data in Figure 12A were recorded with a lower digitizer resolution of 20 ns/channel in order to display a wide range of flight times. The sharp feature at about 41 µs corresponds to parent ions. The somewhat broader peak at 38.5 µs corresponds to fragment ions produced in the field-free drift tube. These may be generated through metastable dissociation or collisions with the walls, gas-phase molecules, or grid G3. Fragment ions move ahead of the parents in the postacceleration region of the instrument. Those with masses between 1 and 130 Da are all predicted to arrive at the detector during the time period corresponding to this peak. This would include individual amino acids. The broad, underlying pedestal that appears between flight times of 38 and 43 µs corresponds predominantly to unresolved and somewhat heavier fragment ions. In addition, some ions that lose kinetic energy as a result of collisions can arrive at the detector after the parent ions. A more thorough examination of these signals has been previously reported.36 An expanded view of the parent ion region is displayed in Figure 12B. As with the insulin spectrum of Figure 10C, the parent ion peak is only 12 ns wide. This is limited by electronics jitter and the existence of an unresolved isotope distribution. Since space-velocity correlation focusing is not mass independent and optimal instrument conditions are valid for just a single mass, it is of interest to experimentally observe how mass spectral resolution deteriorates for nonoptimized masses. The spectrum of chicken egg lysozyme in Figure 13 exemplifies this
Figure 10. Mass spectra of insulin recorded using three different sets of conditions. (A and B) Wiley-McLaren space focusing, (C) spacevelocity correlation focusing, and (D) the conventional MALDI approach of accelerating ions to 30 keV in the first acceleration region. Parts B, C, and D are all plotted over a time range of 2 µs.
A
B Figure 11. Mass spectra of insulin recorded with different delay times (τ) between ion desorption and extraction. A negative τ is equivalent to dc ion drawout.
problem. To record it, mass spectrometric conditions were set up for optimal focusing of the parent ion. The spectrum displays both a parent peak, at ∼27.6 µs and a doubly charged parent ion at ∼19.7 µs. When examined on expanded scales, these peaks are found to be 14 and 54 ns fwhm, respectively. The doubly charged peak is about 150 ns wide across its base, in rough agreement with that predicted in Figure 6. DISCUSSION A number of factors, critical to the improvements in resolution that we have demonstrated, distinguish space-velocity correlation focusing. Principal among these is the fact that a correlation between spatial and velocity distributions is found and exploited. This enables the identification of conditions under which the effect of variations in both the initial position and velocity on the ion time of flight is minimized. In other words, both distributions are simultaneously focused. Wiley and McLaren specifically pointed out that this was not possible with the initial spatial and velocity
Figure 12. Mass spectrum of trypsinogen recorded with (A) 20 ns/ channel and (B) 2 ns/channel digitizer resolution. In A the parent peak at ∼41 µs is surrounded by signal due to fragments and ions that underwent collisions. In B the postacceleration conditions have been changed in order to remove these signals. See ref 36.
distributions produced by conventional gas-phase ionization methods.4 The correlation of distributions is now possible because sample is desorbed from a surface, a case they did not consider. The calculations shown above are intended to predict the effect that space-velocity correlation focusing has on the mass resolution of our instrument. As previously mentioned, only the contribution of the initial velocity distribution is considered. When its influence is reduced, we expect other factors such as isotope distributions, collisional effects, and electronic bandwidth to limit Analytical Chemistry, Vol. 68, No. 8, April 15, 1996
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Figure 13. Mass spectra of chicken egg lysozyme showing mass dependence of space-velocity correlation focusing. The parent and doubly charged peaks are seen at ∼27.6 and ∼19.7 µs, respectively.
experimental peak widths. (For small proteins, isotope distributions have already been resolved.32,33) We can choose to eliminate either x0 or v0 from the basic time-of-flight equation (eq 1). However, since the velocity distribution that MALDI ions are desorbed with has been experimentally examined,43-45 we find it most logical to eliminate x0 and use the reported range of values for v0. Our model makes no assumptions about the shape of the initial velocity distribution. The calculated “peak widths” reported represent the full range of flight times based on considering initial velocities from 0 to 1200 m/s. Since the actual distribution of velocities is expected to include fewer ions at the extremes of the velocity range, the values reported are intended to reflect the widths of ion peak bases; fwhms should be smaller. We also assume that the extraction field is applied with an instantaneous rise time. When an electric field of the form
E(t) ) E0(1 - e-t/tr)
(4)
is incorporated into the model, the results of the calculations differ only by a small shift in the optimal value of τ. This shift is found to be comparable to the rise time of the pulse, tr. The narrowest range in calculated flight times does not always correspond to the best mass resolution. Conditions can often be found for which an increase in the overall flight time compensates for a slightly wider peak. The overall flight time is especially important when factors other than the initial spatial and velocity distributions affect the observed resolution. For example, the data shown in Figure 4C predict a peak width of only 1 ns and resolution that is better than that found in parts D or E. However, when the peak width is limited to 12 ns by the isotope distribution and electronics (as in Figure 12B) then the best experimental resolution may be achieved using the conditions of Figure 4D for which the flight time is longest. The slope or shape of the calculated time-of-flight vs initial velocity curves is of assistance in locating optimal conditions. For example, as seen in Figure 5, τ values greater or less than the optimal one result in the generation of curves having positive and negative slopes, respectively. At the optimal τ values shapes such as those shown in Figure 4 are observed. For a given set of grid distances and voltages one can calculate time-of-flight vs initial velocity curves for a series of τ values and in each case quickly locate the optimum. As the acceleration fields are changed, the shape of the curve at optimal τ changes from concave to convex. 1426 Analytical Chemistry, Vol. 68, No. 8, April 15, 1996
This is seen in parts A and B of Figure 4. The very best conditions are found at the transition between these two shapes. In this region of parameter space higher order relationships are observed, as shown in parts C-E of Figure 4. The presence of these higher order relations makes the identification of optimal operating conditions more complicated than finding the solution of ∂TOF/ ∂x0 ) 0, as done by Wiley and McLaren. To optimally minimize the dependence of ion flight time on initial ion position (or velocity) the derivative of the flight time with respect to either of these parameters should be zero at more than one value of x0 (or v0). As predicted by our calculations, dramatic improvements in resolution compared to traditional high voltage dc drawout methods are achievable using optimized pulsed ion extraction. This is illustrated by Figures 2 and 10. Figures 2A and 10A,B represent (dc) Wiley and McLaren space-focusing conditions. While the range in flight times predicted by Figure 2A is wider than the base of the peak seen in Figure 10B, the calculation makes no assumption about the shape of the initial velocity distribution. A center-weighted distribution, for example, would result in a narrower experimental peak. The reason that Figure 2 compares the flight time spread produced under space-velocity correlation focusing conditions with that predicted for Wiley-McLaren space-focusing conditions (rather than Wiley-McLaren time-lag focusing conditions) is that it is not possible to calculate a set of instrument operating parameters that can be used to accomplish time-lag focusing. Wiley and McLaren specify how to calculate the pulse delay τ given a set of dc and pulser voltages; however, the latter must be determined empirically. Figures 2B and 10D were obtained using conventional MALDI conditions in which ions are accelerated to a high energy in the first region. In this case, the predicted range in flight times is much narrower than that found experimentally. This difference may be caused by the spread of positions over which ions are formed due to the morphology of the crystalline matrix and the gas-phase chemistry that occurs above it. To the extent that this occurs, the approximation represented by eq 2 may break down. (However, this situation can be quite complicated. For example, if a neutral molecule were desorbed from the surface and collisionally ionized without its velocity changing, eq 2 would still accurately describe its position at the time that the pulsed drawout field is applied.) In a very high acceleration field, small differences in position result in substantial variations in electrostatic potential. For example, variations in ion formation position of ∼500 µm are sufficient to cause the peak broadening seen in Figure 10D. This illustrates the importance of operating the spectrometer under conditions in which the flight times of ions are relatively insensitive to both their initial positions and their initial velocities. It is evidently incorrect to assume that all MALDI ions are formed in the same plane and that only the velocity spread needs to be focused. The broad width of the peak displayed in Figure 10D may also be due to events that occur in the source region during the desorption process. These include collisions, adduct formation, and metastable fragmentation. These phenomena are undoubtedly affected by the application of a high electric field. Elimination of this field, through the use of delayed ion extraction, is a significant advantage. Figures 2C and 10C were generated using similar space-velocity correlation focusing conditions. The 12 ns peak width shown in the experimental result of Figure 10C is limited by the jitter of the Biomation waveform
recorder and the isotope distribution of the analyte (which by itself is 9 ns wide). The small flight time discrepancy between Figure 2C and 10C is due to internal electronic delays that were not accounted for. An important test of eq 3 is its ability to predict optimal ion focusing conditions. In Figure 3, we showed how peak width is expected to change as the delay time between desorption and extraction (τ) deviates from the optimum. To either side of the optimum, the peak width is predicted to increase dramatically. The optimum value of τ determined through calculation, 2.32 µs, is close to the optimal τ of 2.38 µs obtained experimentally. The small difference between these two values can be attributed to the precision to which the potentials used for extraction and acceleration are known. As illustrated by the experimental data of Figure 11, the insulin peaks become substantially wider as the delay time is shifted away from the optimum. The smallest value of τ examined experimentally was -0.27 µs. In this case, the extraction pulse was applied before the desorption light, effectively producing dc ion acceleration. An added advantage of optimized pulsed ion extraction is observed in Figure 11. As the analyte peak is narrowed, its height increases. (Signal to background ratio does not appear to improve in the data displayed. However, fewer shots were used to record the central spectra.) In addition to the agreement between the predicted and experimentally measured optimal τ values, Figure 11 also shows that peak widths become wider as delay times become either shorter or longer than the optimum. This would not be true if the improvement in resolution that we observe were primarily due to a reduction in metastables, space charge, or the severity of collisions in the source region. An important aspect of space-velocity correlation focusing is its mass dependence. This is a serious problem that has limited the use of time-lag focusing in linear instruments.16 As shown in Figure 6, conditions optimized for one mass (14 306 Da) are less than optimal for other masses. There is an unusual relationship between mass and expected peak width. The experimental mass spectrum shown in Figure 13 is consistent with the calculations of Figure 6. For the doubly charged lysozyme (m/z 7153), the calculation predicts a range in flight times of ∼175 ns. This is similar to the width of the base of the doubly charged peak in Figure 13. The 54 ns fwhm of this peak is still much narrower than would be obtained with dc ion drawout despite the fact that its mass to charge ratio is half of that for which the experimental conditions were optimized. Good focusing conditions can be found for modest size peptides and large proteins. Figure 7 shows initial velocity vs timeof-flight curves for bradykinin and bovine serum albumin. For bradykinin, our experimental results are limited by the resolution of the waveform recorder and the isotope distribution of the analyte. The best experimental result that we obtained for this molecule was an 8-10 ns fwhm peak. Sharper peaks and unit mass resolution have been obtained by Whittal and Li for this compound.32 For higher masses, changes in instrument geometry are sometimes necessary. This was the case for bovine serum albumin shown in Figure 7B. By changing the lengths of the acceleration regions we were able to predict a flight time spread of only 2.4 ns. With the original distances the best result achieved was 8 ns. Our best experimental result for this analyte is a peak 220 ns fwhm (∼300 Da). We believe that this broad line width is due to a variety of unresolved adducts and/or counterions that can easily attach to very large proteins and particularly albumin.
Bigger analytes also have more opportunities for metastable decay and larger collisional cross sections. Our assumption that the initial velocity distribution is the primary limit to mass resolution may, therefore, become inaccurate above a certain mass range. Factors, such as those above, that limit the resolution of bradykinin and bovine serum albumin may be even more mass dependent than space-velocity correlation focusing itself. As indicated in Figures 8 and 9, larger masses require longer delay times or higher extraction potentials. This is due to the increasingly wide range of kinetic energies that the initial velocity distribution corresponds to. With longer values of τ, the analyte can then disperse into a volume with a wider range of electrostatic potential. Likewise, if a greater extraction field is used, the required range of electrostatic potential can be reached in a shorter delay period. Because of the improvements introduced by space-velocity correlation focusing, certain instrumental factors require special attention. For example, our data clearly shows that peak widths can be limited by electronic resolution. This had not been a serious concern when peaks were hundreds of nanoseconds wide. The use of conversion dynodes and postacceleration can also lead to complications. As was shown in Figure 12, postacceleration separates parent ions and metastables that are formed in the drift region. This may cause additional peaks and background signal in the mass spectrum.36 Similarly, conversion dynodes may generate a variety of secondary ions that are now resolvable. Because space-velocity correlation focusing employs delayed extraction, it can reduce the effect that varying ion formation times have on mass spectral peak broadening. It is even possible to record an ion signal whose temporal width is shorter than that of the desorption laser pulse. This is possible because the pulsed extraction field determines the start of the time-of-flight measurement. The distribution of ion formation times merely results in a small spatial distribution at the time of extraction. During the period between desorption and extraction, τ, ions travel with a velocity that is much lower than their drift velocity after extraction. The distance that molecules travel during the time period over which ions are formed is therefore extremely small compared to the overall flight distance. For example, if ions are formed over a 50 ns time interval with initial velocities of 1000 m/s, then those formed first will be displaced by only 50 µm relative to those formed last. This distance spreads out the overall flight time by much less than 50 ns. Use of delayed ion extraction may have other advantages. As suggested by Lennon and Brown,30,31 the absence of a strong initial field affects collisions in the source region in a manner that enhances the resolution. However, we believe that the agreement between the predicted and experimental optimal values of τ suggests that the focusing of the spatial and velocity distributions is the primary reason that we observe improved resolution. Further work is necessary to fully understand the effects of fields on the formation of ions, adducts, and fragments. Although mass spectral peaks can be dramatically narrowed using the methods described in this paper, the ratio of signal to background noise can but does not necessarily improve. As seen in Figure 12, the analyte signal is dominated by contributions from fragment ions. When these are repressed, as in Figure 12B, the analyte signal is actually rather weak and the signal to noise ratio is not very good. This problem can be overcome by eliminating the postacceleration field between the ion drift tube and detector. When this is done, information about metastable fragmentation Analytical Chemistry, Vol. 68, No. 8, April 15, 1996
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is then, of course, lost, but we have found that the parent ion signal to noise ratio improves significantly. As noted earlier, there are a number of other applications besides MALDI to which space-velocity correlation focusing may be applied. These include fast-atom bombardment, secondary ion mass spectrometry, and laser desorption/ionization. Even though these techniques tend to produce ions of lower mass than those observed in MALDI, improved resolution is still important. For example, in the analysis of surfaces by laser desorption/ionization,47 a resolution of 3000 is needed to distinguish between isobaric species such as Si2+ and 56Fe+. Computer simulations predict that space-velocity correlation focusing should be just as effective in this lower mass range as it has been in MALDI. While the results reported above were obtained with a linear instrument only 25 cm in length, space-velocity correlation focusing can also be applied to longer instruments or to reflectrons. Two groups have recently reported delayed ion extraction studies with longer linear and reflectron instruments.33,34 We have shown several examples of how critical the correct instrument parameters are for obtaining optimal space-velocity correlation focusing. It is easy to see how pulsed extraction could be used in MALDI experiments by a number of groups over several years without producing dramatic resolution improvements. Two factors contribute to this. First, optimal focusing conditions require voltage pulses and source distances that are somewhat different from those typically used. Second, the complexity of the MALDI phenomenon allows improvements in instrumental performance to be attributed to a variety of factors whose relative importance differs from one instrument to the next. The improved resolution observed with space-velocity correlation focusing will help facilitate a variety of interesting experiments. These include the study of adducts and counterions. Without sufficient resolution, it is impossible to identify these species. Their complete separation is necessary for accurate mass determinations and instrument calibration. The same mathematical algorithm that is used to optimize instrument operating parameters to produce the sharpest possible time-of-flight peaks can obviously be used to predict the location of these peaks. We have found that when a DNA 27-mer is enzymatically digested and mass spectra of the resulting oligonucleotide fragments are recorded, the experimentally measured and theoretically calculated flight times of all peaks agree within 2 ns. Both the improved mass resolution and the capability of accurately assigning peak masses should be helpful in future macromolecule sequencing applications. Finally, with a high-resolution MALDI/TOF instrument, one can also examine peak shifts and peak broadening due to gas-phase collisions3,48 and can identify subtle modifications to proteins. SUMMARY AND CONCLUSIONS Space-velocity correlation focusing represents a new computational algorithm that enables substantial improvements in the resolution of some time-of-flight mass spectrometers with certain source geometries. Resolution enhancement of more than 1 order of magnitude is demonstrated for matrix-assisted laser desorption/ ionization. The improvements observed are the result of a number of elements. First among these is the observation that the initial spatial and velocity distributions can be correlated in a certain (47) Becker, J. S.; Dietze, H.-J. Fresenius J. Anal. Chem. 1993, 346, 134-137. (48) Christian, N.; Reilly, J. P. Manuscript in preparation. (49) Tang, K.; Tarenko, N. E.; Allman, S. L.; Chang, L. Y.; Chen, C. H. Rapid Commun. Mass Spectrom. 1994, 8, 727-730.
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source geometry. This enables the simultaneous focusing of both distributions and distinguishes this method from past delayed extraction techniques. Optimal focusing of both distributions was previously postulated to be mutually exclusive.4 It also permits a more effective focusing of the initial velocity distribution than techniques previously used in linear instruments. While both the Wiley-McLaren time-lag focusing algorithm and space-velocity correlation focusing algorithm are based on the same physical mechanism, the compensation for variations in initial ion kinetic energy through time-dependent variations in initial ion electrostatic potential energy, the two approaches differ in both computational detail and in what they can accomplish. The Wiley-McLaren algorithm requires an assumption that the slope ∂TOF/∂x0 has a certain sign. No such assumption is built into the space-velocity correlation focusing algorithm. As seen by the various curves in Figure 4, this derivative can be positive, negative, or zero at various points within the ion velocity (or ion position) range considered by the calculation, although it is advantageous for it to be zero at least somewhere within this range. More significantly, the Wiley-McLaren time-lag focusing algorithm provides an estimate for τ, the time delay between ion production and ion drawout, when all of the other instrument parameters (distances and voltages including that of the ion drawout pulse) have been set and when an average initial ion velocity has been selected. All of these other parameters must be found empirically, through trial and error. In contrast, use of the space-velocity correlation focusing algorithm leads to a complete set of optimized instrument operating parameters while accounting for the effects of a range of initial ion velocities. Furthermore, the effect of initial ion velocity spread over a range of interest is immediately evident, without the assumption of any particular ion velocity distribution. Finally, space-velocity correlation focusing can easily be adapted to include other experimental factors that affect the quality of mass spectra. These might include, for example, a spread in the position where ions are formed or the use of a low voltage field in the source region before the ion drawout pulse is applied. Space-velocity correlation focusing enables a number of predictions about mass spectrometer performance that are experimentally confirmed. It demonstrates that the initial velocity distribution is the primary factor limiting mass resolution in the mass range that we have examined by correctly identifying optimal conditions. The improvement in resolution obtained should lead to a variety of new experiments. For example, by resolving small adduct or counterions, the accuracy of exact mass measurements can be improved and ways to remove these ions can be studied. It is also possible to observe small differences in proteins and investigate posttranslational modifications. When factors other than the initial spatial and velocity distributions are found to limit resolution, space-velocity correlation focusing can be helpful in analyzing their contributions. ACKNOWLEDGMENT This work was supported by the National Science Foundation and the Environmental Protection Agency.
Received for review July 18, 1995. Accepted January 22, 1996.X AC950716Q X
Abstract published in Advance ACS Abstracts, March 1, 1996.
