Kinetics and Mechanisms of Dissolution and Growth of Acicular Triclinic Calcium Pyrophosphate Dihydrate Crystals Margaret R. Christoffersen,† Tonci Balic-Zunic,‡ and Jørgen Christoffersen*,†
CRYSTAL GROWTH & DESIGN 2002 VOL. 2, NO. 6 567-571
Department of Medical Biochemistry and Genetics, Biochemistry Laboratory A, The Panum Institute, University of Copenhagen, Blegdamsvej 3, DK-2200 Copenhagen N, Denmark, and Geological Institute, University of Copenhagen, Østervoldgade 10, DK-1350 Copenhagen K, Denmark Received August 8, 2002;
Revised Manuscript Received September 7, 2002
ABSTRACT: Formation of calcium pyrophosphate (diphosphate) dihydrate (CPPD) crystals in articular cartilage and synovial fluid leads to CPPD deposition disease and pseudogout. Rates of dissolution and growth in the pH range of 5-7 of triclinic CPPD (t-CPPD) microcrystals of acicular (needlelike) shape are reported here. As previously found for columnar t-CPPD, the mechanism of dissolution of acicular t-CPPD is best described by the polynuclear model. The rates of dissolution per unit area of acicular t-CPPD are about a factor of 2 faster than the corresponding rates for columnar t-CPPD. Growth of acicular t-CPPD also appears to be explained by the polynuclear mechanism, as previously found for growth of columnar t-CPPD. At low pH (4.5), the rates of growth per unit area of acicular and columnar t-CPPD are similar. At higher pH (5.5 and 6.5), the rates of growth per unit area of acicular t-CPPD are slower than corresponding rates for columnar t-CPPD. At constant pH, this effect increases as the supersaturation decreases. The main difference between the two morphologies is the edge length per unit area. The larger solution volume around edges may facilitate acicular crystal dissolution but lead to inhibition of acicular growth by chelation of pyrophosphate to calcium ions blocking normal growth. Introduction The increasing age expectancy of the population leads to an increase in interest in diseases that afflict the elderly. Deposition of calcium pyrophosphate (diphosphate) dihydrate (CPPD) crystals in soft tissues such as cartilage, meniscus, and synovial tissue is clearly agerelated. These crystals have been radiographically identified in a large percent (25-50%) of the population by the age of 80. The appearance of these crystals in the synovial fluid can give rise to an acute arthritic attack with pain and inflammation of the joint, a condition called pseudogout.1-6 Formation in vivo of triclinic CPPD (t-CPPD) and monoclinic CPPD (mCPPD) is usually detected in synovial fluid by compensated polarized light microscopy. Smaller crystals, also found to be t- and m-CPPD, have been identified in electron microscopic studies.7-10 There is also an increasing interest in the possible interplay between the formation of these types of crystals in joints and osteoarthritis.6,11-13 An understanding of the mechanisms of growth, formation, and dissolution of calcium pyrophosphate (CPP) crystals is of importance if these processes are to be controlled in vivo. We have previously reported14,15 results of in vitro studies of growth and dissolution of columnar t-CPPD. The crystal structure of a possible precursor of t-CPPD, a monoclinic calcium pyrophosphate tetrahydrate (m-CPPTβ), has also been reported.16 The kinetics of growth and precipitation of m-CPPTβ and possible autoinhibition of these processes has been reported.17 * To whom correspondence should be addressed. Tel: (+45)35327740. Fax: (+45)35327741. E-mail:
[email protected]. † The Panum Institute, University of Copenhagen. ‡ Geological Institute, University of Copenhagen.
In this paper, we report kinetics of growth and dissolution of t-CPPD crystals with a needlelike (acicular) morphology and compare these rates with those previously reported for columnar t-CPPD. Materials and Methods The stock crystals of acicular t-CPPD were prepared by conversion of m-CPPTβ at pH 4.5 and 50 °C. A solution approximately saturated with respect to m-CPPTβ was prepared by dissolving 1.16 mmol of Na4P2O7‚10H2O in 1800 mL of water. The pH was adjusted to 4.5 with 2.05 mL of 1 M HNO3, and 2.32 mmol Ca(NO3)2 was slowly added to the stirred solution in the form of a 0.1 M solution. The solution was heated to 50 °C, and 2 g of m-CPPTβ crystals of the preparation described17 was slowly added in the form of a suspension containing 50 mg/mL. The preparation was stirred and kept at 50 °C for 12 d. Scanning electron microscopy (SEM) micrographs of the acicular crystals are given in Figure 1a,b. The specific surface area, Asp0, from a single point Brunauer-Emmett-Teller (BET) measurement is 2.8 m2/g, a factor of approximately 5 greater than that of the columnar t-CPPD (0.6 m2/g) reported.14,15 The specific surface area of needles is approximately independent of the length of their longest dimension. The longest dimension of the present crystals is of the order 10-30 µm. Assuming the two short dimensions to be in the ratio 2:1 (see below), their lengths can be calculated from the specific surface area to be about 0.8 and 0.4 µm. Thermal analysis of the crystals resembles that of the columnar t-CPPD with the loss of 0.5H2O in the range of 160-290 °C (maximum 234 °C) and 1.5H2O in the range of 290-440 °C (maximum 330 °C). The IR spectra of the acicular and columnar t-CPPD crystals are identical, as are the X-ray diffraction diagrams. Both diagrams correspond to the theoretical for triclinic Ca2P2O7‚2H2O. The seed crystals were kept and used in the growth and dissolution kinetics experiments in the form of an aqueous suspension (20 mg/mL). All kinetic experiments were made at 37.0 °C, the dissolution experiments as described15 and the growth experiments as described.17
10.1021/cg025571c CCC: $22.00 © 2002 American Chemical Society Published on Web 09/27/2002
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Christoffersen et al. four-circle diffractometer with a CCD detector and Mo KR radiation was used. The temperature of measurement was 25 °C. Although the large acicular t-CPPD crystal exceeds in linear dimensions 10 times the stock crystals used for the experiments reported here, it can be concluded from a comparison with SEM photographs that no significant change in morphology has occurred. The dominating faces parallel to the needle axis are the two main pinacoids, which give a characteristic almost rectangular cross-section. The same faces dominate also the significantly larger columnar crystals where also a terminal {011 h } pinacoid has developed (seen also on SEM photographs of the latter14,15), which, however, cannot be seen on the acicular crystals.
Results and Discussion Experiments were analyzed as previously described14,15 using the same values of constants, in particular the value of pKs ) 18.35 for the solubility constant of t-CPPD. The rate of growth or dissolution, J, can be expressed by
J ) |dnCPPD/dt| ) kJm0F(m/m0)g(C)
Figure 1. SEM micrographs of the acicular t-CPPD stock crystals. The bars represent (a) 20 µm and (b) 5 µm. Crystals of acicular t-CPPD large enough for a monocrystal X-ray diffraction study were grown at pH 4.0 and 37 °C over 60 d from a small sample of the stock crystals. The crystals were suspended in 940 mL of a solution of 1.9 mM Ca(NO3)2 and 0.95 mM Na4P2O7 with the pH adjusted to 4.0. This solution was supersaturated only with respect to t-CPPD. The solution was renewed twice a week. One of these crystals was used for the X-ray study. It was approximately 110 µm in length and 20 µm × 10 µm in the shorter dimensions. From a measurement on 38 reflections, crystal lattice parameters were determined as follows: a ) 7.335(5) Å, b ) 8.269(7) Å, c ) 6.677(6) Å, R ) 102.88(3)°, β ) 72.74(5)°, γ ) 94.92(5)°. Apart from a minor difference in the length of the a-axis of 0.01 Å, the parameters were identical to those obtained for a columnar t-CPPD crystal for 30 reflections: a ) 7.347(7) Å, b ) 8.270(7) Å, c ) 6.689(5) Å, R ) 102.87(4)°, β ) 72.70(5)°, γ ) 94.99(5)°. The values were also in a good agreement with those obtained in another crystal structure study of this phase.18 By an optical inspection of the crystal oriented on the diffractometer, the elongation direction was determined as [001] or parallel to the c-axis, and the dominating faces as pinacoids {100} (10) and {010} (20). The values in normal brackets are perpendicular diameters in micrometers. The terminal faces could not be determined due to the small diameter of the crystal. In a similar study of a large columnar t-CPPD crystal, the same pinacoids were determined together with the {011 h } as a terminal one. The crystal diameters were in the latter case 30, 90, and 150 µm for {100}, {010}, and {011 h }, respectively. This crystal was selected from crystals formed by mixing 0.25 g of CaH2P2O7 and 25 mL of water and letting the suspension stand unstirred at room temperature for 1-2 d (pH ≈ 3.0). In both X-ray studies, a Bruker-AXS
(1)
in which kJ is a rate constant proportional to the initial specific surface area, m0 is the initial mass of crystals, F(m/m0) is a function representing the change in the morphology/surface area of the crystals, and g(C) is a function of the solution composition. For purely bulk diffusion-controlled growth and dissolution, g(C) is proportional to |Cs - C| and approximately proportional to |S - 1|, where S is the cube root of the ratio of the ionic activity product to the solubility product. For surface reaction-controlled processes, g(C) can be approximated empirically by |S 1|p. For spiral-controlled processes, p e 2. For polynuclear surface nucleation-controlled processes, p > 2 for relatively low values of S. A detailed description of dissolution and growth processes controlled by the polynuclear mechanism is given.19 The following expressions are used here
g(C) ) gp(C)e-R/3β
(2)
in which R is a substance-dependent constant proportional to the square of the surface tension, β ) |lnS|, and gp(C) is a function mainly describing the rate of the lateral growth of surface nuclei.19
kJ ) Hνin
(3)
in which νin is the frequency for a cation to enter a suitable kink site. H is a substance-dependent constant proportional to Asp0. H ) 4.6 × 10-10 m3/g for the crystals used here. Dissolution. Figures 2 and 3 are empirical logarithmic plots of rates per initial surface area, A0 ) m0Asp0, as a function of the supersaturation, defined as g(C) ) |S - 1|p. Rates were measured at the point in each experiment where 20% of the crystals had dissolved (m/ m0 ) 0.8), except for experiments with pH values of 6.5 and 7.0 where 10% had dissolved (m/m0 ) 0.9). In Figure 3, results for dissolution of acicular and columnar t-CPPD at pH 5.0 and 5.5 are plotted for comparison. As in ref 14, Asp0 ) 0.6 m2/g is used here for the columnar crystals in place of the estimate Asp0 ) 1 m2/g previously used.15 In Figure 4, results for dissolution of
Dissolution and Growth of Acicular Triclinic Crystals
Figure 2. Logarithmic plot of rates of dissolution per unit area, J/A0, in molCPPD/s m2, against the undersaturation 1 S for acicular t-CPPD. Triangles, pH ) 5.0; squares, pH ) 5.5; +, pH ) 6.0; circles, pH ) 6.5; ×, pH ) 7.0. The slopes of the lines are 2.6, 2.1, 2.5, 2.3, and 2.7, respectively.
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Figure 4. Plot of rates of dissolution of acicular t-CPPD according to the polynuclear mechanism. Triangles, pH ) 5.0; squares, pH ) 5.5; +, pH ) 6.0; circles, pH ) 6.5; ×, pH ) 7.0. The slopes of the lines are 0.5, 0.4, 0.7, 0.5, and 0.8, respectively. The intercepts with -1/β ) 0 are ln(νin) with νin given in Table 1. Table 1. Results of Analysis of Rates of Dissolution According to the Polynuclear Mechanism acicular t-CPPD
Figure 3. Comparison of rates of dissolution per unit area of acicular (present work) and columnar t-CPPD dissolution.15 Triangles, pH ) 5.0; squares, pH ) 5.5; solid symbols, acicular t-CPPD; open symbols, columnar t-CPPD.
acicular t-CPPD are plotted according to the polynuclear mechanism as explained.15 The surface energy can be calculated from the slopes of the lines. The intercept of a line with -1/β ) 0 is the natural logarithm of the frequency for a calcium ion to enter a kink site, νin. These values together with corresponding values found for columnar t-CPPD are given in Table 1. As compared under the same conditions of pH, degree of saturation of the solution, and degree of dissolution of the crystals, rates of dissolution per unit area, J/A0, of acicular t-CPPD are about a factor of 2 faster than those of columnar t-CPPD. If we assume the lengths of sides of the columnar crystals to have the ratio 5:3:1, we find from the specific surface area (0.6 m2/g) that an average crystal has the dimensions 10 µm × 6 µm × 2 µm and a surface area of approximately 180 µm2. An acicular crystal of the stock used here with shortest
pH
10-5 νin (s-1)
σ (mJ/m2)
4.5 5.0 5.5 6.0 6.5 7.0
3.5 2.0 2.1 1.1 1.1
27 24 30 26 33
columnar t-CPPD15 10-5 νin (s-1)
σ (mJ/m2)
3.4 1.6 1.1
33 30 31
dimensions 0.8 and 0.4 µm and with this surface area would have a length of approximately 75 µm. The acicular crystal has a total edge length of approximately four times that of the columnar crystal per unit surface area. There is a larger solution volume close to an ion in an edge position than to an ion in a surface position. Formation of dissolution nuclei (holes) from the {100} and {010} faces parallel to the long c-axis [001] may therefore be expected to be faster near edges than in regions with no edges. This may explain that νin for acicular t-CPPD is about a factor of 2 greater than νin for columnar t-CPPD under the same conditions. Growth. Figure 5 is a logarithmic plot of the rates of growth of acicular and columnar t-CPPD as a function of supersaturation, S - 1, for pH values 4.5, 5.5, and 6.5. These rates are plotted according to the polynuclear mechanism in Figure 6. The surface energy, calculated from the slopes of the lines in Figure 6, and the frequency for an ion to enter a growth site, given by the intercept of the lines with x ) 0, are given in Table 2. At low pH (4.5), rates of growth per unit area, J/A0, of acicular and columnar t-CPPD are very similar when compared under the same conditions. As pH increases (4.5 f 5.5 f 6.5), the rates are slower for acicular than for columnar crystals. At pH 5.5 and pH 6.5, the retardation is seen to increase with decreasing supersaturation. The latter effect is well-known for inhibition of crystal growth and dissolution of other crystals.20 We found17 that concentrations of P2O74- and CaP2O72ions in solution increase with increasing pH despite the decreasing total concentrations of PP and Ca. Chelation of P2O74- with Ca2+ in crystal surfaces could explain
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rate expression to rates affected by inhibition will give rise mathematically to higher apparent values of the surface energy and νin, as seen in Table 2. Conclusion
Figure 5. Logarithmic plot of rates of growth per unit area, J/A0, in molCPPD/s m2, against the supersaturation S - 1 for acicular t-CPPD (present work) and columnar t-CPPD.14 Diamonds, pH ) 4.5; squares, pH ) 5.5; circles, pH ) 6.5; solid symbols, acicular t-CPPD; open symbols, columnar t-CPPD. The slopes of the lines are 3.5, 3.9, and 3.9 for acicular t-CPPD and 3.0, 2.4, and 2.9 for columnar t-CPPD for pH 4.5, 5.5, and 6.5, respectively.
Figure 6. Plot of rates of growth of acicular t-CPPD (present work) and columnar t-CPPD14 according to the polynuclear mechanism. Diamonds, pH ) 4.5; squares, pH ) 5.5; circles, pH ) 6.5; solid symbols, acicular t-CPPD; open symbols, columnar t-CPPD. The slopes of the lines are 3.6, 7.3, and 9.1 for acicular t-CPPD and 4.2, 3.7, and 4.9 for columnar t-CPPD for pH 4.5, 5.5, and 6.5, respectively. The intercepts with -1/β ) 0 are ln(νin) with νin given in Table 2. Table 2. Results of Analysis of Rates of Growth According to the Polynuclear Mechanism acicular t-CPPD pH 4.5 5.5 6.5
10-5 ν
in
2.0 7 5
(s-1)
σ
(mJ/m2) 70 100 112
columnar t-CPPD14 10-5 ν
in
3.1 1.1 2.2
(s-1)
σ (mJ/m2) 76 71 82
the decreasing rates of growth and precipitation of m-CPPTβ with increasing supersaturation at pH 7. This effect, called autoinhibition, may also explain the present decrease in rates of acicular t-CPPD as compared to columnar t-CPPD, if chelation, and thereby inhibition, is particularly promoted by the larger solution volume available at edges. Application of a normal polynuclear
In vivo, the columnar morphology of t-CPPD has been observed and reported more often than t-CPPD with acicular morphology. In in vivo investigations, the acicular morphology may have been overlooked due to the smaller size of crystals with this morphology. There is also the possibility that in vivo conditions favor the formation of columnar crystals. This has not been addressed in the present work. If, on the other hand, crystals of both morphologies are formed in vivo, the results reported here that the columnar type has a slower dissolution rate per unit area and a faster growth rate per unit area as compared to acicular crystals and that the acicular morphologies show signs of autoinhibition in growth at neutral pH favor existence of the columnar type. List of Symbols Asp ) specific surface area of crystals; Asp0 ) 2.8 m2/g for acicular t-CPPD here a ) mean ionic activity; a ) IP1/3 for CPPD as ) mean ionic activity in a saturated solution; as ) Ks1/3 for CPPD d ) mean ionic diameter in crystal; d(CPPD) ) 3.36 × 10-10 m F(m/m0) ) term expressing the influence that the relative change in the mass of the crystals has on the geometry of the crystals and thereby on the overall rate of growth or dissolution g(C) ) term expressing the influence of solution composition on the rate of growth or dissolution gp(C) ) preexponential concentration term, polynuclear mechanism H ) constant; H ) kJ/νin ) 2dπ1/2Asp0/31/3ν, H ) 4.6 × 10-10 m3/g for the CPPD crystals used here IP ) ionic product J ) overall rate of growth or dissolution; J ) kJm0F(m/ m0)g(C) Ks ) ionic product for solubility product; pKs(CPPD) ) 18.35 used here k ) Boltzmann constant kJ ) overall rate constant m ) mass of crystals at time t n ) amount of substance (mol) PP ) pyrophosphate S ) supersaturation ratio; (IP/Ks)1/3 for CPPD; S ) a/as T ) absolute temperature t ) time R ) π(σd2/kT)2 β ) lnS ν ) number of particles in formula unit; for Ca2P2O7‚2H2O, ν)5 νin ) frequency for a calcium ion to enter a growth site F ) density; for CPPD, F ) 2.56 × 106 g/m3 σ ) Gibbs surface energy per unit area; surface tension subscript 0 ) value at t ) 0
Acknowledgment. We are most grateful for the technical assistance of Ms. Mette Kjær Schou and Ms. Julita Kuzimska, The Panum Institute. We acknowledge with thanks financial support from the Danish
Dissolution and Growth of Acicular Triclinic Crystals
Medical Research Council (J.C., M.R.C.), Gigtforeningen (The Arthritis Society), Denmark (J.C., M.R.C.), and the Vera and Carl Johan Michaelsen Foundation (J.C.). References (1) McCarty, D. J. In Arthritis and Allied Conditions; Koopman, W. J., Ed.; Williams and Wilkins: Baltimore, 1997; pp 81102. (2) Ryan, L. M.; McCarty, D. J. In Arthritis and Allied Conditions; Koopman, W. J., Ed.; Williams and Wilkins: Baltimore, 1997; pp 2103-2125. (3) Kaplan, J. eMedicine J. 2001, 2, 5. (4) Rothschild, B. M.; Bruno, M. A. eMedicine J. 2001, 2, 12. (5) Barkin, N. J. eMedicine J. 2002, 3, 1. (6) Saadeh, C.; Malacara, J. eMedicine J. 2002, 3, 3. (7) Pritzker, K. P. H. J. Am. Geriatr. Soc. 1980, 28, 439-445. (8) Beutler, A.; Rothfuss, S.; Clayburne, G.; Sieck, M.; Schumacher, H. R. Arthritis Rheum. 1993, 36, 704-715. (9) Swan, A.; Chapman, B.; Heap, P.; Seward, H.; Dieppe, P. Ann. Rheum. Dis. 1994, 53, 467-470. (10) Swan, A.; Heyward, B.; Chapman, B.; Seward, H.; Dieppe, P. Ann. Rheum. Dis. 1995, 54, 825-830.
Crystal Growth & Design, Vol. 2, No. 6, 2002 571 (11) Pritzker, K. P. H. In Osteoarthritis; Brandt, K. D., Doherty, M., Lohmander, L. S., Eds.; Oxford University Press: Oxford, 1998; pp 50-61. (12) Schumacher, H. R. In Osteoarthritis; Brandt, K. D., Doherty, M., Lohmander, L. S., Eds.; Oxford University Press: Oxford, 1998; pp 137-144. (13) Ryan, L. M.; Cheung, H. S. Osteoarthritis 1999, 25, 257267. (14) Christoffersen, M. R.; Balic-Zunic, T.; Pehrson, S.; Christoffersen, J. Cryst. Growth Des. 2001, 1, 463-466. (15) Christoffersen, M. R.; Seierby, N.; Balic-Zunic, T.; Christoffersen, J. J. Cryst. Growth 1999, 203, 234-243. (16) Balic-Zunic, T.; Christoffersen, M. R.; Christoffersen, J. Acta Crystallogr. 2000, B56, 953-958. (17) Christoffersen, M. R.; Balic-Zunic, T.; Pehrson, S.; Christoffersen, J. J. Cryst. Growth 2000, 212, 500-506. (18) Mandel, N. S. Acta Crystallogr. 1975, B31, 1730-1734. (19) Christoffersen, J.; Christoffersen, M. R.; Johansen, T. J. Cryst. Growth 1996, 163, 304-310. (20) Christoffersen, J.; Christoffersen, M. R.; Christensen, S. B.; Nancollas, G. H. J. Cryst. Growth 1983, 62, 254-264.
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