© 2001 by The Society for Integrative and Comparative Biology
Comparative Analysis of Hox Gene Expression in the Polychaete Chaetopterus: Implications for the Evolution of Body Plan Regionalization1
1 Department of Cellular, Molecular and Developmental Biology, Yale University, P.O. Box 208103, New Haven, Connecticut 06520-8103
2 Kewalo Marine Lab, PBRC/Univ. of Hawaii, 41 Ahui St., Honolulu, HI 96813
| SYNOPSIS |
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The Hox genes are widely regarded as candidates for involvement in major evolutionary changes in body plan organization. We examine Hox gene expression data for several taxa, in relation to recent work on the polychaete annelid Chaetopterus. The work in Chaetopterus shows the basic conservation of colinearity of anterior expression boundaries seen in other groups. It also reveals novel patterns including early expression in the larval growth zone and later formation of posterior boundaries that correlate with morphological transitions in the polychaete body plan. The polychaete gene expression pattern is compared with those of Hox gene homologs in other taxa to reveal differences that represent evolutionary changes in Hox gene regulation between lineages. Correlations between Hox gene expression differences and morphological differences are examined, focussing on a number of cases in which posterior Hox gene expression boundaries correlate with morphological transitions. Differential regulation of these posterior expression boundaries is proposed as a possible mechanism for changes body plan regionalization.
| INTRODUCTION |
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Hox genes in body plan evolution: the paradigm
Mutational studies in flies and mice have clearly shown that Hox genes play an important role in the development of discrete regions of the adult body plan (Carroll, 1995
In a very simplified view (to be elaborated below), metazoans are armed with a complement of Hox genes clustered together in a contiguous region of their genomes. The spatial and temporal expression of these genes is regulated by the position of the genes from 3' to 5' along the chromosome, a feature termed colinearity.
For example, in vertebrates the temporal onset of expression of Hox genes is largely colinear with chromosomal location, i.e., 3' genes are expressed earlier than more 5' genes (De Robertis, 1994
). There also appears to be a biphasic temporal pattern of expression in which the morphogenetic function of Hox genes changes during development. Early expression has been characterized as imparting positional information to cells which "remember" the initial Hox code (Gonzalez-Reyes and Morata, 1990
). Expression during later stages of development involves the fine tuning of Hox gene expression within and between segments to transduce complex morphogenetic information and specify unique cell fates (Akam, 1998b
).
The hallmark of Hox gene expression is their coordinated nested spatial patterns. Individual Hox genes are generally expressed from an anterior boundary along the body axis caudallywith or without a defined posterior boundary. The anterior boundaries of consecutive genes in the cluster are arranged in rank order from anterior to posterior in the same register as their 3' to 5' positions along the chromosome.
The paradigmatic view of Hox gene expression is that the most significant feature of the expression pattern is the anterior boundary. Ectopic expression of Hox genes in segments anterior to their normal domain generally results in posteriorization of the affected segment, i.e., the more anterior segment acquires the "Hox code" of the ectopically expressed gene. Similarly if a Hox gene anterior boundary is shifted caudally, the segment losing that gene product takes on the more anterior identity. This general principle is called "posterior dominance" (reviewed in Manak and Scott [1994]
).
In the case of posterior boundaries, shifting the expression domain may or may not affect segmental identity. Gene overexpression studies in flies and mice indicate that in some cases posterior boundaries of expression do have functional significance. Ubiquitous expression of a heat-shock-Dfd transgene causes a partial transformation of the more posterior labial and thoracic segments towards a maxillary identity (Kuziora and McGinnis, 1988
) and ectopic expression of Scr results in the cuticle in the second and third thoracic segments being converted to the form of the first thoracic segment (Andrew et al., 1994
; Pederson et al., 1996
). In the mouse, overexpression of Hoxc-6 results in one or more supernumerary ribs in the lumbar region, caudal to the normal posterior expression boundary of this gene (Jegalian and DeRobertis, 1992
). Similarly, overexpression of Hoxb-8 and Hoxc-8 posterior to their normal domains result in atavistic changes in posterior vertebral morphology (Pollock et al., 1995
). These experiments indicate that in certain cases of genes with defined posterior boundaries of expression, dominance by more posteriorly expressed genes does not hold and therefore changes in posterior expression boundaries could be a mechanism of morphological change.
Hox genes in Chaetopterus
The annelids are one of the three great segmented animal phyla (along with the arthropods and chordates). Each of these groups belong to a distinct metazoan clade, the Lophotrochozoa, Ecdysozoa, and Deuterostomia, respectively. While a great deal of work has concentrated on body plan development and evolution in the arthropods and chordates, comparatively little is know about these issues in any members of the Lophotrochozoa (Shankland and Seaver, 2000
). The polychaete annelid Chaetopterus is of interest because of the complex regionalization of its body plan (Fig. 1). As is typical of polychaetes, the body axis consists of a pre-segmental "head" (the prostomium and peristomium), followed by a series of many distinct "trunk" segments called setigers, each separated by a septum and having its own set of muscles, portion of the ventral nerve cord, blood vessels, nephridia, and lateral appendages called parapodia. The post-segmental posterior terminus is called the pygidium. For most annelids, polychaetes included, the morphology of segments is very similar along the body axis, a trait called homonomy. Chaetopterus is unusual for the extent of its segmental specialization, termed heteronomy, resulting in a tagmatized body plan with three functional regions, called here A, B, and C (Fig. 1C) (Crossland, 1904
).
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The developmental mode of polychaetes is characterized by the production at hatching of an initially unsegmented trochophore larva. (In the case of Chaetopterus the trochophore is a modified form [Okada, 1957
Because the Hox group of homeobox genes have been shown to be instrumental in specifying segmental identity and mediating segmental morphology in such a wide array of metazoan taxa (Ruddle et al., 1994
; Slack et al., 1993
), we were interested in studying Hox genes in Chaetopterus, with its tagmatized body plan and highly specialized segmental morphology. A survey of the Chaetopterus genome using the polymerase chain reaction (PCR), along with cDNA library screening, uncovered nine Hox genes (Irvine et al., 1997
; Irvine and Martindale, 2000
). Phylogenetic sequence analysis determined that these genes can be related to Hox genes found in another polychaete Ctenodrilus, and to Hox genes in flies and mice. From this analysis a hypothetical Chaetopterus Hox cluster was constructed which has putative orthologs of each of the Hox genes in Drosophila, except Abd-B. Subsequently we cloned cDNAs from the Hox1-Hox5 orthologs of Chaetopterus for use in in situ hybridization experiments to determine gene expression patterns.
Three major findings emerged from these gene expression studies. First, we discovered an unexpected and apparently novel pattern of very early expression of all five of the Hox genes examined in the putative growth zone of the larva, as compared with other taxa with teloblastic growth. This expression appears well before any segmentation occurs and obeys the paradigm of temporal colinearity. Second, we observed basic spatial colinearity of anterior expression boundaries like those seen in other taxa (with some important exceptions). Third, we found that some of the genes have posterior expression boundaries that relate to transitions in the tagmatized body plan of Chaetopterus.
Each of these findings will be discussed in relation to Hox expression data from other segmented protostomes, namely the leeches within the annelid group, and insects, crustaceans and chelicerates among the arthropods. We will pay special attention to the issue of whether changes in the domains of Hox gene expression between animal groups relate to differences in body plan morphology, and argue that posterior boundaries of expression may deserve special attention.
| COMPARISON OF HOX GENE EXPRESSION PATTERNS |
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Chaetopterus Hox gene expression patterns
We have examined the expression patterns of five Chaetopterus Hox genes by whole-mount in situ hybridization (Irvine and Martindale, 2000
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During larval growth the early zones of expression expand from the growth zone as the larval body is formed. By the late larval stages (stage L5, Irvine et al., 1999
Interestingly, two of the genes, CH-Hox1 and CH-Hox2 have defined posterior boundaries at the ninth segment, which corresponds to the caudal edge of the anterior region, tagma A (Fig. 1C, arrowhead 1). Likewise, CH-Hox5 expression is downregulated at the posterior boundary of segment B2, which corresponds to the morphological transition to the three palette-bearing segments (Fig. 1C, arrowhead 2). Thus, the posterior limits of expression of CH-Hox1 and CH-Hox2 correlate with a major morphological transition, the caudal terminus of the A tagma, while downregulation of CH-Hox5 corresponds to the significant morphological change from the B2 segment bearing the accessory feeding organ to the palette morphology of segments B3-B5.
Expression domains of CH-Hox3 and CH-Hox4 generally overlap throughout tagmata B and C during mid to late larval stages. However, on a finer scale, each of the genes are expressed in different, only partially overlapping portions of the ventral ganglia of those segments. The expression in the growth zone persists for all the genes examined, so that CH-Hox1, CH-Hox2, and CH-Hox5 must be down-regulated in the region between the A tagma and the caudal growth zone.
Hox gene expression in other annelids
The closest phylogenetic comparison currently possible, given present data, is with the leeches, members of the other major annelid group the clitellates. In contrast to Chaetopterus, leeches have a largely homonomous body plan, with very similar segmental morphology along the body axis. Although they have a highly derived mode of direct development, without a larval stage, they share with polychaetes teloblastic growth of the segmental body from a prepygidial growth zone (Anderson, 1973
; Weisblat and Shankland, 1985
).
In the leeches Helobdella and Hirudo, expression patterns for paralogy group Hox1, Hox4, Hox5, Hox6, and Hox7/8 genes have been reported (Fig. 2B). As in Chaetopterus the major site of expression for all the genes is the CNS. Within the CNS both Chaetopterus and Hirudo exhibit a complex partially non-overlapping sublocalization of expression within ventral ganglia where more than one Hox gene transcript is present (Kourakis et al., 1997
; Wong and Macagno, 1998
; Irvine and Martindale, 2000
). Spatial colinearity is observed, with the expected staggered anterior expression boundaries from anterior to posterior. Paralog groups 1, 4, 5, and 6 show anterior boundaries of expression in the CNS of four consecutive segments (Kourakis et al., 1997
). Paralog group 2 and 3 genes have yet to be recovered in leeches. If present their pattern of expression would be very interesting as there is no segmental gap between the paralog group 1 and 4 anterior boundaries (as would be expected according to the spatial colinearity principle) into which the paralogy group 2 and 3 genes could fit (see Fig. 2B).
Direct comparisons can be made between the Chaetopterus Hox1, 4, and 5 genes and their corresponding homologs in the leech. In the homonomous leech Lox7/Hox1 is expressed from a rostral boundary in the R1 rhombomere and the expression domain extends all along the ventral nerve cord to the posterior extend of the caudal ganglion, i.e., in all 32 body segments (Kourakis et al., 1997
). The leech Hox4 gene, Lox6, is expressed in a similar fashion to Lox7/Hox1 but with an anterior boundary displaced one segment caudally, in R2. Detectable expression of CH-Hox1, on the other hand, has an anterior boundary at the second segment and a posterior boundary at the segment 9/10 junction corresponding to the terminus of the A tagma. In Chaetopterus, CH-Hox1 expression occupies the corresponding segmental register as Lox6/Hox4, i.e., being one segment posterior to the next-most anterior Hox gene, owing to the violation of colinearity between the Chaetopterus Hox1 and Hox2 genes. Thus the CH-Hox2 anterior boundary occupies the same relative segmental register of leech Lox7/Hox1. Interestingly, the leech Lox20/Hox5 has a very restricted expression domain, being limited to two ganglia and some anterior mesodermal tissues, as opposed to the broader a-p domain of the Chaetopterus Hox5 gene. Comparison of leech Hox4 and Hox5 expression with that of their orthologs in Chaetopterus also shows a relative rostral shift in segmental register in the leech (Fig. 2B). These differences in expression domains indicate changes in the regulation of these genes somewhere in the annelid lineage.
Two central class leech genes we did not examine in Chaetopterus, Lox2 and Lox4 (paralogy group 7/8), have defined posterior boundaries corresponding with a major morphological transition (Fig. 2B). Expression of each either terminates or is down-regulated at the boundary with the caudal ganglion, a major morphological transition in the CNS (Nardelli-Haefliger and Shankland, 1992
; Wong et al., 1995
). On a cellular level, boundaries in the differentiation of the MPS neurons in the CNS correlate precisely with the boundaries of Helobdella-Lox2 expression (Berezovskii and Shankland, 1996
).
Hox gene expression in arthropods
In addition to the detailed expression data available for the highly specialized developmental mode of the long germ band insect Drosophila, a rich source of comparative data is accumulating rapidly for other arthropod taxa. Chelicerates, crustaceans, and short germ band insects all have an analogous developmental mode to annelids, with formation of segments in anterior-posterior succession from a posterior growth zone. However, as mentioned above, no early expression pattern of Hox genes in the growth zone has been described for these taxa. The earliest expression of Hox genes for these arthropods is in the already formed segmental anlage, in the presumptive position of the developing segment.
In both insects and crustaceans mid-late stage expression of Hox genes is predominantly in the segmental ectoderm and CNS. Examination of the general character of expression domains in Drosophila and the combination of data for the crustaceans Porcelio (an isopod) and Artemia (a branchiopod) indicates a basic difference between the highly restricted antero-posterior (a-p) domains of expression of Hox genes in the head and the broader, largely overlapping domains in the trunk in both the uniramian insect and the crustaceans (Fig. 3AC). Apparently, cephalization in the complex body plans of mandibulates (insects and crustaceans) has resulted in complex regulation of both the anterior and posterior expression boundaries in the head. In addition to this gross pattern of restricted a-p expression domains, the segmental localization of expression for certain genes is conserved between the insect and crustaceans. For example, labial is expressed in the intercalary segment of the fly and the homologous second antennal segment of Porcelio, while Dfd is expressed in the two homologous gnathal segments of both fly and crustacean. On the other hand the pb and Scr homologs have somewhat shifted expression domains between the two groups (Fig. 3A, B) (Abzhanov and Kaufman, 1999a, b
).
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In the trunk of flies, the Antp, Ubx, abd-A, and Abd-B genes mediate the morphology of segments along the body axis and the morphological boundary between thorax and abdomen. It has been shown that fine temporal and spatial regulation of these genes is responsible for much of the variation in segmental morphology within and between segments (e.g., Castelli-Gair and Akam, [1995]
In the other arthropod subphylum, the Chelicerata, Hox gene expression has been sampled in three species of spiders and a mite (Abzhanov et al., 1999
; Damen et al., 1998
; Damen and Tautz, 1998, 1999
; Telford and Thomas, 1998a,b
). Taken together, the spider data (Fig. 3D) gives a fairly complete picture of Hox gene expression along the body axis (ignoring possible interspecific differences in gene expression that might confound this simplification). In this group the major sites of expression are initially in the ventral ectoderm and later in the appendages. The chelicerate body plan is characterized by two tagmata, the prosoma, including head structures, and the opisthosoma. The pattern of expression in the opisthosoma for the Hox6 through Hox8 genes is reminiscent of the insect and crustacean pattern of the trunk. While there is evidence of independent gene duplication in chelicerates, which have been found in PCR surveys (Abzhanov et al., 1999
; Cartwright et al., 1993
), the general pattern remains one of colinear staggered anterior expression borders with expression extending along the whole body axis caudally. A striking characteristic of the spider data is the posterior termination of expression for Hox1 through Hox5 genes at the prosoma/opisthosoma boundary (Damen and Tautz, 1999
; Abzhanov et al., 1999
). These coincident posterior boundaries are not seen in another chelicerate, the mite Archegozetes, where the expression domains of the Hox3, Hox4, and Hox6 orthologs overlap the prosoma/opisthosoma boundary (Telford and Thomas, 1998a, b
). This difference may relate to differences in regionalization of the body axis between spiders and mites, including the less pronounced morphological transition between the two tagma in the oribatid mite examined.
Unlike the very narrow a-p restriction of Hox expression patterns in the insect and crustacean head, the pattern in the spider prosoma has broad, only partially staggered expression zones. This lack of apparent complexity in gene regulation may reflect less extensive cephalization in the spider head than that of insects or crustaceans, reducing the required levels of control of gene expression. Alternatively, as mentioned above, the additional paralogs of some spider Hox genes, indicative of independent gene or cluster duplications, could confer more specificity in the Hox code within the basically overlapping pattern of expression. Or, of course, the developmental genetic program for the chelicerate prosoma may be very different from that of the insect or crustacean head owing to major differences in the downstream effects of the Hox genes, or the influence of unknown gene pathways.
| CONCLUSIONS |
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Conservation of colinearity
In the annelids and arthropods discussed here the basic tenet of anterior expression boundary colinearity is conserved. Since this pattern is also seen in chordates it appears that colinearity of anterior boundaries is a general characteristic of Hox gene expression. A significant exception in certain taxa are the Hox2 genes. In both Chaetopterus and the vertebrates, zebrafish and mouse, the Hox2 genes have anterior boundaries rostral to those of the Hox1 gene (Krumlauf, 1993
Correlation of changes in Hox gene expression pattern with body plan changes
Among the protostomes there are several examples of Hox gene posterior expression boundaries that correlate with morphological differences in body plan. One example is the distinction between Hox gene expression in the head versus the trunk in mandibulates. We saw above that both Drosophila and the crustacean Porcelio exhibit tightly restricted a-p domains of expression for the Hox genes in the head and anterior thorax as compared with the broader a-p domains of the trunk. This appears to be a derived condition, since the spiders and annelids do not have such limited expression domains. They also do not have the degree of cephalization seen in the mandibulates. Since colinearity of anterior boundaries is the primitive condition, these restricted a-p expression domains are likely due to changes in regulation of the posterior boundaries of expression, possibly related to cephalization and segmental specialization in the evolution of the mandibulate head.
Other examples of correlation between posterior boundary regulation and body plan regionalization are seen in Chaetopterus and the spiders. In Chaetopterus both CH-Hox1 and CH-Hox2 have distinct posterior boundaries of expression coinciding with the transition between the A and B tagma of the body axis (Fig. 2A). Similarly, in spiders there is a common posterior boundary for five of the anteriorly expressed Hox genes coinciding with the division between the two body tagma, the prosoma and opisthosoma (Fig. 3D). Other cases are seen in leeches, with expression of Lox2 in Helobdella and Lox4 in Hirudo terminating at the anterior side of the caudal ganglion (Fig. 2B). Finally, in the brine shrimp Artemia, the Hox6, Hox7, and Hox8 genes all share a posterior boundary at the junction of the thorax and the genital region (Fig. 3C). The relationships of posterior boundaries for these genes is modified in the more highly differentiated trunk of Drosophila (Fig. 3A).
Changes in regulation of posterior expression boundaries: an avenue for evolutionary change?
From the foregoing, it is apparent that correlation of posterior Hox gene expression boundaries with morphological boundaries in various taxa is common. One observation that could be made is that posterior expression boundaries do not appear to be under a constraint comparable to the colinear constraint of anterior boundaries, and that the position of the posterior boundary can be independent of the relative segmental register of the anterior boundary. For example CH-Hox1 and CH-Hox2 share a posterior boundary even though their anterior boundaries are staggered, and this boundary is rostral to that of CH-Hox3. On the other hand, CH-Hox5 has a posterior expression boundary rostral to that of CH-Hox4, the opposite relationship in terms of colinearity (Fig. 2A). A similar opposition is found between the leech genes Lox20/Hox5 and Lox5/Hox6 as versus Lox5/Hox6 and Lox2 and Lox4 (paralogy groups 7/8) (Fig. 2B). In the arthropods, as in annelids, posterior boundaries are free to "bunch up," as seen for the Artemia Hox6, 7, and 8 genes (Fig. 3C), and for the spider Hox15 genes (Fig. 3D).
If posterior boundaries are under looser regulatory constraints than anterior boundaries they may be more available for evolutionary change. The effect of changes in posterior boundaries would be to change the Hox code, or combination of Hox genes acting in a segment or portion of a segment. Restriction of posterior boundaries of multiple Hox genes together, such as CH-Hox1 and CH-Hox2 in Chaetopterus and the Hox15 genes in spiders could amount to a radical change in Hox code allowing a major transition in body plan morphology, like that from tagma A to tagma B in Chaetopterus or from prosoma to opisthosoma in spiders.
Patterns of Hox gene regulatory changes
Evidence of intermediate-scale regulatory changes, as compared to these more phylogenetically distant examples of differences in Hox gene expression patterns, have been found in arthropods. Averof and Patel (Averof and Patel, 1997
) showed in comparisons of Ubx expression in crustaceans that the anterior boundary of this gene shifted posteriorly in species which had evolved differences in the morphology of thoracic appendages. In species, such as Artemia, with homonomous thoracic appendages, Ubx has an anterior boundary of expression in the T1 segment, a condition considered primitive for crustaceans with uniform trunk segments. In separately derived groups, however, with anterior thoracic swimming appendages recruited to aid in feeding (called maxillipeds) the Ubx expression boundary shifted from one to four segments posteriorly in correspondence to the morphological change.
A study of Scr expression in insects from five different orders (Rogers et al., 1997
) demonstrated an expansion of late patterns of expression into lateral and ventral portions of the first thoracic segment in more derived groups. This expansion of the posterior expression boundaries was examined in detail and correlated with derived morphological structures of the prothorax as compared with the most primitive apterygote species.
These examples lend evidence to a view that both anterior and posterior expression boundaries can change in small steps within lineages and correlate with observed differences in morphology. If these small changes in Hox gene regulation continue in the evolution of various groups they could reflect a gradual mechanism for generating the pattern observed in more broad phylogenetic comparisons (Akam, 1998a
).
Future directions
Further exploration of the involvement of regulatory changes in Hox gene expression will require sampling patterns from more diverse animal groups with differing body plan organization. The polychaete annelids are an ideal group for these types of studies because of the radically different body plans derived within various polychaete families. In particular, a comparison could be made between the Hox expression patterns seen in Chaetopterus with those of a more homonomous species from the same order, such as Polydora cornuta. This comparison would provide evidence to test the hypothesis, for example, that posterior boundaries of Hox expression are involved in changes in body plan regionalization. If the posterior boundaries of expression for respective orthologs differ in segmental register, and especially if they also correlate with the more subtle morphological transitions in Polydora, it would lend support to the hypothesis. If, on the other hand, the segmental register of posterior boundaries is the same in both species, the changes in body plan regionalization seen in Chaetopterus must be ascribed to downstream events, or different molecular genetic pathways altogether. This is not to say, however, that if the hypothesis is supported that changes in Hox gene regulation are the direct cause of the morphological differences. Rather, the Hox gene expression pattern differences are a read-out of changes in a developmental pathway likely to be involved in the evolutionary events leading to changes in body plan regionalization. As described in part above, these types of comparisons are underway in a subphylum of arthropods with much morphological variation between families, the crustaceans, owing to the comparative studies undertaken most extensively by the Kaufman, Akam, and Patel laboratories.
Moving beyond Hox genes as markers for the developmental pathway changes resulting in morphological evolution will then require looking to the actual regulatory mechanisms behind the Hox gene expression patterns currently being sampled. One approach to this work is the dissection of cis-regulation using cross-species transgenic analysis (e.g., Carr et al., 1998
). A recent study by (Locascio et al., 1999
) examined the cis regulation of the ascidian CiHox3 gene in reciprocal transgenic reporter experiments between Ciona and mouse. Regulatory elements identified in Ciona were tested in transgenic mouse embryos, and known regulatory sequences from mouse were inserted in the ascidian genome. The authors were able to conclude that though mouse Hox3 regulatory elements failed to reproduce any neural expression in Ciona, an ascidian enhancer fragment could produce a segmental expression pattern in the mouse hindbrain. Further studies of this sort could help determine the specific regulatory changes responsible in part for divergent morphology between animal groups. Another ongoing approach is the comparative analysis of genomic sequences to identify differences in enhancer elements followed by the site-directed knock-in of the enhancer from one species into another to study its functional significance. An example of this approach is an analysis of sequences of the Hoxc-8 early enhancer in mammals, which revealed a specific cis-element deletion in the baleen whales (Shashikant et al., 1998
). A study is now in progress to insert this whale enhancer into the homologous genomic location in the mouse to assay its functional consequence (F. H. Ruddle and H. Juan, personal communication). While these types of studies have only just begun, they promise to help reveal the actual evolutionary events behind regulatory changes in Hox gene regulation and their involvement in the evolution of regionalized body plans.
| ACKNOWLEDGMENTS |
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The authors thank the organizers of the Hox symposium, Drs. Billie J. Swalla and Jeffrey L. Ram, as well as SICB for inviting our participation in this important opportunity for interchange of ideas in the field. Thanks also to Drs. Terri A. Williams and Elaine C. Seaver for incisive comments on the manuscript. SQI acknowledges the support of Dr. Frank Ruddle at Yale University and an NSF/Sloan Foundation Postdoctoral Fellowship. MQM acknowledges the support of the NSF.
| FOOTNOTES |
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1 From the Symposium HOX Clusters and the Evolution of Morphology presented at the Annual Meeting of the Society for Integrative and Comparative Biology, 48 January 2000, at Atlanta, Georgia.
2 E-mail: mqmartin{at}hawaii.edu ![]()
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