Introduction

Top Abstract Introduction Materials and Methods Results Discussion References

CDDP¹ exerts its antitumor activity by binding to cellular DNA (Rosenberg, 1971; Gelasco and Lippard, 1999). When the drug enters the cell, it passes through the cytosol, enters the nuclear envelope, binds to nitrogen atoms on the bases of DNA, and promotes cell death by apoptosis (Bellon et al., 1991; Demarcq et al., 1994). The cytotoxic activity of CDDP thus seems to correlate with the amount of platinum (Pt) bound to DNA (Zwelling et al., 1979; Lindauer and Holler, 1996).

Biological thiols such as GSH, metallothionine, and other protein thiols defend the cell against CDDP (Kraker et al., 1985; Pattanaik et al., 1992; Ishikawa and Ali-Osman, 1993; Reedijk and Teuben, 1999). Pt ions entering the cell may preferentially bind to GSH and metallothionine (Dedon and Borch, 1987), both present in millimolar concentrations in the cytoplasm (Souid et al., 1999, 2001; A.-K. Souid personal observation). Because Pt-thiol adducts interact less well with DNA (Volckova et al., 2002), formation of these complexes limits the amount of drug available for binding to DNA. Furthermore, continued exposure to CDDP can increase the cytosolic sulfhydryl level (Schilder et al., 1990; Eastman 1991; Godwin et al., 1992), which may produce CDDP resistance.

The sulfhydryl agents WR-1065 and mesna are often administered to mitigate toxicities of Pt-based compounds and alkylating agents, such as cyclophosphamide (Brock et al., 1982; Souid et al., 2001; Tacka et al., 2002). The protective mechanism of WR-1065 and mesna involves reaction of the thiolate ion with CDDP in a manner analogous to that of GSH (Leeuwenkamp et al., 1991; Treskes et al., 1991).

Previously, we measured the rate of CDDP binding to DNA in peripheral blood mononuclear cells and ovarian cancer cells (Sadowitz et al., 2002). By blocking the cellular thiol groups and by adding known concentrations of WR-1065 or mesna, we showed how the amount of CDDP reaching the DNA is affected by thiol concentration. For example, blocking all cellular thiol groups with N-ethylmaleimide increased DNA platination by ~8-fold. These data were used to generate a simple kinetic model that reproduced the measured Pt bound to DNA as a function of incubation time and CDDP and thiol concentrations. The model included passage of CDDP through the cell membrane, binding of CDDP to cellular thiols, and platination of DNA. We also studied the reaction of GSH with 4-hydroperoxycyclophosphamide and acrolein (Tacka et al., 2002); the latter is a toxic metabolite of cyclophosphamide.

Although CDDP reaction with thiols has been studied extensively (Berners-Price and Kuchel, 1990a,b; Ishikawa and Ali-Osman, 1993; Bernareggi et al., 1995; Perez-Benito et al., 1995; Bose et al., 1997; El-Khateeb et al., 1999), there is little kinetic data under clinically relevant conditions. In this work, we use UV absorption, HPLC, and atomic absorption spectroscopy (AAS) to measure the rates of CDDP reaction with GSH, WR-1065, and mesna, using a therapeutic concentration of CDDP and conditions that mimic passage of CDDP through the cytosol. The data obtained improve our understanding of how cellular GSH and drug thiols influence DNA platination by CDDP.

	Materials and Methods

Top Abstract Introduction Materials and Methods Results Discussion References

Chemicals. CDDP (1 mg/ml, ~3.3 mM in 154 mM NaCl) was obtained from American Pharmaceutical Partners (Los Angeles, CA); mesna (mol. wt. 164.18, 100 mg/ml solution) was obtained from Bristol-Myers Squibb Co. (Princeton, NJ); WR-1065·2HCl (mol. wt. 207.16) was obtained from U.S. Bioscience (West Conshohocken, PA); Tris was purchased from Fluka Chemical Corp. (Ronkonkoma, NY); GSH, 5,5'-dithio-bis(2-nitrobenzoic acid), dihexylamine, glacial acetic acid, NaCl, and pH Test Strips (4.5-10.0) were purchased from Sigma-Aldrich (St. Louis, MO); and Pt atomic spectroscopy standard (H₂PtCl₆, 1 mg/ml in 10% HCl) was purchased from PerkinElmer Instruments (Norwalk, CT).

Solutions. GSH, WR-1065, and mesna solutions were prepared in dH₂O and stored at 70°C in small aliquots; their concentrations were determined by titration with 5,5'-dithio-bis(2-nitrobenzoic acid) (Souid et al., 1998). Dihexylammonium acetate (DHAA, 2.5 mM) HPLC solvents were prepared in the hood by the addition of 590 µl of 4.24 M dihexylamine and 144 µl of 17.4 M glacial acetic acid to each liter of dH₂O or methanol. The pH was adjusted to ~7.0 by small additions of dihexylamine or acetic acid.

Reaction of CDDP with Thiol (GSH, WR-1065, or Mesna). Reactions were carried out in the dark at 37 ± 0.1°C in a total volume of 1.0 ml. In a typical experiment, the mixture contained 100 mM Tris-NO₃, pH 7.4; 33, 66, or 99 µM CDDP (from a 3.3 mM stock solution in 154 mM NaCl); and 16.5 mM thiol. For all reactions, the final concentration of NaCl was adjusted to 4.62 mM, the approximate concentration of NaCl in the cytoplasm, by the addition of appropriate amount of 154 mM NaCl solution. Reactions were initiated by mixing CDDP with the buffer and NaCl followed by immediate addition of the thiol. The [CDDP]:[GSH] ratio in the reaction mixture is 1:500, which mimics that of cells exposed to a therapeutic concentration of CDDP (see Discussion).

View larger version (13K): [in this window] [in a new window]   Scheme 1.   Hydrolysis of CDDP.

UV Absorbance. The absorbance at 260 nm as a function of time (reflecting formation of Pt-sulfur bonds and disulfides) was measured using a single beam spectrophotometer (model DU 640B; Beckman Coulter, Inc., Fullerton, CA). Samples were in a 1-cm path length quartz cuvette with a Teflon stopper, which was thermostatted at 37 ± 0.1°C. The reaction contained 33 µM CDDP, 16.5 mM thiol, 4.62 mM NaCl, and 100 mM Tris-NO₃, pH 7.4, at a final volume of 1.0 ml. The spectrophotometer was "zeroed" immediately after thiol addition, which initiated the reaction. The control experiments for determining the rate of disulfide formation (thiol oxidation) contained the exact same reaction mixture without CDDP.

HPLC-UV. Analysis was performed on a reversed-phase HPLC system (Beckman Coulter, Inc.), which consisted of an automated injector (model 507e), a pump (model 125), and a UV detector (model 166). UV detection at 260 nm was used; at this wavelength the GS-Pt adducts absorb strongly (Ishikawa and Ali-Osman, 1993; Perez-Benito et al., 1995). Solvent A was 2.5 mM DHAA in dH₂O and solvent B 2.5 mM DHAA in HPLC-grade methanol. The column, a 4.6 × 250-mm Ultrasphere IP column (Beckman Coulter, Inc.), was operated at RT at a flow rate of 0.5 ml/min.

AAS. The Pt analysis was performed using the graphite furnace of an AAS (model AA-6800; Shimadzu, Kyoto, Japan), with an ist (Imaging and Sensing Technology, Horseheads, NY) hollow cathode Pt lamp, deuterium arc background correction, and pyrolytically coated graphite tubes (Sadowitz et al., 2002). A calibration curve (using H₂PtCl₆) was generated before each measurement and proved to be linear from 0 to 10 pmol (r > 0.99). The lower limit of detection was ~20 pg of atomic Pt (~0.1 pmol). A background reading of ~0.0060 optical density (for dH₂O) was subtracted from each of the determinations containing Pt. The injection volume was 20 µl.

	Results

Top Abstract Introduction Materials and Methods Results Discussion References

Reaction of CDDP with GSH as Monitored by UV Absorption. UV absorption at 260 nm of solutions containing different concentrations of CDDP, 16.5 mM GSH, 100 mM Tris-NO₃, pH 7.4, and 4.62 mM NaCl (final volume of 1.0 ml) as a function of time is shown in Fig. 1. The increased absorption with time resulted partially from the reaction of CDDP with GSH (formation of Pt-sulfur bounds) and partially from the oxidation of GSH (formation of the disulfide GSSG), as shown by the increased absorption with time for GSH alone (Fig. 1, dashed lines). Because the rate of disulfide formation is slow (Fig. 1, dashed lines), the concentration of GSH was assumed not to change much over the time course of the GSH-CDDP reaction (several hours). This assumption was also verified by HPLC, which showed a large excess of GSH at the end of each incubation period. Because the GSH concentration is 500 times that of the concentration of CDDP, the reaction of GSH with CDDP likewise does not deplete GSH.

View larger version (23K): [in this window] [in a new window]   Fig. 1.   UV absorbance associated with the reaction of CDDP with GSH. Absorbance at 260 nm is shown as a function of time for a 20-h incubation at 37°C of CDDP and 16.5 mM GSH in 100 mM Tris-NO3, pH 7.4, buffer containing 4.62 mM NaCl. The concentration of CDDP is 33 µM (top), 66 µM (middle), or 99 µM (bottom). The absorbance (260 mm) of a solution containing no CDDP (GSH alone) is shown, as well as the result of subtracting this curve from the total absorbance change for the reaction of GSH with CDDP.

5

5

View this table: [in this window] [in a new window]   TABLE 1 Initial rates of reactions of CDDP with thiols obtained from UV absorption data For GSH and mesna, the absorption at 260 nm as a function of time (0  t  1200 min) for CDDP concentration = 0 was subtracted from the absorption for each CDDP concentration. The difference was fitted to C + A1 exp(b1t) + A2 exp(b2t), and the initial slope (Sin) was calculated as (A1b1 + A2b2). For WR-1065, the difference of absorptions for each CDDP concentration was fitted to a linear function of time (0  t  30 min) to obtain the slope. The concentrations and condition were: Thiol, 16.5 mM; NaCl, 4.62 mM; and Tris-NO3, 100 mM, pH 7.4 at 37°C.

Reactions of CDDP with WR-1065 and Mesna as Monitored by UV Absorption. UV absorption at 260 nm was also observed during 20-h incubations at 37°C of 0 to 99 µM CDDP, 16.5 mM mesna, 100 mM Tris-NO₃, pH 7.4, and 4.62 mM NaCl. With no CDDP present, the UV absorption of mesna varied with time in a more complicated way than that of GSH. Nevertheless, when the absorption for mesna alone is subtracted from the absorption for mesna plus 33, 66, and 99 µM CDDP, we obtained plots similar to those in Fig. 1. Fitting these difference plots to eq. 1, we calculated the initial slopes as S_in = (A₁b₁ + A₂b₂), giving the results in Table 1. Plotted versus [CDDP], these S_in values give a fit (r² = 0.96) to a straight line, S_in = 0.00181 + 6.01 × 10⁵ [CDDP]/µM, showing that the initial reaction is first order in [CDDP].

5

Reaction of CDDP with GSH as Monitored by HPLC-AAS. A typical chromatogram of the reaction of CDDP with GSH is shown in Fig. 2. The reaction mixture (at 37°C) contained 33 µM CDDP, 16.5 mM GSH, 100 mM Tris-NO₃, pH 7.4, and 4.62 mM NaCl (final volume of 1.0 ml). It shows about 45 peaks on a curved baseline, with retention times (t_R) between ~4 and 48 min. Values of t_R in minutes for some peaks are as follows: Tris-NO₃, ~21.0; GSH, ~25.0; and GSSG, ~26.5. The chromatogram also contained a significant number of peaks from DHAA, which do not change with reaction time.

View larger version (20K): [in this window] [in a new window]   Fig. 2.   HPLC chromatogram of the reaction of CDDP with GSH. A representative chromatogram of the reaction (at 37°C) of 33 µM CDDP and 16.5 mM GSH in 100 mM Tris-NO3, pH 7.4, buffer containing 4.62 mM NaCl is shown. About 45 peaks (detected at 260 mm) appear with tR between ~4 and 48 min. The peak at tR of ~4.5 min contains unreacted CDDP. The peaks at 21 min < tR < 25 min and 26.5 min < tR < 31 min contain Pt-thiol products (as shown by AAS). Values of tR in minutes for some peaks are Tris-NO3, ~21.0; GSH, ~25.0; and GSSG, ~26.5.

View this table: [in this window] [in a new window]   TABLE 2 AAS-Pt absorptions for various HPLC elutes for the reaction of CDDP with GSH AAS-Pt absorptions of elutes from reaction of 33 µM CDDP with 16.5 mM GSH in 4.62 mM NaCl and 100 mM Tris-NO3, pH 7.4, at 37°C for the indicated reaction times. Reaction mixtures were separated on HPLC and fractions were collected for various tR and analyzed using AAS as described under Materials and Methods. The peaks at 3.0  tR  6.0 min and 4.25  tR  5.75 min correspond to unreacted CDDP. The remaining peaks correspond to Pt-sulfur products. For the unreacted CDDP peaks, the k1 averaged ~2.2 × 104 s1 (Fig. 3).

1

1

4

1

1

1

4

1

2

1

1

View larger version (16K): [in this window] [in a new window]   Fig. 3.   Kinetics of the reaction of CDDP with GSH determined using HPLC-AAS. CDDP (33 µM) was incubated in the dark at 37°C with 16.5 mM GSH, 4.62 mM NaCl, and 100 mM Tris-NO3, pH 7.4. At the end of each incubation period, an aliquot of the reaction was loaded on the HPLC. Elutes representing unreacted CDDP were collected and their Pt contents were determined by AAS as described under Materials and Methods. Triangles and dashed line correspond to experiment 1 (elutes, 3.0  tR  6.0 min) and squares and solid line experiment 2 (elutes, 4.25  tR  5.75 min), Table 2. Circles and long-dashed curve correspond to an experiment (elutes, 3.0  tR  6.5 min) in which CDDP was aged for 4 h before being mixed with GSH (see text). The k1 values (derived from the slopes of the curves) for the unaged CDDP reaction average ~2.2 × 104 s1 and t1/2 of ~53 min. For the 4-h aging time, the reaction is biphasic; the initial k1 value is ~2.0 × 104 s1 and later (using the last 4 points) ~0.4 × 104 s1, corresponding to t1/2 of 60 and 290 min, respectively.

ct

1

1

4

1

1

4

1

0.00547t

1

4

1

View this table: [in this window] [in a new window]   TABLE 3 AAS-Pt absorptions for various HPLC elutes for the reaction of aged CDDP with GSH AAS-Pt absorption of elutes from reaction of 24-h aged 33 µM CDDP with 16.5 mM GSH in 4.62 mM NaCl and 100 mM Tris-NO3, pH 7.4, at 37°C for the indicated reaction times. The amount of Pt in the fractions was analyzed using AAS as described under Materials and Methods. For the 4.50 min  tR  5.75 min peak (unreacted CDDP), the intensities fit (r2 = 0.998) 0.649 e0.00547t, giving k1 of ~0.9 × 104 s1.

Reaction of CDDP with WR-1065 and Mesna as Monitored by HPLC-AAS. The reaction rate constants for CDDP with WR-1065 and mesna (Fig. 4) were determined in the same way as for the reaction of CDDP with GSH. After establishing that the chromatographic peak for CDDP corresponded to t_R of ~4.5 min, elutes were collected from the HPLC for times including this t_R. A 20-µl sample was injected into the AAS and the absorbance, proportional to Pt concentration, was measured.

View larger version (15K): [in this window] [in a new window]   Fig. 4.   Kinetics of the reaction of CDDP with WR-1065 and mesna determined using HPLC-AAS. CDDP (33 µM) was incubated in the dark at 37°C with 16.5 mM WR-1065 (squares) or mesna (triangles) with 4.62 mM NaCl and 100 mM Tris-NO3, pH 7.4. At the end of each incubation period, an aliquot of the reaction was loaded on the HPLC; elutes representing CDDP (4.25  tR  5.75 min) were collected, and their Pt contents were determined by AAS. The natural logarithms of the Pt-AAS absorbance are plotted as a function of incubation time. The slopes give k1 = 12.0 × 104 s1 (t1/2 ~10 min) for WR-1065 and k1 = ~1.8 × 104 s1 (t1/2 ~65 min) for mesna.

1

1

4

1

2

1

1

4

1

2

1

1

	Discussion

Top Abstract Introduction Materials and Methods Results Discussion References

The reactions of CDDP with GSH and thiols affect the amount of CDDP that is available for binding to DNA (Berners-Price and Kuchel, 1990a,b; Ishikawa and Ali-Osman, 1993; Bernareggi et al., 1995; Perez-Benito et al., 1995; Bose et al., 1997; El-Khateeb et al., 1999). For example, blocking the cellular thiol groups with N-ethylmaleimide increases the amount of DNA-Pt adducts by ~8-fold (Sadowitz et al., 2002). Although previous work provides valuable information on the structure, rate, and mechanism of product formation, most studies were not performed using biologically relevant conditions. For example, the concentration of CDDP was in the millimolar range (too high to be clinically relevant) and/or the concentration of thiol was relatively low.

Clinically, typical CDDP doses are 20 to 120 mg/m², administered intravenously over 1 h. In a recent trial, after infusion of 30 mg/m² of CDDP, the maximum concentration of unbound Pt in the plasma was [mean ± S.D.(n)] 4.5 ± 1.6(19) µM and the t_1/2 was 25.4 ± 5.4 min; Souid et al., 2003]. Other studies showed peak plasma Pt levels of ~10 µM after infusion of 70 mg/m² CDDP (Corden et al., 1985; Korst et al., 1998). Thus, CDDP concentrations of ~5 to 30 µM mimic most conditions encountered in the clinical administration of the drug.

Therefore, we selected the following conditions for measuring the rate constants of the reactions of CDDP with GSH and drug thiols: 1) The source of the drug used in our work is platinol, the formulation used for treating patients. Platinol contains 3.3 mM cis-diamminedichloroplatinum(II) in a slightly acidic solution, pH ~5.5, which also contains 154 mM NaCl. 2) The concentration of CDDP used is 33 µM, which is at the high end of the therapeutic range and still provides sufficient Pt to be detected by AAS. 3) The ratio of CDDP to GSH approximates that in the cell. Because the concentration of GSH in the cell is 1 to 3 mM (Eastman, 1991; Souid et al., 1999, 2001) and the low end of the therapeutic range for CDDP in the cell is ~5 µM, the ratio of thiol to drug in the cytoplasm is ~500:1. In most of our studies, the mixture contained 33 µM CDDP and 16.5 mM thiol, making the reaction pseudo first order with rate proportional to [CDDP]. The low CDDP concentration and the large excess of GSH would favor formation of mononuclear thiolate complexes. 4) The pH of the study was maintained at 7.4, using either 100 mM Tris-NO₃ (or 50 mM NaPO₄; data not shown). These buffer concentrations were the minimum for maintaining the pH at ~7.4 during the course of the reaction. The nitrate ion was chosen because it binds to Pt²⁺ only weakly. Nevertheless, both buffers gave the same results. 5) Reactions were studied at 37 ± 0.1°C.

It is well known that CDDP (1) reacts in water to produce the chloro-aquo (2) and diaquo (3) forms of the drug, shown in Scheme 1 (Miller and House, 1990). In platinol, the clinical formulation of CDDP, the aquation is suppressed by a high chloride concentration (154 mM), and the drug exists mainly as the dichloro form (1). When the chloride content in the medium is reduced, e.g., to 4.62 mM, CDDP begins to aquate but the time to produce 2 and 3 is relatively long (hours). Because the t_1/2 for the reaction of unaged CDDP with GSH is ~50 min (Fig. 3), the major species reacting with GSH is the dichloro form (1). Aging solutions of CDDP at low chloride concentration (4.62 mM) before the addition of GSH allows the drug to aquate to the chloro-aquo (2) and diaquo (3) forms (Scheme 1), with more 2 than 3. Because the pK_a for 2 is 6.85 and the pH of the reaction is 7.4, the major form present is the chloro-hydroxo (4) (Miller and House, 1990). Hydroxide ion, being a poor leaving group compared with water (4), should be much less reactive than 2 in a displacement reaction with GSH. As shown in Fig. 3, the aging clearly affects the kinetics of CDDP reaction with GSH. For a 4-h aging time, the reaction is biphasic; initially the k₁ = ~0.012 min¹ (~2.0 × 10⁴ s¹) and later (using the last 4 points) ~0.0024 min¹ (~0.4 × 10⁴ s¹), corresponding to t_1/2 of 60 and 290 min, respectively (Fig. 3, circles). Because 4 h at RT would be insufficient time for equilibrium between 1 and 2 (or 3), a significant amount of 1 is present, corresponding to the short t_1/2 GSH reaction observed in Fig. 3 (circles). At longer aging times, only the slower reaction of GSH with the chloro-hydroxo 4 is observed. From the value of t_1/2, this compound reacts with GSH more slowly than 1 (Table 3).

The absorbance versus time curves for solutions containing both CDDP and thiol (Fig. 1) could be fit very accurately by a constant plus (or minus) two exponentials of the form A_j exp(b_jt), j = 1 or 2. This indicates that at least two reactions take place. However, one can fit the data as well with a number of other 5-parameter functions, so it is not justified to assume that b₁ and b₂ represent rate constants for two first order reactions. Only an explicit kinetic model, based on evidence from HPLC as well as UV absorption, can indicate the proper interpretation of the UV data. We have used the fit to exponentials only to calculate the initial slope (Table 1), which was proportional to [CDDP], proving that the reaction is first order in CDDP (as proven by HPLC-AAS).

The ability of GSH and other thiols to bind Pt may help explaining how cells resist CDDP therapy (Richon et al., 1987; Eastman, 1991; Mistry et al., 1991). CDDP binding to thiols in the cytoplasm diminishes the concentration of drug capable of binding to DNA. However, the results presented herein show that the reaction of 1 with a large excess of GSH is relatively slow (t_1/2 ~50 min). For comparison, the k₂ for GSH binding to 4-hydroperoxycyclophosphamide (~38 M¹ s¹) is ~3 orders of magnitude higher than that for GSH binding to CDDP, ~1.3 × 10² M¹ s¹ (Tacka et al., 2002). This fact and the expected rapid diffusion of CDDP, suggest that a significant amount of CDDP, as 1 and 4, can reach the nuclear envelope unchanged by reaction with GSH. Further work on the rate of CDDP transfer across the cellular membrane and the rate of its reaction with other cellular thiols (e.g., metallothionein and large molecular weight protein thiols) will provide a better picture of the amount of the drug available for binding to DNA under clinical conditions.

The thiol drugs WR-1065 and mesna exhibit different reactivity toward CDDP (Fig. 4). The higher k₁ value for WR-1065 is probably related to the fact that, of the three thiols studied, WR-1065 has the lowest pK_a value (7.7) for the thiol group; mesna, 9.1, and GSH, 8.7 (Shaked et al., 1980; Newton et al., 1992). Thus, at pH 7.4, WR-1065 would have the highest concentration of the thiolate ion, the attacking nucleophile in the substitution reaction.

Other studies have reported the reaction rates for CDDP with mesna and WR-1065 by measuring the amount of UV absorption of the CDDP peak from HPLC. In one study, the k₂ value decreased from 1.5 × 10² to 0.7 × 10² M¹ s¹ for 200 µM CDDP reacting with 5 to 500 mM mesna in the presence of 150 mM NaCl (Leeuwenkamp et al., 1991); our k₂ value of 1.08 × 10² M¹ s¹ is in the middle of the range.

In another study, k₂ decreased from 2.8 × 10² to 1.1 × 10² M¹ s¹ for 100 µM CDDP reacting with 5 to 20 mM WR-1065 (NaCl concentration was not given) (Treskes et al., 1991); our k₂ value of 7.3 × 10² M¹ s¹ is larger. However, in our hands, measurements of UV absorption of the HPLC-CDDP peak produced inconsistent results, partly from difficulty in establishing the baseline. Note also that the peak probably contains species other than CDDP, whereas measurement of Pt content by AAS is unambiguous.

Mesna and WR-1065 (the active metabolite of WR-2721) are used to reduce the cytotoxicity of CDDP and other anticancer drugs (Dedon and Borch, 1987; Leeuwenkamp et al., 1991; Treskes et al., 1991; Souid et al., 1999, 2001; Reedijk and Teuben, 1999). Unlike mesna, which is an anion, WR-1065 is a cation, which can readily cross the cell membrane and distribute in the nuclear matrix. Because it can bind to DNA (Smoluk et al., 1986) and it has the largest rate constant for reaction with CDDP, WR-1065 may be more efficient in decreasing the concentration of CDDP reaching the DNA.

The rate constants reported herein for the reactions of CDDP with thiols are important for accurate modeling of cellular DNA platination by CDDP (Sadowitz et al., 2002). Although we have previously constructed a simple model, describing complex processes with simple rate laws, it involves several undetermined kinetic parameters. With values for more parameters fixed by measurement, the model should lead to more reliable values for the others. This would enable a serious test of the model and possibly make it useful as a guide to clinical practice.