A nullstellensatz for sequences over F_p

Let p be a prime and let A=(a_1,...,a_l) be a sequence of nonzero elements in F_p. In this paper, we study the set of all 0-1 solutions to the equation a_1 x_1 + ... + a_l x_l = 0. We prove that whenever l >= p, this set actually characterizes A up to a nonzero multiplicative constant, which is no longer true for l < p. The critical case l=p is of particular interest. In this context, we prove that whenever l=p and A is nonconstant, the above equation has at least p-1 minimal 0-1 solutions, thus refining a theorem of Olson. The subcritical case l=p-1 is studied in detail also. Our approach is algebraic in nature and relies on the Combinatorial Nullstellensatz as well as on a Vosper type theorem.Comment: 23 page

A rigorous method for multigenic families' functional annotation: the peptidyl arginine deiminase (PADs) proteins family example

BACKGROUND: large scale and reliable proteins' functional annotation is a major challenge in modern biology. Phylogenetic analyses have been shown to be important for such tasks. However, up to now, phylogenetic annotation did not take into account expression data (i.e. ESTs, Microarrays, SAGE, ...). Therefore, integrating such data, like ESTs in phylogenetic annotation could be a major advance in post genomic analyses. We developed an approach enabling the combination of expression data and phylogenetic analysis. To illustrate our method, we used an example protein family, the peptidyl arginine deiminases (PADs), probably implied in Rheumatoid Arthritis. RESULTS: the analysis was performed as follows: we built a phylogeny of PAD proteins from the NCBI's NR protein database. We completed the phylogenetic reconstruction of PADs using an enlarged sequence database containing translations of ESTs contigs. We then extracted all corresponding expression data contained in EST database This analysis allowed us 1/To extend the spectrum of homologs-containing species and to improve the reconstruction of genes' evolutionary history. 2/To deduce an accurate gene expression pattern for each member of this protein family. 3/To show a correlation between paralogous sequences' evolution rate and pattern of tissular expression. CONCLUSION: coupling phylogenetic reconstruction and expression data is a promising way of analysis that could be applied to all multigenic families to investigate the relationship between molecular and transcriptional evolution and to improve functional annotation

Co-existence of acute myeloid leukemia with multilineage dysplasia and Epstein-Barr virus-associated T-cell lymphoproliferative disorder in a patient with rheumatoid arthritis: a case report

Rheumatoid arthritis (RA) is an autoimmune disease mediated by inflammatory processes mainly at the joints. Recently, awareness of Epstein-Barr virus (EBV)-associated T-cell lymphoproliferative disorder (T-LPD) has been heightened for its association with methotraxate usage in RA patients. In the contrary, acute myeloid leukemia with multilineage dysplasia (AML-MLD) has never been documented to be present concomitantly with the above two conditions. In this report we present a case of an autopsy-proven co-existence of AML-MLD and EBV-associated T-LPD in a patient with RA

Evaluation of X chromosome inactivation with respect to HLA genetic susceptibility in rheumatoid arthritis and systemic sclerosis

Background: Autoimmune diseases, including rheumatoid arthritis (RA) and systemic sclerosis (SSc) are characterized by a strong genetic susceptibility from the Human Leucocyte Antigen (HLA) locus. Additionally, disorders of epigenetic processes, in particular non-random X chromosome inactivation (XCI), have been reported in many female-predominant autoimmune diseases. Here we test the hypothesis that women with RA or SSc who are strongly genetically predisposed are less susceptible to XCI bias. Methods: Using methylation sensitive genotyping of the androgen receptor (AR) gene, XCI profiles were performed in peripheral blood mononuclear cells from 161 women with RA, 96 women with SSc and 100 healthy women. HLA-DRB1 and DQB1 were genotyped. Presence of specific autoantibodies was documented for patients. XCI skewing was defined as having a ratio ≥ 80:20 of cells inactivating the same X chromosome. Results: 110 women with RA, 68 women with SSc, and 69 controls were informative for the AR polymorphism. Among them 40.9% of RA patients and 36.8% of SSc patients had skewed XCI compared to 17.4% of healthy women (P = 0.002 and 0.018, respectively). Presence of RA-susceptibility alleles coding for the "shared epitope" correlated with higher skewing among RA patients (P = 0.002) and such correlation was not observed in other women, healthy or with SSc. Presence of SSc-susceptibility alleles did not correlate with XCI patterns among SSc patients. Conclusion: Data demonstrate XCI skewing in both RA and SSc compared to healthy women. Unexpectedly, skewed XCI occurs more often in women with RA carrying the shared epitope, which usually reflects severe disease. This reinforces the view that loss of mosaicism in peripheral blood may be a consequence of chronic autoimmunity. © 2016 Kanaan et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited