The accuracy of merging approximation in generalized St. Petersburg games

Merging asymptotic expansions of arbitrary length are established for the distribution functions and for the probabilities of suitably centered and normalized cumulative winnings in a full sequence of generalized St. Petersburg games, extending the short expansions due to Cs\"org\H{o}, S., Merging asymptotic expansions in generalized St. Petersburg games, \textit{Acta Sci. Math. (Szeged)} \textbf{73} 297--331, 2007. These expansions are given in terms of suitably chosen members from the classes of subsequential semistable infinitely divisible asymptotic distribution functions and certain derivatives of these functions. The length of the expansion depends upon the tail parameter. Both uniform and nonuniform bounds are presented.Comment: 30 pages long version (to appear in Journal of Theoretical Probability); some corrected typo

Convergence to Stable Limits for Ratios of Trimmed Lévy Processes and their Jumps

We derive characteristic function identities for conditional distributions of an $r$-trimmed L\'evy process given its $r$ largest jumps up to a designated time $t$. Assuming the underlying L\'evy process is in the domain of attraction of a stable process as t\dto 0, these identities are applied to show joint convergence of the trimmed process divided by its large jumps to corresponding quantities constructed from a stable limiting process. This generalises related results in the 1-dimensional subordinator case developed in \cite{KeveiMason2014} and produces new discrete distributions on the infinite simplex in the limit

Tail probabilities of St. Petersburg sums, trimmed sums, and their limit

We provide exact asymptotics for the tail probabilities $\mathbb{P} \{S_{n,r} > x\}$ as $x \to \infty$, for fix $n$, where $S_{n,r}$ is the $r$-trimmed partial sum of i.i.d. St. Petersburg random variables. In particular, we prove that although the St. Petersburg distribution is only O-subexponential, the subexponential property almost holds. We also determine the exact tail behavior of the $r$-trimmed limits.Comment: 24 pages, 2 figure

Resequencing

[ES] La revolución que supone la secuenciación de próxima generación está permitiendo la resecuenciación del genoma completo (WGRS) de cientos o incluso miles de ejemplares de cultivos básicos y especies modelo. Con el lanzamiento de su genoma de referencia, progresivamente se están emprendiendo proyectos WGRS también para otras especies de plantas en una amplia variedad de estudios. En berenjena común (Solanum melongena L.), aunque se ha publicado un primer borrador de la secuencia del genoma de referencia, hasta el momento no se han realizado estudios de resecuenciación. En este capítulo presentamos los primeros resultados de la resecuenciación de ocho accesiones, siete de berenjena común y una del pariente silvestre S. incanum L., que corresponden a los progenitores de un cruce multiparental de generación avanzada (MAGIC) población que se encuentra actualmente en desarrollo utilizando la secuencia del genoma de la berenjena recién desarrollada que se presenta en el Cap. 7 de este libro. Se identificaron más de diez millones de polimorfismos entre las accesiones, el 90% de ellos en el S. incanum silvestre relacionado, lo que confirma la erosión genética de la berenjena común cultivada. Entre los progenitores de la población MAGIC, el patrón de distribución de polimorfismos comunes a lo largo de los cromosomas ha revelado posibles huellas de introgresión ancestral de cruces interespecíficos. El conjunto de polimorfismos se ha anotado extensamente y actualmente se está utilizando para análisis adicionales con el fin de genotipar eficientemente la población MAGIC en curso y diseccionar rasgos agronómicos y morfológicos importantes. La información proporcionada en este primer estudio de resecuenciación en berenjena será extremadamente útil para ayudar al fitomejoramiento a desarrollar nuevas variedades mejoradas y resistentes para enfrentar futuras amenazas y desafíos.[EN] The next-generation sequencing revolution is allowing the whole-genome resequencing (WGRS) of hundreds or even thousands of accessions for staple crops and model species. With the release of their reference genome, progressively also other plants, species are undertaking WGRS projects for a broad variety of studies. In common eggplant (Solanum melongena L.), although a first draft of the reference genome sequence has been published, no resequencing studies have been performed so far. In this chapter, we present the first results of the resequencing of eight accessions, seven of common eggplant and one of the wild relative S. incanum L., that correspond to the parents of a multi-parent advanced generation inter-cross (MAGIC) population that is currently under develop- ment using the newly developed eggplant genome sequence presented in Chap. 7 of this book. Over ten million polymorphisms were identified among the accessions, 90% of them in the wild related S. incanum, confirming the genetic erosion of the cultivated common eggplant. Among the MAGIC population parents, the common polymorphism distribu- tion pattern along the chromosomes has revealed possible footprints of ancestral intro- gression from interspecific crosses. The set of polymorphisms has been extensively anno- tated and currently is being used for further analyses in order to efficiently genotype the ongoing MAGIC population and to dissect important agronomic and morphological traits. The information provided in this first resequencing study in eggplant will be extremely helpful to assist plant breeding to develop new improved and resilient varieties to face future threats and challenges.This work has received funding from the European Union’s Horizon 2020 Research and Innovation Programme under grant agreement No 677379 (G2P-SOL project: Linking genetic resources, genomes and phenotypes of Solanaceous crops) and from Spanish Ministerio de Economía, Industria y Competitividad and Fondo Europeo de Desarrollo Regional (grant AGL2015-64755-R from MINECO/FEDER).Prohens Tomás, J.; Vilanova Navarro, S.; Gramazio, P. (2019). Resequencing. En The Eggplant Genome. Springer. 81-89. http://hdl.handle.net/10251/181875S818

A loss-of-function allele of a TAC1-like gene (SlTAC1) located on tomato chromosome 10 is a candidate for the Erectoid leaf (Erl) mutation

The genetic basis of an erectoid leaf phenotype was investigated in distinct tomato breeding populations, including one derived from Solanum lycopersicum ‘LT05’ (with the erectoid leaf phenotype and uniform ripening, genotype uu) × S. pimpinellifollium ‘TO-937’ (with the wild-type leaf phenotype and green fruit shoulder, genotype UU). The erectoid leaf phenotype was inherited as a semi-dominant trait and it co-segregated with the u allele of gene SlGLK2 (Solyc10g008160). This genomic location coincides with a previously described semi-dominant mutation named as Erectoid leaf (Erl). The genomes of ‘LT05’, ‘TO-937’, and three other unrelated accessions (with the wild-type Erl+ allele) were resequenced with the aim of identifying candidate genes. Comparative genomic analyses, including the reference genome ‘Heinz 1706’ (Erl+ allele), identified an Erectoid leaf-specific single nucleotide polymorphism (SNP) in the gene Solyc10g009320. This SNP caused a change of a glutamine codon (present in all the wild-type genomes) to a TAA (= ochre stop-codon) in the Erl allele, resulting in a smaller version of the predicted mutant protein (221 vs. 279 amino acids). Solyc10g009320, previously annotated as an ‘unknown protein’, was identified as a TILLER ANGLE CONTROL1-like gene. Linkage between the Erl and Solyc10g009320 was confirmed via Sanger sequencing of the PCR amplicons of the two variant alleles. No recombinants were detected in 265 F2 individuals. Contrasting S7 near-isogenic lines were also homozygous for each of the alternate alleles, reinforcing Solyc10g009320 as a strong Erl candidate gene and opening the possibility for fine-tuning manipulation of tomato architecture in breeding programs

APC/C-Mediated Degradation of dsRNA-Binding Protein 4 (DRB4) Involved in RNA Silencing

Background: Selective protein degradation via the ubiquitin-26S proteasome is a major mechanism underlying DNA replication and cell division in all Eukaryotes. In particular, the APC/C (Anaphase Promoting Complex or Cyclosome) is a master ubiquitin protein ligase (E3) that targets regulatory proteins for degradation allowing sister chromatid separation and exit from mitosis. Interestingly, recent work also indicates that the APC/C remains active in differentiated animal and plant cells. However, its role in post-mitotic cells remains elusive and only a few substrates have been characterized. Methodology/Principal Findings: In order to identify novel APC/C substrates, we performed a yeast two-hybrid screen using as the bait Arabidopsis APC10/DOC1, one core subunit of the APC/C, which is required for substrate recruitment. This screen identified DRB4, a double-stranded RNA binding protein involved in the biogenesis of different classes of small RNA (sRNA). This protein interaction was further confirmed in vitro and in plant cells. Moreover, APC10 interacts with DRB4 through the second dsRNA binding motif (dsRBD2) of DRB4, which is also required for its homodimerization and binding to its Dicer partner DCL4. We further showed that DRB4 protein accumulates when the proteasome is inactivated and, most importantly, we found that DRB4 stability depends on APC/C activity. Hence, depletion of Arabidopsis APC/C activity by RNAi leads to a strong accumulation of endogenous DRB4, far beyond its normal level of accumulation. However, we could not detect any defects in sRNA production in lines where DRB4 was overexpressed

E4 ligase–specific ubiquitination hubs coordinate DNA double-strand-break repair and apoptosis

Multiple protein ubiquitination events at DNA double-strand breaks (DSBs) regulate damage recognition, signaling and repair. It has remained poorly understood how the repair process of DSBs is coordinated with the apoptotic response. Here, we identified the E4 ubiquitin ligase UFD-2 as a mediator of DNA-damage-induced apoptosis in a genetic screen in Caenorhabditis elegans. We found that, after initiation of homologous recombination by RAD-51, UFD-2 forms foci that contain substrate-processivity factors including the ubiquitin-selective segregase CDC-48 (p97), the deubiquitination enzyme ATX-3 (Ataxin-3) and the proteasome. In the absence of UFD-2, RAD-51 foci persist, and DNA damage-induced apoptosis is prevented. In contrast, UFD-2 foci are retained until recombination intermediates are removed by the Holliday-junction-processing enzymes GEN-1, MUS-81 or XPF-1. Formation of UFD-2 foci also requires proapoptotic CEP-1 (p53) signaling. Our findings establish a central role of UFD-2 in the coordination between the DNA-repair process and the apoptotic response

Conserved CDC20 Cell Cycle Functions Are Carried out by Two of the Five Isoforms in Arabidopsis thaliana

The CDC20 and Cdh1/CCS52 proteins are substrate determinants and activators of the Anaphase Promoting Complex/Cyclosome (APC/C) E3 ubiquitin ligase and as such they control the mitotic cell cycle by targeting the degradation of various cell cycle regulators. In yeasts and animals the main CDC20 function is the destruction of securin and mitotic cyclins. Plants have multiple CDC20 gene copies whose functions have not been explored yet. In Arabidopsis thaliana there are five CDC20 isoforms and here we aimed at defining their contribution to cell cycle regulation, substrate selectivity and plant development.Studying the gene structure and phylogeny of plant CDC20s, the expression of the five AtCDC20 gene copies and their interactions with the APC/C subunit APC10, the CCS52 proteins, components of the mitotic checkpoint complex (MCC) and mitotic cyclin substrates, conserved CDC20 functions could be assigned for AtCDC20.1 and AtCDC20.2. The other three intron-less genes were silent and specific for Arabidopsis. We show that AtCDC20.1 and AtCDC20.2 are components of the MCC and interact with mitotic cyclins with unexpected specificity. AtCDC20.1 and AtCDC20.2 are expressed in meristems, organ primordia and AtCDC20.1 also in pollen grains and developing seeds. Knocking down both genes simultaneously by RNAi resulted in severe delay in plant development and male sterility. In these lines, the meristem size was reduced while the cell size and ploidy levels were unaffected indicating that the lower cell number and likely slowdown of the cell cycle are the cause of reduced plant growth.The intron-containing CDC20 gene copies provide conserved and redundant functions for cell cycle progression in plants and are required for meristem maintenance, plant growth and male gametophyte formation. The Arabidopsis-specific intron-less genes are possibly "retrogenes" and have hitherto undefined functions or are pseudogenes

REVEILLE8 and PSEUDO-REPONSE REGULATOR5 Form a Negative Feedback Loop within the Arabidopsis Circadian Clock

Circadian rhythms provide organisms with an adaptive advantage, allowing them to regulate physiological and developmental events so that they occur at the most appropriate time of day. In plants, as in other eukaryotes, multiple transcriptional feedback loops are central to clock function. In one such feedback loop, the Myb-like transcription factors CCA1 and LHY directly repress expression of the pseudoresponse regulator TOC1 by binding to an evening element (EE) in the TOC1 promoter. Another key regulatory circuit involves CCA1 and LHY and the TOC1 homologs PRR5, PRR7, and PRR9. Purification of EE–binding proteins from plant extracts followed by mass spectrometry led to the identification of RVE8, a homolog of CCA1 and LHY. Similar to these well-known clock genes, expression of RVE8 is circadian-regulated with a dawn phase of expression, and RVE8 binds specifically to the EE. However, whereas cca1 and lhy mutants have short period phenotypes and overexpression of either gene causes arrhythmia, rve8 mutants have long-period and RVE8-OX plants have short-period phenotypes. Light input to the clock is normal in rve8, but temperature compensation (a hallmark of circadian rhythms) is perturbed. RVE8 binds to the promoters of both TOC1 and PRR5 in the subjective afternoon, but surprisingly only PRR5 expression is perturbed by overexpression of RVE8. Together, our data indicate that RVE8 promotes expression of a subset of EE–containing clock genes towards the end of the subjective day and forms a negative feedback loop with PRR5. Thus RVE8 and its homologs CCA1 and LHY function close to the circadian oscillator but act via distinct molecular mechanisms

FHY1 Mediates Nuclear Import of the Light-Activated Phytochrome A Photoreceptor

The phytochrome (phy) family of photoreceptors is of crucial importance throughout the life cycle of higher plants. Light-induced nuclear import is required for most phytochrome responses. Nuclear accumulation of phyA is dependent on two related proteins called FHY1 (Far-red elongated HYpocotyl 1) and FHL (FHY1 Like), with FHY1 playing the predominant function. The transcription of FHY1 and FHL are controlled by FHY3 (Far-red elongated HYpocotyl 3) and FAR1 (FAr-red impaired Response 1), a related pair of transcription factors, which thus indirectly control phyA nuclear accumulation. FHY1 and FHL preferentially interact with the light-activated form of phyA, but the mechanism by which they enable photoreceptor accumulation in the nucleus remains unsolved. Sequence comparison of numerous FHY1-related proteins indicates that only the NLS located at the N-terminus and the phyA-interaction domain located at the C-terminus are conserved. We demonstrate that these two parts of FHY1 are sufficient for FHY1 function. phyA nuclear accumulation is inhibited in the presence of high levels of FHY1 variants unable to enter the nucleus. Furthermore, nuclear accumulation of phyA becomes light- and FHY1-independent when an NLS sequence is fused to phyA, strongly suggesting that FHY1 mediates nuclear import of light-activated phyA. In accordance with this idea, FHY1 and FHY3 become functionally dispensable in seedlings expressing a constitutively nuclear version of phyA. Our data suggest that the mechanism uncovered in Arabidopsis is conserved in higher plants. Moreover, this mechanism allows us to propose a model explaining why phyA needs a specific nuclear import pathway