The matrix equation XA − BX = R and its applications

AbstractWe study the well-known Sylvester equation XA − BX = R in the case when A and B are given and R is known up to its first n - 1 rows. We prove new results on the existence and uniqueness of X. Our results essentially state that, in case A is a nonderogatory matrix, there always exists a solution to this equation; a solution is uniquely determined by its first row x1; and there is an interesting relationship between x1 and the rows of R. We also give a complete characterization of the nonsingularity of X in this case. As applications of our results we develop direct methods for constructing symmetrizers and commuting matrices, computing the characteristic polynomial of a matrix, and finding the numbers of common eigenvalues between A and B. Some well-known important results on symmetrizers, Bezoutians, and inertia are recovered as special cases

Auxin + KNO₃ inducted regeneration of leguminous tree-Leucaena leucocephala through tissue culture

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Genetic stability developed for β-carotene synthesis in BR29 rice line using dihaploid homozygosity

Obtaining transgenic crop lines with stable levels of carotenoids is highly desirable. We addressed this issue by employing the anther culture technique to develop dihaploid lines containing genes involved in β-carotene metabolism. First, we used Agrobacterium- mediated transformation to develop primary transgenic plants containing the β-carotene biosynthetic genes, phytoene synthase (psy) and phytoene desaturase (crtl), which were engineered for expression and accumulation in the endosperm. Transgenic plants were recovered by selecting for the expression of the phosphomannose isomerase (pmi) gene. Dihaploid plants in addition to haploid and tetraploid plant were generated from anther cultures of these primary transgenic plants. In addition to anatomical features of stomata, pollen of different ploidy-plants, molecular analyses confirmed the stable integration of the genes in the anther culture-derived dihaploid plants, and the yellow color of the polished seeds indicated the accumulation of carotenoids in the endosperm. High performance liquid chromatography (HPLC) analysis of the carotenoid extract further confirmed the levels of β–carotene accumulation in the endosperms of the transgenic dihaploid rice seeds

Development of low phytate rice by RNAi mediated seed-specific silencing of Inositol 1,3,4,5,6-Pentakisphosphate 2-Kinase Gene (IPK1)

Phytic acid (InsP6) is considered to be the major source of phosphorus and inositol phosphates in most cereal grains. However, InsP6 is not utilized efficiently by monogastric animals due to lack of phytase enzyme. Furthermore, due to its ability to chelate mineral cations, phytic acid is considered to be an antinutrient that renders these minerals unavailable for absorption. In view of these facts, reducing the phytic acid content in cereal grains is a desired goal for the genetic improvement of several crops. In the present study, we report the RNAi-mediated seed-specific silencing (using the Oleosin18 promoter) of the IPK1 gene, which catalyzes the last step of phytic acid biosynthesis in rice. The presence of the transgene cassette in the resulting transgenic plants was confirmed by molecular analysis, indicating the stable integration of the transgene. The subsequent T4 transgenic seeds revealed 3.85-fold down-regulation in IPK1 transcripts, which correlated to a significant reduction in phytate levels and a concomitant increase in the amount of inorganic phosphate (Pi). The low-phytate rice seeds also accumulated 1.8-fold more iron in the endosperm due to the decreased phytic acid levels. No negative effects were observed on seed germination or in any of the agronomic traits examined. The results provide evidence that silencing of IPK1 gene can mediate a substantial reduction in seed phytate levels without hampering the growth and development of transgenic rice plants

Overexpression of Arabidopsis and rice stress genes’ inducible transcription factor confers drought and salinity tolerance to rice

Rice yield is greatly affected by environmental stresses such as drought and salinity. In response to the challenge of producing rice plants tolerant to these stresses, we introduced cDNA encoding the transcription factors DREB1A and DREB1B under the control of the stress inducible rd29 promoter. Two different indica rice cultivars were used, BR29, an improved commercially cultivated variety from Bangladesh and IR68899B, an IRRI bred maintainer line for hybrid rice. Agrobacterium mediated transformation of BR29 was done independently with DREB1A isolated from rice and Arabidopsis and DREB1B isolated from rice, whereas biolistic transformation was done with rice- DREB1B in the case of IR68899B. Initial genetic integration was confirmed by PCR and Southern blot analysis. Salinity tolerance was assayed in very young seedlings. Drought stress tests were found to be more reliable when they were carried out at the pre-flowering booting stage. RNA gel blot analysis as well as quantitative PCR analysis was performed to estimate the transcription level under stressed and unstressed conditions. Agronomic performance studies were done with stressed and unstressed plants to compare the yield losses due to dehydration and salt loading stresses. Noticeably enhanced tolerance to dehydration was observed in the plants transformed with DREB1A isolated from Arabidopsis while DREB1B was found to be more effective for salt tolerance

Field performance of transgenic elite commercial hybrid rice expressing Bacillus thuringiensis δ-endotoxin

Here we describe development of transgenic elite rice lines expressing a Bt fusion gene derived from cryIA(b) and cryIA(c) under the control of rice actinI promoter. The lines used in the study were indica CMS restorer line of Minghui 63 and its derived hybrid rice Shanyou 63. The level of Bt fusion protein CryIA(b)/CryIA(c) detected in Minghui 63 (T51-1) plants was 20 ng/mg soluble protein. The Bt Shanyou 63 was field-tested in natural and repeated heavy manual infestation of two lepidopteran insects, leaffolder and yellow stem borer. The transgenic hybrid plants showed high protection against both insect pests without reduced yield

Site-independently integrated transgenes in the elite restorer rice line Minghui 63 allow removal of a selectable marker from the gene of interest by self-segregation

In this study, we have demonstrated that two independent loci are involved in the integration of the insecticidal protein gene cryIAb/cryIAc and selectable marker gene hph in the recipient genome of the elite Chinese CMS restorer line Minghui 63. We have also documented the structural organization of these transgenes in each locus by restriction enzyme digestion and Southern blot analysis. The independent locus integration of different transgenes allowed us to remove the selectable marker gene hph from the gene of interest simply by self-segregation. Not having the selectable marker gene will enhance the commercial value of our transgenic line TT51-1, which showed a consistently high level of resistance against repeated infestations of yellow stem borers and natural outbreaks of leaf-folders, without a reduction in yield potential

Tissue-specific localization of β-carotene and iron in transgenic indica rice (Oryza sativa L.)

Tissue-specific distribution and localization of β-carotene and iron were characterized in transgenic rice seeds by histochemical studies. Histochemical reactions clearly revealed the accumulation of β-carotene in the endosperm of transgenic seeds in comparison with non-transgenic control where no β-carotene could be detected. A similar observation was made for iron-colour reaction in the endosperm. Since histochemical tests can be carried out easily and are fairly specific for determining particular compounds both qualitatively and to some extent quantitatively (based on the intensity of colour), this method could be used for identifying the desirable transgenic material with high β-carotene and iron content

Bioengineered ‘golden’ indica rice cultivars with β-carotene metabolism in the endosperm with hygromycin and mannose selection systems

Vitamin-A deficiency (VAD) is a major malnutrition problem in South Asia, where indica rice is the staple food. Indica-type rice varieties feed more than 2 billion people. Hence, we introduced a combination of transgenes using the biolistic system of transformation enabling biosynthesis of provitamin A in the endosperm of several indica rice cultivars adapted to diverse ecosystems of different countries. The rice seed-specific glutelin promoter (Gt-1 P) was used to drive the expression of phytoene synthase (psy), while lycopene β-cyclase (lcy) and phytoene desaturase (crtI), fused to the transit peptide sequence of the pea-Rubisco small subunit, were driven by the constitutive cauliflower mosaic virus promoter (CaMV35S P). Transgenic plants were recovered through selection with either CaMV35S P driven hph (hygromycin phosphotransferase) gene or cestrum yellow leaf curling virus promoter (CMP) driven pmi (phophomannose isomerase) gene. Molecular and biochemical analyses demonstrated stable integration and expression of the transgenes. The yellow colour of the polished rice grain evidenced the carotenoid accumulation in the endosperm. The colour intensity correlated with the estimated carotenoid content by spectrophotometric and HPLC analysis. Carotenoid level in cooked polished seeds was comparable (with minor loss of xanthophylls) to that in non-cooked seeds of the same transgenic line. The variable segregation pattern in T1 selfing generation indicated single to multiple loci insertion of the transgenes in the genome. This is the first report of using nonantibiotic pmi driven by a novel promoter in generating transgenic indica rice for possible future use in human nutrition