Mass-to-charge ratio upper limits for matrix-assisted laser desorption Fourier transform ion...

Anal. Chem. 1992, 64, 1461-1469 1461

Mass-to-Charge Ratio Upper Limits for Matrix-Assisted Laser Desorption Fourier Transform Ion Cyclotron Resonance Mass Spectrometry Troy D. Wood, Lutz Schweikhard,’ and Alan G. Marshall’J

Department of Chemistry, The Ohio State University, 120 West 18th Avenue, Columbus, Ohio 43210

One of the well-known analytical uses of Fourler transform Ion cyclotron resonance mass spectrometry (FT/ICR/MS) Is lts high theoretical upper mass Ilmlt. FT/ICR/MS upper mass llmlts wlth respect to radlal or axlal loss of trapped Ions have prevlously been derived and computed for Ions whlch are In thermal equlllbrlum wlth thelr surroundlngs (Le., follow Boltr- mann preexcltatlon Ion lnltlal veloclty dlstrlbutlons). However, recent results by Beavls and Chalt show that Ions formed by the matrlx-assisted laser desorptlon (MALD) lonlratlon tech- nlque are clearly not In thermal equlllbrlum wlth thelr surroundings, but rather exhlblt a nearly symmetrlc non-Bolts- mann lnltlal Ion veloclty dlstrlbutlon about a substantially su- prathermal most probable Ion velocity (-780 m s-l) whlch Is essentlally Independent of polypeptlde Ion mass. I n thls paper, we derlved radlal and axlal m/q upper llmlts (deflned by 50% trapplng efflclency In the absence of ICR excltatlon) as a functlon of magnetlc fleld strength and trapplng potentlal for cublc, tetragonal, screened tetragonal, cylhrdrlcal, and hyperbollc traps, evaluated at the most probable Ion preexcltatlon lnltlal veloclty found emplrlcally by Beavls and Chalt. Flnally, because an Increase In trapplng voltage lowers the radlal m/q upper llmlt but ralses the axlal m/q upper Ilmlt, an “optlmum trapplng potentlal” lo derlved and evaluated as a functlon of trapplng voltage and magnetlc fleld strength for varlous trap geometrles. The present theoretlcal upper mass lhnlts account semlquantltatlvely for prlor experlmental MALD/ FT/ICR/MS results; lmpllcatlons for future MALD/FT/ICR/ MS dlrectlons are dlscussed.

INTRODUCTION

The analytical advantages and capabilities of Fourier transform ion cyclotron resonance mass spectrometry (FTl ICR/MS) have been the subject of numerous recent reviews.l-13 A prime advantage of FTIICRIMS is its high theoretical upper

* To whom correspondence should be addressed. + On leave from the University of Mainz, Mainz, Germany. 8 Also a member of the Department of Biochemistry. (1) Marshall, A. G.; Grosshans, P. B. Anal. Chem. 1991, 63, 215A-

229A. (2) Marshall, A. G.; Schweikhard, L. Int. J. Mass Spectrom. Ion Proc.,

in press. (3) Asamoto, B.; Dunbar, R. C. Analytical Applications of Fourier

Transform Ion Cyclotron Resonance Mass Spectrometry; VCH: New York, 1991.

(4) Wanczek, K.-P. Znt. J. Mass Spectrom. Zon Proc. 1989, 95, 1-38. (5) Wilkins, C. L.; Chowdhury, A. K.; Nuwaysir, L. M.; Coates, M. L.

Mass Spectrom. Reu. 1989,8, 67-92. (6) Nibbering, N. M. M. Acc. Chem. Res. 1990, 23, 279-285. (7) Freiser, B. S. InBonding Energies in Organometallic Compounds;

American Chemical Society: Washington, D.C., 1990; Vol. 428, pp 55-69. (8) Lasers in Mass Spectrometry; Lubman, D. M., Ed.; Oxford,

University Press: New York, 1990. (9) Fourier Transform Mass Spectrometry: Evolution, Innovation,

and Applications; Buchanan, M. V., Ed.; American Chemical Society: Washington, D.C., 1987; Vol. 359, 205 pp.

(10) Marshall, A. G. Acc. Chem. Res. 1985, 18, 316-322.

mass limit,’ whose importance lies chiefly in the determination of the mass and structure of large biopolymers.14 Observation by Lebrilla and co-workers of cesium iodide cluster ions up to mass-to-charge ratio, m/q = 31 830 u/e, demonstrates the practicality of FT/ICR/MS for high-mass applications.l5 The ultimate upper mass limit for FTlICRl MS can be expressed in terms of a “critical” mass, above which ions do not have stable cyclotron radii,16 no matter how big the trap. In a finite-size trap, however, ions of sufficiently large mass-to-charge ratio will be lost by collisions with the walls of the trap at mlq values somewhat smaller than the “critical” mlq value. For ions at thermal equilibrium (Le., Boltzmann distribution of ion initial velocities before excitation) in a finite-size trap, the mlq upper limit may be defined by the fraction of ions whose cyclotron radii and/or trapping oscillation amplitudes are less than the corresponding trap dimensions.17 Those calculations indicate that even relatively heavy ions (several thousand ule) formed by the laser desorption (LD) ionization process (with suprath- ermal kinetic energy) can be trapped efficiently for FT/ICR/ MS.

Matrix-assisted laser desorption (MALD), a revolutionary mass spectrometric ionization technique for generating massive gas-phase polypeptide ions, was reported in 198818J9 and has recently been reviewed.20 A laser is used to irradiate a sample in a large excess of a matrix molecule which absorbs at the frequency of the laser. The MALD ionization method has been found to increase dramatically the accessible mass range and sensitivity for mass spectrometric analysis of biopolymers.21 Whereas nicotinic acid was initially used as the matrix, other suitable matrices have also been applied.22-25 The technique has been demonstrated at various UV18J9v26-28

(11) Ghaderi, S. Ceram. Trans. 1989,5,73-86. (12) Hanson. C. D.: Kerlev. E. L.: Russell. D. H. In Treatise in

Analytical Chemistry, 2nd ed.:Winefordner, J. D., Ed.; Wiley: New York,

(13) Sharpe, P.; Richardson, D. E. Coord. Chem. Reu. 1989,93,59-85. (14) Marshall, A. G.; Verdun, F. R. Fourier Transforms in NMR,

Optical, and Mass Spectrometry: A User’s Handbook: Elsevier: Am-

1988; Vol. 11, pp 117-187.

sterdam, 1990; 460 pp.

Anal. Chem. 1990, 62,878-880. (15) Lebrilla, C. B.; Wang, D. T.-S.; Hunter, R. L.; McIver, R. T., Jr.

(16) Ledford, E. B., Jr.; Rempel, D. L.; Gross, M. L. Anal. Chem. 1984,

(17) May, M. A.; Grosshans, P. B.; Marshall, A. G. Int. J. Mass Spec- 56, 2744-2748.

trom. Ion Proc., in press. (18) Karas, M.; Hillenkamp, F. Anal. Chem. 1988,60, 2299-2301. (19) Tanaka, K.; Waki, H.: Ido, Y.:Akita, S.: Yoshida, Y.: Yoshida, T.

Rapid Commun. Mass Spectrom. 1988,2, 151-153. (20) Hillenkamp,F.;Karas, M.;Beavis, R. C.; Chait,B.T.Anal. Chem.

(21) Karas, M.; Hillenkamp, F. Trends Anal. Chem. 1990,9,321-325. (22) Beavis, R. C.; Chait, B. T. Rapid Commun. Mass Spectrom. 1989,

(23) Beavis, R. C.; Chait, B. T. Rapid Commun. Mass Spectrom. 1989,

(24) Zhao, S.; Somayajula, K. V.; Sharkey, A. G.; Hercules, D. M. Z. Anal. Chem. 1990,338, 588-592.

(25) Zhao, S.; Somayajula, K. V.; Sharkey, A. G.; Hercules, D. M.; Hil- lenkamp, F.; Karas, M.; Ingendoh, A. Anal. Chem. 1991, 63, 450-453.

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0003-2700/92/0364-146 1$03.00/0 0 1992 American Chemical Society

1462 ANALYTICAL CHEMISTRY, VOL. 64, NO. 13, JULY 1, 1992

and IR29J0 wavelengths and with different mass analyzers: time-of-flight instruments of various geometries,l8,22131,32 FT/ ICR,33J4 and double-focusing magnetic sector35 instruments. The MALD technique has been extended to oligonucleotide,33 gly~opept ide,~~ and poly~accharide3~ analysis.

In a critical recent experiment, Beavis and Chait measured the initial ion velocity distributions for three polypeptide ions formed by MALD ionization in the source region of a time-of-flight mass spectrometer and noted the relevance of their results for the upper mass limit of MALD/FT/ICR/ MS.38 They found that ions formed by the MALD ionization technique are not in thermal equilibrium with their surroundings, but rather exhibit a nearly symmetric (slightly skewed in favor of high velocity) initial ion velocity distribution which is virtually independent of polypeptide ion mass! Because the initial most probable ion velocity corresponds to a translational energy which exceeds that expected for ion formation at thermal equilibrium, desorption is proposed38939 to proceed by means of a supersonic expansion, in which matrix molecules are excited by laser photons, followed by a rapid phase transition of matrix molecules from a solid to a high-pressure fluid. This high-pressure fluid is then free to expand adiabatically into the vacuum chamber to form a supersonic jet. The jet transports large polypeptides into the gas phase, accelerating them to virtually identical velocity, independent of mass. Other groups have also measured MALD initial ion velocity distributions.32@~41 Those results, performed at UV (26632141 and 308 nm49 and IR (10.6 pm)41 laser wavelengths exhibited initial velocity distributions different than that found by Beavis and Chait38 at 354 nm. Evidently the initial ion velocity distribution is wavelength- dependent. In this paper, we use the Beavis and Chait value; the others could easily be substituted into our equations if desired.

Prior FT/ICR/MS upper mass limitsl7 based on Boltzmann- distributed ions are inappropriate for MALD/FT/ICR/MS because the MALD ionization process is nonthermal. In this paper, we derive m/q upper limit expressions based on the maximum ICR orbital radius (radial m/q upper limit) or translational z-velocity (axial m/q upper limit) a t which ions are still confined in the trap, based on the initial ion velocity

(26) Hillenkamp, F.; Karas, M.; Ingendoh, A.; Stahl, B. In Biological Muss Spectrometry; Burlingame, A. L., Ed.; Elsevier: Amsterdam, 1990; p 49.

(27) Beavis, R. C.; Chait, B. T. Rapid Commun. Muss Spectrom. 1989, 3,436-439.

(28) Salehpour, M.; Perera, I.; Kjellberg, J.; Hedin, A.; Islamian, M. A,; Hakansson, P.; Sundqvist, B. U. R. Rapid Commun. Muss Spectrom.

(29) Overberg, A.; Karas, M.; Hillenkamp, F. Rapid Commun. Mass Spectrom. 1991,5, 128-131.

(30) Overberg, A.; Karas, M.; Bahr, U.; Kaufmann, R.; Hillenkamp, F. Rapid Commun. Muss Spectrom. 1990,4, 293-296.

(31) Perera, I. K.; Uzcategui, E.; Hakansson, P.; Brinkmalm, G.; Petter- son, G.; Johansson, G.; Sundqvist, B. U. R. Rapid Commun. Muss Spec- trom. 1990,4, 285-289.

(32) Spengler, B.; Cotter, R. J. Anal. Chem. 1990, 62, 793-796. (33) Hettich, R.; Buchanan, M. V. J. Am. SOC. Mass Spectrom. 1991,

(34) Hettich, R. L.; Buchanan, M. V. J. Am. SOC. Muss Spectrom.

(35) Hill, J. A.; Annan, R. S.; Biemann, K. Rapid Commun. Mass Spec- trom. 1991,5,395-399. '

(36) Hillenkamp, F. In Proceedings of 38th Ainerican Society of Mass Spectrometry Conference on Muss Spectrometry & Allied Topics; American Society of Mass Spectrometry: East Lansing, MI, Tucson, AR,

(37) Stahl, B.; Steup, M.; Karas, M.; Hillenkamp, F. Anal. Chem. 1991,

(38) Beavis, R. C.; Chait, B. T. Chem. Phys. Lett . 1991,181,479-484. (39) Beavis, R. C.; Chait, B. T. In Methods and Mechanisms for

Producing Ions from Large Molecules; Standing, K. G., Ens, W., Eds.; Plenum: New York, 1992.

(40) Ens, W.; Mao, Y.; Mayer, F.; Standing, K. G. Rapid Commun. Muss Spectrom. 1991,5, 117-123.

(41) Pan, Y.; Cotter, R. J. Org. Mass Spectrom. 1992,27, 3-8.

1989,3, 259-263.

2,402-412.

1991,2, 22-28.

1990; pp 8-9.

63,1463-1466.

D E \ I D

T

Figure 1. Static electromagnetic traps of various geometry for which the MALD/FT/ICR/MS upper mass limits are derived and evaluated in this paper: (a) cubic, (b) tetragonal, (c) screened tetragonal, (d) cylindrical, and (e) hyperbolic. B indicates the static magnetic fieid direction. The excitation, detection, trapping, and screen electrodes are designated E, D, T, and S, respectively.

expected for MALD/FT/ICR/MS, as a function of magnetic field strength and electrostatic trapping potential, for the various ion traps shown in Figure 1. As initial ion velocity, we choose the center of gravity of the velocity distribution observed by Beavis and Chait,38 averaged over their three polypeptides, namely, uo = 760 m s-l. Thus, our trapping criterion corresponds to a trapping efficiency of -50 ?6 . Finally, because the radial m/q upper limit decreases with increasing trapping voltage, whereas the axial m/q upper limit increases with trapping voltage, we can combine the two results to determine the optimal trapping voltage and its corresponding overall m/q upper limit. The results and under- lying assumptions of the theory are analyzed and compared with experiment, and implications for future MALD/FT/ ICR/MS are discussed.

THEORY

An ion moving in the presence of spatially uniform electric (E, in V m-1) and magnetic (B, in Tesla) fields in an ICR ion trap is subjected to a Lorentz force

dv dt force = (mass)(acceleration) = m- = qE + qvB (1)

in which m is ionic mass (kg), q is ionic electrostatic charge (C), and v is ion velocity (m s-l), and the magnetic field is directed toward the positive z-direction: B = Bok. For all of the following radial FT/ICR/MS upper m/q limit models, it is assumed that the ion's initial translational z-velocity, u, (initial), is converted partly into cyclotron velocity (u,. =

dm) in the trap and/or that there is an initial radial velocity component. If r is the ion cyclotron orbital radius, then angular acceleration about the z-axis, dvldt, is equal to

ANALYTICAL CHEMISTRY, VOL. 64, NO. 13, JULY 1, 1992 1483

sidered to occur near the probe tip surface (Le., on the z-axis such that x = 0 and y = 0 as ions enter the trap), and that no trapping potential is applied (i.e. trapping potential is gated to zero) until the ions have entered the trap. In the presence of a trapping potential, ion motion in the xy-plane is distributed between the cyclotron motion at frequency, w+, and magnetron motion at frequency, w-

(6) vXy - w+r+ - w-r-

with equal magnetron and cyclotron orbital radii, r- and r+ (see Figure 2)

r+ = r- (7)

-

In eq 6, the ion cyclotron orbital frequency, w+, is given by

Flgure 2. Pictorial representation of ion cyclotron (radius, r+) and magnetron (radius, r-) orbits in the xy-plane relative to trap boundaries for an Ion formed along the z-axis (magnetic field symmetry axis). Because the ICR orbit Istangent to the center of the trap, the maximum possible ICR orbital radius Is only half the radius of the trap (rtrap).

uxy2/r, and eq 1 becomes 2

dv uxy m- = m- = qE + qvB dt r

Radial m/q Upper Limit in the Absence of Electric Field, E . In the absence of an electric field, E, eq 2 simplifies to

2

m s r = qv,$, (3)

or

(4)

Thus, for sufficiently high mlq, the ICR orbital radius will exceed the radius of the trap, and ions will be lost by colliding with the trap electrodes. Moreover, for ions formed along the z-axis ( x = y = O), the maximum possible ICR orbital radius is only half the radius of the trap, because the ICR orbit of an unexcited ion is tangent to (rather than centered on) the z-axis (see Figure 2). Equation 4 and Figure 2 thus define a "radial" m/q upper limit in the absence of dc trapping or rf excitation electric field, given by eq 514

( 5 )

Axial (i.e., z-direction) motion imposes no mass constraint on eq 5, because in the absence of trapping potential, ions of all m/q move freely along the z-axis. It is worth noting that eq 5 is stated as an m / q upper limit, rather than simply an upper mass limit for singly-charged ions. The distinction is important because multiply-charged ions are a common feature of MALD mass spectra;20*21 hence, observation of multiply- carged ions by FT/ICR could significantly extend the mass range of biopolymers to be analyzed by the MALD/FT/ICR/ MS technique.

Radial FT/ICR/MS m/qUpper Limit in the Presence of Trapping Potential. In order to estimate the radial and axial FT/ICR/MS m / q upper limits, we assume that ion translational energy is partitioned equally in all directions on ion entry into the trap. Thus, for a matrix-desorbed ion velocity, uo, we assume that ions in the trap will have ux = uy = uz = v d f i . Thus, uXy = u O ~ . We also neglect ion-ion and ion-neutral interactions. MALD ion formation is con-

Bortrap =- (:)upper 2 U Z Y

w+ = "( 1 + dl - -) 2 mcrit

and the magnetron frequency is given by

w.. = -

in which the unperturbed ion cyclotron frequency, w, = qB, / m, and the "critical" mass, merit, is given by16

qa2B: mcrit = aLYv, (9)

in which a is the distance between opposed excite or detect electrodes (or trapping electrodes, for a cubic trap), a is a constant determined by the trap geometry, and V , is the trapping potential applied to each of two opposed trap electrodes (see Figure 1). An ion with mass greater than the critical mass spirals outward exponentially while orbiting the z-axis a t 4 2 . The electrostatic potential, V(x,y,z) , is approximately related to the trapping potential by42-44

in which a, p, A, and are constants based on trap geometry (defined in refs 42 and 43). Thus, the following derivations are valid only for traps which follow an approximately quadrupolar potential at the trap center-a good approximation for typical ICR traps. Equations 6 and 7 may be combined to yield

-- - (w+ - w-) '+

Substitution of eqs 8a,b into eq 11 yields

(12)

Substitution of eq 9 for the critical mass and qB, / m = wc leads to

Solving the quadratic eq 13 for m yields two roots, one of which leads to a negative mass, and the other is given below:

(42) Sharp, T. E.; Eyler, J. R.; Li, E. Int. J. Mass Spectrom. Ion Phys.

(43) Hunter, R. L.; Sherman, M. G.; McIver, R. T., Jr. Int. J. Mass

(44) Byrne, J.; Farago, P. S. Proc. Phys. SOC. 1965,86, 801-815.

1972, 9,421-439.

Spectrom. Ion Phys. 1983,50, 259-274.


In the absence of rf electric field excitation, the maximum ion cyclotron orbital radius is equal to half the trap radius, rtrap, for ions formed on the z-axis (see Figure 2 and ref 44). Finally, we may factor out q from all of the terms of the numerator on the right-hand side of eq 14 to yield an m/q upper limit

\'trap/

It is readily verified that in the limit that VT - 0, eq 15 reduces to eq 5.

The radial FT/ICR/MS m/q upper limit proceeds similarly for a hyperbolic trap45 as it does for other traps up through eq 13; as long as the quadrupolar approximation holds, the derivation given in eq 15 is good for all other traps and geometry factors. The exact radial hyperbolic trap solution resembles that given in eq 15 for other traps, except that in the derivation of the radial upper m/q limit solution, the critical mass is not given by eq 9, but by45

qB;(r: + 22:) (16)

in which ro is the minimum distance from the trap center to the ring electrode and zo is the minimum distance from the trap center to the end cap electrodes. Substitution of this factor into eq 13 leads to the radial FT/ICR/MS m/q upper limits in terms of initial ion velocity

m - -

8VT "it =

( 7 ) u P p e r

2 ( 2 ) 2 (17)

For the hyperbolic trap, the relation 2r+ = ro is used because the maximum ion cyclotron radius is half the minimum distance from the FT/ICR trap center to the ring electrode based on the argumenta given above.

Axial FT/ICR/MS m/q Upper Limit in the Presence of Trapping Potential. To be detected, ions must be radially and axially confined to remain within the trap; radially, that condition is met when the ion cyclotron orbital radius is less than or equal to half the ion trap radius (see eqs 15 and 17). For axial confinement, an ion cannot have a greater total energy than the potential applied to the trap electrodes (which are placed along the z-axis); otherwise, the ion will pass through the trap along the magnetic field lines and either escape (if the ion is on-axis) or collide with the trap electrode (if the ion is far enough off-axis). In the present model, we assume that the trapping voltage is switched on only when ions have reached the center of the trap (gated trapping). In the laser desorption FT/ICR/MS experimental event sequence, a brief delay period between the ionization event (the laser pulse) and the moment at which the trap potential is applied enables ions to enter the trap even though they

(45) Yin, W. W.; Wang, M.; Marshall, A. G.; Ledford, E. B., Jr. J . Am. SOC. Mass Spectrom. 1992, 3, 188-197.

were not originally formed within it. Applying a potential to the trapping electrodes adds additional potential energy to the ions. The axial potential energy, U(z ) , is at a minimum, Umin, when an ion is in the center of the ion trap. At the ion trap center ( x = 0, y = 0) , Umin = V(O,O,O) from eq 10

The maximum total z-energy that an ion may have and still be trapped axially is that of the potential applied on the trap electrodes

(19) in which K(z ) is the axial kinetic energy and U(z ) is the axial potential energy of the ion. The axial kinetic energy is given

K(Z) + U(z ) = qvT

by

mu ' K(Z) = 2 2

in which uz is velocity along the z-axis. rewritten as

mu,' ~ + u(z) = qvT 2

(20)

Thus, eq 19 can be

which leads to the upper mass limit expression

uz'

Substitution of Umin for U(z ) results in the desired solution for the axial FT/ICR/MS upper m/q limit

[orthorhombic; cylindrical traps] m - V,[ l+ 271 -

2 (,)upper u-

(23) The solution given in eq 23 is valid for both orthorhombic

and cylindrical traps. For the hyperbolic trap, potential as a function of position has the form given by46

For the hyperbolic trap, the same procedure that led to eq 23 leads to eq 25 for the axial FT/ICR/MS upper m/q limit

2vT( 2202 ') ro2 + 22, (3 = 0 [hyperbolic t vz- \ c1 I upper

As for the FTIICRIMS radial upper mass limit, the axial upper mass limit is also directly proportional to charge and may therefore be expressed as an m/q upper limit in eqs 23 and 25.

Optimal Trapping Potential for FT/ICR/MS. A com- parison of the radial and axial FT/ICR/MS solutions derived in eqs 15 and 23 (orthorhombic and cylindrical traps) and eqs 17 and 25 (hyperbolic trap) shows that the radial m/q upper limit decreases whereas the axial upper limit increases with increasing trapping voltage. When VT is close to zero, the FT/ICR/MS upper m/q limit is axially limited, whereas at higher trapping potential, the upper m/q is radially limited. Thus, there is an "optimal" trapping potential at which both FT/ICR/MS upper m/q limits coincide, so that ions of the highest mass-to-charge ratio may be trapped.

The m/q value corresponding to the optimal trapping potential can be found simply by equating the trapping

(46) Brown, L. S.; Gabrielse, G. Rev. Mod. Phys. 1985, 58, 233-310.


potential for the radial and axial mass-to-charge ratio (mlq) upper limits and then solving for mlq. The optimal trapping potential may then be found by substituting that mlq value back into the original mlq upper limit expressions. For example, eq 13 may be rearranged to yield the trapping potential at the radial upper mlq limit

(26)

Similarly, eq 23 may be rearranged to give the trapping potential at the axial upper mlq limit

Equating eqs 26 and 27 and substituting the translational energy equipartition assumption, u, = v d f i and uZy = a v o , yields

Substitution of 2r+ = rtrap, and rearrangement yields the mlq at the optimal trapping potential

Finally to obtain the optimal trapping potential, the result of eq 29 can be set equal to eq 15 or 23 and solved for VT

(30) U O B O V,(optimal) =

For the hyperbolic trap, the derivation follows the same steps. The trap potential from the radial mlq upper expression, eq 17, leads to the following expression for VT:

whereas from the axial limit, one obtains

(32)

which leads to the solution of optimal trapping potential for a hyperbolic trap

V,(optimal) =

RESULTS AND DISCUSSION

Radial MALDIFTIICRIMS mlq Upper Limits. Equa- tion 5 yields the highest mass-to-charge ratio a t which ions of known xy-velocity can be radially confined in an ICR ion trap, in the absence of trapping potential. For thermal ions, whose velocities are relatively low, eq 5 leads to a very high mlq upper limit: 2 700 000 u/e at 3.0 T for a 1-in.-diameter cubic tra~.~4+17 For matrix-assisted laser desorption, Beavis and Chait found a relatively symmetric ion velocity distribution, centered at a mass-independent most probable velocity of uo = 760m 9-1.38 If we assume that the translational

laool

\ tetragonal screened cylindrical

128004 " ' ' ' " 7 ' 4

0 2 4 6 8 10

6000 1

50004 . ' . . 8 . . I

0 2 4 6 8 10

0 2 4 6 8 1 0

Trapping Voltage (V) Figure 3. Radial MALD/FT/ICR/MS m/q upper limit as a function of trapping voltage for cubic, tetragonal, screened, and cylindrical traps at each of three magnetic fieM strengths. See text for trap dimensions.

energy of such ions equilibrates among all three orthogonal directions on entry of the ions into an ICR ion trap, then the xy-velocity can be taken as u O a . In the absence oftrapping potential, eq 5 then predicts a radially-limited FT/ICR/MS mlq upper of 2400,5900, and 14 000 ule for MAL9-generated ions in a 1-in.-radius cubic ICR ion trap a t the three typical respective FT/ICR magnetic field strengths of 1.2, 3.0, and 7.0 T, as shown by the y-intercepts in Figure 3. Cubic Trap. Equation 15 predicts the FTIICRIMS radial

mlq upper limit for any orthorhombic trap, as a function of trapping potential, magnetic field induction, trap plate-to- plate separation, and ion preexcitation initial xy-speed. In particular, for the cubic ion trap:? a = 1.386 86.43 For a cubic

~ ~ ~ ~~

(47) Comisarow, M. B. Int. J. Mass Spectrom. Ion Phys. 1981, 37, 251-257.


trap of 1-in. radius (plate-to-plate separation of 5.08 cm), Figure 3 (lowest curve in each diagram) shows the depend- ence of MALD/FT/ICR/MS m/q upper limit on trapping potential, for initial injected ion z-velocity, uo = 760 m s-l (to give uxy = 620 m s-l after equilibration) a t magnetic field strengths of 1.2, 3.0, and 7.0 T. The radial m/q upper limit decreases with increasing trapping voltage, because application of a trapping potential to generate an electric field in the z-direction necessarily requires (because of Laplace's equation) a radially outward-directed electric field which opposes the Lorentz magnetic force in eq 1. In other words, application of the trapping potential effectively weakens the magnetic field strength, and since ICR orbital radius is inversely proportional to Bo (eq 4), the ICR orbital radius increases, thereby lowering the m/q upper limit. For example, at 3.0 T, the radial m/q upper limit drops from -5900 u/e at 0 V to -5100 ule at 10 V trapping potential for a 2-in.- diameter cubic trap. Alternatively, Figure 3 shows that a cubic trap should be able to radially confine singly-charged MALD ions with mlq up to - 13 800 u/e at 7.0 T a t sufficiently low trapping potential ( 1 2 V).

Tetragonal Trap. Equation 15 also predicts the MALDi FT/ICR/MS m/q upper limit for a tetragonal (i.e., orthorhombic of square cross section) trap, because the quadrupolar potential given in eq 10 is approximately correct near the center of a tetragonal trap. For example, for a tetragonal trap of aspect (Le., length-to-width) ratio, 4.75, cy = 4.183 19 X 10-4.43 We therefore used eq 15 to evaluate the m/q upper limit for a tetragonal trap of radius, r = 2.54 cm, and trapping plate separation, c = 24.13 cm at 1.2, 3.0, and 7.0 T for ions with initial ion z-velocity, uo = 760 m/s (Le., initial uXy = 620 m s-1 after equilibration). Figure 3 shows that the MALD/ FT/ICR/MS mlq upper limit is almost independent of trapping potential (since the radial electrostatic field a t the center of the trap is nearly zero) over the range, VT = 0-10 V, at any of three typical magnetic field strengths (1.2, 3.0, and 7.0 T). Figure 3 shows that a tetragonal trap of long aspect ratio should be superior to a cubic trap for MALDi FTIICRIMS of high-mass singly-charged ions.

Screened Tetragonal Trap. Equation 15 may also be used to generate a MALDIFTIICRIMS mlq upper limit for the screened tetragonal trap.48 Although the value of the geometric constant, a, for the screened tetragonal trap has not been derived analytically, it may be estimated (in the quadrupolar potential approximation) from the experimentally observed rate of change of ICR orbital frequency with trapping potential:

(34)

b~0/6V~ in ref 48 was found to be -0.67 Hz/V. From eq 34, with a = 5.08 cm and Bo = 3.058 T, a is evaluated as 1.661 08 x 10-2. The m / q upper limit for the screened tetragonal ion trap of ref 48 (length = 6.35 cm or 2.5 in.) as a function of trapping voltage for initial ion velocity, uo = 760 m s-l (Le., initial uXy = 620 m s-' after equilibration) a t 1.2,3.0, and 7.0 T is also shown in Figure 3 (topmost curve in each graph). Again the M/q upper limit is essentially independent of trapping potential over the range, VT = 0-10 V. Basically, the screens reduce the effective radial electrostatic field a t the center of the trap, just as increasing the separation between the trapping electrodes; however, the screened trap achieves superior reduction without having to lengthen the trap. In any case, either a screened trap of nearly unit aspect ratio or a tetragonal trap of larger aspect ratio is predicted to be superior to the cubic trap with respect to higher radial MALD/ FT/ICR/MS mlq upper limit (-13 800 at 7.0 T).

~ ~~ ~

(48) Wang, M.; Marshall, A. G. Anal. Chem. 1989,61, 1288-1293.

8ooo 1 Hyperbolic Trap ::::h 7.0 tesla

5000'

4000;

20001,

1000 1.2 tesla

0 ' " " 0 2 4 6 8 1 0

Trapping Voltage (V) Figure 4. Radial MALD/FT/ICR/MS m/q upper limit for a hyperbolic trap at each of three magnetic field strengths. See text for trap dimensions.

Cylindrical Trap. Equation 15 also applies to the cylindrical trap.49 The formula to obtain the geometric constant a of the cylindrical trap (4ST: in ref 49) is obtained using a program50modified by the present authors, to yield the result

This formula for determining the value of a corrects a previously published expression5l in which the quantity (2m + 1) in the summation incorrectly appeared in the denom- inator rather than the numerator and is defined according to prior convention.42~~3 For a cylindrical trap of dimensions, r = 2.54 cm and c = 5.08 cm, cy = 1.420 18. The MALD/FT/ ICR/MS m/q upper limit as a function of trapping voltage for ions with initial uo = 760 m/s (i.e., initial uxy = 620 m s-l after equilibration) at magnetic field strengths of 1.2,3.0, and 7.0 T is plotted in Figure 3. It is evident that the resulting m/q upper limit for the cylindrical trap is similar to that for the cubic trap, but is significantly lower than for the tetragonal and screened orthorhombic traps, because the a value for the cylindrical trap is approximately the same as that for the cubic trap but is much larger than the values for the tetragonal or screened traps.

Hyperbolic Trap. Finally, the MALD/FT/ICR/MS radial mlq upper limits (eq 17) for a hyperbolic ion trap with dimensions, 20 = 6.35 X 10-3 m and ro = 1.27 X m45 as a function of trapping potential for initial ion velocity, uo = 760 m/s (i.e., initial uxy = 620 m s-l after equilibration) are plotted in Figure 4 at 1.2,3.0, and 7.0 T. These plots clearly predict that the hyperbolic trap is not a good choice for trapping high-mass ions formed by the MALD process. For example, even at 7.0 T, a hyperbolic trap of the above dimensions can trap ions only up to a maximum mlq = 6000 u/e at ordinary trapping potentials. Basically, the minimum radius of the ring electrode limits the maximum ion cyclotron orbital radius. Some improvement could be achieved by constructing an axially elongated hyperbolic trap with larger zo, provided that compensation electrodes are introduced between the endcaps and ring electrode to maintain a precise quadrupolar field.52

(49) Kofel, P.; Allemann, M.; Kellerhals, H.; Wanczek, K.-P. Int. J.

(50) Xiang, X.; Grosshans, P. B.; Marshall, A. G., unpublished results. (51) Grosshans, P. B.; Marshall, A. G. Anal. Chem. 1991, 63, 2057-

(52) Van Dyck, R. S., Jr.; Wineland, D. J.; Eckstrom, P. A.; Dehmelt,

Muss Spectrom. Ion Proc. 1986, 74, 1-12.

2061.

H. G. Appl. Phys. Lett. 1976, 28, 446-448.


-

Axial MALD/FT/ICR/MS m/qUpper Limit. The axial MALD/FT/ICR/MS m/q upper limit expressions given by eq 23 (orthorhombic and cylindrical traps) and eq 25 (hyperbolic trap) show that the axial limit is directly proportional to the applied trapping potential and (for the orthorhombic and cylindrical traps) depends strongly on the geometrical constant, y. SIMION53 calculations for the screened tetragonal trap indicate that its electrostatic potential approaches zero near the trap ~ e n t e r ; ~ 8 thus, Umin approaches zero. We can thus expect similar axial ion behavior (y - 0.5) for both the screened and elongated tetragonal traps (as for the radial ion behavior at the trap mid- plane) and hence have not evaluated the axial m/q upper limit for the screened trap.

The axial MALD/FT/ICR/MS m/q upper limits (eqs 23 and 25) as a function of trapping potential for ions with an initial velocity of uo = 760 m/s (Le., uz = 440 m s-l after equilibration) as a function of trapping potential are plotted in Figure 5 for the same-dimensions cubic, tetragonal, cylindrical, and hyperbolic traps as for the preceding radial limits. The y values used were (according the convention established by Sharp et al.42 0.166 667 for the cubic trap, 0.499 915 for the tetragonal and 0.221 33 for the cylindrical trap. The value for the cylindrical trap is equivalent to the quantity (&,O -0.5) of ref 49, and thus is the same y defined in our eq 10. In contrast to the radially limited case, the axial m/q upper limit increases with increasing trapping voltage because heavier ions (which have higher translational energy, since MALD produces ions of approximately constant speed, independent of mass) can be trapped a t higher trapping potential. Moreover, the axial motion is independent of BO.

As for the radial m/q upper limit, the axial mlq upper limit is highest for the tetragonal trap (due to its high y value) throughout the trapping potential range, 0 I VT I 10 V. For example, at VT = 10 V, a tetragonal trap has an axial MALD/ FT/ICR/MS m/q upper limit of 10000 u/e, whereas a cylindrical trap has a limit of 7200 u/e, a cubic trap, 6700 d e , and a hyperbolic trap, only 3400 u/e. The low axial m/q upper limit for the hyperbolic trap can again be ascribed to its dimensions, which define the potential at the trap center (see eq 24) such that the potential energy minimum, Umin, is larger than for the other traps. Again, the axial m/q upper limit for the hyperbolic trap could be increased by use of a trap with a larger 20. Based on axial considerations only, an elongated trap again seems poised as the best candidate for MALD/ FT/ICR/MS because of its extended mass range.

(53) Dahl, D. A.; Delmore, J. E. SIMION PCiPSP Version 4.0. Idaho National Engineering Laboratory, 1988.

1 5000 1 Optimal Vi

- 7.0 T radial

3.0 T radlal

1.2 T radial .- E 3 8 n n 3

5000

O d ' 4 8 1'2 1'6 ' 2 0

Trapping Voltage (V) Flgure 6. Graphical determination of the optimal trapplng potential for a cubic trap at 1.2,3.0, and 7.0 T from the intersection of the MALDl FTlICRlMS radial and axial mlq upper limits.

Table I. Optimal Trapping Potential (V) for Various Ion Traps at Different Magnetic Field Strengths.

1.2 T 3.0 T 7.0 T cubic 3.16 7.90 18.43 tetragonal 2.36 5.91 13.79 cylindrical 2.94 7.34 17.13 hyperbolic 2.51 6.27 14.63

a See text for dimensions of each trap.

Optimal Trapping Potential for MALD/FT/ICR/MS. A particularly useful result of the present analysis is the prediction from eq 30 (orthorhombic and cylindrical traps) and eq 33 (hyperbolic trap) that an optimal trapping potential can be found for trapping high-mass ions, if the initial ion velocity is known. The optimal trapping potential is directly proportional to the magnetic field strength and the initial ion velocity and has been used to evaluate the optimal trapping potential (see Table I) for ions with initial velocity, LJO = 760 m/s at 1.2, 3.0, and 7.0 T for the above-listed cubic, tetragonal, cylindrical, and hyperbolic traps. Note that the optimal trapping potential is smallest for the elongated (or screened) trap. The origin of the optimum trapping potential becomes clear from Figure 6, which consists of plots of the MALD/ FT/ICR/MS radial and axial m/q upper limits for a cubic trap as a function of trapping potential. For a given magnetic field strength, the intersection of the radial and axial limit curves defines the optimal trapping potential reported in Table I.

The lower optimum trapping potential for the elongated (or screened) trap compared to the other traps is a direct consequence of its larger y value [note that VT varies inversely with (1 + 27) in eq 301. However, at 7.0 T, the optimal trapping potential for all traps (including the elongated tetragonal), exceeds the 10 V limit on most commercial FT/ ICR/MS instruments. Hogan et al." have demonstrated that trapping potential may be extended above 10 V by use of an additional external power source. Thus, even the (high) optimal trapping potential needed at 7.0 T is accessible for MALD/FT/ICR/MS experiments designed to maximize the accessible upper mass limit.

The optimal trapping potential also defines an overall (Le., radial and axial combined) m/q upper limit for a given trap, because a t higher or lower trapping voltage, ions of higher m/q will be lost radially or axially, respectively (see Figure 6). The overall m/q upper limit may be calculated exactly from eq 15 or 23 (orthorhombic or cylindrical traps) or from eq 17 or 25 (hyperbolic trap), once the optimal trapping

(54) Hogan, J. D.; Laude, D. A., Jr. Anal. Chem. 1991,63,2105-2109.


Table 11. Overall Mass-to-Charge Ratio Upper Limits ( d e ) for Various Ion Traps at Different Magnetic Field Strengths*

1.2 T 3.0 T 7.0 T cubic 2,100 5,300 12,300 tetragonal 2,400 5,900 13,800 cylindrical 2,100 5,300 12,400 hyperbolic 840 2,100 4,900

See text for dimensions of each trap.

potential (Table I) has been calculated. Overall mlq upper limits are listed in Table I1 for three magnetic field strengths (for ions with the initial velocity, uo = 760 m/s, equilibrated over all three dimensions). Table I1 indicates that the cubic, tetragonal, and cylindrical traps should have significant analytical utility for MALD/FT/ICR/MS applications because each is able to confine ions with m/q beyond 12 000 ule at 7.0 T. The hyperbolic trap would require zo extension in order to reach the same overall m/q upper limit. Finally, the overall m/q upper limit was not evaluated for the screened orthorhombic trap but would be expected to be similar to that found for the elongated tetragonal trap.

Analysis of Prior Experimentally Determined MALD/ FTIICRIMS mlq Upper Limits. The presently derived axial MALD/FT/ICR/MS mlq upper limit for a cubic trap helps to explain why high mass ions above mlq = 2000 u/e were not observed by Hettich and Buchanan,34 whose experiments were conducted at 3.0 T in a 4.76-cm-diameter cubic trap at a trapping potential of 2 V. Beavis and Chait38 correctly predicted that high-mass MALD-generated ions would not readily be trapped at small trapping potential, and that increasing the applied trapping potential should increase that (axial) upper mass limit. We can now quantitate those predictions. For example (eq 23), for an ion with the initial velocity of uo = 760 m/s, the calculated axial MALD/FT/ ICR/MS mlq upper limit is only 1300 ule. Since Hettich and Buchanan observed ions up to mlq -2000, then (a) the MALD-produced ions may have suffered one or more collisions with neutrals so as to lose enough energy to become trapped and/or (b) the observed ions may have originated from the low-velocity tail of the MALD ion velocity distribution [Beavis and Chait observed ions with initial velocities as low as 450 m 9-1, for which the axial mlq upper limit predicted from eq 23 would be -33800 ulel. A recent acceleratinglretarding potential experiment in MALD/FT/ ICR/MS exhibited maximum ICR signal when there was no bias between the probe and the front trap plate.55 Some ions were trapped even at 5 V acceleration voltage, indicating that other experimental factors (e.g. collisional relaxation) influ- ence trapping of ions with kinetic energy larger than the trap plate potential (nongated trapping), in support of our suggestion that MALD-generated ions may suffer collisions with neutrals, thereby losing enough energy to become trapped. Moreover, the retarding field did not significantly affect trapping efficiency, indicating that the ion packet generated by MALD might be partially shielded from the relatively small trapping potential (< lo V) by space charge.56

Equation 23 also qualitatively explains the recent observation by Russell et al.57 that higher trap voltage is required to trap singly-charged ions of higher mass: -1 V for gram- icidin S (1214 ule), -2 V for angiotensin I (MW = 1296.5), -6 V for renin substrate (1759.0 We), and -9 V for melittin (2846.6 u/e), at 3.0 T in a 2-in.-diameter cubic trap. In these

(55) Hettich, R. L.; Buchanan, M. V. Int. J . Mass Spectrom. Ion Proc.

(56) Beu, S. C.; Hendrickson, C. L.; Vartanian, V. H.; Laude, D. A., Jr.

(57) Solouki, T.; Russell, D. H., unpublished results.

1991, 111, 365-380.

Int. J . Mass Spectrom. Ion Proc. 1992, 113, 59-79.

cases, it appears that axial ion loss is more important than radial ion loss, since high-mass detection is facilitated by use of higher trap voltage.

Analysis of Assumptions for the Present Model. In the present theoretical treatment, we assume that the trapping voltage is switched on when the ions have reached the center of the trap.58,59 We also assume that the ion cyclotron orbits are tangent to the z-axis (i.e., as would be the case if ions are formed or injected along the z-axis). That assumption remains valid if ions are intentionally deflected on entry to the trap.60 The most questionable assumption is that the initial ion translational energy in the z-direction is equilibrated (presumably by ion-neutral collisions or electrostatic deflection on injection of ions into the trap) among all three directions before subsequent ICR excitation and detection. Incomplete equilibration would raise the radial mlq upper limit (since ions would not acquire as much xy-velocity as we have assumed) but would reduce the axial mlq upper limit [since ions would retain somewhat (factor of 4) more z-velocity than we have assumed]. Without any equilibration, the mlq upper limit would be dominated by axial ion loss. Therefore, our overall m / q upper limit would probably remain approximately correct even if equilibration of ion translational energy is incomplete.

Of course, the present mass limits are for unexcited ions (i.e., ions whose ICR orbital radii or axial trapping amplitude just touch the electrodes of the trap before ICR excitation). Obviously, if ions are to be excited for subsequent detection, then the ICR orbital radius before excitation should be no more than (say) one-fifth the trap radius in order to produce coherent ICR orbital motion.61 Therefore, the radial mlq upper limits from the present treatment should probably be lowered by a factor of (say) 5 to allow for ICR excitation.

Conclusions and Suggestions for Optimization of Future MALDlFTlICRlMS Experiments. The radial and axial m / q upper limit equations for MALD/FT/ICR/MS in the absence and presence of trapping potential have been derived for cubic, tetragonal, screened tetragonal, cylindrical, and hyperbolic traps. In addition, an optimal trapping potential has been derived for MALD/FT/ICR/MS from the combined radial and axial mlq upper limits. The elongated and screened traps appear best-suited (radial m/q upper limit of - 14 000 u/e at 7.0 T) for trapping MALD-produced high- mass singly-charged polypeptide ions. Although well below the mlq of the highest mass polypeptide ion observed by MALDl time-of-flight mass spectrometry,21 the present results suggest that MALDlFTlICRlMS has the potential to provide molecular weight information for many proteins, with mass accuracy substantially beyond the capability of time-of-flight detection. Although the radial and axial upper mlq limits of the cubic trap are not as high as those of the elongated or screened tetragonal traps at high trapping potential, the cubic trap nevertheless should reach mlq 2 12 000 u/e for MALDl FT/ICR/MS applications. Moreover, adding grounded screens to a cubic trap48 should extend the mlq upper limit consid- erably at high trap potential. The cylindrical trap also appears viable for MALD/FT/ICR/MS due to slightly higher radial and axial m/q upper limits than the comparable-size cubic trap; elongation of a cylindrical trap along the z-axis will lower its a value and increase its y value, thereby increasing both its radial and axial mlq upper limits. The hyperbolic trap appears to be viable for use in MALD/FT/ICR/MS only if extended along the z-axis.

(58) Hofstadler, S. A.; Laude, D. A., Jr. Anal. Chem. 1991, 63, 2001-

(59) Chen, R.; Grosshans, P. B., unpublished results. (60) Caravatti, P., US. Patent No. 4,924,089, issued 8 May 1990. (61) Wang, M.; Marshall, A. G. Int. J. Muss Spectrom. Ion R o c . 1990,

2007.

100, 323-346.


a biopolymer could be frozen in cryocooled water ice before laser ablation.66 Biasing of the probe voltage to low potential could slow the ions as they enter the trap, although such potential retarding effects will presumably result in less efficient trapping.55 Other possibilities include various possible gating58 or ramping67 of the trapping voltage, again designed to reduce the ion z-velocity before trapping.

ACKNOWLEDGMENT We thank Ronald Beavis and Brian Chait for providing us

with prepublication information. We gratefully acknowledge prepublication information with Peter Grosshans, Michael May, and Xinzhen Xiang and helpful discussions with Patrick Limbach. T.D.W. gratefully acknowledges financial assis- tance from a Department of Education National Needs Graduate Fellowship. L.S. thanks The Ohio State University and the Deutsche Forschungsgemeinschaft for postdoctoral fellowships. This work was supported by grants (to A.G.M.) from the National Science Foundation (CHE-90-21498) and The Ohio State University.

RECEIVED for review January 3, 1992. Accepted April 6, 1992.

(65) Marshall, A. G.; Comisarow, M. B.; Parisod, G. J. Chem. Phys.

(66) Nelson, R. W.; Rainbow, M. J.; Lohr, D. E.; Williams, P. Science

(67) Nikolaev, E. N.; Neronov, Y. I.; Gorshov, M. V.; Talroze, V. L.

1979, 71, 4434-4444.

1989, 246, 1585-1587.

JETP Lett . 1984, 39, 534-536.

As noted above, multiply-charged ions are sometimes observed in MALD mass spectra. Because the presently derived upper limits are for mlq rather than m, the upper mass limit for MALD/FT/ICR/MS is clearly multiplied by the number of charges per ion. For example, eq 15 predicts that doubly-charged ions formed by MALD of a biopolymer of mass -28 000 u can be confined radially at 7.0 T. In any case, future uses of FT/ICR/MS for detection of MALD- generated ions will likely concentrate on MS/MS a n a l y s i ~ ~ ~ , ~ ~ for sequence and structural information of lower-mass biopolymers (say, 115 000 Ne), rather than simply molecular weight determination of high-mass proteins.

The MALD/FT/ICR/MS m/q upper limit can also be increased by reducing the initial axial and cyclotron ion velocities. For example, ion-neutral collisions in the ion trap have been used to cool supersonically injected cluster ions.64 Helium is an excellent choice as the neutral because a collision between it and a massive biomolecule ion is unlikely to deflect the ion out of the trap. In order to minimize pressure- broadening of the subsequently detected ICR signal,65 either dual-trap or pulsed gas inlet should be used. Alternatively,

(62) Tandem Mass Spectrometry; McLafferty, F. W.,Ed.; Wiley: New York, 1983.

(63) Busch, K. L.; Glish, G. L.; McLuckey, S. Mass Spectrometry/ Mass Spectrometry: Techniques and Applications of Tandem Mass Spectrometry; VCH: Deerfield, FL, 1988.

(64) Maruyama, S.; Anderson, L. R.; Smalley, R. E. Rev. Sci. Instrum. 1990, 61, 3686-3693.

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