MATHEMATICAL MODELS AND POLYHEDRAL STUDIES FOR INTEGRAL SHEET METAL DESIGN

We deal with the optimization of the production of branched sheet metal products. New forming techniques for sheet metal give rise to a wide variety of possible profiles and possible ways of production. In particular, we show how the problem of producing a given profile geometry can be modeled as a discrete optimization problem. We provide a theoretical analysis of the model in order to improve its solution time. In this context we give the complete convex hull description of some substructures of the underlying polyhedron. Moreover, we introduce a new class of facet-defining inequalities that represent connectivity constraints for the profile and show how these inequalities can be separated in polynomial time. Finally, we present numerical results for various test instances, both real-world and academic examples.

Functional markers for gene mapping and genetic diversity studies in sugarcane

Abstract Background The database of sugarcane expressed sequence tags (EST) offers a great opportunity for developing molecular markers that are directly associated with important agronomic traits. The development of new EST-SSR markers represents an important tool for genetic analysis. In sugarcane breeding programs, functional markers can be used to accelerate the process and select important agronomic traits, especially in the mapping of quantitative traits loci (QTL) and plant resistant pathogens or qualitative resistance loci (QRL). The aim of this work was to develop new simple sequence repeat (SSR) markers in sugarcane using the sugarcane expressed sequence tag (SUCEST database). Findings A total of 365 EST-SSR molecular markers with trinucleotide motifs were developed and evaluated in a collection of 18 genotypes of sugarcane (15 varieties and 3 species). In total, 287 of the EST-SSRs markers amplified fragments of the expected size and were polymorphic in the analyzed sugarcane varieties. The number of alleles ranged from 2-18, with an average of 6 alleles per locus, while polymorphism information content values ranged from 0.21-0.92, with an average of 0.69. The discrimination power was high for the majority of the EST-SSRs, with an average value of 0.80. Among the markers characterized in this study some have particular interest, those that are related to bacterial defense responses, generation of precursor metabolites and energy and those involved in carbohydrate metabolic process. Conclusions These EST-SSR markers presented in this work can be efficiently used for genetic mapping studies of segregating sugarcane populations. The high Polymorphism Information Content (PIC) and Discriminant Power (DP) presented facilitate the QTL identification and marker-assisted selection due the association with functional regions of the genome became an important tool for the sugarcane breeding program.

An in-depth analysis of the HIV-1/AIDS dynamics by comprehensive mathematical modeling

This work presents major results from a novel dynamic model intended to deterministically represent the complex relation between HIV-1 and the human immune system. The novel structure of the model extends previous work by representing different host anatomic compartments under a more in-depth cellular and molecular immunological phenomenology. Recently identified mechanisms related to HIV-1 infection as well as other well known relevant mechanisms typically ignored in mathematical models of HIV-1 pathogenesis and immunology, such as cell-cell transmission, are also addressed. (C) 2011 Elsevier Ltd. All rights reserved.

Relationship between Vitamin D Receptor gene polymorphisms and the components of metabolic syndrome

Abstract Background The Vitamin D Receptor gene (VDR) is expressed in many tissues and modulates the expression of several other genes. The purpose of this study was to investigate the association between metabolic syndrome (MetSyn) with the presence of VDR 2228570 C > T and VDR 1544410 A > G polymorphisms in Brazilian adults. Methods Two hundred forty three (243) individuals were included in a cross-sectional study. MetSyn was classified using the criteria proposed by National Cholesterol Educational Program - Adult Treatment Panel III. Insulin resistance and β cell secretion were estimated by the mathematical models of HOMA IR and β, respectively. The VDR 2228570 C > T and VDR 1544410 A > G polymorphisms were detected by enzymatic digestion and confirmed by allele specific PCR or amplification of refractory mutation. Results Individuals with MetSyn and heterozygosis for VDR 2228570 C > T have higher concentrations of iPTH and HOMA β than those without this polymorphism, and subjects with recessive homozygosis for the same polymorphisms presented higher insulin resistance than those with the heterozygous genotype. There is no association among VDR 1544410 A > G and components of MetSyn, HOMA IR and β, serum vitamin D (25(OH)D3) and intact parathormone (iPTH) levels in patients with MetSyn. A significant lower concentration of 25(OH)D3 was observed only in individuals without MetSyn in the VDR 1544410 A > G genotype. Additionally, individuals without MetSyn and heterozygosis for VDR 2228570 C > T presented higher concentration of triglycerides and lower HDL than those without this polymorphism. Conclusions Using two common VDR polymorphism data suggests they may influence insulin secretion, insulin resistance an serum HDL-cholesterol in our highly heterogeneous population. Whether VDR polymorphism may influence the severity of MetSyn component disorder, warrants examination in larger cohorts used for genome-wide association studies.

Multimodality and flexibility of stochastic gene expression

We consider a general class of mathematical models for stochastic gene expression where the transcription rate is allowed to depend on a promoter state variable that can take an arbitrary (finite) number of values. We provide the solution of the master equations in the stationary limit, based on a factorization of the stochastic transition matrix that separates timescales and relative interaction strengths, and we express its entries in terms of parameters that have a natural physical and/or biological interpretation. The solution illustrates the capacity of multiple states promoters to generate multimodal distributions of gene products, without the need for feedback. Furthermore, using the example of a three states promoter operating at low, high, and intermediate expression levels, we show that using multiple states operons will typically lead to a significant reduction of noise in the system. The underlying mechanism is that a three-states promoter can change its level of expression from low to high by passing through an intermediate state with a much smaller increase of fluctuations than by means of a direct transition.

Differential Expression of Genes Involved in the Degeneration and Regeneration Pathways in Mouse Models for Muscular Dystrophies

The genetically determined muscular dystrophies are caused by mutations in genes coding for muscle proteins. Differences in the phenotypes are mainly the age of onset and velocity of progression. Muscle weakness is the consequence of myofiber degeneration due to an imbalance between successive cycles of degeneration/regeneration. While muscle fibers are lost, a replacement of the degraded muscle fibers by adipose and connective tissues occurs. Major investigation points are to elicit the involved pathophysiological mechanisms to elucidate how each mutation can lead to a specific degenerative process and how the regeneration is stimulated in each case. To answer these questions, we used four mouse models with different mutations causing muscular dystrophies, Dmd (mdx) , SJL/J, Large (myd) and Lama2 (dy2J) /J, and compared the histological changes of regeneration and fibrosis to the expression of genes involved in those processes. For regeneration, the MyoD, Myf5 and myogenin genes related to the proliferation and differentiation of satellite cells were studied, while for degeneration, the TGF-beta 1 and Pro-collagen 1 alpha 2 genes, involved in the fibrotic cascade, were analyzed. The result suggests that TGF-beta 1 gene is activated in the dystrophic process in all the stages of degeneration, while the activation of the expression of the pro-collagen gene possibly occurs in mildest stages of this process. We also observed that each pathophysiological mechanism acted differently in the activation of regeneration, with distinctions in the induction of proliferation of satellite cells, but with no alterations in stimulation to differentiation. Dysfunction of satellite cells can, therefore, be an important additional mechanism of pathogenesis in the dystrophic muscle.

Differential expression of HINT1 in schizophrenia brain tissue

Recent findings in the literature suggest a relation between histidine triad nucleotide-binding protein-1 (HINT1) and psychiatric disorders such as major depression, anxiety, and schizophrenia, although its physiological roles are not completely comprehended. Using Western blot, we compared HINT1 protein expression in the postmortem dorsolateral prefrontal cortex and thalamus of schizophrenia patients and healthy controls for contributing to elucidate the role of HINT1 in schizophrenia pathophysiology. HINT1 was found to be downregulated in the dorsolateral prefrontal cortex and upregulated in the thalamus. Our results combined to previous studies in human samples and preclinical models support the notion that HINT1 must be more explored as a potential target for psychiatric disorders.

Modeling the Emergence of Circadian Rhythms in a Clock Neuron Network

Circadian rhythms in pacemaker cells persist for weeks in constant darkness, while in other types of cells the molecular oscillations that underlie circadian rhythms damp rapidly under the same conditions. Although much progress has been made in understanding the biochemical and cellular basis of circadian rhythms, the mechanisms leading to damped or self-sustained oscillations remain largely unknown. There exist many mathematical models that reproduce the circadian rhythms in the case of a single cell of the Drosophila fly. However, not much is known about the mechanisms leading to coherent circadian oscillation in clock neuron networks. In this work we have implemented a model for a network of interacting clock neurons to describe the emergence (or damping) of circadian rhythms in Drosophila fly, in the absence of zeitgebers. Our model consists of an array of pacemakers that interact through the modulation of some parameters by a network feedback. The individual pacemakers are described by a well-known biochemical model for circadian oscillation, to which we have added degradation of PER protein by light and multiplicative noise. The network feedback is the PER protein level averaged over the whole network. In particular, we have investigated the effect of modulation of the parameters associated with (i) the control of net entrance of PER into the nucleus and (ii) the non-photic degradation of PER. Our results indicate that the modulation of PER entrance into the nucleus allows the synchronization of clock neurons, leading to coherent circadian oscillations under constant dark condition. On the other hand, the modulation of non-photic degradation cannot reset the phases of individual clocks subjected to intrinsic biochemical noise.

Molecular Characterization and Physical Mapping of Two Classes of 5S rDNA in the Genomes of Gymnotus sylvius and G. inaequilabiatus (Gymnotiformes, Gymnotidae)

The nucleotide sequences of the 5S rRNA multigene family and their distribution across the karyotypes in 2 species of Gymnotiformes, genus Gymnotus (G. sylvius and G. inaequilabiatus) were investigated by means of fluorescence in situ hybridization (FISH). The results showed the existence of 2 distinct classes of 5S rDNA sequences in both species: class I and class II. A high conservative pattern of the codifying region of the 5S rRNA gene was identified, contrasting with significant alterations detected in the nontranscribed spacer (NTS). The presence of TATA-like sequences along the NTS of both species was an expected occurrence, since such sequences have been associated with the regulation of the gene expression. FISH using 5S rDNA class I and class II probes revealed that both gene classes were collocated in the same chromosome pair in the genome of G. sylvius, while in that of G. inaequilabiatus, class II appeared more disperse than class I. Copyright (C) 2012 S. Karger AG, Basel

Modeling gene expression regulatory networks with the sparse vector autoregressive model

Abstract Background To understand the molecular mechanisms underlying important biological processes, a detailed description of the gene products networks involved is required. In order to define and understand such molecular networks, some statistical methods are proposed in the literature to estimate gene regulatory networks from time-series microarray data. However, several problems still need to be overcome. Firstly, information flow need to be inferred, in addition to the correlation between genes. Secondly, we usually try to identify large networks from a large number of genes (parameters) originating from a smaller number of microarray experiments (samples). Due to this situation, which is rather frequent in Bioinformatics, it is difficult to perform statistical tests using methods that model large gene-gene networks. In addition, most of the models are based on dimension reduction using clustering techniques, therefore, the resulting network is not a gene-gene network but a module-module network. Here, we present the Sparse Vector Autoregressive model as a solution to these problems. Results We have applied the Sparse Vector Autoregressive model to estimate gene regulatory networks based on gene expression profiles obtained from time-series microarray experiments. Through extensive simulations, by applying the SVAR method to artificial regulatory networks, we show that SVAR can infer true positive edges even under conditions in which the number of samples is smaller than the number of genes. Moreover, it is possible to control for false positives, a significant advantage when compared to other methods described in the literature, which are based on ranks or score functions. By applying SVAR to actual HeLa cell cycle gene expression data, we were able to identify well known transcription factor targets. Conclusion The proposed SVAR method is able to model gene regulatory networks in frequent situations in which the number of samples is lower than the number of genes, making it possible to naturally infer partial Granger causalities without any a priori information. In addition, we present a statistical test to control the false discovery rate, which was not previously possible using other gene regulatory network models.