J . Phys. Chem. 1989, 93, 1628-1633
1628
Hydroxyapatite Formation in a Dynamic Collagen Gel System: Effects of Type I Collagen, Llplds, and Proteoglycans Adele L. Boskey Laboratory f o r Ultrastructural Biochemistry, The Hospital for Special Surgery, and Department of Biochemistry, Cornell University Medical College, New York, New York 10021 (Received: March 1 , 1988; In Final Form: July 15, 1988)
Hydroxyapatite formation was monitored in a denatured collagen gel system through which calcium and phosphate solutions circulated at a constant rate from an "infinite reservoir". With the use of 10%gelatin gels, 2-6 mL in volume, the diffusion coefficients for calcium and phosphate were 6.0 X 10" and 3.9 X lod cm2/s, respectively. In the absence of any other macromolecules, hydroxyapatite formation was detectable in the 3-mL gels at a point 1.54 0.02 mL (3.08 cm) from the end through which the calcium solution was being circulated after 5.5 & 0.5 days. At this time point the observed calcium and phosphate content adjacent to the central precipitant band was 37 mM2. The presence of hydroxyapatite was verified by X-ray diffraction, electron microscopy, and chemical analyses. Inclusion of 0.1 mL of lathyritic type I collagen fibers (1 mg/mL) or synthetic complexed acidic phospholipids (0.3-1.2 mg/mL) at the site where mineralization occurred in control gels decreased the time required for the formation of the first observable mineral deposit. The lipids increased the amount of mineral formed relative to the control gels at day 5 . Inclusion of 0.1 mL of 4-10 mg/mL articular cartilage proteoglycan aggregate or monomer preparations prevented mineral deposition during the 5-day period. Hydroxyapatite seeds (0.5-5 mg/mL) included in the 0.1 -mL central band proliferated, showing highly reproducible, detectable increases in mineral content at 2-6 days. The advantages of this unique dyhamic gel system for the study of hydroxyapatite formation and/or proliferation in the presence of other macromolecules include reproducibility and the need for only small amounts of macromolecules.
*
Introduction Crystal growth in gels is frequently used in the preparation of large crystals.' Recently, several investigators2-" have used gel growth systems for the study of the deposition of biologic minerals, and calcium pyrophosphate die.g., hydr~xyapatite~*~*~**-l~ h ~ d r a t e . ~Denatured .~~ collagen (gelatin) or intact collagenous matrices were used in several of these system^^,'"'^ in place of agar or silicates in order to allow mineral deposition to occur in a matrix analogous to that in calcifying tissues. However, with the exception of one study that used a polymer film as the matrix,12 the previously described systems suffered from the disadvantage that high concentrations of precipitating ions had to be included within or adjacent to the gels in order to allow mineral deposition to occur in a reasonable period of time. These high concentrations resulted in nonphysiologic concentration gradients and the formation of precipitates in Liesegang rings.ls The reactants in these static gel systems were also rapidly exhausted. In the above studies, macromolecules believed to be involved in control of biologic calcification were included throughout the gel, requiring large amounts of the suspect macromolecules and often changing the diffusion properties of the matrix. (1) Henisch, H. K. Crysrul Growth in Gels; Pennsylvania State University Press: University Park, PA, 1970. (2) Mandel, N . S.; Mandel, G. S. Scanning Electron Microsc. 1985, 4. 1779. (3) Pokric, B.; Pucar, Z. Calcif. Tissue Int. 1979, 27, 171. (4) Kibalczkyc, W.; Sokolowski, T.; Wiktorowska, B. Cryst. Res. Techno/. 1982, 17, Kl05: ( 5 ) LeGeros, R. 2.; LeGeros, J. P. J. Cryst. Growth 1972, 13, 476 (6) LeGeros. R. 2.: Morales. P. J. Inuest. Urol. 1973, 11, 12. (7) Rubin, B.; Saffir, A. Nuture!Imdon) 1970, 225, 78. (8) Udich, H. J.; Hoeft, H.; Boerring, H. Biomed. Biochim. Acta 1985, 44, 547. (9) Fujisawa, R.; Kuboki, Y.; Sasaki, S. Culcif. Tissue Inr. 1987, 41, 44. (IO) Hunter, G.K.; Allen, B. L.; Grynpas, M. D.; Cheng, P-T. Biochem. J . 1985, 226, 463. ( 1 1) Wilhelm, G. 2.Nuturforsch., C Biosci. 1977, 32C, 979. (12) de Jong, A. S. H.; Hak, T. J.; van Duijn, P. Connect. Tissue Res. 1980, 7 , 73. (13) Hunter, G. K.; Grynpas, M. D.; Cheng, P-T.; Pritker, K. A. Culcu. Tissue Int. 1987, 41, 164. (14) Pritzker, K. P. H.; Cheng, P-T.; Omar, S. A,; Nyburg, S. C. J. Rheumutol. 1981, 8, 451. (15) Liesegang, R. E. 2. Phys. Chem. 1914, 88, 1.
0022-3654/89/2093-1628$01.50/0
The purpose of this study was to develop a method for the study of hydroxyapatite formation and growth using a "biologic matrix" in which the effect of agents believed to be involved in the control of calcification could be examined. A system is described that is reproducible, requires relatively small amounts of matrix macromolecules, and is not subject to errors due to alteration in diffusion properties.
Materials and Methods The gels used for this study consisted of 10 wt % gelatin (Bloom No. 275, Fisher Chemical, Springfield, NJ) dissolved in 0.10 M NaCl and containing 0.01% sodium azide to prevent bacterial growth. The pH of the gelatin solution, prepared by stirring at 50 "C, was adjusted to 7.40 with 0.1 N NaOH. These conditions were selected, on the basis of preliminary studies, to give a matrix that was workable, was stable, and approximated physiologic solution composition. The gels were poured into 4-1 2 cm long sections cut from 10-mL (0.79-cm i.d.) serological polystyreneplugged sterile pipets (Kimble) and cooled to room temperature. The gels were then mounted on a device as shown in Figure 1. Calcium and phosphate solutions circulated at a continuous rate through this device, in separate loops at opposite ends of the gel. Solution flow was maintained by using an air pump, with the air washed through two separate saturated barium hydroxide solutions to remove carbon dioxide. The calcium and phosphate solutions were maintained at 3-4 L, providing an "infinite reservoir" relative to the 3-6" contents of the six to nine gels used for each experiment. The device was not thermostated, but the ambient temperature around the device was monitored, and experiments were not done if the temperature was outside the range of 20-25 "C. Physiologic temperatures could not be used, since the gelatin began to melt at 35 "C. Based on preliminary studies in which 1, 10, or 100 mM solutions were circulated through the system, the solution concentrations in the "infinite reservoirs", monitored at the start and end of each experiment, were maintained at 100 mM in order to allow for precipitate formation within a 1-week period. Diffusion coefficients, based on Fick's second-order differential equation, were calculated16 on the basis of single diffusion experiments with the gel exposed to either the calcium or phosphate (16) Pucar, 2.;Pokric, B.; Graovac, A. Anal. Chem. 1974, 46, 403
0 - 1989 American Chemical Societv
Hydroxyapatite Formation
Figure 1. Schematic diagram of the dynamic hydroxyapatite growth formation system. Calcium and phosphate solutions are pumped from infinite reservoirs (Ca, P) by using an air pump and regulators (AI-3). The carbon dioxide is removed from the air by washing through saturated barium hydroxide solutions (B). The gels are connected in parallel to the lines through which the calcium and phosphate arc being pumped. Mineral depasitian can be observed perpendicular to the direction of flow in the central band of the gel
solution. According to Fick’s law (eq 1) diffusion through a substance can be described as dc/dr = D d2c/d.9 (1) where x is the distance travelled from the origin, c the concentration, I the time, and D the coefficient of diffusion. Assuming an infinite cylinder exists at either side of the gelsolution interface, then initially at x < 0, c = co (the concentration of the circulating fluid), and c = 0 inside the gel (x > 0). The solution to the equation then becomes c = %co erf c ((x/2(D1)~/~))
(2) where erf (y) is the Gaussian error function. Diffusion coefficients were calculated by using eq 2, tabulations of the Gaussian error function, the measured c/co ratios as a function of x (calculated as the center of each sequential 0.3-cm slice) of gel analyzed, and I (time of sampling). For all experiments, gels were removed from the polystyrene tubes by using a Parafilm coated wooden plunger, which made a tight fit with the inner walls of the tube. The gel was then cut with a device consisting of equally spaced (0.3 cm apart) wires. The calcium” and phosphate18contents of the 0.3-cm-thick slices were measured at selected time periods during the course of the experiment (1-15 days). For these analyses, gel slices were dissolved by heating (50 “C) in 10 mL of 1.0 N HCI. (Repro(17) Willis. I. S. Sperrmhim. Aero 1960, 16. 259. (18) Hcinonen. J. K.;Lahti, R. J. Ami. Bimhcm. 1981. 113, 313.
The Journal of Physical Chemislry, Vol. 93, No. 4, 1989 1629 ducibility of slicing and analytical methods was assessed by weighing of random slices and by preparing uniform gels from solutions of known calcium or phosphate concentrations. These “test” gels were not used for gel growth studies, hut rather were analyzed immediately after preparation, and their composition was compared to that of the solution from which they were prepared. The “concentration factor” derived from these studies was used to convert the measured Ca and P contents of gel slices into millimolar concentration units. For all experiments other than those in which diffusion coefficients were monitored, calcium and phosphate solutions diffused through the gels from opposite ends (double diffusion). After a lag period (lag time) a thin opaque band (precipitant band) formed perpendicular to the direction of flow. In preliminary experiments, the lag time and the location of the band were monitored by using 4-12-cm-long gels. The location of the precipitant band was monitored by using the calibrated Kimble pipet and recorded in milliliters (1 mL being approximately 2 cm). The precise time required for initial precipitant band formation was determined by repeating the above experiment with the use of 2-, 3- and 4-mL gels, starting each gel 1.O h after the preceding one. Immediately after the band was observed, the gel was cut and the Ca and P contents of the 0.3-cm-thick slices on either side of the slice containing the precipitant band were determined. From the diffusion coefficients and by conversion of milliliters to centimeters in eq 2, the calcium and phosphate concentrations in the precipitant band at the time of observation were calculated and compared to the observed concentrations of these ions in the adjacent bands. The precipitant bands were used for mineral analyses (X-ray diffraction and SEM) as described below. Since the 2- and 3-mL gels were most reproducible, these were used for all further experiments. The applicability of the gel system for the characterization of promoters and inhibitors of hydroxyapatite formation and growth was tested by using well-characterized macromolecules. In preliminary studies these macromolecules were included throughout the 3-mL gel. However, this greatly altered the measured diffusion coefficients. The system was therefore modified so that 0.1 mL (consisting of 50 p L of the macromolecule in 0.1 M pH 7.4 Tris (tris(hydroxymetby1)aminomethane HCl) buffer and 50 p L of 20% gelatin) was placed a t the point that the precipitant band formed in control experiments. After 1.0 cm3 (4-cm gels) or 1.50 cm3 ( 6 c m gels) of the 10%gelatin had sct, the 0.1-mL suspension of macromolecule and 10% gelatin was added. Once this gel had set, without formation of any interfaces, it was covered with the IO% gel, providing a “sandwich” of blank gel, gel with macromolecule, blank gel. To verify that there was no spreading of components from the LOO-pL gel, control gels containing Tris buffer and methylene blue were prepared, and the spectroscopic properties of the central and adjacent hands were used to demonstrate the absence of mixing. The following macromolecules were included in the gels: 0.3-1.2 mg/mL synthetic complexed acidic phospholipids, 0-10 mg JmL protwglycan aggregate or monomer-containing fractions, and 1 mg/mL fibrillar collagen. The complexed acidic phospholipids, prepared from bovine bone as described elsewhere,19 promote hydroxyapatite formation in solution. They were prepared as a liposome dispersion for inclusion in the gel, by brief sonication ( I O X 1 min, 0 OC, Branson Heat Systems Sonicator, 100 W) of a dry lipid film in Tris buffer. The proteoglycans (kindly provided by Dr. L. Rosenberg, Montefiore Hospital, Bronx, NY) were extracted from fetal bovine articular or epiphyseal cartilage. In solution, similar proteoglycan aggregate and monomer-containing preparations are inhibitors of hydroxyapatite formation and g r o ~ t h . ” ~ ‘ Lathrytic rat skin collagen fibers (kindly pro(19) Baskey. A. L. Melob. Bone Dis. Relnl. Res. 1978. 1. 137. (20) Cuervo. A.: Pita, I. C.: Howell, D. S. ColciJ T i m e Res. 1973, 31, 1.
(21) Blumenthal. N. C.: Pasnu, A. S.: Silverman, L. D.: Roscnberg, L. C. Colcif. Tisrue Inl. 1979. 27, 75. (22) Chen. C. C.: Baskey. A. L.:Rascnberg. L. C. ColciJ Tislue Inl. I N , 36, 285.
Boskey
1630 The Journal of Physical Chemistry, Vol. 93, No. 4, 1989 $Measured value f SO 0 Theoretical value
0 l o t c L
e
+
.eo-
lag time?
a, C
gel vol 4 mL 3 cm 2 cm
.bo-
s H 0
E
TABLE I: Appearance of First Precipitant Band“ in Gelatin Gels
4
.40-
is
.20-
2
I
I 0
i
LO5
.35
1,75
2.45
3.15
Distance ( c m )
A
* SD
$Measured value Theoretical value
1 .O+ C
.e
e .EO-
days 8 f le,/ 5.5 f 0.41 3.2 f 0.9
critical concnC Ca P obsd calcd obsd calcd 6.8 6.7 6.8
5.8c*/ 4.6 5.2
6.1 5.5 6.1
5.61 5.0 5.7
Ca/pd 1.78 1.80 1.70
All central bands were shown to be hydroxyapatite by X-ray diffraction analyses. bTime at which first observable band (width 50.05 cm) was noted in a series of experiments (n = 12) staggered by I-h intervals. Critical concentration is concentration (mM) at which first precipitation occurs. It is estimated here from the observed Ca and P contents of bands adjacent to the precipitant band, and from the calculated concentration (based on Fick’s law) of the central band at the lag time. All values are means; SD 5 12%. dCa:P molar ratio of the central precipitant band, SD I8%. CSignificantlydifferent from 3-mL gels, p 6 0.010. /Significantly different from 2-mL gels, p 6 0.015.
c
0)
C
2 60-
I
0
.35
1.05
1.75
v
2.45
a 3.15
Distance (cm)
B
Figure 2. Observed and calculated Ca (A) and P (B) contents of 4-cmlong (2 mL) gels at 2 days. Diffusion coefficients calculated from Fick’s
second law of diffusion were used for calculations. Values are normalized relative to the concentrations in the solutions that entered the gels. vided by Dr. A. Veis, Northwestern University, Chicago, IL) were prepared for inclusion in the gel (1 mg/mL) by dialysis of an acetate solubilized extract (1.13 mg/mL) against Tris buffer, centrifugation of large fibrils, and thermal gelation of the supernate at 35 “C. For each concentration of matrix molecule, the time and location of appearance of the precipitant band was noted, and gels were analyzed for Ca and P content, as described above, 5.0 days after the start of the experiment. For those experiments in which no precipitant band was seen at 4 days, additional gels were analyzed after the appearance of the band. (Gels containing bands greater than 0.1 cm wide or more than one band Liesegang ringsi5 were excluded since the initial band had been missed; this occurred for seven out of 91 total experiments). In some experiments, to correct for Ca or P binding by the matrix molecules, single-diffusion experiments including the macromolecules being tested were run parallel to each double-diffusion experiment, and diffusion constants were verified for each concentration of macromolecule. The increase in Ca and P content of the precipitant band, beyond that due to diffusion, was calculated by comparison to the single-diffusion data. All experiments were repeated at least in triplicate: control gels, containing the same buffers in the absence of macromolecules, were included for all analyses. At least one gel containing each of the macromolecules studied was used to supply a precipitant band for X-ray diffraction or SEM analysis. For X-ray diffraction, the gelatin was removed by heating the slice to 50 “ C followed by immediate microcentrifugation. The pellet obtained after repeating the melting procedure was immediately subjected to wide-angle X-ray diffraction analysis using Cu K-cu radiation on a Siemens automated powder diffractometer. A second gel band was dehydrated in graded ethanols, Pd-coated, and examined with an Amray scanning electron microscope. Hydroxyapatite-seeded growth was examined in the gel growth system by placing 100-pL volumes containing 0.5-5 mg/mL ~~~
I
t
I
40
30
20
28 Figure 3. Wide-angle X-ray diffraction pattern (Cu Ka radiation) demonstrating the presence of hydroxyapatitein the precipitant band of a 3-mL gelatin gel at 5 days. Similar patterns were observed for all
experiments in which precipitant bands were subjected to diffraction analyses. well-characterized hydroxyapatite (prepared by refluxing at 75 OCZ5),sieved to uniform (45 pm) size and incubated in Tris buffer for 24 h, in 10% gelatin, above 1.5 mL of collagen gel in the 3-mL gel. At 1-4 days, the gels were sliced, and the Ca and P contents of the hydroxyapatite-containing band were determined and compared to that in similar hydroxyapatite-containing gels that had not been exposed to the circulating calcium and phosphate solutions. Results Diffusion coefficients were calculated by using the data from 3-, 4- and 6-mL gels at 2-4 days. The calculated diffusion coefficients (6.0 f 0.5 X 10” and 3.9 f 0.2 X 10” cm2/s; mean f SD, n = 12) for calcium and phosphate, respectively, gave excellent agreement with the measured calcium and phosphate contents of the gels (Figure 2a,b). The reproducibility of the slicing technique used to make these measurements is seen both from the constancy of the gel weights (0.320 f 0.008 g; mean f SD, n = 30) and from the calcium and phosphate analyses of gels prepared with either 10.0 mM calcium or 10.0 mM phosphate, shown to contain 10.39 f 0.1 1 mM Ca and 9.77 f 1.61 mM P (n = 27). The time at which the first precipitant band (width 5 0 . 2 cm) was noted in control (gelatin only) gels of different lengths, and the “critical concentrations”, defined as either the observed Ca and P content of the gel adjacent to the precipitant band3 or the calculated Ca and P content in the precipitant band at the time the band was detected, are presented in Table I. The lag times were significantly different in the 2-, 3- and 4-mL gels. The critical concentrations measured (6.7-6.8 X 5.5-6.1 mMZ) were not
~
(23) Chen, C. C.; Boskey, A. L. Calcif. Tissue In!. 1985, 37, 395. (24) Chen, C. C.; Boskey, A. L. Calcif. Tissue In?. 1986, 38, 324.
(25) Blumenthal, N. C.; Posner, A. S.;Holmes, J. M. Mater. Res. Bull. 1972, 7, 1181.
The Journal of Physical Chemistry, Vol. 93, No. 4 , 1989 1631
Hydroxyapatite Formation TABLE 11: Appearance of First Precipitant Band in Gelatin Gels" Containing Other Macromoleculesb
macromolecule proteoglycan monomersC 5 mg/mL 10 mg/mL proteoglycan aggregatese 10 mg/mL complexed acidic phospholipids 0.3 mg/mL 0.6 mg/mL 1.2 mg/mL fibrillar collagen 1 mg/mL gelatin only
lag time, days
TABLE IV: Mineral Accumulation" in Central Precipitant Band at 7 Daw
gel contents proteoglycan aggregatesb 1 mg/mL 2 mg/mL 4 mg/mL gelatin only
5.3 f 0.6d 6 f Id
Ca, mM
P, mM
34.5 f 4.6 25.1 f 1.6c 26.8 f l C 36.3 i 0.9
20.3 f 2 18.7 f 1.9c 18.7 f 3c 23.1 f 2
"Corrected for Ca and P present in gel due to diffusion or binding to the matrix. Mineral shown to be hydroxyapatite by XRD and/or EM. Bovine fetal epiphyses proteoglycan aggregate preparation. 'Significantly different from gelatin gels, p 5 0.05, n = 6 for gels containing proteoglycans, n = 9 for gelatin only.
2.7 f 0.2 2.5 f 0.3d 2.4 f 0.2d
2.5 f 0.6 3.2 f 0.8
'Data for 2-mL (4 cm long) gels. 100-pL solutions of the macromolecules in 10%gelatin gels were included 2.0 cm from the end of the 4-cm-long (2 mL) gels; n = 3 for all but gelatin only (n = 12). Bovine articular proteoglycan preparations. dSignificantly different from gels without macromolecules (gelatin only), P 5 0.05 on the basis of Student I test.
0
mM C a i S D (n.3)
o mM P i + S D (n.3)
TABLE 111: Calcium and Phosphate Content of Center Precipitant Bands in 3-mL Gels at 5 Days
gel constituents' gelatin only single diffusion double diffusion fibrillar collagen 1 mg/mL complexed acidic phospholipids 1.2 mg/mL proteoglycan monomer 10 mg/mL 5 mg/mL 2.5 mg/mL I .25 mg/mL proteoglycan aggregate 5 mg/mL 10 mg/mL
Ca. mM
_ _ _ ~ ~
P. mM
6.95 f 1.4
n HAb 9 9
20.1 f 3.2c
7.96 f 1.4 11.1 f 1.4e
16.2 f 2.5c
11.4 f 3.6'qd
9 X
24.8 f 1.8C3d 12.1 f 1.3c
5 X
7 X, S
5.55 f 3d 3.03 f 1.7c3d 3 6.94 f 0.9d 4.06 f lcvd 4 7.35 f I d 3.44 f 2c.d 4 11.1 f 5.55 f 2d 3 X, S jcsd
5.45 f 3d 4.53 f 2d
2.50 f qCsd 4 2.03 f 0.7C*d3
"Central band contained 100 pL or constituent listed. bPresenceof hydroxyapatite (or mineral crystals) was demonstrated by X-ray diffraction (X) or scanning electron microscopy (S). CSignificantlydifferent from single-diffusion control, p 5 0.01. dSignificantlydifferent from double-diffusion gelatin-only control, p 5 0.001, significantly different. The calculated critical concentrations were always lower than that measured in the adjacent bands. Only calculated critical concentrations in the 4-mL gel differed from the others (p < 0.015). Throughout these experiments, the precipitant band occurred closer to the side of the gel through which the phosphate entered. In the 3-mL gels, for all control gels ( n = 4 9 , the band was 1.54 f 0.02 mL (3.1 cm) from the side from which the calcium entered. The presence of hydroxyapatite in these bands was confirmed by X-ray diffraction analysis (Figure 3). N o mineral phases other than hydroxyapatite were detected in any of the experiments. A limited number of experiments were performed to determine the effect of different macromolecules on the observed lag time (Table 11). The 2-mL gel was used because of concern about proteoglycan degradation during the extensive lag times noted in preliminary 3-mL gel experiments. Complexed acidic phospholipids promoted hydroxyapatite formation while the proteoglycans inhibited mineral deposition. In the 2-mL gels, proteoglycan monomers increased the lag time, although the apparent dose response was not statistically significant. The proteoglycan-aggregate-containing preparation (in physiologic concentrations of IO mg/mLZ6did not show precipitant bands after 2 weeks. In gels with fibrillar collagen, precipitant bands were detected earlier (26) Howell, D. S.; Pita, J. C . Clin. Orthop. Relat. Res. 1916, 118, 208.
"
0
1
2
3
4
5
6
Days Figure 4. Time-dependent accumulation of calcium and phosphate in gels containing 1 mg/mL hydroxyapatite in a 100-pL central band. Values are seen f SD for three determinations.
than in control gels, although the measured lag times did not differ significantly. Table 111 presents the total concentrations of Ca and P in the 0.3-cm-thick precipitant bands at 5 days. At this time, when initial mineral bands were visible in controls, the Ca and P contents of the central bands were not significantly different from the Ca or P content due to diffusion only, in gels containing 2.5-10 mg/mL bovine articular cartilage proteoglycan monomers, or 5 and 10 mg/mL bovine articular cartilage proteoglycan aggregates. In these gels, in fact, the P content was significantly less than that of the single-diffusion gelatin-only controls. The gels with 1.25 mg/mL proteoglycan monomers acquired more Ca than the diffusion controls, although P contents were not different. The mineral ion contents of gels with and without fibrillar collagen were not significantly different, while gels with 1.2 mg/mL complexed acidic phospholipids had significantly more mineral ions than the control. X-ray diffraction analyses confirmed the presence of hydroxyapatite in all precipitant bands. Precipitant bands formed in the presence of proteoglycans showed the presence of Ca, P, Na, C1, and S by X-ray microanalysis, while all other precipitates lacked S (not shown). By including single-diffusion experiments containing the same concentration of macromolecules as in the double-diffusion experiments, the Ca and P contents of the central precipitant band could be corrected for the presence of ions due to diffusion or binding to the matrix. Table IV shows a series of experiments using three concentrations of bovine epiphyseal proteoglycan aggregates, in which 1 mg/mL was not an effective inhibitor, accumulating as much mineral, beyond that due to matrix binding and diffusion, as the gelatin-only gels. Higher concentrations of this proteoglycan aggregate preparation (2 and 4 mg/mL) significantly decreased the amount of Ca and P accumulated. The mineral contents of the gels containing 2 and 4 mg/mL proteoglycan, however, were not significantly different. Calculated
1632
The Journal of Physical Chemistry, Vol. 93, No. 4, 1989
diffusion coefficients from these experiments did not differ from gelatin-only controls. Figure 4 shows the time-dependent accumulation of Ca and P in the central band of the gels containing 1 mg/mL hydroxyapatite. Similar data were seen with 0.5, 2, and 5 mg/mL. The average Ca:P molar ratio of these central bands was 1.64 f 0.16, in contrast to 1.44 f 0.21 for samples of the hydroxyapatite imbedded in the gel but not mounted on the gel apparatus. The hydroxyapatite seeds used for these experiments had a Ca:P molar ratio of 1.57 f 0.05, the difference between the 1.44 and 1.57 ratios being attributable to the small but detectable phosphate content of the collagen gel.
Discussion This study has demonstrated that a dynamic gel growth system can be used as a model for the study of mineralization by physiologically relevant macromolecules. In this system, independent of Ca X P concentrations and the presence of macromolecules, hydroxyapatite deposited at a constant location, slightly closer to the end of the gel through which the phosphate entered. Brushite, octacalcium phosphate, and amorphous calcium phosphate found in static gel growth systems@ were not detected. Even where Ca/P ratios were less than the stoichiometric 1.7:1,no other phases were detected. The unique feature of the gel growth system described in this study is the continuous flow of calcium and phosphate ions into the matrix. This flow is from a reservoir that approximates an infinite reservoir relative to the volume of the matrix. This elimination problems inherent in layering a concentrated solution within or on top of the gel and/or of using a gel in which the diffusing solution is exhausted due to binding to constituent macromolecules. In addition, including the macromolecule to be tested in a small region determined to be the site of mineral deposition eliminates problems due to alteration in diffusion constant and enables analyses using macromolecules available in limited supply. The Liesegang rings,I5 formed in other gel systems5-6*'0J3 as one ionic reactant diffuses into a concentrated solution of the other, can be avoided since at the low supersaturation in the center of the gel, nucleation will pred~minate:~while at the higher supersaturations that are reached as the concentration in the center of the gel increases, crystal growth on these initial crystal nuclei will p r e d ~ m i n a t e . ' ~With . ~ ~ time, as the Ca X P product increases, Liesegang rings will form in this system; selecting sufficiently short time points to see the actions of promoters or inhibitors of mineral deposition can eliminate this problem. Within the dynamic gel system, Fick's second law is obeyed16 until precipitation occurs. Measured diffusion coefficients can thus be used to approximate the concentrations at the time of initial mineral deposition. The diffusion rates are relatively slow; thus the inclusion of a narrow segment with potentially altered diffusion properties did not appear to alter the measured diffusion properties of the system. Several different parameters can provide insight into the effect of macromolecules on mineralization in the dynamic gel system. Recording the time at which the initial precipitant band is visible provides an estimate of the potentiating or inhibitory effects of the macromolecules in the central band. This is the least reliable measurement, since it is dependent on constant observation of the gels and is subject to observer error. Measuring the Ca and P contents adjacent to the precipitant band or calculating the Ca and P content at the estimated time of precipitation provides only a slightly more quantitative assessment. Ion clusters and nuclei present in these regions cause overestimation of the "critical concentration". These measurements are also dependent on noting a reproducible time of initial precipitant band formation. The most reliable parameter is the Ca and P content of the precipitant band at a fixed time point. This parameter can be corrected for the presence of Ca and P due to diffusion or binding to the macromolecules present and can be compared to values in the absence of macromolecules. Although the concentrations of the solutions circulating into the gels in this in vitro mineralization model were much higher
Boskey than physiologic, hydroxyapatite formation (as indicated by X-ray diffraction, SEM, and chemical analysis) occurred when the Ca X P mM2 product was less than or equal to 7 mM X 6 mM. This is in agreement with the static double-diffusion study of Pokric et aL3in which the concentrations at the time of initial precipitation (10% gelatin, 0.15 M NaC1, pH 7.4, 25 "C) were 4.5 X 4.7 mM2. Inclusion of type I fibrillar collagen decreased the time required to see the first precipitate, but did not affect the Ca and P content of the central band at 5.0 days. Pokric et aL3 also reported that 10% reconstituted collagen (at 37 "C) had a lower (3.7 X 3.7 mM2) critical concentration, but similar to the results found here, the fibrillar collagen did not promote calcium phosphate formation. Recent data2' suggest that collagen itself is not a hydroxyapatite nucleator, although it was originally proposed to serve this f ~ n c t i o n . ~It. ~is ~more likely that the fibrillar collagen, as distinct from the gelatin, is providing an oriented framework that facilitates initial oriented mineral deposition. The decreased critical concentration (the Ca X P product at the time of initial mineral deposition) may be related to the ability to see the mineral when it is aligned on the collagen fibrils. The dynamic gel system provides a reproducible means for characterizing the effects of macromolecules that were available in limited quantities. A mineralization promoter, the complexed acidic phospholipids, and an inhibitor, the proteoglycans, were examined as model systems. The complexed acidic phospholipids lowered the time required for mineral formation and the critical concentration required for mineralization while increasing the amount of mineral present at 5 days. The complexed acidic phospholipids are in vitro and in vivo promoters of hydroxyapatite f ~ r m a t i o n . ' They ~ ~ ~ appear to have a similar effect in the collagen gel system, decreasing the concentration of Ca and P needed for initial mineral deposition to values closer to those that exist in the fluids around mineralizing tissues.31 Proteoglycans, which are inhibitors of hydroxyapatite formation and growth in s ~ l u t i o n , ~retarded *~~ hydroxyapatite formation in this system. Since certain (dermatan sulfate) proteoglycans are known to interact with ~ o l l a g e n , ~it" ~is~possible that such interactions between the chondroitin sulfate proteoglycans and the collagen could have contributed to this inhibition. Hunter et a1.I0 similarly observed that the predominant glycosaminoglycan of cartilage proteoglycans, chondroitin sulfate (10-30 mg/mL), prevented hydroxyapatite formation in a gel system, but at this high concentration, the predominant effect was likely one of calcium binding. Ca chelation by proteoglycans in the present study was minimized due to the presence of 0.1 M NaC1.35 By subtraction of the Ca or P content of the central band exposed to either Ca or P (single-diffusion) from the ion contents of the precipitant band, any effects of such chelation are eliminated. Thus the data for the bovine epiphyseal proteoglycan aggregates show an inhibitory effect in the absence of Ca chelation. Since nucleation may occur at lower critical concentrations in the presence of certain macromolecules, this data treatment has certain limitations. The lack of difference between gels with 2 and 4 mg/mL proteoglycan aggregates might be attributed to such limitations. The mineral content of the precipitant bands at 5-7 days provides insight into both crystal growth and nucleation rather than nucleation alone. Experiments using hydroxyapatite seed crystals suggest the effects on mineral proliferation can be (27) Termine, J. D., Kleinman, H. K.; Whitson, S. W.; Conn, K. M.; McGarvery, M. L.; Martin, G. R. Cell, (Cambridge, Mass.) 1981, 26, 99. (28) Glimcher, M. J. Reu. Mod. Phys. 1959, 31, 359. (29) Glimcher, M. J.; Krane, S. M. In Treatise on Collagen I Z B Ramachandran, G.N . , Gould, B. S., Eds.; Academic: New York, 1968; p 68. (30) Raggio, C. L.; Boyan, B. D.; Boskey, A. L. J . Bone Miner. Res. 1986, I , 5. (31) Howell, D. S . ; Pita, J. C.; Marquez, J. F.; Madruga, J. E. J . Clin. Inuest. 1968, 47, 1121. (32) Toole, B. P.; Lowther, D. A. Biochem. J . 1968, 109, 857. (33) Vogel, K. S.;Paulsson, M.;Heinegard, D. Biochem. J . 1984,223,587. (34) Scott, J . E.; Haigh, M. Biochem. SOC.Trans. 1985, 14, 933. (35) Blumenthal, N. C. In The Chemistry and Biology of Mineralized Connectiue Tissues; Veis, A,, Ed.; Elsevier: New York, 1981; p 509.
J . Phys. Chem. 1989, 93, 1633-1637 monitored in this dynamic gel system. In the future, combining matrix molecules with fibrillar collagen or hydroxyapatite seed crystals will greatly expand the potential of the dynamic gel system.
Acknowledgment. I especially thank Mr. Andrew J. Burstein for designing the gel system, and Dr. A. Veis and Dr. L. Rosenberg for supplying the macromolecules tested in this study. The assistance of Mr. Tony Labastierre and the staff of the Department
1633
of Pathology at the Hospital for Special Surgery, who helped in the preparation and evaluation of the electron micrographs, and of Mr. Darryl Jonas, Ms. Pegeen Mularchuk, Ms. Mary Mckeveny, Mr. Wil Armentano, and Mr. Michael Maresca is gratefully acknowledged. This work was supported by NIH Grant DE 04141. Registry No. Ca, 7440-70-2; PO:-,
14265-44-2.
Long-Range Electron Transfer within the Hexamer of the Photosynthetic Reaction Center Rhodopseudomonas viridis P. 0. J. Scherer and Sighart F. Fischer* Technische Universitat Munchen, Theoretische Physik, 0-8046 Garching, FRG (Received: April 22, 1988; In Final Form: June 30, 1988)
Quantum calculations of the INDO-SCI type are performed for the hexamer of the central prosthetic groups of the reaction center Rhodopseudomonas uiridis. The lowest electronic excitations including 28 charge-transfer states are analyzed with regard to their configuration interactions.
Introduction In photosynthetic reaction centers such as Rps. Viridis or Rb. sphaeroides a very rapid charge separation takes place after excitation of the bacteriochlorophyll dimer P. The first detected charge-separated state P+HL- is formed in 2.8 ps'J and has the negative charge on the bacteriopheophytine HL. This pigment is separated from P by about 17 A. Between P and HL an accessory bacteriochlorophyll BL is located so that it can mediate the electron transfer. These pigments belong to the so-called L branch of the protein. An almost symmetrically arranged pair BM and HM on the so-called M branch seems to be inactive in the charge-separation process. Since the structure of the reaction centers Rps. viridis3 and Rb. sphaeroides4 has been resolved, several attempts have been made to understand its function from a quantum mechanical point of vie^.^-^ The high interest in these systems is motivated by the observations that the charge separation is extremely efficient (lOO%)'O and the energy loss into the surrounding medium is relatively small (less than 20%). Once it becomes clear which structural features are essential for the function, it might be possible to construct artificial systems with similar properties that could be useful for solar energy conversion and energy storage. In this article we present quantum calculations for the full hexamer consisting of four bacteriochlorophyll monomers BM, PL, PM, and BL as well as two bacteriopheophytins HM and HL together with four histidines, which are attached to the Mg atoms
of the four bacteriochlorophylls. The monomers PLand PMform the dimer P. The results indicate that the rapid charge separation may be an outcome of a special molecular engineering of the pigments. Due to an energetically close arrangement of the lowest unoccupied orbitals a certain delocalization of these orbitals is achieved. This delocalization depends on the coupling between localized orbitals as well as their relative energy differences. Here we show that the energy spacing of these self-consistent field (SCF) orbitals affects the configuration interaction (CI) between the excited states in a very sensitive way. Within our calculations charge-transfer states such as P'HLare treated as excited configurations in the same way as the initially excited dimer state P*. We analyze the final interaction responsible for a transition from P* to P'HL- in terms of oneparticle interactions, CI coupling constants, and energy differences between orbitals as well as those between states. Compared to the energy differences, the extracted coupling constants should be less sensitive to further refinements of the coordinates and model assumptions about the calculated reaction center complex. We consider three mechanisms, the direct electron transfer from P* to P+HL-and two indirect transfers invoking P+BL- or BL'HLas intermediates. We show how the energetics can favor one or the other. It is interesting to note that the direct coupling becomes relatively large in the basis of partially delocalized orbitals. To understand this new result, it is essential to distinguish between orbital tuning and the energetics of states.
(1) Martin, J. L.; Breton, J.; Hoff, A. J.; Migus, A.; Antonetti, A. Proc. Natl. Acad. Sci. U.S.A. 1986, 83, 957. (2) Breton, J.; Martin, J. L.; Migus, A.; Antonetti, A.; Orsay, A. Proc. Natl. Acad. Sci. U.S.A. 1986, 83, 5121. (3) Deisenhofer, J.; Epp, 0.;Huber, R.; Michel, H. J. Mol. B i d . 1984, 180, 385. Michel, H.; Epp, 0.; Deisenhofer, J. EMDO J. 1986, 5, 2445. (4) Allen, J. P.; Feher, G.; Yeates, T. 0.;Komiya, H.; Rees, D. C. Proc. Natl. Acad. Sci. U.S.A. 1987, 84, 5730. (5) Fischer, S. F.; Scherer, P. 0. J. Chem. Phys. 1987, 115, 151. (6) Scherer, P. 0. J.; Fischer, S. F. Chem. Phys. Lett. 1987, 141, 179. (7) Kuhn, H. Phys. Rev. A: Gen. Phys. 1986, 34, 3409. (8) Warshel, A.; Creighton, S.; Parson, W. W. J . Phys. Chem. 1988, 92, 2696. (9) Michel-Beyerle, M. E.; Plato, M.; Deisenhofer, J.; Michel, H.; Bixon, M.: Jortner, J. Bimhim. Biophys. Acta 1987, 932, 52. (IO) Wraight, C. A.; Clayton, R. K. Biochim. Biophys. Acta 1974, 246, 333.
Methods We included 518 atoms (1400 atomic orbitals of the s and p type). We used a modified version of the QCPE 372 program (INDO-SCI). The parametrization was chosen as in ref 11. However, we preferred to takefy = 1 to have y = e Z / Rfor large distances. The Mg atoms were treated in the sp approximation. The Slater exponent for Mg was taken from ref 12. For distances larger than 2.8 8, the resonance integrals Pij were reduced as in ref 13.
0022-3654/89/ 2093-1633$01.50/0 . , I
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(11) Ridley, J.; Zerner, M. Theor. Chim. Acto. 1973, 32, 111. (12) Gordon, M. S.; Bjorke, M. D.; Marsh, F. J.; Korth, M. S . J. Am. Chem. SOC.1978, 100, 2670.
0 1989 American Chemical Society
