Relative Sensitivity Factors of Inorganic Cations in Frozen-hydrated

Mar 15, 2006 - We describe the measurement, at 100 K, of the SIMS relative sensitivity factors (RSFs) of the main physiological cations Na+, K+, Mg2+,...
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Anal. Chem. 2006, 78, 2471-2477

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Relative Sensitivity Factors of Inorganic Cations in Frozen-hydrated Standards in Secondary Ion MS Analysis C. De´rue,† D. Gibouin,† F. Lefebvre,† D. Studer,‡ M. Thellier,† and C. Ripoll*,†

Laboratoire Assemblages mole´ culaires: mode´ lisation et imagerie SIMS (AMMIS), FRE CNRS 2829, Faculte´ des Sciences de l’Universite´ de Rouen, 76821 Mont Saint Aignan Cedex, France

We describe the measurement, at 100 K, of the SIMS relative sensitivity factors (RSFs) of the main physiological cations Na+, K+, Mg2+, and Ca2+ in frozen-hydrated (FH) ionic solutions. Freezing was performed by either plunge freezing or high-pressure freezing. We also report the measurement of the RSFs in flax fibers, which are a model for ions in the plant cell wall, and in F-H ionic samples, which are a model for ions in the vacuole. RSFs were determined under bombardment with neutral oxygen (FAB) for both the fibers and the F-H samples. We show that referencing to ice-characteristic secondary ions is of little value in determining RSFs and that referencing to K is preferable. The RSFs of Na relative to K and of Ca relative to Mg in F-H samples are similar to their respective values in fiber samples, whereas the RSFs of both Ca and Mg relative to K are lower in fibers than in F-H samples. Our data show that the physical factors important for the determination of the RSFs are not the same in F-H samples and in homogeneous matrixes. Our data show that it is possible to perform a SIMS relative quantification of the cations in frozen-hydrated samples with an accuracy on the order of 15%. Referencing to K permits the quantification of the ionic ratios, even when the absolute concentration of the referencing ion is unknown. This is essential for physiological studies of F-H biological samples. Quantification in secondary ion mass spectrometry (SIMS) cannot be performed directly by measuring the current intensity * Corresponding author. Phone: (33) 235146681. Fax: (33) 235147020. E-mail: [email protected]. † Universite ´ de Rouen. ‡ Current address: Anatomizches Institut, University of Bern, Bu ¨ hlstrasse 26, CH-3000 Bern 9, Switzerland. 10.1021/ac051518u CCC: $33.50 Published on Web 03/15/2006

© 2006 American Chemical Society

of a secondary ion characteristic of the analyzed species. Elements at the same concentration may produce signals differing by orders of magnitude,1,2 depending on the nature of the element analyzed (differences in ionization yield), the chemical composition of the matrix (matrix effects), the nature of the primary ions (oxygen, as compared with Ar+ or Ga+, enhances the ionization yield for positive secondary ions), and instrumental parameters (current density, spectrometer transmission, detection yield, etc.). Such quantification problems are usually overcome using standards to measure the so-called relative sensitivity factor (RSF) of an element, j. This is defined3 by

RSFj/ref ) (ij/iref)/(Cj fj/Cref fref) where i is the secondary ion intensity, C is the concentration, and f is the isotopic abundance of the analyte (subscript j) and of a reference element (subscript ref). An abundant element, homogeneously distributed in the sample matrix, is generally chosen as the reference element. Carbon has been used as a reference element in the semiquantitative processing of SIMS images of freeze-dried or resin-embedded biological samples4,5 or in SIMS analysis of gelatine calibration standards.6 Elements such as K or P have also been used as a reference in analyzes of a variety of biological samples.3 When the concentration of the reference (1) Benninghoven A.; Rudenauer F. G.; Werner H. W. Secondary Ion Mass Spectrometry: Basic Concepts, Instrumental Aspects, Applications and Trends; Wiley: New York; 1987. (2) Thellier, M.; Ripoll, C.; Quintana, C.; Sommer, F.; Chevallier, P.; Dainty, J. Methods Enzymol. 1993, 227, 535-586. (3) Ramseyer, G. O.; Morrison, G. H. Anal. Chem. 1983, 55, 1963-1970. (4) Fragu, P.; Brianc¸ on, C.; Halpern, S.; Larras-Regard, E. Biol. Cell 1988, 62, 145-155. (5) Follet-Gueye, M.-L.; Verdus, M.-C.; Demarty, M.; Thellier, M.; Ripoll, C. Cell Calcium 1998, 24, 205-215. (6) Zhu, D.; Harris, J. R.; Morrison, G. H. Anal. Chem. 1982, 54, 419-422.

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element is unknown but constant in the different analyzed samples, the following simpler definition of the RSFs may be used.7

RSF′j/ref ) (ij/iref)/(Cj fj) The ratio 〈ij〉 ) ij/iref is termed the normalized intensity.5 It is, therefore, expected that in different matrixes, different values of the RSFs will be found for the same element with a given primary ion. In this article, we describe the measurement of the RSFs and their ratios for the main physiological cations Na+, K+, Mg2+, and Ca2 in frozen-hydrated ionic solutions used as standards. Very few SIMS analyzes of frozen-hydrated electrolyte solutions have been reported so far. Tantsyrev et al. have published measurements at 144 K under neutral argon bombardment;8,9 however, they did not give values for the RSFs of alkaline and alkaline earth cations. The experiments reported here were carried out to quantify the concentrations of the cations in the different compartments of frozen-hydrated plant cells using a device developed in our laboratory.10 We used frozen-hydrated ionic standard solutions as a model matrix of aqueous compartments, such as the vacuole in plant cells, which often occupies more than 90% of the cell volume (the relevance of such simple solutions to the highly complex cell cytoplasm remains to be determined). Flax is a plant that has been extensively studied in our laboratory.11,12 Flax fibers can be used as a model matrix for ions in the cell wall, and in another set of experiments, we measured the RSFs in isolated flax fibers. The RSFs were determined under bombardment with neutral oxygen O2 for both the frozen-hydrated samples and the fibers. This fast atom bombardment mode (FAB mode) allowed us to analyze thick, insulating samples. We investigated the physical factors that determine the RSFs and showed that they are not the same in F-H samples and in homogeneous matrixes. MATERIALS AND METHODS Frozen-Hydrated Standards. Our SIMS analyzer (Cameca IMS 4f) has been modified and permits the analysis and imaging of frozen-hydrated samples as described elsewhere.10 This equipment consists of (i) a cold stage that maintains the temperature of the sample at 100 K (at such a temperature, the vapor pressure of the ice is low enough not to perturb the high vacuum in the specimen chamber) and (ii) a modified Oxford Instruments CT 1500 transfer and freeze-fracturing system attached to the specimen chamber of the Cameca IMS 4f ion analyzer (in place of the original air-lock of the IMS4f). The Oxford Instruments specimen holder was therefore used in place of the Cameca standard holder. Holes were drilled (3 mm deep, 0.7 mm in diameter) in the Oxford sample holder perpendicular to its surface (7) Ausserer, W. A.; Ling, W. C.; Chandra, S.; Morrison, G. H. Anal. Chem. 1989, 61, 2690-2695. (8) Tantsyrev, G. D.; Lyapin, G. Yu. Z. Anal. Chem. 1991, 49, 1767-1771. (9) Tantsyrev, G. D.; Pronchev, G. B. J. Trace Microprobe Techniques 1999, 17, 49-61. (10) De´rue, C.; Gibouin, D.; Lefebvre, F.; Rasser, B.; Robin, A.; Le Sceller, L.; Verdus, M.-C.; Demarty, M.; Thellier, M.; Ripoll, C. J. Trace Microprobe Techniques 1999, 17, 451-460. (11) Verdus, M.-C.; Thellier, M.; Ripoll, C. Plant J. 1997, 12, 1399-1410. (12) De´rue, C.; Gibouin, D.; Verdus, M.-C.; Lefebvre, F.;. Demarty, M.; Ripoll, C.; Thellier, M. Microsc. Res. Techniques 2002, 58, 104-110.

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in four places along the axis of the holder. These drilled holes allowed the introduction, under liquid nitrogen, of small copper tubes (3 mm long, 0.25-mm i.d.) filled with frozen aqueous solutions containing a mixture of Na, Mg, K, and Ca chlorides at known concentrations (frozen-hydrated standards). With this setup, when a 3-mm-long copper tube containing a frozen solution has been dropped into a hole, its upper end is flush with the surface of the holder. The frozen solution in the tube was then exposed to the primary beam in the SIMS analyzer to allow both microanalysis and imaging of the frozen-hydrated standard. The frozen-hydrated standard solutions in the tubes were obtained by either plunge freezing (PF) or high-pressure freezing (HPF). HPF was carried out using a Leica Empact machine as described in Studer et al.13 Copper tubes 16 mm in length and 0.25-mm i.d. were cleaned by sonication in ultrapure water (ACS reagent, Aldrich) and dried in an oven at 60 °C. They were then filled with a standard solution (see below) using an Eppendorf pipet fitted with a narrow tip and mounted in the sample holder of the Empact machine. Freezing was then performed at 2000 bar and 77 K following the protocol of the manufacturer (see also Studer et al.13). After freezing, the tube was retrieved in liquid nitrogen (LN2) and mounted under LN2 in a modified version of the punching tool supplied with the Empact machine. This modified tool allowed a 3-mm-long piece to be punched out from the central part of the tube, and this piece, still under LN2, was introduced into one of the drilled holes of the Oxford sample holder as explained above. The sections of the 3-mm tubes and, therefore, of the frozen solution to be analyzed were flat enough to give reliable SIMS measurements (see below). The preparation of samples using PF was identical to that for HPF, except that instead of mounting the 16-mm copper tube in the sample holder of the Empact machine, it was fixed at the tip of tweezers on a laboratory-made device to allow rapid plungefreezing in supercooled propane at the temperature of LN2 (77 K). After freezing, the other steps of the preparation were the same as for HPF. Flax Fiber Preparation. Bundles of mature flax fibers (Linum usitatissimum L., var. Ariane) were manually isolated and dried in an oven. Samples ∼10 mm in length were cut from the bundles and immersed in pure Spurr’s resin for 24 h at room temperature without any previous chemical treatment. Pieces were then cut from these samples and put into a silicone polymerization mold (Agar-Oxford, Saclay). The wells were then filled with fresh Spurr’s resin, and polymerization was carried out at 60 °C for 24 h to give blocks. SIMS analyses were performed using thick slices, 3 mm in width, cut from these blocks. The slices were mounted on the arm of an ultramicrotome (Leica Ultra Cut S, Rueil-Malmaison, France), and their surfaces were planed using a diamond knife until a perfectly flat surface was obtained to allow reliable SIMS analyses. The planed slices were then mounted in the sample holder of the SIMS analyzer. It should be noted that semithin sections (1 µm) of the embedded bundles are not useful for SIMS analysis because their surface has many cracks around the bundles of fibers (probably because of a poor embedding of the bundles, which form a very compact material). (13) Studer, D.; Graber, W.; Al-Amoudi, A.; Eggli, P. J. Microsc. 2001, 203, 285294.

Determination of Ion Concentrations. Calculation of RSFs requires measurement of the ionic contents of the fibers and of the frozen-hydrated standard solutions. Small batches of dried fibers were weighed and placed in silica crucibles (that had been cleaned in 1 M nitric acid and carefully rinsed with Milli-Q water). The fibers were burned at 500 °C in a laboratory furnace for 150 min. The ashes were then suspended in 1 mL of 2 M nitric acid, and the resulting solution was transferred to a 50-mL gauged flask. The crucibles were washed 3 times with a 1 M solution of nitric acid containing 1 g L-1 lanthanum nitrate. The washing solutions were pooled with the solution of ashes in the gauged flask, and the volume was brought to 50 mL with the solution of lanthanum nitrate in 1 M nitric acid. After appropriate dilutions with the solution of lanthanum nitrate in 1 M nitric acid, Ca2+, Na+, K+, and Mg2+ were assayed using a Perkin-Elmer (model 230) atomic absorption spectrophotometer. Blanks were run in parallel. The solutions used to produce the frozen-hydrated standards were prepared by dilution of a stock solution containing the Na, Mg, K, and Ca chlorides at known concentrations (see results for the values). The stock solutions were prepared using analytical grade chemicals and ACS reagent ultrapure water purchased from Aldrich. SIMS Analysis and Imaging. SIMS analysis and imaging was carried out using a Cameca IMS 4f ion analyzer (Cameca, Courbevoie, France) operating in the “isotope” mode for microanalysis and in the microscope mode for imaging. In these experiments, the primary bombarding particles were neutral oxygen molecules obtained after neutralization of O2+ ions 15 keV in energy (FAB source). The mass spectrometer of the IMS 4f instrument was set at a mass resolution of 1600, which in our case was high enough to prevent most risks of mass interference when acquiring the images. The analyzed or imaged secondary ions were 23Na+, 24Mg+, 39K+, and 40Ca+ with resin-embedded samples and 1H+, 1H316O+, 23Na+, 24Mg+, 39K+, and 40Ca+ with frozen-hydrated samples. Instrumental parameters were as follows. The O2+ primary current before neutralization was 6 µA. For microanalysis (isotope mode) the field aperture was FA2 (750 µm), and the contrast aperture was CA1 (400 µm). For imaging purposes (microscope mode), the transfer optics was set for a 250-µm field of view, the field aperture was FA1 (1800 µm), and the contrast aperture was CA4 (20 µm). With these parameters, the theoretical lateral resolution on the images was ∼1 µm. Images were produced on the microchannel plate of the IMS 4f and photographed (Ilford 400 ISO films) using 0.5-, 1-, 2-, and 5-s exposure times. RESULTS AND DISCUSSION Normalization of Cations RSFs to Ice-Characteristic Secondary Ions. SIMS experiments at 100 K showed that oxygen bombardment of frozen-hydrated samples sputtered H(H2O)n+ positive clusters from ice.10,14 In principle, these secondary ions might be used as matrix-characteristic reference ions. We therefore chose 1H+ and 1H316O+ ions, which are intensely emitted, to measure the RSFj/H and RSFj/H3O of the different cations (j ) Na, Mg, K, Ca) in the frozen-hydrated standards. Two series of

standards were prepared. The first series was made from a stock solution containing 100 mM NaCl, 40 mM MgCl2, 200 mM KCl, and 40 mM CaCl2, which was diluted 2-, 4-, 8-, and 16-fold to give five different standard solutions; these were frozen either by plunge freezing or by high-pressure freezing. The second series of standards was prepared from the same stock solution, but the dilutions were in 200 mM KCl instead of in pure water, such that the K+ concentration was 200 mM in each of the five standards. This second series of standards was frozen by PF. The normalized currents ij/iH and ij/iH3O were measured as described in Materials and Methods. The results presented in Figure 1 show the values of the RSFj/ref as a function of RSFK/ref (j ) Na, Mg, Ca; ref ) H, H3O) using a log-log scale. The RSF values are spread over 2 or 3 orders of magnitude. If the RSFs had been constant, the experimental points would have been clustered around the points (RSFj/H, RSFK/H) and (RSFj/H3O, RSFK/H3O). Figure 1 shows, however, that despite the variability of the RSFs, there is a good correlation between the values of the RSFj/ref and RSFK/ref. Indeed, whatever the reference species and the freezing method, the points lie on a straight line (of slope 1 in the log-log scale). The calculated regression coefficients are r2 ) 0.9852, 0.7881, and 0.8587 for the RSFs of Na, Mg, and Ca, respectively, vs the RSFs of K, and r2 ) 0.9879 for the RFSs of Ca vs those of Mg. This figure also shows that the correlation is better between ions of the same valence. One interpretation of these results is that even in the case of a freezing that is “good” (in the sense that only very small crystals are formed), ice excludes electrolyte crystals.15 A frozen standard is, thus, composed of a complex mixture of numerous different microphases with dimensions ranging from nanometers to micrometers, depending on the freezing rate. These microphases include the ice and different crystals of the alkaline and alkaline earth chlorides. Ice is sputtered out more rapidly than the crystals of the salts, as shown by the rapid decrease in the current of the ice-characteristic secondary ions H+ or H3O+, as compared with that of the inorganic cations (not shown). In other words, the “reference current” may vary with time in an uncontrollable manner during a SIMS experiment. This is an important factor in the variability of the RSFj/H and RSFj/H3O. The results presented in Figure 1 show that a broad range of values of RSF/ice-characteristic species is observed in both freezing modes (PF or HPF). The coefficient of variation (standard deviation/mean) of the RSFs is a measure of this range. These coefficients are almost the same for the four cations, but they change with the reference species and the freezing method. The mean of the coefficients of variation of the four cations (( standard error) are 2.28 ( 0.04 and 3.13 ( 0.16 for references H+ and H3O+, respectively, for samples frozen using PF and, similarly, 1.65 ( 0.27 and 2.33 ( 0.22 for samples frozen using HPF. These values show that the variability is, indeed, considerable but is lowered by taking H+ as a reference. This corresponds to changes in the secondary current being faster and more erratic with H3O+ than with H+ (not shown). These values also show that the variability is much lower for the samples frozen using HPF than for those frozen using PF. This is probably due to the production of a more homogeneous solid phase with high-pressure freezing than with

(14) Lancaster, G. M.; Honda, F.; Fukuda, Y.; Rabalais, J. W. J. Am. Chem. Soc. 1979, 108, 1951-1958.

(15) Zierold, K.; Steinbrecht, R. A. In Cryotechniques in Biological Electron Microscopy; Steinbrecht, R. A., Zierold, K., Eds.; Springer-Verlag: Berlin, 1987; pp 272-282.

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Figure 1. Relative sensitivity factors RSFj/ref of Na (upper left), Mg (lower left), and Ca (lower right) as a function of RSFK/ref. Circles are for samples frozen by PF, and squares are for samples frozen by HPF. Filled symbols are for reference H+ and open symbols for reference H3O+. Also shown (upper right) is the RSFCa/ref vs RSFMg/ref; symbols are the same for all frames. Each point is the mean of 10 successive determinations using the “isotope” program of the SIMS analyzer (see Materials and Methods). The standard deviation of these measurements is typically of the order of 1% and thus the uncertainty bars are smaller than the symbols.

Figure 2. SIMS images of the surface of the frozen-hydrated standards acquired using the microscope mode under FAB bombardment. Field of view, 250 µm. Left column, 1H+; middle, 1H316O+; and right, 40Ca+. Upper row, HPF; lower row, PF. These images were produced on the microchannel plate of the IMS 4f ion analyzer and photographed (Ilford 400 ISO films) using exposure times of upper left, 0.5 s; upper middle, 5 s; upper right, 2 s; lower left, 0.5 s; lower middle, 2 s; and lower right, 0.5 s.

classical plunge freezing. The images of Figure 2 were obtained using the IMS 4f ion analyzer in microscope mode because the primary beam of neutral oxygen can be neither focused nor rastered on the sample surface, and thus, scanning imaging was 2474

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not possible. Even though the resolution is poor (1 or 2 µm, at best) the images of the HPF samples are more homogeneous than those of the PF samples. Moreover, the distribution of the bright areas is similar on the images of H+ and H3O+ but different from that on the Ca+ image (although the distribution in this case is, in many places, complementary to that of H+ or H3O+); a similar conclusion can be drawn from the images of the other cations, (not shown). This is evidence for phase segregation. In conclusion, normalizing the current of a cation to H+ or H3O+ is not advisable, because these species are collected from different microphases that are sputtered at different rates. The uncorrelated sputtering of these microphases is a serious drawback for image normalization and, thus, for the comparison of images obtained from different experiments. As expected, HPF is to be preferred to PF as the freezing method, since it gives more reliable results due to the smaller microphases; however, even in this case, phase segregation could not be prevented in our samples due to their size, and normalization to ice ions should be avoided. Measurement of Cation RSFs in Frozen-Hydrated Standards and in Flax Fibers. The correlation between the values of the RSFj/ref and RSFK/ref (Figure 1) indicates, as discussed above, that one of the cations should be used as a reference species. Potassium would be a good choice because it is present in cells at around 150 mM, a concentration that is both high and relatively constant. That said, it may also be worth reconsidering the use

of RSF for heterogeneous systems, such as the frozen-hydrated standards. The whole idea of the RSF depends on the two analytes in the ratio being in the same matrix. This would occur in the case of frozen-hydrated standards if these were vitrified, since the amorphous structure of the solid state is similar to that of the solution. To interpret the RSF, we can use the fundamental equation of SIMS,

ij ) SIpYXjRjT

Table 1. RSFs of Na, Mg, and Ca Relative to K and of Ca Relative to Mga

Na/K Mg/K Ca/K Ca/Mg b

where ij is the measured current (counts per second, cps) of species j, S is the analyzed surface, Ip is the primary current density (cps per unit surface), Y is the total sputtering yield, Xj is the atomic fraction of the species j in the sputtered volume, Rj is the ionization probability of j, and T is the instrumental transmission function (which includes the detection yield). Assuming a homogeneous matrix and an identical T for j and for the reference species, this equation gives,

ij/iref ) (RjXj)/(RrefXref) ) (RjCj)/(RrefCref) in which the ratio of the atomic fractions, Xj/Xref is replaced by that of the molarities, Cj/Cref. Hence, this last equation and the definition of the RSF give

RSF frozen-hydrated standard (this work)

RSF flax fibers (this work)

“biological mean” (after Ramseyer and Morrison3)

0.67 ( 0.05 (66) 0.22 ( 0.03 (66) 0.31 ( 0.04 (66) 1.45 ( 0.04 (66)

0.83 ( 0.09 (20) 0.14 ( 0.01 (20) 0.19 ( 0.02 (20) 1.39 ( 0.10 (20)

1.10 ( 0.52b 0.16 ( 0.04b 0.25 ( 0.07b

a Mean ( 95% confidence interval (number of measurements). Mean ( standard error.

the same homogeneous phase. Nevertheless, using the definition RSFj/ref ) (ij/iref)/(Cj f j/Cref f ref), a formal RSF can be calculated (note the italics to state that this is not a true RSF). If this RSF value is constant, that is, if the currents ij and iref are linearly dependent on the concentrations of the elements j and ref before freezing the solution, it can be used for quantification purposes in a heterogeneous matrix just as a true RSF is used for a homogeneous matrix. In the following, we discuss the conditions that have to be fulfilled to obtain a constant RSF. This RSF may be written as

RSFj/ref ) (YjX°j R°j fref/YrefX°ref R°ref fj)(SjCref/SrefCj)

RSFj/ref ) (Rj fref)/(Rref fj) which is a constant value related to the ionization probabilities of the species in the analyzed matrix. Quantification may then be carried out using the equation

Cj ) (1/RSFj/ref)Cref(fref/fj)〈ij〉 where, again, 〈ij〉 ) ij/iref is the normalized current. In the case of a frozen-hydrated standard in which j and the reference species are sputtered from different microphases, the current of j is written

ij ) SjIpYj X°j R°j T

where an identical transmission function is again assumed for both species. It is apparent that the RSF has a constant value only if the term in the second set of brackets is constant, that is, if Sj is proportional to Cj (and Sref to Cref). After freezing, the volume occupied by the phase containing the species j is

Vj ) CjVVj where V is the total volume to be frozen and Vj is the molar volume of the compound containing j in the crystallized solid phase (we suppose for the sake of simplicity that a single phase contains j, but this assumption is not critical). The ratio of the volumes of the solid phases containing j and the reference species is, therefore

Vj/Vref ) (CjVj)/(CrefVref) A similar equation can be written for the reference species. Sj is the surface of the microphases containing the species j (which is a part of the total bombarded surface); Yj is the total sputtering yield of this microphase and is not necessarily the same for all the microphases; X°j is the atomic fraction of j in the crystal microphase that contains j and is, thus, a constant value, depending only on the stoichiometry of the crystallized compound; hence, X°j is independent of the concentration Cj; R°j is the ionization probability of j in this microphase. In the case of a heterogeneous medium, ij depends on the concentration of j, because the surface Sj exposed to the primary beam is a function of Cj, and not on Xj, which in this case is equal to X°j, a constant value. Indeed the greater the Cj in the standard solution, the greater the fraction represented by Sj in the total sputtered surface of the FH standard. If, however, Sj is not proportional to Cj, ij is not linearly related to Cj. An RSF calculated from a frozen-hydrated matrix is misleading because the analyte and the reference elements are not within

If the frozen medium can be considered as isotropic, Vj /Vref ) Sj/Sref, and therefore,

(SjCref/SrefCj) ) Vj/Vref The RSF may now be written as

RSFj/ref ) (Yj X°j R°j fref Vj)/(YrefX°ref R°ref fjVref) Hence, if the assumption of “isotropy” is valid, the RSF value is constant and can be used for quantification purposes. This is the case if the sizes of the microphases are small compared with the size of the analyzed surface over which the secondary currents are integrated. Because HPF produces smaller microphases (see Analytical Chemistry, Vol. 78, No. 8, April 15, 2006

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Figure 3. Calibration curves in frozen-hydrated standards containing a constant concentration of K+. Points are mean values with their standard error. Straight lines have been drawn with slopes calculated using the RSFs from Table 1 and using a potassium concentration value of 200 mM. C_ ) concentration of.

also Figure 2) it is certainly a better freezing technique in this respect. However, errors in interpretations could result from quantification in very small analyzed areas because of the variation of the term (SjCref/SrefCj) in the equation giving the RSF value. The RSFj/K’s in the frozen-hydrated standards were calculated (Table 1) from the results in Figure 1, taking into account the fractional abundance fj of the isotopes used to trace the cations (namely, 1 for 23Na, 0.7899 for 24Mg, 0.96941 for 40Ca, and 0.932581 for 39K). The calculated RSFCa/Mg is also given in Table 1. Assuming that the values of the RSFs are randomly distributed around a mean value, the central limit theorem17 justifies the estimation of confidence intervals using the expression derived from the normal law. From the data in Table 1 (F-H values), the precision (100 × confidence interval/mean, %) of the determination of the RSFs in the frozen-hydrated samples is 7, 14, 13, and 3% for RSFNa/K, RSFMg/K, RSFCa/K, and RSFCa/Mg respectively. We can, thus, take 15% as a reasonable estimate of the overall precision. With the results of the chemical assays of the cations in flax fibers and the SIMS measurements described in the Material and Methods, we calculated the RSFs in a matrix representative of plant cell walls (assumed here to be a homogeneous matrix). The values are shown in Table 1. From the data in Table 1 (fiber values), the precision of the determination of the fiber RSFs is 11, 7, 10, and 7% for RSFNa/K, RSFMg/K, RSFCa/K, and RSFCa/Mg respectively. We can, thus, again take 15% as an estimate of the overall precision. Even though the chemical and the SIMS analyses were carried out using samples collected from fiber batches as homogeneous as possible, there is a considerable variability in the ion content of these fibers. This variability, however, is much lower for divalent ions than for monovalent ions. For example, we obtained in the fibers CNa/CK and CCa/CMg values of 0.14 and 7.1, respectively, whereas Morvan et al.16 reported values of 0.34 and 6.8. The “biological means” reported by Ramseyer and Morrison3 are given in Table 1 (last column) for comparison. These “biological means” were measured using a variety of biological samples (animal and plant tissues, flours, gelatine standards) under O2+ bombardment. We estimated from their data the corresponding standard errors, but these are (16) Morvan, C.; Abdul-Hafez, A.; Morvan, O.; Jauneau, A. Plant Physiol. Biochem. 1989, 27, 451-459. (17) Korn, G. A.; Korn, T. M. Mathematical Handbook for Scientists and Engineers; McGraw-Hill: New York, 1968. (18) www.webelements.com. (19) Klewe, B.; Pedersen, B. Acta Crystallogr. 1974, B30, 2363-2371.

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characteristic of the variability between samples different in nature and not of the variability in the measurements within a given type of sample. It is noteworthy that all of the RSFs values we measured (Table 1), both in frozen-hydrated and in fiber samples, are consistent with the previous estimates of Ramseyer and Morrison. It can be seen from the results presented in Table 1 that the RSF values in the frozen-hydrated standards are similar to the RSF values in flax fibers for Na/K and Ca/Mg, that is, for ions of the same valence. This is particularly clear for the divalent ions. Mean values for Mg/K and Ca/K are much lower in flax fibers than in frozen-hydrated standards. To find a possible cause for such a difference, consider again the expressions for the RSFs in a homogeneous matrix (fibers) and in a heterogeneous isotropic matrix (frozen-hydrated samples). The ratio R ) RSF(frozenhydrated)/RSF(homogeneous) may be written

R ) (YjR°j RKX°j Vj)/(YKR°K Rj X°KVK) Assuming that the ratio of the ionization probabilities is not very different from 1, this expression can be simplified to

R ) (YjX°j Vj )/(YKX°KVK) To estimate R, we consider that in the frozen standards, KCl crystallizes in the form of an anhydrous compound (no KCl hydrate has ever been described18), NaCl in anhydrous form or as a dihydrate,19 and CaCl2 and MgCl2 as sesquihydrates.18 Using data in the literature,18 the term (X °j Vj)/(X°KVK) is then easily calculated. Therefore, the measured ratio R allows estimation of the ratio of the total sputtering yields Yj/YK. We calculated values of 1.5, 5.0, and 4.8 for YNa/YK, YMg/YK, and YCa/YK respectively. This result suggests a higher sputtering yield for highly hydrated crystal matrixes (at least under oxygen bombardment). Calibration experiments were then carried out using the second series of standards in which potassium is at a constant concentration of 200 mM. The results are shown in Figure 3 in which Cj is plotted against the corresponding current normalized to that of potassium. The slopes of the straight lines have been calculated using the mean values of the RSFs from data in Table 1. The experimental points lie close to these straight lines. It is clear that the fit is best at the low concentrations of the ions, and it is these low concentrations that are physiologically relevant. The slope of the line that best fits the points at low concentrations,

however, corresponds to an RSF value 20% lower than that given in Table 1. The departure from linearity for a given freezing process could result from ion concentration-dependent differences in the nucleation process and in the growth of crystals. In conclusion, our experiments show that it is possible to perform a SIMS relative quantification of the main physiological cations in frozen-hydrated samples with acceptable accuracy (estimated on the order of 15%). Using potassium as a reference, that is, measurement of the normalized current 〈ij/iK〉, permits the quantification of the ionic ratios, even when the absolute concentration of the referencing ion is unknown. This is a valuable result for physiological studies in frozen-hydrated biological samples.

ACKNOWLEDGMENT Our SIMS analyzer was purchased with grants from Re´gion de Haute Normandie, Ministe`re de la Recherche et de la Technologie and CAMECA company. We thank Gradimir Misevic for helpful discussions and Laurence Chevalier (UMR 6037 CNRS/ Universite´ de Rouen and Centre commun de microscopie e´lectronique) for her help in the performance of the high pressure freezing of the samples. We also thank Vic Norris for his help with English. Received for review August 24, 2005. Accepted February 17, 2006. AC051518U

Analytical Chemistry, Vol. 78, No. 8, April 15, 2006

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