Published online before print July 3, 2008, doi: 10.1161/CIRCRESAHA.108.178996
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© 2008 American Heart Association, Inc.
Molecular Medicine |
Protein Kinase A–Mediated Phosphorylation of cMyBP-C Increases Proximity of Myosin Heads to Actin in Resting Myocardium
From the Department of Physiology (B.A.C., M.R.L., D.P.F., R.L.M.), University of Wisconsin Medical School, Madison, Wis; and CSRRI and the Department of BCPS (T.B., T.C.I.), Illinois Institute of Technology, Chicago, Ill.
Correspondence to Brett Colson, 601 Science Drive, Madison, WI 53711. E-mail bacolson{at}wisc.edu
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Abstract |
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Protein kinase A–mediated (PKA) phosphorylation of cardiac myosin binding protein C (cMyBP-C) accelerates the kinetics of cross-bridge cycling and may relieve the tether-like constraint of myosin heads imposed by cMyBP-C. We favor a mechanism in which cMyBP-C modulates cross-bridge cycling kinetics by regulating the proximity and interaction of myosin and actin. To test this idea, we used synchrotron low-angle x-ray diffraction to measure interthick filament lattice spacing and the equatorial intensity ratio, I11/I10, in skinned trabeculae isolated from wild-type and cMyBP-C null (cMyBP-C–/–) mice. In wild-type myocardium, PKA treatment appeared to result in radial or azimuthal displacement of cross-bridges away from the thick filaments as indicated by an increase (approximately 50%) in I11/I10 (0.22±0.03 versus 0.33±0.03). Conversely, PKA treatment did not affect cross-bridge disposition in mice lacking cMyBP-C, because there was no difference in I11/I10 between untreated and PKA-treated cMyBP-C–/– myocardium (0.40±0.06 versus 0.42±0.05). Although lattice spacing did not change after treatment in wild-type (45.68±0.84 nm versus 45.64±0.64 nm), treatment of cMyBP-C–/– myocardium increased lattice spacing (46.80±0.92 nm versus 49.61±0.59 nm). This result is consistent with the idea that the myofilament lattice expands after PKA phosphorylation of cardiac troponin I, and when present, cMyBP-C, may stabilize the lattice. These data support our hypothesis that tethering of cross-bridges by cMyBP-C is relieved by phosphorylation of PKA sites in cMyBP-C, thereby increasing the proximity of cross-bridges to actin and increasing the probability of interaction with actin on contraction.
Key Words: contractile protein structure • cross-bridge kinetics • cMyBP-C • protein kinase A phosphorylation • x-ray
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Introduction |
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In myocardium, the phosphorylation status of myofibrillar proteins affects protein function, which leads to changes in Ca2+-activated force and the rate at which force is developed, presumably by changing myofilament structure. In response to β-adrenergic stimulation of the heart, phosphorylation by protein kinase A (PKA) is a short-term modulator of myocardial work capacity. Cardiac myosin binding protein C (cMyBP-C), which binds tightly to myosin, is a substrate for PKA, and its phosphorylation is likely to play an important role in the regulation of cardiac contractility,1,2 possibly by accelerating the rates of force development in systole and the rates of relaxation in diastole.3,4 Conversely, the lack of cMyBP-C3–8 or decreased levels of cMyBP-C phosphorylation9 lead to cardiac dysfunction.
Although cAMP activation of PKA targets cMyBP-C in the thick filament, PKA targets primarily troponin I (cTnI) in the thin filament. In skinned myocardium, phosphorylation of cTnI regulates the Ca2+-sensitivity of force, and phosphorylation of cMyBP-C regulates the rates of cross-bridge cycling.3,4 With regard to the role of cMyBP-C in the regulation of contraction kinetics, we favor a working model of regulation in which PKA phosphorylation of cMyBP-C accelerates the kinetics of cross-bridge cycling and stretch activation (and presumably systolic ejection) by regulating the proximity and subsequent interaction of myosin and actin. In examining low-resolution electron micrographs of isolated thick filaments, PKA phosphorylation of cMyBP-C appears to increase the diameter of thick filaments, which has been interpreted as radial displacement of cross-bridges away from the thick filament backbone10,11; however, this interpretation has yet to be tested in intact muscles.
Emerging evidence suggests that cross-bridge kinetics and the level of cooperative activation of the thin filament change by a structural mechanism in which cMyBP-C affects the location of cross-bridges relative to the thick filament backbone. We have recently shown that myocardium from mutant mice lacking cMyBP-C (cMyBP-C–/–) differ from wild-type (WT) myocardium in that myosin heads are located further from the surface of the thick filament and closer to actin.12 Similar to the effect of ablation, PKA-mediated phosphorylation of cMyBP-C has been postulated to relieve the collar-like constraint of myosin heads.10 In this regard, both phosphorylation and ablation of cMyBP-C appear to have similar effects to accelerate cross-bridge cycling kinetics.3,4 It remains unresolved whether the structural mechanisms underlying the accelerated kinetics are the same in the 2 cases.
The kinetics of myocardial force development are accelerated by β-adrenergic agonists, in part due to PKA-mediated phosphorylation of myofibrillar proteins, especially cMyBP-C.13 We propose that phosphorylation of cMyBP-C causes myosin cross-bridges to move radially or azimuthally toward the thin filament by alleviating a physical constraint, similar to the model proposed by Winegrad,10 thereby accelerating the rate of binding to actin during contraction. To determine whether cMyBP-C phosphorylation affects cross-bridge position, we treated WT and cMyBP-C–/– myocardium with PKA to induce phosphorylation of myofibrillar proteins (including cMyBP-C in WT and excluding cMyBP-C in cMyBP-C–/–) and then assessed the ratio of the 1,1 to the 1,0 equatorial reflections (I11/I10) as a measure of the proximity of myosin heads to actin in myocardium under resting conditions. We found that only WT myocardium exhibited changes in equatorial intensities due to PKA phosphorylation from a typical relaxed pattern toward that of a contracting or rigor pattern. In contrast, cMyBP-C–/– null myocardium showed no change before and after PKA treatment, presumably because the structural constraint on myosin position was already relieved due to ablation of cMyBP-C.5,12
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Materials and Methods |
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Experimental Animals
Homozygous cMyBP-C null mice (cMyBP-C–/–) were generated as described.4 WT SV/129-strain mice (6 to 12 months old; either sex) were obtained from Taconic Farms (Germantown, NY). Animal use was conducted in accordance with institutional guidelines using protocols approved by the Animal Care and Use Committee of the University of Wisconsin School of Medicine and Public Health.
Experimental Solutions
Experimental solutions for dissections and x-ray diffraction measurements were prepared as described.12 Additionally, mechanical measurements made on skinned trabeculae used solutions containing different amounts of [Ca2+]free (pCa 6.1 to 5.3), which were made by mixing pCa 9.0 and pCa 4.5 solutions (pCa 4.5 solution contained the same concentrations of chemicals as pCa 9.0 except for [mM] 7.01 CaCl2, 5.29 MgCl2, and 4.72 ATP). Preactivating solution alternatively contained (mM) 0.07 EGTA, 5.29 MgCl2, and 4.67 ATP.
Isolation of Skinned Trabeculae
Mice were anesthetized and euthanized as described.12 Hearts were rapidly excised and placed in a petri dish containing modified Tyrodes solution ([mM] 120 NaCl, 5 KCl, 1.2 MgSO4, 19 NaHCO3, 1.2 Na2HPO4, 10 glucose, 1 CaCl2, and 30 2,3-butanedione monoxime, and the pH was adjusted to 7.0 by bubbling with 95% O2/5% CO2 for 30 minutes16,17). Trabeculae were dissected, skinned, and stored as described.12
Trabeculae Mounting
Trabeculae were mounted in a simple x-ray chamber18 and sarcomere length was set19,20 to approximately 2.15±0.01 µm as described.12 For PKA treatment experiments, mounted trabeculae were incubated for 1 hour (22°C) in pCa 9.0 solution, which contained 1 U/µL PKA catalytic subunit from bovine heart (Sigma; #P2645) and 6 mmol/L dithiothreitol. PKA was washed out of the myocardial preparations by 3 washes of pCa 9.0 in the approximately 250 µL volume of the chamber for a total of 30 minutes3,4,21 followed by a final soak in a fresh bath of pCa 9.0 used during exposure of myocardium to the x-ray beam.
X-ray Diffraction and Analysis
X-ray experiments were performed at 22°C using the small-angle instrument on the BioCAT undulator-based beamline 18-D at the Advanced Photon Source, Argonne National Laboratory20,22 as described.12 Spacings of the 1,0 and 1,1 equatorial reflections were converted to d10 lattice spacings using Bragg’s Law and can be converted to interthick filament spacing by multiplying d10 by 2/
3.23 Intensities of the 1,0 and 1,1 equatorial reflections were determined from one-dimensional projections along the equator and analyzed as described23 independently by 4 people and the results averaged. I11/I10 intensity ratios can be used to estimate shifts of mass (presumably cross-bridges) from the region of the thick filament to region of the thin filament.24,25
Phosphoprotein Staining
After exposure to the x-ray beam, the region of trabeculae between aluminum t-clips were dissolved and stored in 12-µL-aliquots of SDS buffer. Proteins in myocardial samples were separated by 10% SDS (wt/vol) PAGE. Pro-Q Diamond Phosphoprotein gel stain analysis (Molecular Probes) was performed to confirm phosphorylation state of individual phosphoproteins (Figure 3). The strength of the emitted signal correlates with the number of phosphate groups. SYPRO Ruby protein gel-stain (Molecular Probes) was used in conjunction with Pro-Q Diamond stain to determine the total protein load of individual proteins and thereby provide a measure of the phosphorylation level of specific myofibrillar proteins normalized to the total amount of protein of interest (see Figure 4 for quantitation of cTnI and cMyBP-C phosphorylation) and thus correct for differential protein loading due to variations in experimental preparation size. Preparations were analyzed individually and contained unknown concentrations of total protein. Typically, skinned trabeculae used for x-ray experiments contain approximately 15 µg of total myofibril protein as determined by colorimetric detection and quantification using a bicinchoninic acid assay (Pierce).
A Bio-Rad storage phosphor scanner (Molecular Imager F/X) with laser excitation filter at 532 nm and long-pass emission filter at 555 nm was used to capture Pro-Q Diamond fluorescence image. An EC-3 imaging system (UVP) ultraviolet source with excitation filter at 302 nm and long-pass emission filter at 560 nm was used to capture SYPRO Ruby fluorescence images. The program Laser-Pix (Bio-Rad) was used to determine the total pixel count and relative intensity of individual bands of interest after subtraction of background intensity. The intensity of each band was corrected for variability in gel-to-gel conditions using linear regression analysis of a dilution series of an ova-albumin/albumin weight standard (loading 50 to 1000 ng) to create a standard curve relating band intensity (arbitrary units) to the amount of phosphorylated protein and total protein (ng) for both stains in each gel.
Additionally, myofibril preparations26 from WT and cMyBP-C–/– mice (n=4) were separated by 5% SDS (wt/vol) PAGE and stained with Pro-Q Diamond. Basal phosphorylation of titin does not change with ablation of cMyBP-C, because the average slopes of phosphointensities of the NB2 isoform and T2 degradation products of titin using regression analysis are not different in WT and cMyBP-C–/– myocardium ([in arbitrary units] 29.46±3.27 in WT and 30.22±3.17 in cMyBP-C–/–).
Mechanical Experiments
Total force generated by skinned trabeculae at each pCa and the rate of force development were measured and assessed, as described by Stelzer,5 except that a different motor model (6800HP; Cambridge Tech) was used in the apparatus and sarcomere length was set to approximately 2.16 µm. The changes in motor position and force signals were digitized at 1 kHz using a 12-bit A/D converter (model AT-MIO-16F-5; National Instruments Corp) and displayed and saved to disk for later analysis using computer software (SLControl).28 Rate constants of force redevelopment (ktr) were estimated by fitting the data with a single exponential equation.30,31
Statistics
Data are expressed as means±SEM. A 2-tailed t test for unpaired samples or a paired t test was used to post hoc test of significance (P<0.05), as appropriate.
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X-ray Experiment Analysis
Intensity ratios determined from the 1,0 and 1,1 equatorial reflections from WT and cMyBP-C–/– skinned myocardium (Figure 1) were used to investigate the role of cMyBP-C phosphorylation on the distribution of cross-bridge mass between the thick and thin filaments. These measurements were made under relaxed conditions (pCa 9.0) to avoid possible confounding effects due to attachment of cross-bridges to thin filaments in activated muscle. I11/I10 ratios in trabeculae from WT mice were found to be significantly greater (approximately 50%, P<0.05) in WT myocardium treated with PKA (0.33±0.03, n=17) than in untreated WT myocardium (0.22±0.03, n=6; Figure 2). In contrast, I11/I10 in trabeculae from cMyBP-C–/– mice were not significantly different between cMyBP-C–/– myocardium (0.40±0.06, n=4) and cMyBP-C–/– myocardium treated with PKA (0.42±0.05, n=5). These results suggest that in resting myocardium, phosphorylation of PKA sites in cMyBP-C leads to a net transfer of mass from the region of the thick filaments to the thin filaments.
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The separations of the 1,0 and 1,1 equatorial reflections in diffraction patterns were converted to d10 lattice spacings to investigate the roles of cMyBP-C and cTnI phosphorylation on the interfilament lattice spacing. As shown in Figure 2, d10 lattice spacings did not change in WT myocardium after PKA treatment (45.65±0.99 nm, n=7 versus 45.64±0.64 nm, n=17). Conversely, d10 lattice spacings in cMyBP-C–/– myocardium were significantly increased after PKA treatment (46.80±0.92 nm, n=9 versus 49.61±0.59 nm, n=10). These results suggest that when cMyBP-C is absent, the distance between neighboring thick filaments in the hexagonal lattice is increased after PKA treatment.32
Phosphoprotein Staining
Gel analysis of protein phosphorylation using SYPRO-Ruby and Pro-Q Diamond staining (Figures 3 and 4
) showed that basal levels of cTnI phosphorylation were not different in WT and cMyBP-C–/– myocardium before PKA treatment, consistent with earlier results.3,4 PKA treatment phosphorylated both cTnI and cMyBP-C in WT myocardium, but phosphorylated only cTnI in cMyBP-C–/– myocardium (Figures 3 and 4). Titin is phosphorylated by PKA33 (2.71±0.25 versus 3.75±0.37, P<0.05) in our preparations (not shown), and also a distinct band migrates just slower than desmin in the 60- to 70-kD MW range that appears after PKA treatment (0.88±0.20 versus 3.94±0.69). Because PKA phosphorylation has no impact on the disposition of cross-bridges in cMyBP-C–/– in addition to that caused by ablation, PKA phosphorylation of other myofibrillar proteins appear to have no effect on the location of cross-bridges. However, we note that there are myofibrillar proteins whose effects of phosphorylation have not yet been resolved such as intermediate filament proteins.
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Mechanical Measurements
The decrease in the Ca2+ sensitivity of force with PKA treatment was similar in WT and cMyBP-C–/– myocardium (Table) as reported previously.3,4 During submaximal Ca2+ activation, the rate constant of force development (ktr), a measure of cross-bridge cycling kinetics, increased after PKA treatment in WT myocardium, but did not change after PKA treatment in cMyBP-C–/– myocardium (Table).
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Discussion |
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The primary result of this study is that when the PKA sites in the cardiac isoform of MyBP-C are phosphorylated, myosin cross-bridges assume positions further from the surface of the thick filament and closer to the thin filament. This conclusion follows from the observation that the I11/I10 ratio was significantly greater in WT myocardium treated with PKA than untreated WT myocardium and that PKA treatment did not change the I11/I10 ratio in cMyBP-C–/– null myocardium. This finding suggests that cMyBP-C acts to regulate the proximity and interaction of myosin with actin on contraction, and this mechanism is modulated by β-adrenergic stimulation through phosphorylation of PKA sites in cMyBP-C. cMyBP-C is assumed to normally act as a structural restraint on every third crown of heads in the C zone.34 The structural conformation of myosin heads in the relaxed state was recently revealed by Zoghbi et al.35 It appears that only crown 1 of 3 is constrained and dependent on the presence of cMyBP-C and that at least 3 of the 11 cMyBP-C domains lie on the thick filament surface in this crown. We favor a model in which phosphorylation of cMyBP-C relieves this restraint such that those cross-bridges move closer to the thin filament and thereby increase the probability of their interaction with actin on active contraction. The displacement of cross-bridges accelerates the cooperative recruitment of additional cross-bridges to force-generating states to increase the rate of force development. Such a mechanism is consistent with earlier suggestions that cMyBP-C serves as a mechanical tether on myosin that may be altered by phosphorylation, possibly due to disruption of cMyBP-C binding to the S2 domain of myosin.36–38 Similarly, the closer proximity of myosin heads to the thin filaments, which would presumably decrease the time taken to cooperatively activate the thin filament, could account for the faster kinetics of force development in PKA-treated WT myocardium compared with control myocardium, as reported here and previously.3,4
PKA phosphorylation of myofibrillar proteins such as cMyBP-C involves the addition of a negatively charged phosphate group on a serine or threonine residue, which is thought to induce a conformational change in the structure of the protein. Although we have found PKA phosphorylation of cMyBP-C to modulate the disposition and availability of cross-bridges to actin, it remains to be elucidated whether this mechanism of cMyBP-C function can be attributed to the negative charge associated with phosphorylation. At least 3 domains near the C-terminal region of cMyBP-C run along the thick filament surface35,39 and likely interact with titin and light meromyosin in crown 1 and thereby anchor cMyBP-C to the thick filament. Domains near the N-terminal region of cMyBP-C are thought to extend from the filament surface39–41 and bind to the S2 domain of myosin in crown 1, thereby limiting the availability of S1 to actin. It is possible that the negative charge associated with phosphorylation of cMyBP-C is sufficient to relieve a physical constraint on cross-bridges, possibly by disrupting cMyBP-C binding to the S2 region of myosin.42,43 This, in turn, would allow cross-bridges to move away from the surface of thick filaments at rest and accelerate cross-bridge binding to actin on contraction by increasing the cooperative spread of thin filament activation. It is possible, however, that cMyBP-C influences the binding of heads to actin in a mechanism independent of a tether42 in such a way that S2 could play a regulatory role in contraction39 or that cMyBP-C binds actin,41 but it remains unresolved whether these interactions normally occur in vivo.
Force development in myocardium is a highly cooperative process44 in which initial cross-bridge binding to the thin filaments recruits additional cross-bridge binding to actin and also increases Ca2+ binding to troponin C. In this manner, increasing the availability of cross-bridges to actin would contribute to increasing the number of cross-bridges that are strongly bound to the thin filaments, and consequently, we would expect even a small change in the disposition of myosin heads to considerably change the rates of force development, whereby cross-bridge cycling kinetics would be accelerated by eliminating, or significantly accelerating, cooperative cross-bridge recruitment.3 When we consider our structural measurements in the context of the findings by Stelzer et al,3,4 who used the same mouse lines and PKA treatment, it appears that the cross-bridge kinetics are faster when cross-bridges are closer to actin at resting force. This conclusion follows from the results that both genetic ablation12 and PKA phosphorylation of cMyBP-C (data presented here) result in radial or azimuthal displacement of cross-bridges, and both genetic ablation5 and PKA phosphorylation3 (see also the Table) of cMyBP-C result in faster rates of force development and shorter times to peak of delayed force development after a rapid stretch to a new length (stretch activation). It seems likely, then, that changes in the disposition of cross-bridges during diastole may affect the rate of cross-bridges binding to actin during systole (ie, how fast cross-bridges attach to the thin filament). Indeed, Pearson and colleagues recently demonstrated45 that the number of attached cross-bridges and the rate of force generation proportionally increase as the result of a greater proximity of myosin filaments to actin.
Our finding that interfilament lattice spacing does not change in WT myocardium when subject to PKA phosphorylation is consistent with results by Toh et al,46 whereby β-adrenergic stimulation leading to cascading events, including PKA phosphorylation of cMyBP-C and cTnI, does not change lattice spacing. In contrast to WT myocardium, PKA phosphorylation of cMyBP-C–/– myocardium increased lattice spacing, which is consistent with previous inferences32 that PKA-dependent phosphorylation of cTnI caused expansion of the myofilament lattice and that this effect is greater in the absence of cMyBP-C. Interestingly, Konhilas et al32 found lattice spacing to expand slightly in PKA-treated WT myocardium. We believe our results differ from the previous study because we took care to reduce the level of basal phosphorylation of regulatory myosin light chains (RLCs) by 2,3-butanedione monoxime treatment47 during our trabeculae dissection (see "Materials and Methods"); phosphorylation of RLC has been shown to have similar effects as cMyBP-C phosphorylation on force generation16,47 by inducing movement of the myosin head away from the thick filament backbone48,49 and may have confounding effects on observations concerning myofilament structure. When we compared results of WT myocardium from our previous study,12 in which RLC was basally phosphorylated, with results in the present study, in which RLC was dephosphorylated, we found that dephosphorylation of RLC slightly, but significantly, expanded lattice spacing (42.95±0.43 nm versus 45.65±0.99 nm) and decreased the I11/I10 (0.28±0.01 versus 0.22±0.03). Therefore, it seems likely that the effect of cTnI phosphorylation on lattice spacing observed by Konhilas et al32 was masked in our study by dephosphorylation of RLC. These results also suggest that cMyBP-C and RLC may have similar effects on myofilament structure. With regard to phosphorylation of the contractile proteins related to the inherent mechanical properties of myocardium, such a finding would be expected, because the phosphorylation status of both cMyBP-C and RLC affect the kinetics of force development in cardiac muscle. In either case, it appears that phosphorylation of cTnI in the absence of cMyBP-C increases the spacing between thick filaments.
Our studies using x-ray diffraction of whole muscle are consistent with electron microscopy studies of isolated thick filaments,10,11 in which the filament diameter in the cross-bridge containing regions were greater in PKA treated than in control filaments. Phosphorylation of the thick filament in the absence of the thin filament appeared to result in a looser packing of myosin such that the thickness of PKA-treated filaments was approximately 2 to 5 nm greater than untreated filaments. The increased thickness was interpreted as a population of cross-bridges that extended away from the backbone of the thick filament due to phosphorylation of cMyBP-C. In some cases, however, untreated filaments contained cross-bridges that extended the same distance as the PKA-treated filaments. Weisberg and Winegrad10 suggest that these cases are most likely associated with phosphorylated cMyBP-C in the untreated filament. It is thus important to consider phosphorylation status in cardiac preparations when interpreting the results of structural studies, because phosphorylation appears to change myofilament structure. In our study, phosphoprotein staining analysis was used to determine the phosphorylation status of myocardium used in our x-ray studies; in 2 of 9 cases of untreated WT trabeculae, cMyBP-C phosphorylation was suprabasal by more than 2-fold as compared with all other untreated WT trabeculae, and the ratio of cMyBP-C phosphorylation to cTnI phosphorylation was nearly 3-fold greater than all other WT preparations. These observations are consistent with the variability in the level of basal phosphorylation of contractile proteins reported previously.50,51 Consequently, these cases of suprabasal cMyBP-C phosphorylation were excluded when assessing the effect of cMyBP-C phosphorylation on cross-bridge disposition.
As our understanding of the mechanism by which cMyBP-C modulates cardiac contractility improves, it is becoming clear that its phosphorylation by PKA is an important regulatory mechanism that contributes to increased cardiac output in response to β-adrenergic stimulation. We propose that cMyBP-C normally acts to slow the rates of cross-bridge attachment and the transition to force-generating states. However, during adrenergic stimulation, phosphorylation of cMyBP-C accelerates the rates of cross-bridge cycling early in systole as a consequence of the closer juxtaposition of myosin heads nearer to actin in diastole and thereby matches the increased heart rate. Conversely, PKA phosphorylation of cTnI acts to decrease the Ca2+-binding affinity of troponin, which causes earlier onset of relaxation and thus provides adequate time for diastolic filling. In this scheme, the balance of PKA-mediated phosphorylations of cMyBP-C and cTnI acts to finely tune durations of systolic ejection and diastolic filling to optimize contraction during accelerated systolic ejection.
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Acknowledgments |
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We thank Sandy Dunning (for assistance in data collection) and J. R. Patel (for advice in experimental design). We especially thank Heather King, Anton Kovalsky, and Krystyna Shioura (for assistance in analysis of diffraction patterns).
Sources of Funding
This work was supported by an American Heart Association predoctoral fellowship (BAC) and by National Institutes of Health HL-R01-82900 (RLM). Use of the Advanced Photon Source was supported by the US Department of Energy, Basic Energy Sciences, Office of Science, under contract No W-31-109-ENG-38. BioCAT is a National Institutes of Health-supported Research Center RR-08630. The content is the sole responsibility of the authors and does not necessarily reflect the official views of the National Center for Research Resources or the National Institutes of Health.
Disclosures
None.
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Footnotes |
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Original received January 25, 2008; resubmission received May 6, 2008; revised resubmission received June 15, 2008; accepted June 24, 2008.
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References |
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