Functional genomic analysis of heat stress in Vitis vinifera

Grapevine (Vitis vinifera) is one of most agro-economically important fruit crops worldwide, with a special relevance in Portugal where over 300 varieties are used for wine production. Due to global warming, temperature stress is currently a serious issue affecting crop production especially in temperate climates. Mobile genetic elements such as retrotransposons have been shown to be involved in environmental stress induced genetic and epigenetic modifications. In this study, sequences related to Grapevine Retrotransposon 1 (Gret1) were utilized to determine heat induced genomic and transcriptomic modifications in Touriga Nacional, a traditional Portuguese grapevine variety. For this purpose, growing canes were treated to 42 oC for four hours and leaf genomic DNA and RNA was utilized for various techniques to observe possible genomic alterations and variation in transcription levels of coding and non-coding sequences between non-treated plants and treated plants immediately after heat stress (HS-0 h) or after a 24 hour recovery period (HS-24 h). Heat stress was found to induce a significant decrease in Gret1 related sequences in HS-24 h leaves, indicating an effect of heat stress on genomic structure. In order to identify putative heat induced DNA modifications, genome wide approaches such as Amplified Fragment Length Polymorphism were utilized. This resulted in the identification of a polymorphic DNA fragment in HS-0 h and HS-24 h leaves whose sequence mapped to a genomic region flanking a house keeping gene (NADH) that is represented in multiple copies in the Vitis vinifera genome. Heat stress was also found to affect the transcript levels of various non-coding and gene coding sequences. Accordingly, quantitative real time PCR results established that Gret1 related sequences are up regulated immediately after heat stress whereas the level of transcript of genes involved in identification and repair of double strand breaks are significantly down regulated in HS-0 h plants. Taken together, the results of this work demonstrated heat stress affects both genomic integrity and transcription levels.

Orthogonal models, structure crossing, nesting and inference

We intend to study the algebraic structure of the simple orthogonal models to use them, through binary operations as building blocks in the construction of more complex orthogonal models. We start by presenting some matrix results considering Commutative Jordan Algebras of symmetric matrices, CJAs. Next, we use these results to study the algebraic structure of orthogonal models, obtained by crossing and nesting simpler ones. Then, we study the normal models with OBS, which can also be orthogonal models. We intend to study normal models with OBS (Orthogonal Block Structure), NOBS (Normal Orthogonal Block Structure), obtaining condition for having complete and suffcient statistics, having UMVUE, is unbiased estimators with minimal covariance matrices whatever the variance components. Lastly, see ([Pereira et al. (2014)]), we study the algebraic structure of orthogonal models, mixed models whose variance covariance matrices are all positive semi definite, linear combinations of known orthogonal pairwise orthogonal projection matrices, OPOPM, and whose least square estimators, LSE, of estimable vectors are best linear unbiased estimator, BLUE, whatever the variance components, so they are uniformly BLUE, UBLUE. From the results of the algebraic structure we will get explicit expressions for the LSE of these models.