Role of Delta-like-4/Notch in the Formation and Wiring of the Lymphatic Network in Zebrafish
Objective— To study whether Notch signaling, which regulates cell fate decisions and vessel morphogenesis, controls lymphatic development.
Methods and Results— In zebrafish embryos, sprouts from the axial vein have lymphangiogenic potential because they give rise to the first lymphatics. Knockdown of delta-like-4 (Dll4) or its receptors Notch-1b or Notch-6 in zebrafish impaired lymphangiogenesis. Dll4/Notch silencing reduced the number of sprouts producing the string of parchordal lymphangioblasts; instead, sprouts connecting to the intersomitic vessels were formed. At a later phase, Notch silencing impaired navigation of lymphatic intersomitic vessels along their arterial templates.
Conclusion— These studies imply critical roles for Notch signaling in the formation and wiring of the lymphatic network.
The lymphatic vasculature regulates interstitial fluid homeostasis, fat resorption, immune defense, inflammation, and metastasis.1 In mammals, venous blood vascular endothelial cells (BECs) differentiate to lymphatic endothelial cells (LECs).1 In response to Sox18, prospero homeobox-1 (Prox-1) induces the lymphatic transdifferentiation of venous BECs.1,2 Additional cues must regulate lymphatic development; however, their nature remains unknown. Another outstanding question is how lymphatics become wired into a stereotyped network. Deep lymphatics regularly fasciculate with other vessels and track along arteries.1,3 Similar to blood vessels,4 lymphatic sprouts have tip cells with filopodia to probe guidance cues.5 Although molecules such as vascular endothelial growth factor receptor (VEGFR)-3, VEGF-C, Neuropilin-2, and Ccbe1 regulate lymphatic migration,1,6 the navigation of lymphatics remains poorly understood. Thus, the mechanisms and molecules underlying lymphatic development and wiring remain largely unknown.
See accompanying article on page 1682
Intriguingly, despite the venous origin of lymph vessels, several molecules involved in arterial BEC regulation also regulate lymphangiogenesis. For instance, EphrinB2, an initial marker of arterial BECs,7,8 regulates lymphatics later in development.1 Sox18, together with Sox7, is required for arterial differentiation and later regulates lymphatic competence.2 This relationship between “arterial” factors and lymphangiogenesis, and the anatomical congruence between arteries and lymphatics,8–11 prompted us to investigate whether Notch also regulates lymphatic development. Notch and its ligand delta-like-4 (Dll4) seemed intriguing candidates, given their role in vessel branching.4 By using gene silencing methods in zebrafish, we revealed novel roles for Dll4/Notch signaling at multiple steps during early lymphangiogenesis.
The transgenic zebrafish lines used were Fli1:eGFPy1,12 Flt1:YFP, kdr-l:mCherryRed, Stab1:YFP, Fli1:DsRed,6 Tp1bglob:eGFP,13 and intercrosses. Embryos and fish were grown and maintained as previously described.6,14 All animal experimentation was approved by the institutional ethical committee.
Morpholinos (Gene Tools, LLC, Corvallis, Ore) (supplemental Table I; all supplemental materials are available online at http://atvb.ahajournals.org) were injected at the indicated doses, as previously described.14 Phenotyping data are pooled data from at least 3 independent experiments, with analysis of 33 to 185 injected embryos per dose. Screening methods for the evaluation of lymphatic development and functionality are detailed in the supplemental Methods.
RNA Analysis and Cell Culture Assays
Whole-mount in situ hybridization of dechorionated embryos using antisense probes for the indicated genes (supplemental Methods) was performed as previously described.14 Quantitative RT-PCR was performed on whole embryo extracts or on fluorescence-activated cell sorted embryo cells after in vivo labeling of LECs, as described in the supplemental Methods. The proliferation, migration, and expression analyses of LECs or human umbilical venous ECs are detailed in the supplemental Methods.
Each gene-specific morpholino was always compared with a control morpholino or vehicle. To determine the penetrance of the phenotype, we counted the number of embryos exhibiting different phenotype severities, and analyzed distributions by χ2. Unpaired comparisons were performed by a 2-sided t test. Asterisks represent a significance level of P<0.05.
Knockdown of Dll4 and Notch-1b or Notch-6 Impairs Thoracic Duct Formation
To explore a role for Notch signaling in lymphatic development (supplemental Note I and supplemental Figure I), we silenced every known zebrafish orthologue of the Notch ligands (DeltaA-D, Dll4, Jagged-1a/b, and Jagged-2) and receptors (Notch-1a/b, Notch-5, and Notch-6) and the Notch-activating presenilins-1/2 in Fli1:eGFPy1 zebrafish embryos, in which lymphatic, arterial, and venous ECs are labeled.12,15,16 Submaximal silencing conditions were used (supplemental Note II); these conditions did not affect general or blood vascular development (supplemental Figure II and supplemental Figure III). Development of the thoracic duct (TD), the first functional lymphatic formed in the trunk in between the dorsal aorta (DA) and the posterior cardinal vein (PCV), was analyzed (supplemental Note III defines acronyms).
Dll4 morpholino knockdown (Dll4KD) inhibited TD formation. On injection of a morpholino affecting Dll4 mRNA splicing (Dll4SPL, 10 ng), the TD failed to form at all by 6 days post fertilization (dpf) in 52% of morphant embryos, indicating that lymphatic development was completely aborted (Figure 1A, B, and D). In another 27% of Dll4SPL embryos, the TD formed over only 10% to 30% of its normal length, whereas in another 15% of morphant embryos, the TD formed over 30% to 90% of its normal length (Figure 1D). Follow-up studies at 12 dpf revealed that, in embryos with intermediate defects, the TD segments that did form failed to reconstitute the entire TD and to compensate for the lymphatic failure in nearby somites (not shown). Dll4KD embryos without TD at 6 dpf also failed to form a TD, even partially, at later stages (supplemental Figure IIG and H), indicating that lymphatic development was not simply delayed but aborted. Similarly, incomplete silencing of Notch-1b and, to a lesser extent, Notch-6 impaired TD formation (Figure 1C and E). Of note, their mammalian orthologues, Notch-1 and Notch-2, are expressed in LECs.10,17 Because Notch-1b downregulation causes more penetrant lymphatic defects, only data for Notch-1bKD are shown.
Similar TD defects were obtained with morpholinos, targeting the ATG of Dll4 (Dll4ATG) or Notch-1b (Notch-1bATG) (data not shown); however, silencing of the Notch ligands DeltaA-D, Jagged-1a/b, Jagged-2, or receptors Notch-1a, or Notch-5 (orthologue of mammalian Notch-3) did not induce lymphatic defects (data not shown). Finally, inhibition of the γ-secretase complex (which proteolytically activates Notch)18 confirmed the involvement of Notch in lymphatic development. Both morpholino knockdown of presenilin-1 (PS-1) (but not PS-2) and pharmacological inhibition of γ-secretase activity by N-[N-(3,5-difluorophenacetyl)-L-alanyl]-Sphenylglycine t-butyl ester (DAPT)18 impaired TD formation (Figure 1F, supplemental Figure IVQ and R, and supplemental Note II).
Lymphangiography in 7-dpf kdr-l:mCherryRed Dll4KD embryos (in which only blood vessels express mCherryRed) revealed no drainage of fluorescent dye in the region in which the TD normally forms, confirming that the lack of a GFP+ TD in Fli1:eGFPy1 Dll4KD embryos was not the result of reduced expression of GFP, but the actual absence of the vessel itself (Figure 1G and H). This assay further showed that partial TD fragments were not functional (data not shown).
Notch Is Required for Parachordal Lymphangioblast String Formation
Next, we analyzed whether silencing of Notch impaired development of the parachordal lymphangioblast (PL) cells6 at the horizontal myoseptum because these precursors contribute to TD formation (supplemental Note I and supplemental Figure I). At 52 hours post fertilization (hpf), the formation of the PL string was completely formed in 53% and largely completed in 40% of embryos (Figure 2A). In contrast, in Dll4SPL embryos, the PL string was completely absent in 38% and formed only in a few segments in 27% of embryos (Figure 2A). Largely comparable fractions of Dll4SPL embryos exhibited similar types of PL string and TD defects (compare Figure 1D with Figure 2A), suggesting that the TD defects were, at least in part, attributable to defects in PL string formation. Imaging of lymphangiogenic structures in Dll4SPL embryos using the Stab1:YFP line,6 which primarily visualizes venous and LECs, confirmed these findings (Figure 2B and C). A similar absence of the PL string was observed when using the Dll4ATG morpholino (data not shown) or on knockdown of Notch-1b (Figure 2A) or Notch-6 (data not shown). Because the string of PL cells forms as a result of sprouting from the PCV (supplemental Note I and supplemental Figure I),6 these findings suggest that Notch signaling acts in part at early steps.
Dll4 Silencing Reduces the Fraction of Lymphangiogenic Sprouts
Then, we studied whether inhibition of Notch acts during branching of PL-forming secondary sprouts from the PCV (termed “lymphangiogenic” secondary sprouts, denoting that they participate in the process that leads to the formation of lymphatic structures, but not blood vessels) (supplemental Note I). Whole-mount staining for Tie2, which marks all secondary sprouts,19 showed a normal total number in Dll4KD embryos (N=20) (Figure 2D and E). However, high-resolution imaging of 4-dpf Fli1:eGFPy1 embryos revealed alterations in the proportion of venous intersomitic vessels (vISVs) connected to the PCV. In control embryos, half of the ISVs were vISVs (percentage of total ISVs: 54±1%; mean±SEM; N=49); in contrast, in Dll4SPL embryos, 82±1% of the ISVs were connected to the PCV and, thus, vISVs (mean±SEM; N=97; P<0.05 versus control). Similar findings were obtained in Notch-1bSPL embryos (vISVs, portion of total: 69.0±2.7%; mean±SEM; N=27; P<0.05 versus control). Because vISVs can only be formed via connection of a secondary “angiogenic” sprout to a primary ISV (supplemental Note I), these findings, and the observation that silencing of Dll4, Notch-1b, or Notch-6 aborted PL string formation in a substantial fraction of embryos, show that a fraction of secondary sprouts that would normally have been lymphangiogenic were angiogenic, thereby impairing TD formation.
We also used high-resolution video-imaging of the double transgenic reporter line Flt1:YFPxkdr-l:mCherryRed,6 labeling venous cells red (CherryRed+) and arterial cells yellow (YFP+CherryRed+) in merged images.6 In control embryos, half of the ISVs had a red venous color and the other half had a yellow arterial color (Figure 2F and F′). In contrast, in Dll4KD embryos with severe lymphatic defects, nearly all yellow arterial ISV (aISV) connections with the DA had disappeared (single white arrow in Figure 2G and G′) (supplemental Movies I and II). Thus, a supernumerary fraction of vISV-producing angiogenic sprouts is formed in Dll4KD embryos at the expense of lymphangiogenic sprouts that would otherwise proceed to form the PL string.
Dll4/Notch Promotes Lymphatic Characteristics In Vitro
To evaluate whether Notch activation in venous ECs could induce lymphatic properties, we cocultured human umbilical venous ECs, which express Notch-1, but negligible levels of Prox-1 (data not shown), with monkey kidney COS cells expressing Dll4 (COSDll4) or a control vector (COSCTR), and analyzed by RT-PCR with human gene-specific primers the expression of lymphatic markers. Expression levels of the lymphatic markers PROX-1, VEGFR3, LYVE-1, and SOX18 in COSDll4-activated human umbilical venous ECs were moderately to distinctly elevated (Figure 3). Notably, the expression levels of EPHRINB2, which is regulated by Notch and has been implicated in both arterial and lymphatic processes,1,7 and COUP-TFII, which is expressed in both venous ECs and LECs,20 were also upregulated; however, levels of other blood vessel markers (ENDOGLIN, vascular endothelial [VE]-CADHERIN, and CD31) were not or were only minimally affected (Figure 3). The upregulation of lymphatic markers was abolished by treatment of the cells with DAPT, 30 μmol/L (data not shown).
Silencing of Dll4 Impairs PL Cell Migration Along aISVs
From 60 hpf onward, PL cells switch to radial migration and navigate ventrally and dorsally alongside aISVs, where they form lymphatic ISVs (lISVs) (supplemental Note I). Because the TD failed to form in a fraction of Dll4SPL embryos (25%) despite the presence of a partial PL string, we further explored whether Notch signaling affects lISV formation. In control embryos, lISV-PLs (PL cells that formed lISVs) migrated exclusively along aISVs, suggesting that vISVs are not permissive (Figure 4A and B). Because there were more vISVs and fewer aISVs in Dll4KD embryos, migrating lISV-PLs were deprived from their arterial template and could, therefore, not contribute to TD formation (Figure 4C). This was the most common migration defect. Intriguingly, even when residual aISVs formed in Dll4SPL embryos, lISV-PLs sometimes bypassed the aISV post, failing to turn and migrate along aISVs (Figure 4D). Indeed, in Dll4SPL embryos with a nearly complete PL string (>90% of its length; mean±SEM; N=61), 49±6% of their aISVs were not accompanied by lISV-PLs, compared with only 15±4% in controls (mean±SEM; N=29; P<0.05).
Other, much less frequent, lISV defects included lISV-PLs that turned ventrally alongside the aISV but stalled (Figure 4E) or, even in a few cases, misrouted lISV-PLs migrating along vISVs (Figure 4F). In vitro studies revealed that Notch did not regulate LEC migration/motility, proliferation, or lymphatic capillary tube formation or sprouting (supplemental Figure V and data not shown).
Expression of Dll4 and Notch
Whole-mount in situ hybridization in control embryos at 30 hpf, when secondary sprout formation starts, showed that Dll4 was detectable in the DA but not in the PCV (Figure 5A and B), in line with previous reports.19,21,22 Notch-1b was strongly expressed in the DA (Figure 5C and D), whereas a much weaker signal appeared dispersed in certain ECs of the dorsal part of the PCV, although the low Notch-1b signal approached the detection limit of available techniques (supplemental Figure VI).
We also developed a new technique to isolate LECs from zebrafish embryos. When tetramethylrhodamine B isothiocyanate–dextran dye is injected intramuscularly in 4-week-old Fli1:eGFPy1 embryos, the red dye is taken up by LECs but not by BECs via pinocytosis, allowing fluorescence-activated cell sorting of red or green LECs. By RT-PCR, low Notch-1b transcript levels were detected in these LECs (ratio of copies of Notch-1b to 105 copies of β-actin: 6.90±0.77; N=4). However, tetramethylrhodamine B isothiocyanate–dextran “LEC labeling” is only feasible in large 4-week-old embryos, but not in small early-stage embryos, precluding us from quantifying Notch-1b expression in early lymphatic development.
Dll4 and Notch-1b were also detected by in situ hybridization in primary ISVs at 30 hpf (Figure 5A-C).21,22 Because in situ hybridization is technically challenging in embryos beyond 2 dpf, we analyzed Notch expression during lISV-PL migration in Tp1bglob:eGFPxFli1:DsRed fish, in which all ECs are red and cells with canonical Notch activity are green (GFP driven by a promoter containing 12 Su[H] binding sequences13). Imaging when PL cells turn and switch to radial ventral migration revealed that the DA and aISVs are yellow in the merged image, indicating that canonical Notch signaling was active in arterial vessels but not in lISVs or vISVs (Figure 5E–E‴).
The key finding of this study is that incomplete silencing or pharmacological inhibition of Notch impaired lymphatic development in zebrafish. Phenotypic analysis indicates that Notch signaling regulates the formation of lymphangiogenic sprouts and their descendent PL cells, which produce the TD (Figure 6A and B). At a later stage, Notch is required for guided migration of lISV-PLs along aISVs (Figure 6C-C‴).
Role of Notch in Lymphangiogenic Secondary Sprout Formation
Our results reveal that Notch, in addition to its role in blood vessel morphogenesis and arterial development,4,9 also regulates lymphatic development. Half of the Notch hypomorphant embryos failed to form a TD without later rescue, indicating lymphatic abortion rather than delay. The earliest identifiable abnormality, the increased fraction of venous ISVs, indicated a defect at the level of the secondary sprouts from the PCV, where fewer lymphangiogenic, but more angiogenic, sprouts developed (Figure 6A and B). Also, most embryos, surviving DAPT treatment at stages when lymphangiogenic sprouting was initiated, did not form a TD, further suggesting an early role for Notch in lymphatic development (data not shown). The hypomorphant phenotypic change correlated with defective formation of the PL and TD and could result from defects in LEC fate acquisition, migration, proliferation, survival, and/or other cellular processes contributing to sprout formation and maintenance.
How Notch signaling regulates lymphatic development remains unresolved. Based on the present study and other recent studies, 3 possible (nonexclusive) models can be considered to explain our findings. A first explanation is that Notch silencing altered blood vessel development and, secondarily, influenced lymphatic development. Previous studies documented that arterial differentiation is impaired by inhibition of multiple Notch signaling pathways (eg, by a dominant-negative Su[H]),7 but not by selective silencing of Dll4.21,22 Our imaging and marker expression analyses are consistent with these findings and reveal that initial formation and differentiation of the PCV, DA, and primary ISVs all occurred normally on incomplete silencing of Notch signaling. Thus, at least by generally accepted criteria of arterial and venous identity, these blood vessels developed normally in Dll4KD and Notch-1bKD embryos. Nevertheless, we do not exclude the possibility that subtle alterations in arterial characteristics of the primary ISVs might have favored supernumerary connections with secondary sprouts, thereby “entrapping” sprouts that would otherwise have remained lymphangiogenic. Also, Notch silencing resulted in a greater fraction of venous than arterial ISVs; because arterial ISVs act as guidance templates for lISVs, impaired migration of the latter was indeed attributable to such a change in arterial morphogenesis. However, an outstanding question is whether the aISV changes themselves were, in fact, not caused by defective formation of the lymphangiogenic sprouts in the first instance. Indeed, precisely because lymphangiogenic branches failed to develop in Notch morphants, venous angiogenic sprouts formed instead, which then connected to the primary ISVs and converted them to vISVs.
A second model is that Dll4 and Notch are expressed by the same or adjacent arterial ECs within the DA and that this cis signaling induces the release of paracrine lymphangiogenic factors (eg, EphrinB2, VEGF-D,1,23 or an unknown signal) that indirectly instruct venous ECs of the nearby PCV to induce lymphangiogenic sprout formation in a cell nonautonomous manner. A similar indirect model was proposed to explain segregation of the DA from PCV in zebrafish.8 Likewise, during lISV migration, release of a guidance signal from aISVs in response to Dll4/Notch signaling in arterial cells could assist navigation of lISVs to their target projection.
Finally, a third and perhaps the most appealing, but at this stage still speculative, explanation for our data is that arterial Dll4 in the DA signals in trans to Notch on ECs in the PCV, which lies in close juxtaposition at the time of lymphangiogenic sprouting. There are arguments in support of and against this model. An argument in favor of a cell autonomous role of Notch in PCV cells is that activation of Notch by Dll4 upregulated several LEC-specific markers in venous ECs in vitro. Expression analysis experiments in vivo yielded inconclusive results. Notch-1b expression was weakly detectable in dispersed dorsal PCV cells, but only at a low level that approached the detection limit of the techniques used. Notch-1b was also measurable by RT-PCR in isolated LECs in older embryos; however, this technique could not be used during early lymphatic development. Therefore, we acknowledge that the Notch-1b expression results represent a limitation of this study that precludes us from drawing firm conclusions regarding a cell-autonomous role for Notch in lymphangiogenic sprouting.
Another recent study24 also documented a cell-autonomous role for Notch, whereas a second study25 did not document this role. In LEC cultures, Notch signaling reprogrammed lymphatic to arterial cell fate, whereas Prox-1 counteracted this force, thereby allowing fine-tuning of the LEC fate in a delicately balanced feedback.24 These findings are not necessarily contradictory to our findings because they analyzed reprogramming of fully differentiated LECs away from their lymphatic fate; we used venous BECs to study programming toward the LEC fate in vitro. Kang et al24 note in their discussion that “LEC-fate may not be governed by a two-way turn on-off switch, but rather by a dial switch that allows a gradient increase or decrease in the lymphatic cell fate force.” Reconciling these and our findings, it seems that Notch levels must be tightly controlled to induce and maintain LEC fate. Low levels of Notch signaling might be required to induce lymphatic fate in venous BECs; once differentiated into LECs, Prox-1 would then secure lymphatic fate by preventing overexpression of Notch because this would promote arterial cell fate.24 The lower expression of Notch-1 in LECs (as found in the present study and in previous studies10,24) than in arterial ECs8–11 supports this model and could also explain why incomplete Notch silencing sufficed to abrogate lymphatic, but not arterial, development. However, in the absence of more conclusive evidence that Notch silencing abrogates Prox-1 induction in PCV cells in the zebrafish model in vivo, a role for Notch in programming LEC fate remains unproved. Also, Notch may regulate processes other than LEC specification in lymphangiogenic sprouting.
A recent study in mice further adds complexity to this model. Indeed, conditional inactivation of RbpJ, a mediator of canonical Notch signaling, in ECs did not alter the expression of lymphatic markers in venous ECs.25 Although these data may suggest that Notch signaling is redundant for LEC specification in mammals in vivo, an alternative interpretation is that Notch regulates this process via noncanonical signaling. This might also explain why we could not detect a robust signal in LECs or in their precursors in the Tp1bglob:eGFPxFli1:DsRed line. Also, species-specific differences between mammals and zebrafish could account for some of the observations. Overall, whether Notch signaling regulates lymphatic development in a cell-autonomous manner remains to be further elucidated in the future.
Role of Notch in Lymphatic Migration From the PL
Notch signaling also regulated the formation of lISVs, which arise from the PL cells. Most frequently, the lISV was absent; however, in other rarer cases, migrating lISV-PLs stalled or became misrouted (Figure 6C-C‴). Our findings suggest that lymphangiogenic EC migration per se (motility) was normal. Also, we did not detect signs of lymphatic regression or retraction (data not shown). Therefore, it is tempting to speculate that lISV defects in Notch-silenced embryos reflect impaired lymphangiogenic cell pathfinding. lISV-PLs navigated in close association along aISV templates, raising the question of whether aISVs act as guidance templates for lISV-PLs, reminiscent of how follower axons navigate along a pioneer axon’s pathway or how autonomic nerves use arterial tracks to reach their target.26,27 Therefore, because fewer aISVs are present in Notch morphants as the result of lymphangiogenic sprouting defects, PL cells are deprived of navigation templates and, therefore, cannot form lISVs normally (Figure 6C). Other observations that lISV-PLs failed to switch from tangential to radial migration or, more rarely, stalled or selected incorrect paths (Figure 6C’-C‴) are reminiscent of classic neuronal guidance defects. That arteries may act as navigation templates is evidenced by reports that autonomic nerves stall or become misrouted when these arteries do not produce appropriate guidance cues.27 Su[H]-dependent Notch activity was detectable in aISVs when PL cells switch from tangential to radial migration alongside aISV, indicating that lymphatic navigation is regulated either cell nonautonomously or via noncanonical Notch signaling. Whether and how Notch regulates the production of turning and guidance cues for lISV-PL cells by aISVs or nearby (somitic) cells remain to be determined. Other morphant and mutant zebrafish phenotypes also suggest that lISV development requires arterial-lymphatic congruence.28
In conclusion, this study revealed a role of Notch in lymphatic development, in part by regulating the initial steps of lymphangiogenic sprouting and PL formation. Moreover, the navigation defects of lISV-PL cells along aISVs suggest that Notch also regulates lymph vessel pathfinding along arteries.
We thank A.L. Harris, MD, PhD, for LZRSpBMN-WT and LZRSpBMN-DLL4, H. Pendeville, PhD, for Tbx20, and J. den Hertog, PhD, for the Dab2 probe.
Sources of Funding
This study was supported by the Institute for the promotion of Innovation through Science and Technology in Flanders (IWT-Vlaanderen) (Drs Geudens, Hermans and De Smet, and W Vandevelde); the EU Framework Program 7 (Dr Segura); FEBS (Dr Ruiz de Almodovar); Vrienden Hubrecht Stichting (Dr Bussmann); C. J. Martin Fellowship (Dr Hogan); American Heart Association (AHA) (Dr Moore); Deutsche Krebshilfe (Dr Loges); Operational Network for Excellence in Lombardy’s Biomedicine (CARIPLO-N.O.B.E.L.) (Dr Cotelli); National Institutes of Health (NIH) (Dr Lawson); a VIDI grant from the Netherlands Organisation for Scientific Research (NWO) (Dr Duckers); the Royal Netherlands Academy of Arts and Sciences (KNAW) (Dr Schulte-Merker); and by the Federal Science Policy Office, Belgian State; a grant LSHG-CT-2004-503573 from EU Framework Program 6; and a Methusalem grant (Dr Carmeliet).
Drs Geudens, Herpers, and Hermans contributed equally to this work. Drs Schulte-Merker, Carmeliet, and Dewerchin contributed equally to this work.
Received on: January 9, 2010; final version accepted on: May 3, 2010.
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