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Ann Bot. 2009 October; 104(5): 937–944.
Published online 2009 July 17. doi:  10.1093/aob/mcp175
PMCID: PMC2749544

Ultrastructure and post-floral secretion of the pericarpial nectaries of Erythrina speciosa (Fabaceae)


Background and Aims

The occurrence of nectaries in fruits is restricted to a minority of plant families and consistent reports of their occurrence are not found associated with Fabaceae, mainly showing cellular details. The present study aims to describe the anatomical organization and ultrastructure of the pericarpial nectaries (PNs) in Erythrina speciosa, a bird-pollinated species, discussing functional aspects of these unusual structures.


Samples of floral buds, ovaries of flowers at anthesis and fruits at several developmental stages were fixed and processed by the usual methods for studies using light, and scanning and transmission electron microscopy. Nectar samples collected by filter paper wicks were subjected to chemical analysis using thin-layer chromatography.

Key Results

The PNs are distributed in isolation on the exocarp. Each PN is represented by a single hyaline trichome that consists of a basal cell at epidermal level, stalk cell(s) and a small secretory multicellular head. The apical stalk cell shows inner periclinal and anticlinal walls impregnated by lipids and lignin and has dense cytoplasm with a prevalence of mitochondria and endoplasmic reticulum. The secretory cells show voluminous nuclei and dense cytoplasm, which predominantly has dictyosomes, rough endoplasmic reticulum, plastids, mitochondria and free ribosomes. At the secretory stage the periplasmic space is prominent and contains secretion residues. Tests for sugar indicate the presence of non-reducing sugars in the secretory cells. Nectar samples from PNs contained sucrose, glucose and fructose.


The secretory stage of these PNs extends until fruit maturation and evidence suggests that the energetic source of nectar production is based on pericarp photosynthesis. Patrolling ants were seen foraging on fruits during all stages of fruit development, which suggests that the PNs mediate a symbiotic relationship between ants and plant, similar to the common role of many extrafloral nectaries.

Keywords: Ant–plant interactions, Erythrina speciosa, Fabaceae, Faboideae, fruit anatomy, nectar secretion, nectary, post-floral nectaries


Nectaries on fruits are considered for some authors as post-floral nectaries, structures that can be defined as glands of the reproductive organs after corolla abscission, which predominantly secrete sugars. In this work, the term ‘pericarpial’ will be used instead of ‘post-floral’ to designate the nectaries on the fruit, since the latter is an improper term because floral nectaries are capable of persisting intact and functional during fruit development. Considering Schmid (1988), in this situation ‘post-floral’ refers to the secretion products instead of the secretory structures. ‘Post-floral’ is the general term for any nectar secretion that occurs after fertilization or corolla abscission. Thus, this term must be employed to refer to a nectar secretion stage and not to the nectary itself.

Functionally, the pericarpial nectaries (PNs) are similar to the extrafloral nectaries (EFNs), both being related to plant protection (Fahn, 1979). Occurrence of nectaries with post-floral nectar secretion has been reported in 21 plant families, but not in Fabaceae (see Bernardello, 2007).

PNs have frequently been treated in the literature as EFNs. This can be justified to a certain extent by their morphological and functional similarities (see Elias and Gelband, 1976; Morellato and Oliveira, 1994; Pacini and Nicolson, 2007), although it seems strange that nectaries occurring within floral structures can be considered by some authors as EFNs. This contradiction is due to distortions of the definition of floral and EFNs, as proposed by Caspary (1848 apud Schmid, 1988), who discusses the position of these structures in plants. The term extrafloral nectary has been widely used with the significance first proposed by Delpino (1886) for extranuptial nectaries, and thus took on a broader definition as any nectary that is not directly involved in the process of pollination (see Elias and Gelband, 1976). Given the morphological and functional similarities between PNs and EFNs, information about the structure of EFNs can be useful in discussing PNs.

There have been many reports of EFNs being involved in protection against herbivory (see Oliveira and Freitas, 2004; Kobayashi et al., 2008), and the few published studies available that concern PNs have come to similar conclusions. Thus, the nectar production of the PNs constitutes an adaptative advantage, because they attract ants that, in turn, protect the developing fruit against herbivores (Keeler, 1981).

Approximately 6 % of the Fabaceae (approx. 1027 species) have EFNs (Keeler, 2009). It should be noted that these structures are only functional on very young leaves in many species, which makes their identification difficult and occasionally results in false negatives, which implies that the number presented above is most likely an underestimation. Among the Fabaceae, EFNs are present in large numbers of species in the subfamily Mimosoideae, being most common among the Caesalpinioideae, but less frequent in Faboideae species (Elias, 1983; Keeler, 2009). Among the Faboideae, EFNs are known almost exclusively from the tribes Vicieae and Phaseoleae where they are composed of aggregations of clavate nectariferous trichomes located on the stipules or stipels, while in the other subfamilies they occur on the petioles and leaf blades, and are apparently derived from independent evolutionary lines (Lersten and Brubaker, 1987). In many species of Erythrina, EFNs are composed of pairs of glands at the base of the leaflets (Delpino, 1886; So, 2004). The genus Erythrina is an important member of the Faboideae tribe Phaseoleae, and comprises approx. 112 species widely distributed throughout the tropics, and is characteristically bird pollinated (see Bruneau, 1996).

According to Werker (2000), little is known about secretory trichomes on plant gynoecia which can be extended to these trichomes on fruit. The present work describes the location, histochemistry and ultrastructure of the trichomes that constitute PNs on the fruits of E. speciosa, emphasizing their functional aspects during the secretory stage.


Sampling of plant material, insect visitors and nectar

Samples of floral buds, ovaries of flowers at anthesis and fruits at different developmental stages were collected from specimens of Erythrina speciosa Andrews cultivated at the Pampulha campus of the Universidade Federal de Minas Gerais, Minas Gerais State, Brazil. The developmental stages of sampled fruits were: fruits in expansion stage (about 50 % expanded); immature but fully expanded fruits; mature fruits before dehydration stage.

Ants observed feeding on the nectar produced by the fruits were also collected, fixed and stored in 70 % ethyl alcohol for identification.

Ten immature fruits with completely expanded pericarps were collected in the early morning and their peduncles were cut while immersed in a beaker (500 mL) of water in order to prevent cavitation. The fruits were then placed in a humidity chamber for 24 h (12 : 12 h light/dark; 30 µmol m−2 s−1; room temperature) with the peduncle immersed in water so that nectar would be produced in sufficient volume to assist its collection for subsequent carbohydrate analysis. Due to the naturally small volumes of their secretions, nectar collection was performed by wiping the surface of the fruits with Whatman filter paper strips (10 × 3 mm) until the strips were saturated (one strip per fruit). The nectar collection was carefully conducted in order to avoid damage to the PNs and assure that only nectar was removed. Each strip was then soaked with 0·1 mL of distilled water and the paper was hand compressed to expel the nectar in solution; this extract was applied to plates for thin-layer chromatography (TLC).

Chemical characterization of sugars

The extract with nectar was immediately transferred by capillary tubes to silica gel TLC plates prepared with 0·02 % sodium acetate to detect and identify the sugars. Likewise, standard marker solutions of fructose, glucose and sucrose, as well as distilled water (control), were applied to the same plates. The plates were run with a mobile phase of chloroform:methanol (6 : 4). After running, the plates were dried at room temperature, sprayed with an orcinol-sulfuric acid solution, and heated to 120 °C for 5 min. Sugars stain as dark-purple bands against a yellow background (Stahl, 1988).

Light microscopy and histochemical tests

For anatomical examination of flowers and fruits by light microscopy, samples were fixed in Karnovsky solution (Karnovsky, 1965) for 24 h, dehydrated in an ethanol series, and embedded in hydroxyethyl-methacrylate (Leica Microsystems Inc., Heidelberger, Germany). Transverse and paradermal sections (5 µm) were cut with a rotary microtome and subsequently stained in 0·05 % toluidine blue, pH 4·3 (O'Brien et al., 1964). Paradermal sections of fresh completely expanded fruits were examined using a microscope equipped with a micrometric scale to determine the density of PNs that was evaluated in fields at ×10 magnification, in an Olympus BH-2 light microscope. All data (n = 50 fields) was submitted to variance analysis.

The following histochemical tests were performed on fresh, hand-cut sections: an aqueous solution of ruthenium red to detect the presence of acidic polysaccharides (Johansen, 1940); lugol solution to detect starch (Johansen, 1940), Sudan black B to detect lipids (Pearse, 1980), Fehling reagent to detect reducing sugars (Sass, 1951) and phloroglucinol acid to detect lignin (Johansen, 1940).

Electron microscopy

Samples to be examined using transmission electron microscopy were fixed in Karnovsky solution (Karnovsky, 1965) for 24 h, post-fixed in 1 % osmium tetroxide in 0·1 m phosphate buffer, pH 7·2, and processed using standard methods (Roland, 1978). Ultra-thin sections were treated with uranyl acetate and lead citrate and examined using a Philips CM 100 transmission electron microscope at 60 kV.

Samples to be examined using scanning electron microscopy were fixed in 2·5 % glutaraldehyde in 0·1 m phosphate buffer, pH 7·2, dehydrated in an ethanol series, and dried to their critical point (Robards, 1978). These dried samples were glued on aluminum stubs, gold coated, and examined on a Quanta 200 SEM (FEI Company) at 20 kV.


Distribution, structure and functional aspects

The PNs of Erythrina speciosa are formed during the initial stages of ovary development, differentiating in the floral buds during pre-anthesis. The PNs only become functional after abscission of the corolla, and they remain active until the pericarp becomes completely differentiated and the fruits demonstrate the first signs of maturation. The PNs become senescent when the pericarp begins to dry out.

The PNs of Erythrina speciosa are too small to be seen with the naked eye, but small drops of nectar produced by the nectaries can be seen under low magnification. PNs occur isolated (Fig. 1A) and randomly distributed on the fruit; their densities vary during the process of fruit expansion as they are formed during the initial phases of development. The quite high density of nonsecretory trichomes in young and incompletely expanded fruits makes it difficult to identify the nectaries even when a stereomicroscope is used, once the PNs are transparent and are found under the indumentum.

Fig. 1.
General view of pericarpial nectaries on fruit surface of Erythrina speciosa. These fruits were young (about 50 % expanded). (A, B) SEM images of nectaries (in A, arrows indicate many of them); in (B) a closer view of the trichome nectary consisting of ...

Nonsecretory trichome density becomes significantly reduced in expanded fruits as these structures become senescent, and are eventually shed being largely eliminated in later developmental stages. This loss of pubescence, however, facilitates the visualization of the secretory trichomes (the PNs) in this developmental phase of fruit, and they can be seen to have an average density of 7·52 mm−2.

The PNs are clavate glandular trichomes composed of a basal cell, a single or two-celled stalk, and by approximately eight secretory cells that are covered by a cuticle (Fig. 1B, C). The major axis of the nectary forms an acute angle in relation to the fruit surface that is determined by the basal cell or the basal stalk cell, thus the secretory portion is aligned parallel to the fruit surface (Fig. 1B, C). The pericarp vascular bundles do not appear to have any relationship with the nectaries or with their distribution.

Examinations of diverse developmental stages of the fruit indicated that the presence of starch in the epidermal cells (exocarp) is restricted to the stomatal guard-cells. Starch was not observed in the mesocarp during the pericarp expansion, although in fully expanded fruits starch was notably present and concentrated in the internal layers of the median and inner mesocarp, especially near to the dorsal bundle.

Starch was rarely observed in PNs, especially in the secretory cells. Tests for sugar using Fehling reagent gave positive results only after acid hydrolysis, indicating the presence of non-reducing sugars in the secretory cells. These same compounds were not detected in the basal or stalk cells. Nectar samples from PNs that were analysed by TLC indicated the presence of sucrose, glucose and fructose in the secretion. In the nectaries the lignin seems to be restricted to the anticlinal walls of the apical stalk cell, which showed some lipids too.

Ultrastructural aspects

The basal cell, disposed at epidermal level, shows ultrastructural characteristics of protoplasm similar to the other adjacent epidermal cells. The subjacent parenchymatic cells likewise did not exhibit any characteristics that would distinguish them from the other nearby cells.

The apical (or single) stalk cell of a PN has thick and cellulosic cell walls that are impregnated with lignin and lipidic compounds, which are not seen on the distal face in contact with the secretory cells. The cytoplasm is dense and has many mitochondria and a smooth endoplasmic reticulum (Fig. 2A, B). The mitochondria were longer, numerous, and had dense stroma and highly developed cristae (Fig. 2B). Oil droplets were seen scattered throughout the cytosol and near the plasma membrane, although only in small numbers. When the stalk is two-celled, the basal cell has thick anticlinal cell walls that were impregnated with lipids, but its protoplast is similar to the other epidermal cells.

Fig. 2.
Ultrastructural aspects of pericarpial nectaries of Erythrina speciosa. (A, B) Stalk cells. In (A) note that the basal stalk cell shows phenolic compounds in the vacuoles. The apical stalk cell (B) shows dense cytoplasm with a high mitochondrion population; ...

The secretory cells show large nuclei, and dense cytoplasms that predominantly have dictyosomes, rough endoplasmic reticulum (RER), plastids, mitochondria and free ribosomes (Fig. 2C–E). The connection between the stalk cell and the secretory cells is predominantly symplastic, as indicated by the high number of plasmodesmata between them (Fig. 3A). On the other hand, at the proximal wall, towards the basal cell, there is a complete absence of plasmodesmata. The secretory cells are compactly arranged, with no visible intercellular spaces. A periplasmic space was preeminent during the secretory phase containing an amorphous material that apparently represented secretion residues. The vacuolar component of these cells was quite reduced, and many multi-vesicular bodies were visible in the smaller vacuoles (Fig. 2E).

Fig. 3.
Ultrastructural aspects of secretory cells of the capitate trichome head of pericarpial nectaries of Erythrina speciosa. (A) Detail showing plasmodesmata (arrows) that connect protoplasts of secretory cells. (B) At the peripheral cytoplasm, note the presence ...

The Golgi apparatus is randomly distributed within the cytoplasm, and composed of several dictyosomes with just a few cisternae each (Fig. 2C, D). Dictyosome vesicles were seen in the peripheral cytoplasm and they were frequently joined to the plasma membrane.

The RER was observed to be well developed and distributed throughout the cytoplasm. The RER in the periplasmic region was frequently arranged in parallel series, near to the plasma membrane (Fig. 3B).

Plastids were very numerous and distributed in the perinuclear region, having dense stroma, poorly developed membrane systems, and plastoglobuli (Fig. 2C, E). The mitochondria of the secretory cells were predominantly globe-shaped and showed well-developed cristae (Fig. 2D, E), differing from those of the stalk cell. The formation of an ample subcuticular space (Figs 1C and and3C)3C) is a notable characteristic of the secretory cells, although there were no signs of ruptures, pores or canals through the cuticle (Fig. 3C).

Insect visitors

Ants (Camponotus sp., Cephalotes sp. and Pseudomyrmex sp.) were observed patrolling and foraging on the surface of these fruits during the entire period of fruit development, and actually led to the discovery of these PNs. Herbivore attack was not observed during any stage of fruit development.


Distribution, structure and functional aspects

The PNs observed in E. speciosa are structurally very simple and similar to other glandular trichomes seen in the Faboideae. Healy et al. (2005) noted the presence of glandular trichomes in the gynoecium of soybean (Glycine max) and had considered that the secretion products might supplement the floral nectar, which already had been postulated by Horner et al. (2003). However, Healy et al. (2009) demonstrated that in secretory trichomes of Glycine gynoecia, the secretion products are aqueous, fixative resistant and can be considered as non-water-soluble polysaccharides or glycoproteins. Furthermore, the PNs in E. speciosa only become active after corolla abscission and there is no indication that these structures participate in the elaboration of floral nectar.

According to McKey (1989), the glandular structures on Fabaceae leaves appear to have evolved independently several times. However, evidence suggests that the glandular trichomes may precede other more complex nectar-producing structures. Pascal et al. (2000) reported that Caesalpinieae and Mimosoideae do not possess specialized nectaries, but have patches of glandular trichomes on the rachis that constitute primitive forms homologous to these structures.

Among the Faboideae, stipular nectaries formed by aggregations of secretory trichomes that are similar to those seen in the fruits of E. speciosa, have been reported for the Erythrina (Lersten and Brubaker, 1987), Vicia (Figier, 1971; Davis et al. 1988) and Vigna (Kuo and Pate, 1985). In these cases, however, the nectary consists of crowded trichomes forming a dense cluster, and there are no reports of isolated trichomes in these genera that could be considered individual nectaries similar to those in the fruits of E. speciosa. Vogel (1998) considered nectar glands composed of just a few cells as nectarioles, and described nectar-producing trichomes in Peperomia magnoliifolia (Piperaceae) that were morphologically very similar to those seen in E. speciosa fruits.

Clavate glandular trichomes were observed on both faces of the leaves of E. speciosa and they were morphologically similar to the nectariferous trichomes described for the fruits. However, no secretions were observed to be associated with these foliar trichomes, and histochemical tests designed to detect the presence of sugars gave negative results (E. A. S. Paiva, unpubl. res.).

Observations made in the present work allow us to infer that the PNs of Erythrina precede more complex glandular structures, which corroborate the observations made by Pascal et al. (2000) and Lersten and Brubaker (1987) in Fabaceae, and argue against the hypothesis of Fahn (2002) that mesophyll secretory structures evolutionarily precede secretory trichomes. Additionally, the secretory cells of many structurally complex nectaries originate from the protoderm (Durkee, 1982; McDade and Turner, 1997; Paiva and Machado, 2006a; Paiva et al., 2007); in fact, this is a relatively common developmental pattern for some secretory structures. The participation of the protoderm in the formation of secretory structures has likewise been reported for internal secretory structures such as secretory cavities (Solereder, 1908; Paiva and Machado, 2006b). Nectaries in another species of Erythrina show a clear tendency to form agglomerations of trichomes in restricted areas of the exocarp and their trichomes are very similar to those seen in E. speciosa, which suggests a complexity gradient for these structures in the genus (E. A. S. Paiva, unpubl. res.).

According to Stephenson (1982), when nectar production is distributed among numerous nectaries, ants are forced to patrol large areas while foraging. The distribution of PNs in Erythrina speciosa fruits would therefore constitute an adaptative advantage for the plant, as many small nectaries dispersed in any given area would function as well or better than a single large nectary in terms of ant attraction (see Elias and Gelband, 1976; Paiva and Machado, 2006a; Paiva et al., 2007).

The absence of any indication of vascularization near the PNs is a common characteristic of nectaries composed of secretory trichomes, and has been reported for other species of Faboideae (Kuo and Pate, 1985; Lersten and Brubaker, 1987). Observations of E. speciosa indicate that vascular elements are not redirected towards nectaries even when pericarpial vascular bundles are seen near them. According to Carlquist (1969), the amount of vascularization associated with a plant structure is directly proportional to its size, but is not necessarily related to its evolutionary stage. As such, the absence of vascularization associated with the PNs of E. speciosa would appear to be related only to their small size and their exclusively dermal origin.

The absence of phloem elements near PNs indicates that the nectar precursors are not derived from this tissue. The PN nectar precursors in E. speciosa may originate in the photosynthetic parenchyma of the outer mesocarp, once this tissue is rich in chloroplasts, or in the inner mesocarp which has plastids with starch grains. Pacini and Nicolson (2007) proposed that the natural exposure of these kinds of nectaries to light contributes to nectar secretion, as nectar components are derived from photosynthetic processes taking place either in adjacent tissues or in other nearby regions.

The absence of starch in the PNs and in the subjacent parenchymal cells reinforces the hypothesis that chloroplasts are the immediate source of the carbohydrates to nectar. Starch reserves in nectar secretory structures are more common in species that have abundant secretions during only short periods of time, a situation compatible with pollinators that consume large quantities of nectar (Pacini et al., 2003; Paiva and Machado, 2008). This situation is observed in floral nectaries that act as nuptial nectaries (sensu Delpino, 1886).

Sugar secretion and nectar release

Although the proportions of the different sugars present in the nectar of E. speciosa was not determined, the results of the investigations allow the action of invertases to convert sucrose to monosaccharides to be inferred, as has been reported in studies of nectaries in several plant species (Gottsberger et al. 1984; Pate et al., 1985; Pacini and Nicolson, 2007). The invertase action in secreted nectar is important to assure a chemical gradient that permits a continuous flux from the secretory cells, independently of nectar removal by foragers. According to Fahn (1988) the sucrose hydrolysis can maintain a sucrose concentration gradient that could promote a passive flow of nectar.

The presence of lignin and lipidic substances in the anticlinal cell walls of the stalk cells may prevent nectar reflux towards the mesocarp, and also direct it outwards. The presence of the stalk cells with Casparian bands that avoid the apoplastic flux and consequently the secretion reflux, has been reported in several secretory structures (Lüttge, 1971; Fahn, 1988, 2000; McDade and Turner, 1997).

Ultrastructural aspects

The abundance of mitochondria in the PN stalk cell of E. speciosa suggests a high energy demand for the transport of nectar precursors from the basal cell to the secretory cells. The absence of plasmodesmata at the proximal face of the stalk cell reinforces the apoplastic transport route for the nectar precursors from mesocarp cells towards secretory cells, and corroborates the energetic demand hypothesis for pre-nectar transport. It is important to emphasize that in the apoplastic pathway, sucrose uptake requires metabolic energy (Taiz and Zeiger, 1998).

The ultrastructural characteristics of the terminal secretory cells observed in E. speciosa, such as dense cytoplasm, plastids with plastoglobuli, numerous mitochondria, well-developed endoplasmic reticulum, and active dictyosomes, were also observed in trichomes that constitute the stipel nectaries of Vigna unguiculata (Kuo and Pate, 1985). These same features have been reported in other diverse types of nectaries, and are indicative of high metabolic activities (Fahn, 1979, 1988; Durkee, 1983; Stpiczynska et al., 2005; Paiva and Machado, 2008). Lüttge (1971) likewise observed that reduced vacuolar development is related to intense metabolic activity.

The high numbers of dictyosome-derived vesicles and their fusion with the plasma membrane of the apical cells suggest that granulocrine secretion predominates in these PNs, as is commonly observed in many diverse types of nectaries (Fahn, 1979). Vicia faba has stipel nectaries composed of groups of nectariferous trichomes that have a structure very similar to that observed in the fruits of E. speciosa; in Vicia nectaries, the transport of secretion towards the plasmatic membrane was attributed to vesicles derived from dictyosomes (Figier, 1971), in the same manner as was interpreted in the PNs of E. speciosa.

Various authors have reported the presence of a well-developed RER in nectar-secreting cells (see Fahn, 1988), and according to Durkee (1983), a well-developed RER is one of the chief characteristics of active secretory cells. The presence of endoplasmic reticulum seems to be associated with the transport of nectar precursors, and has been observed in many diverse types of nectaries (Fahn, 1988, 2000; Stpiczynska et al., 2005).

The absence of canals or pores in the cuticles of the secretory cells of the PNs of E. speciosa was also reported for the secretory trichomes of Vigna unguiculata (Kuo and Pate, 1985), and the means by which the nectar passes this cuticular barrier has not been determined in either case. The pressure promoted due to secretion accumulation in the trichome secretory head, as a consequence of being a barrier to apoplastic flux, can explain the transport across the cuticle.

Insect visitors and plant protection

The constant presence of ants patrolling E. speciosa fruits in search of nectar-producing PNs and the innumerous reports of plant–ant relationships protecting the hosts against herbivores all corroborate the hypothesis that the PNs of E. speciosa act to recruit ants. However, the confirmation of this fact and the possible role of PNs in protecting the developing fruits and seeds were not directly tested here and require additional study. Recent research has demonstrated that nectar production in extra-nuptial nectaries increases under stress situations, and suggests that the defensive role of these structures is dynamic and active (see Kobayashi et al., 2008).

According to Sherbrooke and Scheerens (1979), the seed protection system in E. flabelliformis combines chemical deterrents in the seed as well as symbiotic defences that result from plant–ant interactions mediated by EFNs. The analysis of the role of leaf nectaries found on E. speciosa in maintaining beneficial ant populations would constitute a very interesting line of investigation because these leaf nectaries offer food rewards for a longer period of time, making their nectar rewards more predictable than those associated with the fruits.

Secretory trichomes are common in vegetative and reproductive organs of Faboideae and recent data (Healy et al., 2009) suggest that they can exert different functions. The present study marks the first report of trichomes involved on post-floral nectar production in the Fabaceae, and implies a necessity for an accurate evaluation of important ecological interactions mediated by these structures.


The author thanks the technical team of the Centro de Microscopia Eletrônica, Instituto de Biociências, UNESP Botucatu, for their help in preparing the samples. I am indebted to M.Sc. Igor Rismo Coelho for his help with ant identification and to Dr Arthur R. Davis and Dr Denise M. T. Oliveira for valuable suggestions. This work was supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico – CNPq (Brazil) (471444/2008-1). E. A. S. Paiva is supported by a research grant from CNPq (302048/2008-1].


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