Cluster roots

Figure 5 Model of phosphorus (P) deficiency-induced physiological changes associated with the release of P-mobilizing root exudates in cluster roots of white lupin. Solid lines indicate stimulation and dotted lines inhibition of biochemical reaction sequences or mclaholic pathways in response to P deliciency. For a detailed description see Sec. 4.1. Abbreviations SS = sucrose synthase FK = fructokinase PGM = phosphoglueomutase PEP = phosphoenol pyruvate PE PC = PEP-carboxylase MDH = malate dehydrogenase ME = malic enzyme CS = citrate synthase PDC = pyruvate decarboxylase ALDH — alcohol dehydrogenase E-4-P = erythrosc-4-phosphate DAMP = dihydraxyaceConephos-phate APase = acid phosphatase.

An interesting adaptation of the root system to low P is the formation of cluster roots. As they are an adaptation, but not systematically different from other roots (Skene 2003), we will review the knowledge about the well-studied cluster roots in some detail as an example of root functioning. 

From the cluster roots, carboxylates are exuded at high rates (Shane and Lambers 2005), leading to an increasing mobility and uptake of P and other nutrients (Gerke... 

Next to the amount of P, the chemical form of this nutrient (Lambers et al. 2002 Shu et al. 2005 Shane et al. 2008) and the availability of other nutrients, especially nitrogen, potassium, and iron (Shane and Lambers 2005) affects the formation of cluster roots. It seems to be regulated by several plant hormones. Thus, application of auxin led to the production of cluster roots in white lupin at P concentrations that normally suppress cluster roots (Gilbert etal. 2000 Neumann et al. 2000). Cytokinines might also play a role, as kinetin applied to the growth medium of P-deficient white lupin inhibited the formation of cluster roots (Neumann et al. 2000). 

Fig. 6.1 Different plant strategies for dealing with patchy distribution of P in soil (a) initial situation random distribution of roots, (b) increased root production, (c) production of cluster roots in high-P environments, (d) production of cluster roots at random. For discussion, see text...

Although cluster roots form an interesting adaptation, species that do not form clusters generally have the same means of accessing nutrients, albeit not in such a condensed form They use root growth and branching to access nutrient-rich areas, exudation to increase nutrient availability, and absorption for uptake (Skene 2003). 

Thus, the outlined regulating factors and strategies also apply to species that do not form cluster roots. Furthermore, nutrient uplift, i.e., net displacement of nutrients from deep layers to the topsoil (Jobbagy and Jackson 2004), is used by plants to make P more accessible. This leads to the next section, where we discuss the influence of plants on soil P concentrations. 

Neumann G, Massonneau A, Langlade N, Dinkelaker B, Hengeler C, Romheld V, Martinoia E (2000) Physiological aspects of cluster root function and development in phosphorus-deficient white lupin (Lupinus albus L.). Ann Bot 85 909-919. doi http //aob.oxfordjournals.org/cgi/ content/abstract/85/6/909... 

Schachtman DP, Reid RJ, Ayling SM (1998) Phosphorus uptake by plants from soil to cell. Plant Physiol 116 447-453. doi http //www.plantphysiol.org Schindler DW (1974) Eutrophication and recovery in experimental lakes implications for lake management. Science 184 897-899. doi http //www.sciencemag.org/cgi/content/abstract/184/4139/897 Schindler DW, Hecky RE, Findlay DL, Stainton MP, Parker BR, Paterson MJ, Beaty KG, Lyng M, Kasian SEM (2008) Eutrophication of lakes cannot be controlled by reducing nitrogen input results of a 37-year whole-ecosystem experiment. Proc Natl Acad Sci USA 105 11254-11258. doi http //www.pnas.org/content/105/32/l 1254.abstract Scott JT, Condron LM (2003) Dynamics and availability of phosphorus in the rhizosphere of a temperate silvopastoral system. Biol Fert Soils 39 65-73 Shane MW, Lambers H (2005) Cluster roots a curiosity in context. Plant Soil 274 101-125. doi http //dx.doi.org/10.1007/s 11104-004-2725-7... 

Shane MW, De Vos M, De Roock S, Lambers H (2003a) Shoot P status regulates cluster-root growth and citrate exudation in Lupinus albus grown with a divided root system. Plant Cell Environ 26 265-273. doi http //www.blackwell-synergy.com/doi/abs/10.1046/ j. 1365-3040.2003.00957.x... 

Shane MW, de Vos M, de Roock S, Cawthray GR, Lambers H (2003b) Effects of external phosphorus supply on internal phosphorus concentration and the initiation, growth and exudation of cluster roots in Hakea prostrata R.Br. Plant Soil 248 209-219. doi http //dx.doi. org/10.1023/A 1022320416038... 

MATLAB s polynomial-roots finder roots does not handle repeated or clustered roots very well, but otherwise it is the best 0(n3) root finder available. Note that an operations count of 0(nP) for an algorithm signifies that the algorithm performs K n additions and multiplications (for some algorithm specific constants K and j, but depending on n) to obtain its output from n input data. Most of the polynomial-root finders of the last century unfortunately were even slower 0(n4) algorithms and all in all much too slow and inaccurate. 

Impact of Organic Substances on the Bioavailability of Trace Elements in the Rhizosphere The potential of plants to create chemical conditions assuring the accelerated dissolution of micronutrient metals is best exemplified by plants such as Banksia trees and white lupin Lupinus albus L.) that can produce proteoid/cluster roots exuding large amounts of organic, notably carboxylic, acids (Dinkelaker et al., 1995). Indicators of micronutrient availability such as DTPA (diethylenetriaminepentaacetic acid)-extractable Fe, Mn, and Zn were found to... 

Neumann, G., and Martinoia, E. (2002). Cluster roots an underground adaptation for survival in extreme envirorrments. Trends Plant Sci. 7, 162-167. 

Fig. 4.18. a Representative random conformations of six-membered rings in the c(hair), b(oat) and g(eneral) conformers. The arrows indicate symmetry transformations performed during cluster formation in which fragment g2 is arbitrarily chosen as the cluster root, b Cluster formed around randomly chosen cluster roots g2, b, and c. c Symmetry transformation of clusters around b, and C5 to new positions (b, and c which are in closest mutual proximity to g2... 

It is well known that in a high-order polynomial with clustered roots the root location is a very sensitive function of the polynomial coefficients. Therefore, filter poles and zeroes can be much more accurately controlled if higher order filters are realized by breaking them up into the parallel or cascade connection of first- and second-order subfilters. One exception to this rule is the case of linear-phase FIR filters in which the symmetry of the polynomial coefficients and the spacing of the filter zeros around the unit circle usually permits an acceptable direct realization using the convolution summation. 

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