Trifolin: a Rhizobium recognition protein from white clover

A protein agglutinin, trifoliin, was purified from white clover seeds and seedling roots. Trifoliin specifically agglutinates the symbiont of clover, Rhizobium trifolii, at concentrations as low as 0.2 microgram protein/ml, and binds to the surface of encapsulated R. trifolii 0403. This clover protein has a subunit with Mr approximately 50 000, an isoelectric point of 7.3, and contains carbohydrate. Antibody to purified trifoliin binds to the root hair region of 24-h-old clover seedlings, but does not bind to alfalfa, birdsfoot trefoil or joint vetch. The highest concentration of trifoliin on a clover root is present at sites where material in the capsule of R. trifolii binds. 2-Deoxy-D-glucose elutes trifoliin from intact clover-seedling roots, suggesting that this protein is anchored to root cell walls through its carbohydrate binding sites. We propose that trifoliin on the root hair surface plays an important role in the recognition of R. trifolii by clover.     

Regulation by fixed nitrogen of host-symbiont recognition in the Rhizobium-clover symbiosis

Either NO₃⁻ (16 millimolar) or NH₄⁺ (1 millimolar) completely inhibited infection and nodulation of white clover seedlings (Trifoliin repens) inoculated with Rhizobium trifolii. The binding of R. trifolii to root hairs and the immunologically detectable levels of the plant lectin, trifoliin, on the root hair surface had parallel declining slopes as the concentration of either NO₃⁻ or NH₄⁺ was increased in the rooting medium. This supports the role of trifoliin in binding R. trifolii to clover root hairs. Agglutination of R. trifolii by trifoliin from seeds was not inhibited by these levels of NO₃⁻ or NH₄⁺. The results suggest that these fixed N ions may play important roles in regulating an early recognition process in the Rhizobium-clover symbiosis, namely the accumulation of high numbers of infective R. trifolii cells on clover root hairs.     

Receptor Site on Clover and Alfalfa Roots for Rhizobium

Sites on white clover and alfalfa roots that bind Rhizobium trifolii and R. meliloti capsular polysaccharides, respectively, were examined by fluorescence microscopy. Fluorescein isothiocyanate-labeled capsular material from R. trifolii bound specifically to root hairs of clover but not alfalfa. Binding was most intense at the root hair tips. Treatment of clover roots with 2-deoxyglucose (2-dG) prevented binding of R. trifolii capsular material to the roots. The sugar 2-dG enhanced the elution of clover root protein, which could bind to and specifically agglutinate R. trifolii but not R. meliloti or R. japonicum. The mild elution procedure left the roots intact. Agglutination of R. trifolii and passive hemagglutination of rabbit erythrocytes coated with the capsular material of R. trifolii were specifically inhibited by 2-dG. These results suggest that clover roots contain proteins that cross-link complementary polysaccharides on the surface of clover root hairs and infective R. trifolii through 2-dG-sensitive binding sites. Alfalfa root hairs were shown to specifically bind to a surface polysaccharide from R. meliloti.     

Effect of nitrate supply on the in-vivo synthesis and distribution of trifollin A,a Rhizobium trifolii-binding lectin,in Trifolium repens seedlings

In-vivo synthesis of the white-clover lectin, trifoliin A, was examined by the incorporation of labeled amino acids into protein during heterotrophic growth of intact Trifolium repens L. seedlings. Lectin synthesis was quantified by measuring the level of labeled protein immunoprecipitated from root exudate, from the hapten (2-deoxyglucose) eluate of the roots, and from root and shoot homogenates. The presence of labeled trifoliin A was confirmed by non-denaturing and sodium dodecyl sulfate-polyacrylamide gel electrophoresis, followed by fluorography and comparison with trifoliin A standards. In-vivo-labeled trifoliin A was detected in seedling root homogenate 2 h after the addition of labeled amino acids and on the root surface by 8 h. Incorporation of labeled amino acids into protein and trifoliin A was greatest with 2-d-old seedlings and was greater when the plants were grown continuously in the dark than when they were exposed to 14 h light daily. Significantly more labeled lectin accumulated on the root surface of seedlings grown with 1.5 mM KNO₃ than of seedlings grown either without N or with 15.0 mM KNO₃. The labeled lectin from the root surface in all nitrate treatments and from the rootexudate samples of seedlings grown N-free and with 1.5 mM KNO₃ was fully able to bind to Rhizobium trifolii. In contrast, only 2% of the immunoprecipitable protein found in the root exudate of seedlings grown with 15.0 mM KNO₃ was able to bind to the bacteria. Thus, excess nitrate does not repress the synthesis of trifoliin A in the root, but does affect the distribution and activity of this newly synthesized lectin in a way which reduces its ability to interact with R. trifolii. By using Western blot analysis, much more total trifoliin A is detected in the homogenates of shoots than roots. However, greater than 80% of the total labeled protein and 85–90% of the total labeled lectin were found in the root homogenates of 2-d-old dark-grown seedlings incubated for 5 h with labeled amino acids. In addition, Western blot analysis indicated that the shoot homogenate contained smaller-molecular-weight peptides which reacted with the specific anti-trifoliin A antibody. These studies indicate that stored trifoliin A in the seed is degraded in the shoots during seedling development, while newly synthesized trifoliin A in the roots is excreted to the root surface and external environment.Abbreviations IgG immunoglobulin G - LPS lipopolysaccharide - PBS 10 mM potassium-phosphate buffer, pH 7.0, containing 0.8% NaCl - PBS-T 20 mM phosphate-buffered saline, pH 7.4, containing 0.05% Tween 20 - SDS-PAGE sodium dodecyl sulfate-polyacrylamide gel electrophoresis     

Lack of a direct nitrate-trifoliin A interaction in the Rhizobium-clover symbiosis

Summary Nitrate added at critical concentrations to plant growth medium inhibits the infection of legume roots by Rhizobium. The direct interaction, of nitrate and trifoliin A, a Rhizobium-recognition lection from white clover (Trifolium repens L.), was examined as a possible basis for this regulation. Selective molecular ultrafiltration studies to detect ligand-protein interactions showed that radioactive¹³NO₃ ⁻ did not bind directly to trifoliin A when incubated at two molar ratios. Immunoprecipitation of trifoliin A by its homologous antibody was unaffected by 15 mM NO₃ ⁻. In addition, there was no apparent reduction in attachment ofR. trifolii 0403 to root hairs of clover seedings during 1 h of incubation in the presence of 15 mM NO₃ ⁻. These results show that nitrate inhibition of these early steps of the infection process is not due to a direct interaction of nitrate with trifoliin A or its glycosylated receptors.     

Bacterial polysaccharide which binds Rhizobium trifolii to clover root hairs.

Immunofluorescence, quantitative immunoprecipitation, and inhibition of bacterial agglutination and passive hemagglutination indicate that cross-reactive antigenic determinants are present on the surface of Rhizobium trifolii and clover roots. These determinants are immunochemically unique to this Rhizobium-legume cross-inoculation group. The multivalent lectin trifoliin and antibody to the clover root antigenic determinants bind competitively to two acidic heteropolysaccharides isolated from capsular material of R. Trifolii 0403. The major polysaccharide is an antigen which lacks heptose, 2-keto-3-deoxyoctulosonic acid, and endotoxic lipid A. The minor polysaccharide in the capsular material of R. Trifolii 0403 contains the same antigen in addition to heptose, 2-keto-3-deoxyoctonate, and lipid A. The acidic polysaccharides of two strains of R. trifolii share the clover r-ot cross-reactive antigenic determinant despite other differences in their carbohydrate composition. Studies with monovalent antigen-binding fragments of anti-clover root antibody and Azotobacter vinelandii hybrid transformants carrying the unique antigenic determinant suggest that these polysaccharides bind R. trifolii to the clover root hair tips which contain trifoliin.     

Specific phases of root hair attachment in the Rhizobium trifolii-clover symbiosis

The time course and orientation of attachment of Rhizobium trifolii 0403 to white clover root hairs was examined in slide cultures by light and electron microscopy. Inocula were grown for 5 days on defined BIII agar medium and represented the large subpopulation of fully encapsulated single cells which uniformly bind the clover lectin trifoliin A. When 10(7) cells or more were added per seedling, bacteria attached within minutes, forming randomly oriented clumps at the root hair tips. Several hours later, single cells attached polarly to the sides of the root hair. This sequence of attachment to clover root hairs was selective for R. trifolii at inoculum sizes of 10(7) to 4 X 10(8) per seedling, specifically inhibited if 2-deoxy-D-glucose, a hapten for trifoliin A, was present in the inoculum, and not observed when 4 X 10(8) cells were added to alfalfa seedling roots or to large clover root cell wall fragments which lacked trifoliin A but still had trifoliin A receptors. Once attached, R. trifolii 0403 became progressively less detachable with 2-deoxy-D-glucose. At smaller inoculum sizes (10(5) to 10(6) cells per seedling), there was no immediate clumping of R. trifolii at clover root hair tips, although polar binding of bacteria along the root hair surface was observed after 4 h. The interface between polarly attached bacteria and the root hair cell wall was shown to contain trifoliin A by immunofluorescence microscopy. Also, this interface was shown by transmission electron microscopy to contain electron-dense granules of host origin. Scanning electron microscopy revealed an accumulation of extracellular microfibrils associated with the lateral and polar surfaces of the attached bacteria, detectable after 12 h of incubation with seedling roots. At this same time, there was a significant reduction in the effectiveness of 2-deoxy-D-glucose in dislodging bacteria already attached to root hairs and an increase in firm attachment of bacteria to the root hair surface, which withstood the hydrodynamic shear forces of high-speed vortexing. These results are interpreted as a sequence of phases in attachment, beginning with specific reversible interactions between bacterial and plant surfaces (phase I attachment), followed by production of extracellular microfibrils which firmly anchor the bacterium to the root hair (phase 2 adhesion). Thus, attachment of R. trifolii to clover root hairs is a specific process requiring more than just the inherent adhesiveness of the bacteria to the plant cell wall.(ABSTRACT TRUNCATED AT 400 WORDS)     

Specific phases of root hair attachment in the Rhizobium trifolii-clover symbiosis.

The time course and orientation of attachment of Rhizobium trifolii 0403 to white clover root hairs was examined in slide cultures by light and electron microscopy. Inocula were grown for 5 days on defined BIII agar medium and represented the large subpopulation of fully encapsulated single cells which uniformly bind the clover lectin trifoliin A. When 10(7) cells or more were added per seedling, bacteria attached within minutes, forming randomly oriented clumps at the root hair tips. Several hours later, single cells attached polarly to the sides of the root hair. This sequence of attachment to clover root hairs was selective for R. trifolii at inoculum sizes of 10(7) to 4 X 10(8) per seedling, specifically inhibited if 2-deoxy-D-glucose, a hapten for trifoliin A, was present in the inoculum, and not observed when 4 X 10(8) cells were added to alfalfa seedling roots or to large clover root cell wall fragments which lacked trifoliin A but still had trifoliin A receptors. Once attached, R. trifolii 0403 became progressively less detachable with 2-deoxy-D-glucose. At smaller inoculum sizes (10(5) to 10(6) cells per seedling), there was no immediate clumping of R. trifolii at clover root hair tips, although polar binding of bacteria along the root hair surface was observed after 4 h. The interface between polarly attached bacteria and the root hair cell wall was shown to contain trifoliin A by immunofluorescence microscopy. Also, this interface was shown by transmission electron microscopy to contain electron-dense granules of host origin. Scanning electron microscopy revealed an accumulation of extracellular microfibrils associated with the lateral and polar surfaces of the attached bacteria, detectable after 12 h of incubation with seedling roots. At this same time, there was a significant reduction in the effectiveness of 2-deoxy-D-glucose in dislodging bacteria already attached to root hairs and an increase in firm attachment of bacteria to the root hair surface, which withstood the hydrodynamic shear forces of high-speed vortexing. These results are interpreted as a sequence of phases in attachment, beginning with specific reversible interactions between bacterial and plant surfaces (phase I attachment), followed by production of extracellular microfibrils which firmly anchor the bacterium to the root hair (phase 2 adhesion). Thus, attachment of R. trifolii to clover root hairs is a specific process requiring more than just the inherent adhesiveness of the bacteria to the plant cell wall.(ABSTRACT TRUNCATED AT 400 WORDS)     

Interaction of Azospirillum and Rhizobium Strains Leading to Inhibition of Nodulation

Rhizobium-Azospirillum interactions during establishment of Rhizobium-clover symbiosis were studied. When mixed cultures of Azospirillum and Rhizobium trifolii strains were simultaneously inoculated onto clover plants, no nodulation by R. trifolii was observed. R. trifolii ANU1030, which nodulated clover plants without attacking root hairs, i.e., does not cause root hair curling (Hac⁻), did not show inhibition of nodulation when inoculated together with Azospirillum strains. Isolation of bacteria from surface-sterilized roots showed that azospirilla could be isolated both from within root segments and from nodules. Inhibition of nodulation could be mimicked by the addition of auxins to the plant growth medium.     

Root hair deformation in the white clover/Rhizobium trifolii symbiosis

Rhizobium trifolii most frequently infects its host white clover (Trifolium repens L.) by means of infection threads formed in markedly curled root hairs. Rhizobium infections are classified as either lateral or apical based on whether they originate in the branches or at the apex of the root hairs. A quantitative estimate of lateral and apical infection in the region of the host root (Trifolium repens L. cv. Regal Ladino) that possessed mature and immature root hairs at the time of inoculation with Rhizobium trifolii TAI (CSIRO, Canberra City, Australia) indicated that lateral infection occurred more frequently in the mature root hair region of the root. Apical infections were more common in the immature root hair region. Cell free filtrates collected from R. trifolii cultured in association with the host roots induced branching in white clover root hairs. A partially purified preparation of the branching factor was obtained from freeze-dried filtrates by ethanol extraction and ion exchange chromatography. Preliminary studies on the characteristics of these substances suggest that some are dialyzable and heat stable white others are non-dialyzable and heat labile. The dialyzable, heat-stable compounds contain neutral sugars and range between 1200 to 10000 daltons in size. In roots that were exposed to low concentrations (6–25 μg-ml^?1) of these partially purified deformation factors before inoculation, the developmentally mature root hairs were deformed at the time of inoculation. Nodules appeared in the mature and immature root hair region of these plants at the same time. In plants exposed to water, nodules were observed in the immature root hair region and mature root hair regions 3 and 5 days after inoculation, respectively. Based on these results, we conclude that the nodule development was hastened in the plants exposed to the root hair-deforming substances because the mature root hairs of these plants were made infectible at the time of inoculation by this exposure.     

Transient susceptibility of root cells in four common legumes to nodulation by rhizobia

Root cells of four common legumes were found to remain susceptible to nodulation by rhizobia for only a short period of time. Delayed inoculation experiments conducted with these legume hosts indicated that the initially susceptible region of the root became progressively less susceptible if inoculations were delayed by a few hours. Profiles of the frequency of nodule formation relative to marks indicating the regions of root and root hair development at the time of inoculation indicated that nodulation of Vigna sinensis (L.) Endl. cv California Black Eye and Medicago sativa L. cvs Moapa and Vernal roots was inhibited just below the region that was most susceptible at the time of inoculation. This result suggests the existence of a fast-acting regulatory mechanism in these hosts that prevents overnodulation. Nodulation in white clover may occur in two distinct phases. In addition to the transient susceptibility of preemergent and developing root hair cells, there appeared to be an induced susceptibility of mature clover root hair cells. A cell-free bacterial exudate preparation from Rhizobium trifolii cells was found to render mature root hair cells of white clover more rapidly susceptible to nodulation.     

Selective removal of seedling root hairs for studies of the Rhizobium-legume symbiosis

A freeze-fracture method has been developed for the selective removal of root hairs from white clover (Trifolium repens L.) and alfalfa (Medicago sativa L.) seedling. This procedure yields sufficient material for analysis of root hair proteins by polyacrylamide gel electrophoresis and can be adapted to study in vivo protein synthesis in these differentiated epiderman cells. Clover root hairs which have been injected by the nitrogen-fixing symbiont, Rhizobium trifolii 0403, are also detached from roots by this process, yielding appropriate material to study root responses to the bacterial symbiont during the infection process.     

Microscopic analysis of the effect ofRhizobium leguminosarum biovartrifolii host specific nodulation genes in the infection of white clovers

Summary A microscopic assessment is presented of the comparative infection capacity of wild-type and hybrid strains ofRhizobium leguminosarum bv.viciae withR. l. bv.trifolii strain ANU 843 on white clover seedlings. TheR. l. bv.viciae hybrid strains contained defined DNA segments coding for different combinations ofR. l. bv.trifolii host-specific nodulation genes. White clover plants were examined over a 72 h period to assessRhizobium infectivity, the morphological changes in root hair growth; colonisation ability of rhizobia; infection thread initiation and the ability to induce cortical cell division.R. l. bv.viciae strain 300 induced root hair curling more slowly than strain ANU 843 or any of the hybrid strain 300 bacteria, and when curling had taken place, there was poorer colonization by strain 300 within the folded hair cell, no evidence of infection thread formation and only limited cortical cell division 72 h after inoculation. The addition of the host-specific nodulation genes ofR. l. bv.trifolii to strain 300 was necessary to induce infection threads and establish a normal pattern of nodulation of the roots of white clovers.     

Alteration of the Trifoliin A-Binding Capsule of Rhizobium trifolii 0403 by Enzymes Released from Clover Roots

The effect of white clover root exudate on capsules of Rhizobium trifolii 0403 was examined. The clover lectin trifoliin A was detected in root exudate of two clover varieties by indirect immunofluorescence with antibody against this lectin purified from clover seed. Trifoliin A bound uniformly to encapsulated, heat-fixed cells during 1 h of incubation with root exudate. After 4 to 8 h of incubation, trifoliin A was only bound to one pole of the cells. Transmission electron microscopy showed that the capsule itself was altered. The disorganization of the acidic polymers of the capsule began in the equatorial center of the rod-shaped cell and then progressed toward the poles at unequal rates. Trifoliin A could no longer be detected on heat-fixed cells after 12 h of incubation with root exudate. However, trifoliin A was detected in situ on one pole of cells grown for 4 days in the clover root environment of Fahraeus slide cultures. Inhibition studies with the hapten 2-deoxy-d-glucose showed that trifoliin A in root exudate had a higher affinity for one of the cell poles. Immunoelectrophoresis was used to monitor the alteration of the extracellular polysaccharides from R. trifolii 0403 by concentrated root exudate. These polysaccharides were converted into products which eventually lost their ability to immunoprecipitate with homologous antibody. This progressive loss of antigenic reactivity proceeded more rapidly with root exudate from seedlings grown under nitrogen-free conditions than with root exudate from plants grown with 15 mM KNO(3). The root exudate, depleted of trifoliin A by immunoaffinity chromatography, was still able to alter the capsule of R. trifolii 0403. Reconstitution experiments showed that the substance(s) in root exudate which induced this alteration of the capsule was of a high molecular weight, heat labile, trypsin sensitive, and antigenically unrelated to trifoliin A. A variety of glycosidase activities were also detected in the fraction depleted of trifoliin A. These results suggest that enzymes in clover root exudate alter the trifoliin A-binding capsule in a way which would favor polar attachment of R. trifolii to clover root hairs.     

A Structural Comparison of the Acidic Extracellular Polysaccharides from Rhizobium trifolii Mutants Affected in Root Hair Infection

The structures of the acidic extracellular polysaccharides (EPSs) from several R. trifolii mutants were compared by examining their compositions and their sugar linkages as determined by methylation analysis. These mutant strains were derived from the wild-type R. trifolii ANU843 and were unable to induce normal root hair curling (Hac- phenotype) or nodulation response (Nod- phenotype) in clover plants. These strains included several transposon Tn5-induced Nod-mutants, strain ANU871, which possesses a 40 to 50 kilobase deletion of the resident Sym plasmid, and strain ANU845 which is missing the Sym plasmid (pSym-). Strains ANU845(pSym-) containing either plasmid pRt150 or pBR1AN were also used. The recombinant plasmid pRt150 restores only root hair curling capacity to ANU845 while plasmid pBR1AN (an R. trifolii pSym) restores both root hair curling and nodulation capacity to this strain. Our composition and methylation results show that the EPSs from all these strains have the same glycosyl and pyruvyl linkages. Thus we suggest that neither the nod genes involved in root hair curling nor the entire pSym encodes for the arrangement of glycosyl or pyruvyl residues in these EPSs. Whether or not the nod genes dictate the location of acetyl or β-hydroxybutyrate substituent groups remains to be determined.     

Nodulation of specific legumes is controlled by several distinct loci in Rhizobium trifolii

Summary Three distinct loci (designated regions III, IV and V) were identified in the 14 kb Nod region of Rhizobium trifolii strain ANU843 and were found to determine the host range characteristics of this strain. Deletion of region III or region V only from the 14 kb Nod region affected clover nodulation capacity. The introduction to R. Leguminosarum of DNA fragments on multicopy vectors carrying regions III, IV and V (but not smaller fragments) extended the host range of R. leguminosarum so that infection threads and nodules occurred on white clover plants. The same DNA fragments were introduced to the Sym plasmid-cured strain (ANU845) carrying the R. meliloti recombinant nodulation plasmid pRmSL26. Plasmid pRmSL26 alone does not confer root hair curling or nodulation on clover plants. However, the introduction to ANU845 (pRmSL26) of a 1.4 kb fragment carrying R. trifolii region IV only, resulted in the phenotypic activation of marked root hair curling ability to this strain on clovers but no infection events or nodules resulted. Only the transfer of regions III, IV and V to strain ANU845 (pRmSL26) conferred normal nodulation and host range ability of the original wild type R. trifolii strain. These results indicate that the host range genes determine the outcome of early plant-bacterial interactions primarily at the stage of root hair curling and infection.     

Scanning Electron Microscopy of Rhizobium trifolii Infection Sites on Root Hairs of White Clover

White clover root hairs which were inoculated with Rhizobium trifolii 4S (infectious strain) contained infection threads which were observed by light microscopy and scanning electron microscopy. Three morphological types of root hairs retaining infection threads were recognized. The bacteria were strongly attached between the surfaces of two plant cell walls as follows: between surfaces of a root hair tip curled back on itself, between a protuberance from a root hair and its cell surface, or between two root hair tips clinging together. An anatomical analysis documented the attachment site of the infection thread sheath from the inside of the root hair cell.     

Identification of the sym plasmid of Rhizobium leguminosarum strain 1001 and its transfer to and expression in other Rhizobia and Agrobacterium tumefaciens

A plasmid of 150 Mdal from Rhizobium leguminosarum RCC1001 was found to be a Sym plasmid (pSym1) carrying genes for root nodulation and nitrogen fixation on plants of the pea vetch cross-inoculation group. The plasmid was expressed not only in different R. leguminosarum and R. trifolii hosts, but also in Agrobacterium tumefaciens and R. meliloti, although in root nodules induced by A. tumefaciens and R. meliloti hosts no nitrogen was fixed. The host range for root nodule induction appeared to be determined by pSym1 and only included plants of the pea vetch cross-inoculation group; in contrast, the host range for the induction of root hair deformations, which was found also to be determined by pSym1 was less restricted and included besides plants of the pea vetch group in addition plants of the clover group. This corroborates previous findings that host specificity for nodulation and nitrogen fixation is exerted at a stage after the induction of root hair deformations.     

Transient appearance of lectin receptors onRhizobium trifolii

The appearance on the surface ofRhizobium trifolii 0403 of determinants important to both clover lectin (trifoliin) binding and adherence of the bacteria to clover root epithelial surfaces was studied by quantitative agglutination, immunofluorescence, and direct microscopic techniques. These unique determinants were found for only transient periods of time—as cells left lag phase and as they entered stationary phase of growth in broth. When present, these receptors were associated with a fibrillar polyanionic capsule surrounding the cells when grown on solid medium. These studies support earlier proposals that the architecture of the rhizobial cell surface is not constant in composition, but changes with the phase of growth.     

Hair Curling Induced in Heterologous Legumes and Monocots by Flavonoid-Treated Rhizobia

The curling of root hairs and the deformation response wereobserved when white clover was infected with homologous strainsof Rhizobium leguminosarum biovar trifolii 4S and 0403. In thecase of Rhizobium meliloti NZ and Rhizobium leguminosarum biovarviciae 128C53, however, curling was only induced when thesebacteria were pretreated with flavonoids: luteolin in the caseof R. meliloti and naringenin for R.I. viciae. The same resultswere obtained with oat, a monocotyledonous non-leguminous plant.The two flavonoids mentioned are secreted from the host plantsand induce the expression of genes for root hair curling (Hac)on Sym plasmid in homologous rhizobia, therefore, the curlingresponse in both white clover and oat appears to be correlatedwith the activation of the Hac genes. These results suggestthat a factor(s) that activates the Hac genes, such as 7,4'-dihydroxyflavonewhich is known as the factor required by R. I. trifolii, issecreted from the oat roots. (Received June 12, 1989; Accepted November 9, 1989)