Approximations of relations by continuous functions

AbstractLet X be a Tychonoff space, C(X) be the space of all continuous real-valued functions defined on X and CL(X×R) be the hyperspace of all nonempty closed subsets of X×R. We prove the following result. Let X be a countably paracompact normal space. The following are equivalent: (a) dimX=0; (b) the closure of C(X) in CL(X×R) with the Vietoris topology consists of all F∈CL(X×R) such that F(x)≠∅ for every x∈X and F maps isolated points into singletons; (c) each usco map which maps isolated points into singletons can be approximated by continuous functions in CL(X×R) with the locally finite topology. From the mentioned result we can also obtain the answer to Problem 5.5 in [L'. Holá, R.A. McCoy, Relations approximated by continuous functions, Proc. Amer. Math. Soc. 133 (2005) 2173–2182] and to Question 5.5 in [R.A. McCoy, Comparison of hyperspace and function space topologies, Quad. Mat. 3 (1998) 243–258] in the realm of normal, countably paracompact, strongly zero-dimensional spaces. Generalizations of some results from [L'. Holá, R.A. McCoy, Relations approximated by continuous functions, Proc. Amer. Math. Soc. 133 (2005) 2173–2182] are also given

MRE11 and RAD50, but not NBS1, are essential for gene targeting in the moss Physcomitrella patens

The moss Physcomitrella patens is unique among plant models for the high frequency with which targeted transgene insertion occurs via homologous recombination. Transgene integration is believed to utilize existing machinery for the detection and repair of DNA double-strand breaks (DSBs). We undertook targeted knockout of the Physcomitrella genes encoding components of the principal sensor of DNA DSBs, the MRN complex. Loss of function of PpMRE11 or PpRAD50 strongly and specifically inhibited gene targeting, whilst rates of untargeted transgene integration were relatively unaffected. In contrast, disruption of the PpNBS1 gene retained the wild-type capacity to integrate transforming DNA efficiently at homologous loci. Analysis of the kinetics of DNA-DSB repair in wild-type and mutant plants by single-nucleus agarose gel electrophoresis revealed that bleomycin-induced fragmentation of genomic DNA was repaired at approximately equal rates in each genotype, although both the Ppmre11 and Pprad50 mutants exhibited severely restricted growth and development and enhanced sensitivity to UV-B and bleomycin-induced DNA damage, compared with wild-type and Ppnbs1 plants. This implies that while extensive DNA repair can occur in the absence of a functional MRN complex; this is unsupervised in nature and results in the accumulation of deleterious mutations incompatible with normal growth and developmen

MRE11 and RAD50, but not NBS1, are essential for gene targeting in the moss Physcomitrella patens

The moss Physcomitrella patens is unique among plant models for the high frequency with which targeted transgene insertion occurs via homologous recombination. Transgene integration is believed to utilize existing machinery for the detection and repair of DNA double-strand breaks (DSBs). We undertook targeted knockout of the Physcomitrella genes encoding components of the principal sensor of DNA DSBs, the MRN complex. Loss of function of PpMRE11 or PpRAD50 strongly and specifically inhibited gene targeting, whilst rates of untargeted transgene integration were relatively unaffected. In contrast, disruption of the PpNBS1 gene retained the wild-type capacity to integrate transforming DNA efficiently at homologous loci. Analysis of the kinetics of DNA-DSB repair in wild-type and mutant plants by single-nucleus agarose gel electrophoresis revealed that bleomycin-induced fragmentation of genomic DNA was repaired at approximately equal rates in each genotype, although both the Ppmre11 and Pprad50 mutants exhibited severely restricted growth and development and enhanced sensitivity to UV-B and bleomycin-induced DNA damage, compared with wild-type and Ppnbs1 plants. This implies that while extensive DNA repair can occur in the absence of a functional MRN complex; this is unsupervised in nature and results in the accumulation of deleterious mutations incompatible with normal growth and development

The Physiology and Proteomics of Drought Tolerance in Maize: Early Stomatal Closure as a Cause of Lower Tolerance to Short-Term Dehydration?

Understanding the response of a crop to drought is the first step in the breeding of tolerant genotypes. In our study, two maize (Zea mays L.) genotypes with contrasting sensitivity to dehydration were subjected to moderate drought conditions. The subsequent analysis of their physiological parameters revealed a decreased stomatal conductance accompanied by a slighter decrease in the relative water content in the sensitive genotype. In contrast, the tolerant genotype maintained open stomata and active photosynthesis, even under dehydration conditions. Drought-induced changes in the leaf proteome were analyzed by two independent approaches, 2D gel electrophoresis and iTRAQ analysis, which provided compatible but only partially overlapping results. Drought caused the up-regulation of protective and stress-related proteins (mainly chaperones and dehydrins) in both genotypes. The differences in the levels of various detoxification proteins corresponded well with the observed changes in the activities of antioxidant enzymes. The number and levels of up-regulated protective proteins were generally lower in the sensitive genotype, implying a reduced level of proteosynthesis, which was also indicated by specific changes in the components of the translation machinery. Based on these results, we propose that the hypersensitive early stomatal closure in the sensitive genotype leads to the inhibition of photosynthesis and, subsequently, to a less efficient synthesis of the protective/detoxification proteins that are associated with drought tolerance