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1.
Accumulation and ethylene-dependent translocation of free polyamines was studied in various organs, the phloem and xylem exudates of common ice plants (Mesembryanthemum crystallinum L.). Under normal conditions (23–25°C), spermidine predominated among polyamines. Cadaverine was found in old leaves, stems, and, in large quantities, in roots. The heat shock treatment (HS; 47°C, 2 h) of intact plant shoots induced intense evolution of ethylene from leaves but reduced the leaf content of polyamines. Under these conditions, the concentration of polyamines in roots, particularly of cadaverine, increased many times. The HS treatment of roots (40°C, 2 h) induced translocation of cadaverine to stems and putrescine to leaves. An enhanced polyamine content after HS treatment was also found in the xylem and phloem exudates. The exposure of detached leaves to ethylene led to a reduction in their putrescine and spermidine and accumulation of cadaverine, which implies the ethylene-dependent formation of cadaverine and a possible relation between the HS-induced translocation of this diamine to roots and the transient ethylene evolution by leaves. To validate this hypothesis, we compared the ethylene evolution rate and interorgan partitioning of cadaverine and other polyamines for two lines of Arabidopsis thaliana: the wild type (Col-0) and ein4 mutant with impaired ethylene reception. In plants grown in light at 20–21°C, the rate of ethylene evolution by rosetted leaves was higher in the mutant than in the wild type. The content of putrescine and spermidine was reduced in mutant leaves, whereas cadaverine concentration increased almost threefold compared with the wild type. In roots, cadaverine was found only in the wild type and not in the mutant line. Our data indicate the ethylene-dependent formation of cadaverine in leaves and possible involvement of cadaverine and ethylene in the long-distance translocation of stress (HS) signal in plants.  相似文献   

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Recent advances in the field of plant community phylogenetics and invasion phylogenetics are mostly based on plot-level data, which do not take into consideration the spatial arrangement of individual plants within the plot. Here we use within-plot plant coordinates to investigate the link between the physical distance separating plants, and their phylogenetic relatedness. We look at two vegetation types (forest and grassland, similar in species richness and in the proportion of alien invasive plants) in subtropical coastal KwaZulu-Natal, South Africa. The relationship between phylogenetic distance and physical distance is weak in grassland (characterised by higher plant densities and low phylogenetic diversity), and varies substantially in forest vegetation (variable plant density, higher phylogenetic diversity). There is no significant relationship between the proportion of alien plants in the plots and the strength of the physical-phylogenetic distance relationship, suggesting that alien plants are well integrated in the local spatial-phylogenetic landscape.  相似文献   

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How Do Stomata Read Abscisic Acid Signals?   总被引:22,自引:2,他引:20       下载免费PDF全文
When abscisic acid (ABA) was fed to isolated epidermis of Commelina communis L., stomata showed marked sensitivity to concentrations of ABA lower than those commonly found in the xylem sap of well-watered plants. Stomata were also sensitive to the flux of hormone molecules across the epidermal strip. Stomata in intact leaves of Phaseolus acutifolius were much less sensitive to ABA delivered through the petiole than were stomata in isolated epidermis, suggesting that mesophyll tissue and/or xylem must substantially reduce the dose or activity of ABA received by guard cells. Delivery of the hormone to the leaf was varied by changing transpiration flux and/or concentration. Varying delivery by up to 7-fold by changing transpiration rate had little effect on conductance. At a given delivery rate, variation in concentration by 1 order of magnitude significantly affected conductance at all but the highest concentration fed. The results are discussed in terms of the control of stomatal behavior in the field, where the delivery of ABA to the leaf will vary greatly as a function of both the concentration of hormone in the xylem and the transpiration rate of the plant.  相似文献   

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Acta Biotheoretica - Radial growth has long been a subject of interest in tree biology research. Recent studies have brought a significant change in the understanding of some basic processes...  相似文献   

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Understanding the response of soil respiration to climate variability is critical to formulate realistic predictions of future carbon (C) fluxes under different climate change scenarios. There is growing evidence that the influence of long-term climate variability in C fluxes from terrestrial ecosystems is modulated by adjustments in the aboveground–belowground links. Here, we studied the inter-annual variability in soil respiration from a wet shrubland going through successional change in North Wales (UK) during 13 years. We hypothesised that the decline in plant productivity observed over a decade would result in a decrease in the apparent sensitivity of soil respiration to soil temperature, and that rainfall variability would explain a significant fraction of the inter-annual variability in plant productivity, and consequently, in soil respiration, due to excess-water constraining nutrient availability for plants. As hypothesised, there were parallel decreases between plant productivity and annual and summer CO2 emissions over the 13-year period. Soil temperatures did not follow a similar trend, which resulted in a decline in the apparent sensitivity of soil respiration to soil temperature (apparent Q10 values decreased from 9.4 to 2.8). Contrary to our second hypothesis, summer maximum air temperature rather than rainfall was the climate variable with the greatest influence on aboveground biomass and annual cumulative respiration. Since summer air temperature and rainfall were positively associated, the greatest annual respiration values were recorded during years of high rainfall. The results suggest that adjustments in plant productivity might have a critical role in determining the long-term-sensitivity of soil respiration to changing climate conditions.  相似文献   

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How and Why Do Plants Inactivate Homologous (Trans)genes?   总被引:13,自引:0,他引:13       下载免费PDF全文
Matzke MA  Matzke A 《Plant physiology》1995,107(3):679-685
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11.
Do Rotifer Jaws Grow After Hatching?   总被引:3,自引:3,他引:0  
The hard articulated jaws of some pseudocoelomate metazoans were recently used in reconstructing their phylogenetic relationships, but we still do not know if these structures could change in size and shape during the life of individuals, and experimental data are lacking on their post-embryonic development. Rotifers are one of the groups in which hard articulated jaws, called trophi, are well known, and are widely used taxonomically. Here we report on SEM study of trophi of rotifers of different ages, to determine if the trophi structures change in shape and/or in size during post-embryonic development. We used linear measurements and geometric morphometrics analyses from scanning electron microscopic pictures of trophi of Cupelopagis vorax, Dicranophorus forcipatus, Macrotrachela quadricornifera, Notommata glyphura, Rotaria macrura, R. neptunoida, and R. tardigrada. Results for these species show that trophi do not change after hatching, either in size or in shape. In contrast, data on Asplanchna priodonta reveal trophi growth after hatching.  相似文献   

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Work over the past 20 years has implicated electrically nonexcitable astrocytes in complex neural functions. Despite controversies, it is increasingly clear that many, if not all, neural processes involve astrocytes. This review critically examines past work to identify the commonalities among the many published studies of neuroglia signaling. Although several studies have shown that astrocytes can impact short-term and long-term synaptic plasticity, further work is required to determine the requirement for astrocytic Ca2+ and other second messengers in these processes. One of the roadblocks to the field advancing at a rapid pace has been technical. We predict that the novel experimental tools that have emerged in recent years will accelerate the field and likely disclose an entirely novel path of neuroglia signaling within the near future.The year 2014 represents the 20th anniversary of a pair of papers published by the writers that provided the first indication that astrocytes actively signal to neurons, and that these glial cells have the potential to be participants in the control of neural circuit function and behavior (Nedergaard 1994; Parpura et al. 1994). Although we have taken independent paths, we come together on this anniversary to discuss what we have learned since 1994, where we see the field progressing, and, finally, to discuss some key steps that we believe should be taken in the next decade to begin to further clarify the diverse roles that astrocytes play in brain function in health and disease.Without knowledge of one another’s work, we published a pair of papers that provided the first demonstration that physiological changes in astrocytes influence neurons: stimulated Ca2+ changes in astrocytes led to delayed Ca2+ responses in neurons (Nedergaard 1994; Parpura et al. 1994). To set the backdrop to these studies, this was a period of explosive growth in Ca2+ imaging that resulted from the availability of fluorescent Ca2+ indicators and sensitive cameras to permit low-light-level imaging of intracellular biochemistry. As a consequence, there had been several recently published studies revealing that astrocytes show Ca2+ elevations in response to mechanical contact or even to the addition of neurotransmitters, such as glutamate (Cornell-Bell et al. 1990). However, the functional downstream consequences were unknown. In our studies, which used a combination of different stimuli—mechanical, optical, as well as a chemical transmitter bradykinin—we were able to show a robust impact of the astrocytic Ca2+ signal on the adjacent neurons (Nedergaard 1994; Parpura et al. 1994). Despite differences in mechanistic conclusions, these papers stimulated revised thinking about roles of astrocytes in the brain—perhaps these glial cells were actively signaling, albeit on a slower time scale, to modulate neurons, circuits, and, ultimately, behavior.The subsequent two decades have been spent examining the signaling of astrocytes to neurons in more intact systems. As a consequence of this work, it is clear that astrocytes play critical roles in actively modulating brain function, although we are still putting the pieces of the puzzle in place to understand where, when, and how this process occurs naturally in vivo and when dysfunction can lead to disorders of the brain.The field has gone through an explosive growth that has consisted of several phases. Initially, there was the dish phase in which the potential of the astrocyte was revealed in cell culture. These studies were essential as they captured our imagination and stimulated new thinking; however, they were limited by the fact that the properties of astrocytes can be different in vitro and in vivo. Next, we had the in situ phase, in which we asked whether similar processes could be detected in situ in acutely isolated brain slices. Then we began asking about roles in vivo through Ca2+ imaging together with two-photon microscopy as well as with molecular genetic alterations to permit the inhibition and stimulation of astrocytes. Each of these phases has offered unique insights, challenges, and opportunities for the field.Through all of these phases, an emergent picture is developing in which it is without doubt that astrocytes play important roles in vivo but that the mechanisms are so diverse and complex that an understanding is still to emerge.Some of the major challenges that we have faced and continue to face include: What are the endogenous signals of these glial cells? How can we stimulate astrocytes in a physiologically relevant manner? How can we inhibit astrocytes to determine when they are needed for brain function? And last, but by no means least, how diverse are astrocytes?We are still at the early days of understanding astrocytes, and patience regarding functional interpretation is required. We make this statement because there have been apparently contradictory conclusions drawn from different studies. The individual observations are important as they help provide a fuller picture of the biology of these complex cells. However, the jury still needs further evidence before definitive conclusions can be drawn. For example, a plethora of studies have shown that Ca2+ signals stimulate gliotransmission and the consequent modulation of neurons and synapses (see Agulhon et al. 2010), the field was rocked. We do not question the data of the study; instead, we believe this is an important piece of information that ultimately needs to be put in context. In contrast, additional studies have shown that IP3 receptors are important for other aspects of astrocyte-induced synaptic modulation. A more recent study has shown that, in addition to Ca2+ release from internal stores, the influx of Ca2+ through transient receptor potential (TRP) channels is important for gliotransmission (Shigetomi et al. 2013). Clearly, such influx sites were unlikely to have been affected by the IP3R2 knockout and were shown to regulate d-serine release from the astrocyte. Another piece of the puzzle is added. Undoubtedly, there will be further twists and turns, but that is the joy of discovery, and it should be embraced.

Table 1.

Effect of Ca2+ signaling on excitatory or inhibitory potentials, slow inward current, synaptic failure, or neural bistability
PreparationMethod for inducing astrocytic Ca2+ signalingChange in the frequency of EPSP or IPSP (%)aDuration of modulation of EPSP or IPSPaReferences
Hippocampal coculturesMechanical stimulation or photolysis of caged Ca2+-10–50 secAraque et al. 1998
RetinaMechanical stimulationModulation of light- induced neural activity10–20 secNewman and Zahs 1998
Frog neuromuscular junctionInjection of GTP-γS in perisynaptic Schwann cellsModulation of nerve-evoked synaptic responsesFor the duration of the recordingsRobitaille 1998
Hippocampal slicesTrain of depolarization10%–30%∼60–120 secJourdain et al. 2007
Hippocampal slicesPhotolysis20%–30% decrease in synaptic failure50–60 secPerea and Araque 2007
Hippocampal slicesAgonists (ATP, UTP, FMRF)∼20%–30%10–60 secWang et al. 2012a
Hippocampal slicesPhotolysis of caged Ca2+b∼30%10–60 secWang et al. 2013
Slow inward current
Hippocampal slicesAgonist (DHPG) and photolysis of caged Ca2+Slow inward current∼20–50 secFellin et al. 2004
Hippocampal slicesNeuronal depolarizationSlow inward current∼50 secNavarrete and Araque 2008
Decrease in synaptic failure rate
Hippocampal slicesTrain of depolarization∼20%–30%20 minKang et al. 1998
Hippocampal slicesPhotolysis of caged Ca2+∼20%–30%∼60 secPerea and Araque 2007
Hippocampal slicesAgonists∼20%–30%10–60 secWang et al. 2012a
Hippocampal slicesComparison of agonists and photolysis of caged Ca2+∼20%–30%10–60 secWang et al. 2013
Bistability
Cortical slicesTrains of depolarizationUpstate synchronizations-Poskanzer and Yuste 2011
Cerebellar slicesAgonists (ATP, UTP, FMRF)Increase in duration of upstate40–60 secWang et al. 2012b
Open in a separate windowAll of the studies included in the table show that the modulatory effect on neural activity is Ca2+-dependent (BAPTA loading, thapsigargin, and/or use of transgenic mice with deletion of IP3R2 receptors).DHPG, dihydroxyphenylglycine; EPSP, excitatory postsynaptic potential; IPSP, inhibitory postsynaptic potential.aFor simplicity, EPSP and IPSP denote excitatory or inhibitory potentials or currents in both presence and absence of tetrodotoxin (TTX). Details can be found in the original papers.bThe same study compared the effect of photolysis and agonist-induced astrocytic Ca2+ signaling and found that only photolysis, but not agonist exposure, induced changes in the frequency of EPSPs.We believe that it is also important to be constrained when discussing Ca2+ as there is not just one type of Ca2+ signal. For example, there are global Ca2+ signals in which large somatic Ca2+ elevations arise and that can propagate as slow waves between adjacent astrocytes in slices preparation. In vivo, astrocytes in awake mice display global Ca2+ increases that often simultaneously engaged most cells within the field of view. Isolated oscillatory cellular Ca2+ signals can be restricted to one cell, and there are “spotty” Ca2+ signals that can be restricted to local microdomains (Shigetomi et al. 2013). It is possible, even likely, that each of these signals mediates different processes and more effort should focus on understanding the important functional distinction between each.Other areas of interesting debate have concerned how gliotransmitters are released. Evidence exists for multiple mechanisms: exocytosis, anion transporters, and connexin hemichannels, to name a few. Significant evidence exists for each, and it is likely that all are used, although in different locales, and are recruited under differing conditions. A challenge is to perform precise experiments that allow the discrimination between each mechanism and to identify when each is recruited in physiology and/or pathology.  相似文献   

16.
Whether G protein-coupled receptors (GPCRs) exist in plants is a fundamental biological question. Interest in deorphanizing new GPCRs arises because of their importance in signaling. Within plants, this is controversial, as genome analysis has identified 56 putative GPCRs, including G protein-coupled receptor1 (GCR1), which is reportedly a remote homolog to class A, B, and E GPCRs. Of these, GCR2 is not a GPCR; more recently, it has been proposed that none are, not even GCR1. We have addressed this disparity between genome analysis and biological evidence through a structural bioinformatics study, involving fold recognition methods, from which only GCR1 emerges as a strong candidate. To further probe GCR1, we have developed a novel helix-alignment method, which has been benchmarked against the class A-class B-class F GPCR alignments. In addition, we have presented a mutually consistent set of alignments of GCR1 homologs to class A, class B, and class F GPCRs and shown that GCR1 is closer to class A and/or class B GPCRs than class A, class B, or class F GPCRs are to each other. To further probe GCR1, we have aligned transmembrane helix 3 of GCR1 to each of the six GPCR classes. Variability comparisons provide additional evidence that GCR1 homologs have the GPCR fold. From the alignments and a GCR1 comparative model, we have identified motifs that are common to GCR1, class A, B, and E GPCRs. We discuss the possibilities that emerge from this controversial evidence that GCR1 has a GPCR fold.There has been much interest in the identification of novel G protein-coupled receptors (GPCRs) from genome analysis, initially from the human genome, because GPCRs are highly druggable therapeutic targets, and more recently from other genome studies, because GPCRs are vital signaling molecules in diverse organisms. Therefore, whether GPCRs exist in plants is a fundamental biological question.Here, our focus on putative plant GPCRs was initiated with the characterization of G protein-coupled receptor1 (GCR1) as an orphan GPCR that binds to the plant G protein Guanine nucleotide-binding protein alpha-1 subunit (GPA1) and that is involved in the drought response (Hooley, 1999; Pandey and Assmann, 2004). This observation was followed by intense efforts to identify other plant GPCRs (Moriyama et al., 2006; Liu et al., 2007; Gookin et al., 2008; Pandey et al., 2009). For well-established GPCRs, there are two main classification systems. The GRAFS system (Fredriksson et al., 2003) described five classes of human GPCRs: Glutamate, Rhodopsin, Adhesion, Frizzled/Taste2, and Secretin. Others (Attwood and Findlay, 1994; Kolakowski, 1994) described six classes, namely A to E and the Frizzled GPCRs (class F), that additionally include class D (Eilers et al., 2005) found in fungi and class E cAMP receptors associated with Dictyostelium species (Williams et al., 2005); the Adhesion and Secretin receptors, which differ primarily in their N termini (Lagerström and Schiöth, 2008), together form class B. GCR1 is particularly interesting from a bioinformatics perspective, as it has identifiable but distant homology to class E, class B, and class A GPCRs (Pandey and Assmann, 2004), and so has been used to inform the medically important class A-class B GPCR alignment (Vohra et al., 2007, 2013). GCR1 and the other putative plant GPCRs do not naturally fall into the well-characterized GPCR classes, as presented at the GPCRDB (Horn et al., 2003; Vroling et al., 2011) or elsewhere, and so confirmation that GCR1 is a GPCR is difficult. Indeed, the pitfalls of GPCR identification are illustrated by the high profile (Liu et al., 2007) but erroneous identification of GCR2 as a plant GPCR. It has now been confirmed through crystallization that GCR2 is a lantibiotic cyclase-like protein (Chen et al., 2013), as predicted by our fold recognition studies (Illingworth et al., 2008).We are particularly interested in these putative GPCRs to assess whether, as remote homologs, they may similarly be used to address the difficult issue of alignment between GPCR families. In this respect, only GCR1 is useful, as the fold recognition studies indicate that GCR1 is the most likely candidate to have a GPCR fold while the evidence for other plant GPCRs is at best minimal. While many methods have been used to align GPCRs from different classes (Frimurer and Bywater 1999; Sheikh et al., 1999; Bissantz et al., 2004; Miedlich et al., 2004; Eilers et al., 2005; Kratochwil et al., 2005; Dong et al., 2007; Coopman et al., 2011; Gregory et al., 2013), it has not been possible to validate these methods on GPCRs until recently. However, with the recent publication of the structure of the class B glucagon receptor (Siu et al., 2013), the class B corticotropin-releasing factor1 receptor (Hollenstein et al., 2013), and the class F human smoothened receptor (Wang et al., 2013) and the associated structural alignments between class A and these remote homologs, we have been able, to our knowledge for the first time, to successfully test our new method. This method is a variation on that used to produce a well-validated class A-class B alignment (Vohra et al., 2013), in which GCR1 was used as a bridge; in a follow-on article, the alignment formed the basis of a class B calcitonin receptor-like receptor (CLR) active model (Woolley et al., 2013) that was later shown to be in good agreement with the class B glucagon receptor x-ray crystal structure. Consequently, we have aligned the GCR1 homologs to class A, class B, and class F and have generated comparative models of active and inactive GCR1. From the alignment, with the assistance of the models, we have identified a number of motifs that are common to GCR1, class A, class B, and class E GPCRs, thus greatly increasing the evidence that GCR1 has a GPCR fold. In addition, we have provided further evidence that GCR1 homologs have the same fold as class A and class B GPCRs from variability analysis. Here, we imply that the difference between a GPCR and a protein with a GPCR fold is the lack of definitive experimental evidence of conventional signaling partners.Some bioinformatics studies have suggested that there might be about 50 plant GPCRs, including those with large non-membrane domains (Supplemental Table S1) or those with sequence similarities to other plant proteins (Supplemental Table S2), but now it has been questioned whether there are any plant GPCRs (Urano et al., 2012, 2013; Bradford et al., 2013; Urano and Jones 2013), primarily because the plant G protein is self activating and does not need a guanine nucleotide-exchange factor (GEF). One of the presentations of putative plant GPCRs is based on a hidden Markov model, trained on several hundred seven-transmembrane helical (7TM) proteins taken from the GPCRDB (both well-characterized GPCRs and other 7TM proteins such as the mildew resistance locus O [MLO] proteins); the genes were tentatively assigned as GPCRs on the basis of seven predicted transmembrane helices (Moriyama et al., 2006). This assignment has been made against the background of the well-documented and now closed debate regarding whether the 7TM protein bacteriorhodopsin was a suitable template for modeling GPCRs (Hibert et al., 1993; Hoflack et al., 1994), most typified by the article of Hibert et al. (1993): “This is not a G protein coupled receptor.” Given that a number of distinct GPCR x-ray crystal structures have become available (Congreve et al., 2011; Katritch et al., 2013; Venkatakrishnan et al., 2013), it is now possible to analyze these putative plant GPCR sequences to assess whether, in the light of new structural information, they are more or less likely to be GPCRs and, thus, to move beyond the assumption implicit in Moriyama et al. (2006) that a receptor with seven transmembrane helices is a GPCR (e.g. bacteriorhodopsin has seven transmembrane helices but is not a GPCR; Hibert et al., 1993).Here, our approach to analysis of the 56 putative plant GPCRs is to combine transmembrane structure prediction and sequence analysis with fold recognition methods. There are essentially two approaches to fold recognition, namely sequence-based methods, such as genTHREADER (Jones, 1999b), and empirical potential-based methods, such as Threader (Jones et al., 1992; Jones, 1998). The sequence-based methods have the advantage of speed and may be suitable for whole-genome analysis but may not readily identify remote homologs when the sequence identity is low. The empirical potential-based methods may be more efficient at identifying remote homologs but are generally not parameterized for membrane proteins. For this reason, we have taken a heuristic approach and have tested a variety of fold recognition methods to see if they correctly identify characteristic GPCR sequences from classes A to F while at the same time not incorrectly assigning bacteriorhodopsin and GCR2 as GPCRs. In particular, our focus is on fold recognition methods such as I-TASSER (Zhang, 2008; Roy et al., 2010) that have performed well in the critical assessment of protein structure prediction (CASP) fold recognition competitions (Moult et al., 2009). For proteins where the evidence that they are GPCRs was not convincing, the fold recognition (threading) results were used to give a preliminary indication of which other types of membrane proteins they could be; the most likely alternatives were ion channels or transporters. The significance of this study, therefore, is 4-fold. First, it adds clarity to the field of plant GPCRs by indicating from a wide range of evidence that only GCR1 is strongly predicted to have a GPCR fold. Second, it provides evidence that some of the other candidates are more likely to be transporters. Third, it indicates computational approaches that could be taken to follow up initial genome analysis studies to help avoid the confusion that has shrouded the plant GPCR field. Fourth, the new alignment method has given promising results on well-validated alignments in or below the “twilight zone” (Doolittle, 1986) and so could, with development, be used in other more general applications. In addition, we discuss the implications of these results that are difficult to reconcile with current knowledge of the mechanism of the Arabidopsis (Arabidopsis thaliana) G protein, GPA1.  相似文献   

17.
What Do We Really Know about Cellulose Biosynthesis in Higher Plants?   总被引:1,自引:0,他引:1  
Cellulose biosynthesis is one of the most important biochemical processes in plant biology. Despite the considerable progress made during the last decade, numerous fundamental questions related to this key process in plant development are outstanding. Numerous models have been proposed through the years to explain the detailed molecular events of cellulose biosynthesis. Almost all models integrate solid experimental data with hypotheses on several of the steps involved in the process. Speculative models are most useful to stimulate further research investigations and bring new exciting ideas to the field. However, it is important to keep their hypothetical nature in mind and be aware of the risk that some undemonstrated hypotheses may progressively become admitted. In this review, we discuss the different steps required for cellulose formation and crystallization, and highlight the most important specific aspects that are supported by solid experimental data.  相似文献   

18.
Cellulose biosynthesis is one of the most important biochemical processes in plant biology. Despite the considerable progress made during the last decade, numerous fundamental questions related to this key process in plant development are outstanding. Numerous models have been proposed through the years to explain the detailed molecular events of cellulose biosynthesis. Almost all models integrate solid experimental data with hypotheses on several of the steps involved in the process. Speculative models are...  相似文献   

19.
How Do Real Roots Work? (Some New Views of Root Structure)   总被引:13,自引:4,他引:13       下载免费PDF全文
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20.
In “The Origin of Species,” Darwin describes a hypothetical example illustrating that large, slowly reproducing mammals such as the elephant can reach very large numbers if population growth is not affected by regulating factors. The elephant example has since been cited in various forms in a wide variety of books, ranging from educational material to encyclopedias. However, Darwin’s text was changed over the six editions of the book, although some errors in the mathematics persisted throughout. In addition, full details of the problem remained hidden in his correspondence with readers of the Origin. As a result, Darwin’s example is very often misinterpreted, misunderstood or presented as if it were a fact. We show that the population growth of Darwin’s elephant population can be modeled by the Leslie matrix method, which we generalize here to males as well. Darwin’s most often cited figure, about 19 million elephants after 750 years is not a typical outcome, actually a very unlikely result under more realistic, although still hypothetical situations. We provide a recursion formula suggesting that Darwin’s original model corresponds to a tribonacci series, a proof showing that sex ratio is constant over all age classes, and a derivation of a generating function of the sequence.  相似文献   

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