Computability of Probability Distributions and Distribution Functions

We define the computability of probability distributions on the real line as well as that of distribution functions. Mutual relationships between the computability notion of a probability distribution and that of the corresponding distribution function are discussed. It is carried out through attempts to effectivize some classical fundamental theorems concerning probability distributions. We then define the effective convergence of probability distributions as an effectivization of the classical vague convergence. For distribution functions, computability and effective convergence are naturally defined as real functions. A weaker effective convergence is also defined as an effectivization of pointwise convergence

Random Iteration Algorithm for Graph-Directed Sets

A random iteration algorithm for graph-directed sets is defined and discussed. Similarly to the Barnsley-Elton\u27s theorem, it is shown that almost all sequences obtained by this algorithm reflect a probability measure which is invariant with respect to the system of contractions with probabilities

Proteasome-associated ubiquitin ligase relays target plant hormone-specific transcriptional activators

The ubiquitin-proteasome system is vital to hormone-mediated developmental and stress responses in plants. Ubiquitin ligases target hormone-specific transcriptional activators (TAs) for degradation, but how TAs are processed by proteasomes remains unknown. We report that in Arabidopsis, the salicylic acid– and ethylene-responsive TAs, NPR1 and EIN3, are relayed from pathway-specific ubiquitin ligases to proteasome-associated HECT-type UPL3/4 ligases. Activity and stability of NPR1 were regulated by sequential action of three ubiquitin ligases, including UPL3/4, while proteasome processing of EIN3 required physical handover between ethylene-responsive SCF(EBF2) and UPL3/4 ligases. Consequently, UPL3/4 controlled extensive hormone-induced developmental and stress-responsive transcriptional programs. Thus, our findings identify unknown ubiquitin ligase relays that terminate with proteasome-associated HECT-type ligases, which may be a universal mechanism for processive degradation of proteasome-targeted TAs and other substrates

The mechanism of SO2 -induced stomatal closure differs from O3 and CO2 responses and is mediated by nonapoptotic cell death in guard cells.

Plants closing stomata in the presence of harmful gases is believed to be a stress avoidance mechanism. SO2 , one of the major airborne pollutants, has long been reported to induce stomatal closure, yet the mechanism remains unknown. Little is known about the stomatal response to airborne pollutants besides O3 . SLOW ANION CHANNEL-ASSOCIATED 1 (SLAC1) and OPEN STOMATA 1 (OST1) were identified as genes mediating O3 -induced closure. SLAC1 and OST1 are also known to mediate stomatal closure in response to CO2 , together with RESPIRATORY BURST OXIDASE HOMOLOGs (RBOHs). The overlaying roles of these genes in response to O3 and CO2 suggested that plants share their molecular regulators for airborne stimuli. Here, we investigated and compared stomatal closure event induced by a wide concentration range of SO2 in Arabidopsis through molecular genetic approaches. O3 - and CO2 -insensitive stomata mutants did not show significant differences from the wild type in stomatal sensitivity, guard cell viability, and chlorophyll content revealing that SO2 -induced closure is not regulated by the same molecular mechanisms as for O3 and CO2 . Nonapoptotic cell death is shown as the reason for SO2 -induced closure, which proposed the closure as a physicochemical process resulted from SO2 distress, instead of a biological protection mechanism

Mechanosensory trichome cells evoke a mechanical stimuli–induced immune response in Arabidopsis thaliana

Perception of pathogen-derived ligands by corresponding host receptors is a pivotal strategy in eukaryotic innate immunity. In plants, this is complemented by circadian anticipation of infection timing, promoting basal resistance even in the absence of pathogen threat. Here, we report that trichomes, hair-like structures on the epidermis, directly sense external mechanical forces, including raindrops, to anticipate pathogen infections in Arabidopsis thaliana. Exposure of leaf surfaces to mechanical stimuli initiates the concentric propagation of intercellular calcium waves away from trichomes to induce defence-related genes. Propagating calcium waves enable effective immunity against pathogenic microbes through the CALMODULIN-BINDING TRANSCRIPTION ACTIVATOR 3 (CAMTA3) and mitogen-activated protein kinases. We propose an early layer of plant immunity in which trichomes function as mechanosensory cells that detect potential risks

BdWRKY38 is required for the incompatible interaction of Brachypodium distachyon with the necrotrophic fungus Rhizoctonia solani

Rhizoctonia solani is a soil‐borne necrotrophic fungus that causes sheath blight in grasses. The basal resistance of compatible interactions between R. solani and rice is known to be modulated by some WRKY transcription factors (TFs). However, genes and defense responses involved in incompatible interaction with R. solani remain unexplored, because no such interactions are known in any host plants. Recently, we demonstrated that Bd3‐1, an accession of the model grass Brachypodium distachyon, is resistant to R. solani and, upon inoculation with the fungus, undergoes rapid induction of genes responsive to the phytohormone salicylic acid (SA) that encode the WRKY TFs BdWRKY38 and BdWRKY44. Here, we show that endogenous SA and these WRKY TFs positively regulate this accession‐specific R. solani resistance. In contrast to a susceptible accession (Bd21), the infection process in the resistant accessions Bd3‐1 and Tek‐3 was suppressed at early stages before the development of fungal biomass and infection machinery. A comparative transcriptome analysis during pathogen infection revealed that putative WRKY‐dependent defense genes were induced faster in the resistant accessions than in Bd21. A gene regulatory network (GRN) analysis based on the transcriptome dataset demonstrated that BdWRKY38 was a GRN hub connected to many target genes specifically in resistant accessions, whereas BdWRKY44 was shared in the GRNs of all three accessions. Moreover, overexpression of BdWRKY38 increased R. solani resistance in Bd21. Our findings demonstrate that these resistant accessions can activate an incompatible host response to R. solani, and BdWRKY38 regulates this response by mediating SA signaling

Dynamics of Quasi-ordered Structure in a Regio-regulated pi-Conjugated Polymer:Poly(4-methylthiazole-2,5-diyl)

Dynamics of regio-regulated Poly(4-methylthiazole-2,5-diyl) [HH-P4MeTz] was inves tigated by solid-state 1H, 2D, 13C NMR spectroscopies, and differential scanning calorimetry(DSC) measurements. DSC, 2D quadrupolar echo NMR, 13C cross-polarization and magic-angle spinning(CPMAS) NMR, and 2D spin-echo(2DSE) CPMAS NMR spectroscopy suggest existence of a quasi-ordered phase in which backbone twists take place with weakened pi-stackings. Two-dimensional exchange 2D NMR(2DEX) detected slow dynamics with a rate of an order of 10^2Hz for the CD_3 group in d_3-HH-P4MeTz at 288K. The frequency dependence of proton longitudinal relaxation rate at 288K shows a omega^-1/2 dependence, which is due to the one-dimensional diffusion-like motion of backbone conformational modulation waves. The diffusion rate was estimated as 3+/-2 GHz, which was approximately 10^7 times larger than that estimated by 2DEX NMR measurements. These results suggest that there exists anomalous dispersion of modulation waves in HH-P4MeTz. The one-dimensional group velocity of the wave packet is responsible for the behavior of proton longitudinal relaxation time. On the other hand, the 2DEX NMR is sensitive to phase velocity of the nutation of methyl groups that is associated with backbone twists. From proton T_1 and T_2 measurements, the activation energy was estimated as 2.9 and 3.4 kcal/mol, respectively. These were in agreement with 3.0 kcal/mol determined by Moller-Plesset(MP2) molecular orbital(MO) calculation. We also performed chemical shielding calculation of the methyl-carbon in order to understand chemical shift tensor behavior, leading to the fact that a quasi-ordered phase coexist with the crystalline phase.Comment: 14 pages, 11 figures, to appear in Phys.Rev.

Low temperature modulates natural peel degreening in lemon fruit independently of endogenous ethylene

Peel degreening is an important aspect of fruit ripening in many citrus fruit, and previous studies have shown that it can be advanced by ethylene treatment or by low-temperature storage. However, the important regulators and pathways involved in natural peel degreening remain largely unknown. To determine how natural peel degreening is regulated in lemon fruit (Citrus limon), we studied transcriptome and physiochemical changes in the flavedo in response to ethylene treatment and low temperatures. Treatment with ethylene induced rapid peel degreening, which was strongly inhibited by the ethylene antagonist, 1-methylcyclopropene (1-MCP). Compared with 25 degrees C, moderately low storage temperatures of 5-20 degrees C also triggered peel degreening. Surprisingly, repeated 1-MCP treatments failed to inhibit the peel degreening induced by low temperature. Transcriptome analysis revealed that low temperature and ethylene independently regulated genes associated with chlorophyll degradation, carotenoid metabolism, photosystem proteins, phytohormone biosynthesis and signalling, and transcription factors. Peel degreening of fruit on trees occurred in association with drops in ambient temperature, and it coincided with the differential expression of low temperature-regulated genes. In contrast, genes that were uniquely regulated by ethylene showed no significant expression changes during on-tree peel degreening. Based on these findings, we hypothesize that low temperature plays a prominent role in regulating natural peel degreening independently of ethylene in citrus fruit

Phytohormones in red seaweeds: a technical review of methods for analysis and a consideration of genomic data

Emerging studies suggest that seaweeds contain phytohormones; however, their chemical entities, biosynthetic pathways, signal transduction mechanisms, and physiological roles are poorly understood. Until recently, it was difficult to conduct comprehensive analysis of phytohormones in seaweeds because of the interfering effects of cellular constituents on fine quantification. In this review, we discuss the details of the latest method allowing simultaneous profiling of multiple phytohormones in red seaweeds, while avoiding the effects of cellular factors. Recent studies have confirmed the presence of indole-3-acetic acid (IAA), N6-(Δ2-isopentenyl)adenine(iP), (+)-abscisic acid (ABA), and salicylic acid, but not of gibberellins and jasmonate, in Pyropia yezoensis and Bangia fuscopurpurea. In addition, an in silico genome-wide homology search indicated that red seaweeds synthesize iP and ABA via pathways similar to those in terrestrial plants, although genes homologous to those involved in IAA biosynthesis in terrestrial plants were not found, suggesting the epiphytic origin of IAA. It is noteworthy that these seaweeds also lack homologues of known factors involved in the perception and signal transduction of IAA, iP, and ABA. Thus, the modes of action of these phytohormones in red seaweeds are unexpectedly dissimilar to those in terrestrial plants