327 resultados para Knot
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Pós-graduação em Agronomia (Produção Vegetal) - FCAV
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Thesis presented at the Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, to obtain a Master degree in Conservation and Restoration,Specialization in Textiles
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In thee present paper the classical concept of the corpuscular gene is dissected out in order to show the inconsistency of some genetical and cytological explanations based on it. The author begins by asking how do the genes perform their specific functions. Genetists say that colour in plants is sometimes due to the presence in the cytoplam of epidermal cells of an organic complex belonging to the anthocyanins and that this complex is produced by genes. The author then asks how can a gene produce an anthocyanin ? In accordance to Haldane's view the first product of a gene may be a free copy of the gene itself which is abandoned to the nucleus and then to the cytoplasm where it enters into reaction with other gene products. If, thus, the different substances which react in the cell for preparing the characters of the organism are copies of the genes then the chromosome must be very extravagant a thing : chain of the most diverse and heterogeneous substances (the genes) like agglutinins, precipitins, antibodies, hormones, erzyms, coenzyms, proteins, hydrocarbons, acids, bases, salts, water soluble and insoluble substances ! It would be very extrange that so a lot of chemical genes should not react with each other. remaining on the contrary, indefinitely the same in spite of the possibility of approaching and touching due to the stato of extreme distension of the chromosomes mouving within the fluid medium of the resting nucleus. If a given medium becomes acid in virtue of the presence of a free copy of an acid gene, then gene and character must be essentially the same thing and the difference between genotype and phenotype disappears, epigenesis gives up its place to preformation, and genetics goes back to its most remote beginnings. The author discusses the complete lack of arguments in support of the view that genes are corpuscular entities. To show the emharracing situation of the genetist who defends the idea of corpuscular genes, Dobzhansky's (1944) assertions that "Discrete entities like genes may be integrated into systems, the chromosomes, functioning as such. The existence of organs and tissues does not preclude their cellular organization" are discussed. In the opinion of the present writer, affirmations as such abrogate one of the most important characteristics of the genes, that is, their functional independence. Indeed, if the genes are independent, each one being capable of passing through mutational alterations or separating from its neighbours without changing them as Dobzhansky says, then the chromosome, genetically speaking, does not constitute a system. If on the other hand, theh chromosome be really a system it will suffer, as such, the influence of the alteration or suppression of the elements integrating it, and in this case the genes cannot be independent. We have therefore to decide : either the chromosome is. a system and th genes are not independent, or the genes are independent and the chromosome is not a syntem. What cannot surely exist is a system (the chromosome) formed by independent organs (the genes), as Dobzhansky admits. The parallel made by Dobzhansky between chromosomes and tissues seems to the author to be inadequate because we cannot compare heterogeneous things like a chromosome considered as a system made up by different organs (the genes), with a tissue formed, as we know, by the same organs (the cells) represented many times. The writer considers the chromosome as a true system and therefore gives no credit to the genes as independent elements. Genetists explain position effects in the following way : The products elaborated by the genes react with each other or with substances previously formed in the cell by the action of other gene products. Supposing that of two neighbouring genes A and B, the former reacts with a certain substance of the cellular medium (X) giving a product C which will suffer the action, of the latter (B). it follows that if the gene changes its position to a place far apart from A, the product it elaborates will spend more time for entering into contact with the substance C resulting from the action of A upon X, whose concentration is greater in the proximities of A. In this condition another gene produtc may anticipate the product of B in reacting with C, the normal course of reactions being altered from this time up. Let we see how many incongruencies and contradictions exist in such an explanation. Firstly, it has been established by genetists that the reaction due.to gene activities are specific and develop in a definite order, so that, each reaction prepares the medium for the following. Therefore, if the medium C resulting from the action of A upon x is the specific medium for the activity of B, it follows that no other gene, in consequence of its specificity, can work in this medium. It is only after the interference of B, changing the medium, that a new gene may enter into action. Since the genotype has not been modified by the change of the place of the gene, it is evident that the unique result we have to attend is a little delay without seious consequence in the beginning of the reaction of the product of B With its specific substratum C. This delay would be largely compensated by a greater amount of the substance C which the product of B should found already prepared. Moreover, the explanation did not take into account the fact that the genes work in the resting nucleus and that in this stage the chromosomes, very long and thin, form a network plunged into the nuclear sap. in which they are surely not still, changing from cell to cell and In the same cell from time to time, the distance separating any two genes of the same chromosome or of different ones. The idea that the genes may react directly with each other and not by means of their products, would lead to the concept of Goidschmidt and Piza, in accordance to which the chromosomes function as wholes. Really, if a gene B, accustomed to work between A and C (as for instance in the chromosome ABCDEF), passes to function differently only because an inversion has transferred it to the neighbourhood of F (as in AEDOBF), the gene F must equally be changed since we cannot almH that, of two reacting genes, only one is modified The genes E and A will be altered in the same way due to the change of place-of the former. Assuming that any modification in a gene causes a compensatory modification in its neighbour in order to re-establich the equilibrium of the reactions, we conclude that all the genes are modified in consequence of an inversion. The same would happen by mutations. The transformation of B into B' would changeA and C into A' and C respectively. The latter, reacting withD would transform it into D' and soon the whole chromosome would be modified. A localized change would therefore transform a primitive whole T into a new one T', as Piza pretends. The attraction point-to-point by the chromosomes is denied by the nresent writer. Arguments and facts favouring the view that chromosomes attract one another as wholes are presented. A fact which in the opinion of the author compromises sereously the idea of specific attraction gene-to-gene is found inthe behavior of the mutated gene. As we know, in homozygosis, the spme gene is represented twice in corresponding loci of the chromosomes. A mutation in one of them, sometimes so strong that it is capable of changing one sex into the opposite one or even killing the individual, has, notwithstading that, no effect on the previously existing mutual attraction of the corresponding loci. It seems reasonable to conclude that, if the genes A and A attract one another specifically, the attraction will disappear in consequence of the mutation. But, as in heterozygosis the genes continue to attract in the same way as before, it follows that the attraction is not specific and therefore does not be a gene attribute. Since homologous genes attract one another whatever their constitution, how do we understand the lack cf attraction between non homologous genes or between the genes of the same chromosome ? Cnromosome pairing is considered as being submitted to the same principles which govern gametes copulation or conjugation of Ciliata. Modern researches on the mating types of Ciliata offer a solid ground for such an intepretation. Chromosomes conjugate like Ciliata of the same variety, but of different mating types. In a cell there are n different sorts of chromosomes comparable to the varieties of Ciliata of the same species which do not mate. Of each sort there are in the cell only two chromosomes belonging to different mating types (homologous chromosomes). The chromosomes which will conjugate (belonging to the same "variety" but to different "mating types") produce a gamone-like substance that promotes their union, being without action upon the other chromosomes. In this simple way a single substance brings forth the same result that in the case of point-to-point attraction would be reached through the cooperation of as many different substances as the genes present in the chromosome. The chromosomes like the Ciliata, divide many times before they conjugate. (Gonial chromosomes) Like the Ciliata, when they reach maturity, they copulate. (Cyte chromosomes). Again, like the Ciliata which aggregate into clumps before mating, the chrorrasrmes join together in one side of the nucleus before pairing. (.Synizesis). Like the Ciliata which come out from the clumps paired two by two, the chromosomes leave the synizesis knot also in pairs. (Pachytene) The chromosomes, like the Ciliata, begin pairing at any part of their body. After some time the latter adjust their mouths, the former their kinetochores. During conjugation the Ciliata as well as the chromosomes exchange parts. Finally, the ones as the others separate to initiate a new cycle of divisions. It seems to the author that the analogies are to many to be overlooked. When two chemical compounds react with one another, both are transformed and new products appear at the and of the reaction. In the reaction in which the protoplasm takes place, a sharp difference is to be noted. The protoplasm, contrarily to what happens with the chemical substances, does not enter directly into reaction, but by means of products of its physiological activities. More than that while the compounds with Wich it reacts are changed, it preserves indefinitely its constitution. Here is one of the most important differences in the behavior of living and lifeless matter. Genes, accordingly, do not alter their constitution when they enter into reaction. Genetists contradict themselves when they affirm, on the one hand, that genes are entities which maintain indefinitely their chemical composition, and on the other hand, that mutation is a change in the chemica composition of the genes. They are thus conferring to the genes properties of the living and the lifeless substances. The protoplasm, as we know, without changing its composition, can synthesize different kinds of compounds as enzyms, hormones, and the like. A mutation, in the opinion of the writer would then be a new property acquired by the protoplasm without altering its chemical composition. With regard to the activities of the enzyms In the cells, the author writes : Due to the specificity of the enzyms we have that what determines the order in which they will enter into play is the chemical composition of the substances appearing in the protoplasm. Suppose that a nucleoproteln comes in relation to a protoplasm in which the following enzyms are present: a protease which breaks the nucleoproteln into protein and nucleic acid; a polynucleotidase which fragments the nucleic acid into nucleotids; a nucleotidase which decomposes the nucleotids into nucleoids and phosphoric acid; and, finally, a nucleosidase which attacs the nucleosids with production of sugar and purin or pyramidin bases. Now, it is evident that none of the enzyms which act on the nucleic acid and its products can enter into activity before the decomposition of the nucleoproteln by the protease present in the medium takes place. Leikewise, the nucleosidase cannot works without the nucleotidase previously decomposing the nucleotids, neither the latter can act before the entering into activity of the polynucleotidase for liberating the nucleotids. The number of enzyms which may work at a time depends upon the substances present m the protoplasm. The start and the end of enzym activities, the direction of the reactions toward the decomposition or the synthesis of chemical compounds, the duration of the reactions, all are in the dependence respectively o fthe nature of the substances, of the end products being left in, or retired from the medium, and of the amount of material present. The velocity of the reaction is conditioned by different factors as temperature, pH of the medium, and others. Genetists fall again into contradiction when they say that genes act like enzyms, controlling the reactions in the cells. They do not remember that to cintroll a reaction means to mark its beginning, to determine its direction, to regulate its velocity, and to stop it Enzyms, as we have seen, enjoy none of these properties improperly attributed to them. If, therefore, genes work like enzyms, they do not controll reactions, being, on the contrary, controlled by substances and conditions present in the protoplasm. A gene, like en enzym, cannot go into play, in the absence of the substance to which it is specific. Tne genes are considered as having two roles in the organism one preparing the characters attributed to them and other, preparing the medium for the activities of other genes. At the first glance it seems that only the former is specific. But, if we consider that each gene acts only when the appropriated medium is prepared for it, it follows that the medium is as specific to the gene as the gene to the medium. The author concludes from the analysis of the manner in which genes perform their function, that all the genes work at the same time anywhere in the organism, and that every character results from the activities of all the genes. A gene does therefore not await for a given medium because it is always in the appropriated medium. If the substratum in which it opperates changes, its activity changes correspondingly. Genes are permanently at work. It is true that they attend for an adequate medium to develop a certain actvity. But this does not mean that it is resting while the required cellular environment is being prepared. It never rests. While attending for certain conditions, it opperates in the previous enes It passes from medium to medium, from activity to activity, without stopping anywhere. Genetists are acquainted with situations in which the attended results do not appear. To solve these situations they use to make appeal to the interference of other genes (modifiers, suppressors, activators, intensifiers, dilutors, a. s. o.), nothing else doing in this manner than displacing the problem. To make genetcal systems function genetists confer to their hypothetical entities truly miraculous faculties. To affirm as they do w'th so great a simplicity, that a gene produces an anthocyanin, an enzym, a hormone, or the like, is attribute to the gene activities that onlv very complex structures like cells or glands would be capable of producing Genetists try to avoid this difficulty advancing that the gene works in collaboration with all the other genes as well as with the cytoplasm. Of course, such an affirmation merely means that what works at each time is not the gene, but the whole cell. Consequently, if it is the whole cell which is at work in every situation, it follows that the complete set of genes are permanently in activity, their activity changing in accordance with the part of the organism in which they are working. Transplantation experiments carried out between creeper and normal fowl embryos are discussed in order to show that there is ro local gene action, at least in some cases in which genetists use to recognize such an action. The author thinks that the pleiotropism concept should be applied only to the effects and not to the causes. A pleiotropic gene would be one that in a single actuation upon a more primitive structure were capable of producing by means of secondary influences a multiple effect This definition, however, does not preclude localized gene action, only displacing it. But, if genetics goes back to the egg and puts in it the starting point for all events which in course of development finish by producing the visible characters of the organism, this will signify a great progress. From the analysis of the results of the study of the phenocopies the author concludes that agents other than genes being also capaole of determining the same characters as the genes, these entities lose much of their credit as the unique makers of the organism. Insisting about some points already discussed, the author lays once more stress upon the manner in which the genes exercise their activities, emphasizing that the complete set of genes works jointly in collaboration with the other elements of the cell, and that this work changes with development in the different parts of the organism. To defend this point of view the author starts fron the premiss that a nerve cell is different from a muscle cell. Taking this for granted the author continues saying that those cells have been differentiated as systems, that is all their parts have been changed during development. The nucleus of the nerve cell is therefore different from the nucleus of the muscle cell not only in shape, but also in function. Though fundamentally formed by th same parts, these cells differ integrally from one another by the specialization. Without losing anyone of its essenial properties the protoplasm differentiates itself into distinct kinds of cells, as the living beings differentiate into species. The modified cells within the organism are comparable to the modified organisms within the species. A nervo and a muscle cell of the same organism are therefore like two species originated from a common ancestor : integrally distinct. Like the cytoplasm, the nucleus of a nerve cell differs from the one of a muscle cell in all pecularities and accordingly, nerve cell chromosomes are different from muscle cell chromosomes. We cannot understand differentiation of a part only of a cell. The differentiation must be of the whole cell as a system. When a cell in the course of development becomes a nerve cell or a muscle cell , it undoubtedly acquires nerve cell or muscle cell cytoplasm and nucleus respectively. It is not admissible that the cytoplasm has been changed r.lone, the nucleus remaining the same in both kinds of cells. It is therefore legitimate to conclude that nerve ceil ha.s nerve cell chromosomes and muscle cell, muscle cell chromosomes. Consequently, the genes, representing as they do, specific functions of the chromossomes, are different in different sorts of cells. After having discussed the development of the Amphibian egg on the light of modern researches, the author says : We have seen till now that the development of the egg is almost finished and the larva about to become a free-swimming tadepole and, notwithstanding this, the genes have not yet entered with their specific work. If the haed and tail position is determined without the concourse of the genes; if dorso-ventrality and bilaterality of the embryo are not due to specific gene actions; if the unequal division of the blastula cells, the different speed with which the cells multiply in each hemisphere, and the differential repartition of the substances present in the cytoplasm, all this do not depend on genes; if gastrulation, neurulation. division of the embryo body into morphogenetic fields, definitive determination of primordia, and histological differentiation of the organism go on without the specific cooperation of the genes, it is the case of asking to what then the genes serve ? Based on the mechanism of plant galls formation by gall insects and on the manner in which organizers and their products exercise their activities in the developing organism, the author interprets gene action in the following way : The genes alter structures which have been formed without their specific intervention. Working in one substratum whose existence does not depend o nthem, the genes would be capable of modelling in it the particularities which make it characteristic for a given individual. Thus, the tegument of an animal, as a fundamental structure of the organism, is not due to gene action, but the presence or absence of hair, scales, tubercles, spines, the colour or any other particularities of the skin, may be decided by the genes. The organizer decides whether a primordium will be eye or gill. The details of these organs, however, are left to the genetic potentiality of the tissue which received the induction. For instance, Urodele mouth organizer induces Anura presumptive epidermis to develop into mouth. But, this mouth will be farhioned in the Anura manner. Finalizing the author presents his own concept of the genes. The genes are not independent material particles charged with specific activities, but specific functions of the whole chromosome. To say that a given chromosome has n genes means that this chromonome, in different circumstances, may exercise n distinct activities. Thus, under the influence of a leg evocator the chromosome, as whole, develops its "leg" activity, while wbitm the field of influence of an eye evocator it will develop its "eye" activity. Translocations, deficiencies and inversions will transform more or less deeply a whole into another one, This new whole may continue to produce the same activities it had formerly in addition to those wich may have been induced by the grafted fragment, may lose some functions or acquire entirely new properties, that is, properties that none of them had previously The theoretical possibility of the chromosomes acquiring new genetical properties in consequence of an exchange of parts postulated by the present writer has been experimentally confirmed by Dobzhansky, who verified that, when any two Drosophila pseudoobscura II - chromosomes exchange parts, the chossover chromosomes show new "synthetic" genetical effects.
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The three species studied have 19 chromosomes, being one heterochromosome, one pair of microchromosomes and 8 pairs of autosomes. The microchromosomes of Hypselonotus fulvus are amongst the largest we know. During the synizesis, in Hypselonotus fulvus, we can see in several strands that scape from the chromatic knot a place in which they are widley open. As, in that phase the chromosomes have both ends converging to the same place, the openings suggest a side-to-side pairing of the chromosomal threads. The tetrads are like that studied by Piza (1945-1946). The bivalents are united side by side at their entire length. The unpaired part at the midle of the bivalents gives origin to the arms of the cross-shapede tetrads. The chromosomes have a kinetochore at each end. The bivalents sometimes unite their extremities to form ring-shaped figures, which open themselves out before metaphase. The tetrads are oriented parallelly to the spindle axis. At telophase the kinetochores repeli one another, the chiasmata, if present, slip toward the acentric extremities and the chromosomes rotate in order to arrange themselves parallelly to the axis of the new spindle. Separation is therefore through the pairing plane. In the spermatogonial anaphase of Hypselonotus subterpunctatus the chromosomes are curved to the poles, like those described by PIZA (1946) and PIZA and ZAMITH (1946). The sex chromosomes in Hypselonotus interruptus and Hypselonotus fulvus appears longitudinally divided. It is oriented with the ends in the plane of the equator and its chomatids separate by the plane of division. In the second division the sex chromosome, provided as it is with an actve klnetochore at each end, orients itself with its length parallelly to the spindle axis and passes undivided to one pole. Sometimes it is distended between the poles. This corresponds to case (a) established by PIZA (1946) for the sex chromosomes of Hemiptera In Hypselonotus subterpunctatus the sex chromosome, in the first division of the spermatocytes, orients like the tetrads and divides transversaly. In the second division, as its kinetochore becomes inactive, it remans monocentric, does not orient in the spindle, and is finally enclosed in the nearer nucleus. In the secondary telophase it recuperates its dicentricity like the autosomal chromatids. This behavior corresponds to case (c) of PIZA (1946).
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This paper deals with some Millipedes (Diplopoda), which have been verified associated with or attacking on cultivated plants. The following forms are reported: 1) Orthomorpha (Orthomorpha) coarctata (Saussure, 1860) - Enormous numbers of individuals belonging to this species, whose synanthropic habits are frequentely emphasized, were collected around coffee-plants kept in a nursery. Young plants (with 10 cm) are mentioned as damaged by the species, which gnaws the stem, just above the roots. The dusting with benzene hexachloride (BHC) was successfully employed to prevent the invasions. Other occurrences of O. coarctata are reported, ecological and biological informations being also added. 2) Orthomorpha (Kalorthomorpha) gracilis (C. L. Koch, 1847) - Observed frequentely associated with the former species, being however less numerous. Both forms are very active, seemming to be widely distributed throughout the State of S. Paulo. 3) Cylindroiulus (Aneuloboiulus) britannicus (Verhoeff, 1891) - This species represents the first european Millipede verified in Brazil, by O. SCHUBART (1942a). The Author obtained a few specimens associated with O. gracilis, from the roots of lettuce plants. The lesions shown by the stem just above the roots seem to be due to both species. 4) Alloporus setiger Broelemann, 1902; Gymnostreptus olivaceus Schubart, 1944 and Pseudonannolene tricolor Broelemann, 1902 - Total damages determined by these species (mainly G. olivaceus) were observed in cultures of sugar-beet and melon. Actually, the Millipedes destroyed entirely the roots of the former plant and the fruits of the latter, representing a serious pest, here reported by the first time. Ecological and bionomical data are also included. 5) Pseudonannolene sp. (possibly P. paulista Broelemann, 1902) - Verified gnawing sweet-potatoes, about the crackings exhibited by the tubers. The crackings in sweet-potatoes appear to result in certain instances from a root-knot nematodes infection (Meloidogyne sp). P. paulista was recentely observed attacking potatoes, destroying from 6 to 30% of the tubers, according to the variety (BOOCK & LORDELLO, 1952).
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Tomato roots heavily disfigured by root-knot nematodes were throughly mixed with soil. At various time intervals, samples were taken from the mixture and treated in closed containers by each of the folio wing nematicides: D.D., E.D.B. and M.B. The efficacy of the treatment was tested by setting indicator plants in the treated soil and by examining their roots for the presence of galls two months later. In other words, the ability of the three nematicides to penetrate nematode galls after various periods of rotting, which varied from 5 to 30 days was studied. The main conclusions drawn are as follows: a) no nematicide among the three listed above showed the ability for complete destruction of the nematodes protected inside the roots, for a number of small galls developed on the root system of the indicator plant in all treatments; b) smaller and less numerous galls were present on the roots of the indicator plants grown in soil treated after a rotting period of 30 days; c) however, the control obtained seems to be quite satisfactory economically, since the check plants grew poorly and have developed a very unhealthy root system. This is in accordance with STARK & LEAR (1947), LEAR (1951) and CICCARONE's (1951) statements. The results of the present experiments show again that awaiting for the rotting of galls of the root-knot nematodes is not indispensable for an economically convenient soil fumigation. Fields in which many fleshy infected roots from previous crops have been buried can be economically fumigated immediately, without any loss of time. Notwithstanding, when thick woody roots are present in the soil, the above statements may not hold true. This should constitute a new problem calling for further experiments. Another essay dealing with methyl bromide alone, consisted in treating cotton roots heavily disfigured by Meloidogyne incognita in a container (diameter = 28cm, height = 32 cm), which remained closed for five days. After the treatment, the roots were mixed with soil, in which tomato seedlings were planted. After a growing period of two months, the roots of the tomato plants were washed in running water and examined for the presence of galls. As an early infeccion was present in the root system of all plants, the inefficacy of the treatment has been proved.
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The writers report results on the application of four fumigants (D. D., E. D. B.-40, C. B. P. and Vapam) for control of root-knot and meadow nematodes attacking potato in beds filled with soil artificially inoculated. The data obtained were as follows: a) as reported by previous authors, potato is sensitive to C.B.P., the toxical effects of which disapearing only about 6 and half months after application. On the other hand, C.B.P. proved to have a significative residual nematicidal value, protecting the seeds from root-knot nematodes for a period of two years; b) D. D., E. D. B., and Vapam were effective for controling root-knot but with no residual value, having to be used prior to each planting; c) at the rates used, no nematicide was effective to control meadow nematodes; d) in the conditions of the experiments, all nematicides incited attacks bv Streptomyces scabies. Actually, in some cases scab did not affect any tuber from the check while the entire production from the treated beds was heavily desfigured. The writers assume that as the nematicides killed protozoa and too many bacteria-eating nematodes, they destroyed the biological equilibrium existing in the soil, thus allowing the S. scabies population to reach a high level.
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In the State of S. Paulo, Brazil, squash plants (Cucurbita spp.) are attacked by the Javanese nematode (Meloidogyne javanica) and by M. incognita acrita. Squash belongs to that group of plants in which the root-knot nematodes break through the root surface, so that the egg-producing females protrude from the root, showing yellowish or brow nish egg masses attached to them. Washed roots show numerous small dark spots, each corresponding to an ootheca, which is adhering to a mature female. A curious abnormal female of M. i. acrita was obtained from a sample of squash roots. This female's body showed two globular parts, separated by a deep constriction. The convoluted ovaries were found to fill both portions of the body.
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Eight root-knot nematode forms are known to occur in Brazil, namely Meloidogyne exigua, M. incognita, M. j. javanica, M. j. bauruensis, M. inornata, M. hapla, M. arenaria arenaria and M. coffeicola. After presenting a historical resume of the root-knot disease, as well as observations on symptoms, distribution and spread, and life history of the nematodes, a study of the morphological characters used in identification of species is made, a key for separating the forms referred to above being also prepared. As no information on host plants of the coffee root-knot nematode (M. exigua) was available, a few tests were performed, as an attempt to infect several plant species. Pepper (Capsicum annuun) was the only plant attacked by M. exigua, having failed all attempts to infect nine other plants, including tomato var. Rutgers. M. exigua incited formation of galls on roots of cucumber, but no adult female was found in the tissue. In a final chapter dealing with control, a review of all methods available is presented.
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Suppose a genus two handlebody is removed from a 3-manifold M and then a single meridian of the handlebody is restored. The result is a knot or link complement in M and it is natural to ask whether geometric properties of the link complement say something about the meridian that was restored. Here we consider what the relation must be between two not necessarily disjoint meridians so that restoring each of them gives a trivial knot or a split link.
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The aim of this paper is to give an explicit formula for the SL2(C)-twisted Reidemeister torsion as defined in [6] in the case of twist knots. For hyperbolic twist knots, we also prove that the twisted Reidemeister torsion at the holonomy representation can be expressed as a rational function evaluated at the cusp shape of the knot. Tables given approximations of the twisted Reidemeister torsion for twist knots on some concrete examples are also enclosed.
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We present an invariant of a three dimensional manifold with a framed knot in it based on the Reidemeister torsion of an acyclic complex of Euclidean geometric origin. To show its nontriviality, we calculate the invariant for some framed (un)knots in lens spaces. An important feature of our work is that we are not using any nontrivial representation of the manifold fundamental group or knot group.
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KNOTS are usually categorized in terms of topological properties that are invariant under changes in a knot's spatial configuration(1-4). Here we approach knot identification from a different angle, by considering the properties of particular geometrical forms which we define as 'ideal'. For a knot with a given topology and assembled from a tube of uniform diameter, the ideal form is the geometrical configuration having the highest ratio of volume to surface area. Practically, this is equivalent to determining the shortest piece of tube that can be closed to form the knot. Because the notion of an ideal form is independent of absolute spatial scale, the length-to-diameter ratio of a tube providing an ideal representation is constant, irrespective of the tube's actual dimensions. We report the results of computer simulations which show that these ideal representations of knots have surprisingly simple geometrical properties. In particular, there is a simple linear relationship between the length-to-diameter ratio and the crossing number-the number of intersections in a two-dimensional projection of the knot averaged over all directions. We have also found that the average shape of knotted polymeric chains in thermal equilibrium is closely related to the ideal representation of the corresponding knot type. Our observations provide a link between ideal geometrical objects and the behaviour of seemingly disordered systems, and allow the prediction of properties of knotted polymers such as their electrophoretic mobility(5).
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Plant-parasitic nematodes are major agricultural pests worldwide and novel approaches to control them are sorely needed. We report the draft genome sequence of the root-knot nematode Meloidogyne incognita, a biotrophic parasite of many crops, including tomato, cotton and coffee. Most of the assembled sequence of this asexually reproducing nematode, totaling 86 Mb, exists in pairs of homologous but divergent segments. This suggests that ancient allelic regions in M. incognita are evolving toward effective haploidy, permitting new mechanisms of adaptation. The number and diversity of plant cell wall-degrading enzymes in M. incognita is unprecedented in any animal for which a genome sequence is available, and may derive from multiple horizontal gene transfers from bacterial sources. Our results provide insights into the adaptations required by metazoans to successfully parasitize immunocompetent plants, and open the way for discovering new antiparasitic strategies.