Calculating real roots using Chebyshev polynomials

V diplomskem delu bomo predstavili Čebiševe polinome prve in druge vrste, njihove lastnosti ter Čebiševo vrsto. Uporabili bomo Čebiševe polinome prve vrste za iskanje ničel gladke funkcije f na danem intervalu. Najprej bomo funkcijo aproksimirali z Čebiševimi polinomi in nato nad končno Čebiševo vrsto uporabili polinomske iskalnike ničel. V nadaljevanju pa bomo predstavili, kako najti ničle polinomske funkcije na nekem intervalu, ki ga bomo pri nekaterih algoritmih razdelili na podintervale z namenom natančnejšega in tudi hitrejšega iskanja ničel. Predstavljenih bo nekaj algoritmov in njihova uporaba, pa tudi njihove zahtevnosti, slabosti in omejitve. V okviru dela smo algoritme tudi sprogramirali v programu Matlab. Njihova praktična uporaba bo predstavljena na primerih.In this work, Chebyshev polynomials of the first and the second kind, their properties and the Chebyshev series will be examined. We will use Chebyshev polynomials of the first kind to find roots of the smooth function f on the given interval. At first the function will be approximated and then the polynomial root-finders on the truncated Chebyshev series will be used. In the next chapter we will study how to find roots of a polynomial function on the interval which we will, with some algorithms, divide on subintervals with the purpose of more accurate and faster finding of the roots. Different algorithms and their use, their complexity and their strengths and weaknesses will be presented. During this work we have also programmed these algorithms in Matlab. We will show their practical application on some examples

Mitotic Arrest in Teratoma Susceptible Fetal Male Germ Cells

Formation of germ cell derived teratomas occurs in mice of the 129/SvJ strain, but not in C57Bl/6 inbred or CD1 outbred mice. Despite this, there have been few comparative studies aimed at determining the similarities and differences between teratoma susceptible and non-susceptible mouse strains. This study examines the entry of fetal germ cells into the male pathway and mitotic arrest in 129T2/SvJ mice. We find that although the entry of fetal germ cells into mitotic arrest is similar between 129T2/SvJ, C57Bl/6 and CD1 mice, there were significant differences in the size and germ cell content of the testis cords in these strains. In 129T2/SvJ mice germ cell mitotic arrest involves upregulation of p27KIP1, p15INK4B, activation of RB, the expression of male germ cell differentiation markers NANOS2, DNMT3L and MILI and repression of the pluripotency network. The germ-line markers DPPA2 and DPPA4 show reciprocal repression and upregulation, respectively, while FGFR3 is substantially enriched in the nucleus of differentiating male germ cells. Further understanding of fetal male germ cell differentiation promises to provide insight into disorders of the testis and germ cell lineage, such as testis tumour formation and infertility

Copy Number Variation in Patients with Disorders of Sex Development Due to 46,XY Gonadal Dysgenesis

Disorders of sex development (DSD), ranging in severity from mild genital abnormalities to complete sex reversal, represent a major concern for patients and their families. DSD are often due to disruption of the genetic programs that regulate gonad development. Although some genes have been identified in these developmental pathways, the causative mutations have not been identified in more than 50% 46,XY DSD cases. We used the Affymetrix Genome-Wide Human SNP Array 6.0 to analyse copy number variation in 23 individuals with unexplained 46,XY DSD due to gonadal dysgenesis (GD). Here we describe three discrete changes in copy number that are the likely cause of the GD. Firstly, we identified a large duplication on the X chromosome that included DAX1 (NR0B1). Secondly, we identified a rearrangement that appears to affect a novel gonad-specific regulatory region in a known testis gene, SOX9. Surprisingly this patient lacked any signs of campomelic dysplasia, suggesting that the deletion affected expression of SOX9 only in the gonad. Functional analysis of potential SRY binding sites within this deleted region identified five putative enhancers, suggesting that sequences additional to the known SRY-binding TES enhancer influence human testis-specific SOX9 expression. Thirdly, we identified a small deletion immediately downstream of GATA4, supporting a role for GATA4 in gonad development in humans. These CNV analyses give new insights into the pathways involved in human gonad development and dysfunction, and suggest that rearrangements of non-coding sequences disturbing gene regulation may account for significant proportion of DSD cases

Germ cell sex and cell cycle

Germ cells are the only cells in the body capable of transferring an individual’s genetic and epigenetic information to the next generation. However, the developmental processes that provide the foundation for male and female germ line development and later gamete production are complex and poorly understood. In mice the primordial germ cells enter the bipotential gonad at E10.5 and, in response to the testicular or ovarian micro-environment, commit to spermatogenesis or oogenesis. This paper reviews progress in understanding the molecular processes underlying the early stages of male and female germ line development

Pharmacological inhibition of EZH2 disrupts the female germline epigenome

Abstract Background Recently discovered drugs that target epigenetic modifying complexes are providing new treatment options for a range of cancers that affect patients of reproductive age. Although these drugs provide new therapies, it is likely that they will also affect epigenetic programming in sperm and oocytes. A promising target is Enhancer of Zeste 2 (EZH2), which establishes the essential epigenetic modification, H3K27me3, during development. Results In this study, we demonstrate that inhibition of EZH1/2 with the clinically relevant drug, tazemetostat, severely depletes H3K27me3 in growing oocytes of adult female mice. Moreover, EZH2 inhibition depleted H3K27me3 in primary oocytes and in fetal oocytes undergoing epigenetic reprogramming. Surprisingly, once depleted, H3K27me3 failed to recover in growing oocytes or in fetal oocytes. Conclusion Together, these data demonstrate that drugs targeting EZH2 significantly affect the germline epigenome and, based on genetic models with oocyte-specific loss of EZH2 function, are likely to affect outcomes in offspring

FGF-independent MEK1/2 signalling in the developing foetal testis is essential for male germline differentiation in mice

Abstract Background Disrupted germline differentiation or compromised testis development can lead to subfertility or infertility and are strongly associated with testis cancer in humans. In mice, SRY and SOX9 induce expression of Fgf9, which promotes Sertoli cell differentiation and testis development. FGF9 is also thought to promote male germline differentiation but the mechanism is unknown. FGFs typically signal through mitogen-activated protein kinases (MAPKs) to phosphorylate ERK1/2 (pERK1/2). We explored whether FGF9 regulates male germline development through MAPK by inhibiting either FGF or MEK1/2 signalling in the foetal testis immediately after gonadal sex determination and testis cord formation, but prior to male germline commitment. Results pERK1/2 was detected in Sertoli cells and inhibition of MEK1/2 reduced Sertoli cell proliferation and organisation and resulted in some germ cells localised outside of the testis cords. While pERK1/2 was not detected in germ cells, inhibition of MEK1/2 after somatic sex determination profoundly disrupted germ cell mitotic arrest, dysregulated a broad range of male germline development genes and prevented the upregulation of key male germline markers, DPPA4 and DNMT3L. In contrast, while FGF inhibition reduced Sertoli cell proliferation, expression of male germline markers was unaffected and germ cells entered mitotic arrest normally. While male germline differentiation was not disrupted by FGF inhibition, a range of stem cell and cancer-associated genes were commonly altered after 24 h of FGF or MEK1/2 inhibition, including genes involved in the maintenance of germline stem cells, Nodal signalling, proliferation, and germline cancer. Conclusions Together, these data demonstrate a novel role for MEK1/2 signalling during testis development that is essential for male germline differentiation, but indicate a more limited role for FGF signalling. Our data indicate that additional ligands are likely to act through MEK1/2 to promote male germline differentiation and highlight a need for further mechanistic understanding of male germline development

Temperaturedependent sex determination in the American alligator: Expression of SF1, WT1, and DAX1 during gonadogenesis. Gene

ABSTRACT Gonadal morphogenesis is very similar among mammals, birds, and reptiles. Despite this similarity, each group utilises quite different genetic triggers for sex determination. In mammals, testis development is initiated by action of the Y-chromosome gene SRY. Current evidence suggests that SRY may act together with a related gene, SOX9, to activate another gene(s) in the pathway of testicular differentiation. A downstream candidate for regulation by SRY and SOX9 is AMH. In mouse, Sox9 is expressed in the Sertoli cells of the embryonic testis and it precedes the onset of Amh expression. During mouse gonadogenesis, Amh is confined to the embryonic testis, although it later shows postnatal expression in the ovary. Reptiles such as the American alligator, which exhibit temperature-dependent sex determination (TSD) do not have dimorphic sex chromosomes and apparently no SRY orthologue. SOX9 is expressed during testis differentiation in the alligator; however, it appears to be expressed too late to cause testis determination. Here we describe the cloning and expression of the alligator AMH gene and show that AMH expression precedes SOX9 expression during testis differentiation. This is the opposite to that observed in the mouse where SOX9 precedes AMH expression. The data presented here, as well as findings from recent expression studies in the chick, suggest that AMH expression is not regulated by SOX9 in the non-mammalian vertebrates. Dev Dyn 1999;216:411-419. 1999 Wiley-Liss, Inc

PRC2 is required for extensive reorganization of H3K27me3 during epigenetic reprogramming in mouse fetal germ cells

BACKGROUND: Defining how epigenetic information is established in the germline during fetal development is key to understanding how epigenetic information is inherited and impacts on evolution and human health and disease. RESULTS: Here, we show that Polycomb Repressive Complex 2 is transiently localized in the nucleus of mouse fetal germ cells, while DNA methylation is removed from the germline. This coincides with significant enrichment of trimethylated lysine 27 on histone 3 near the nuclear lamina that is dependent on activity of the essential PRC2 catalytic proteins, Enhancer of Zeste 1 and/or 2. CONCLUSIONS: Combined, these data reveal a role for Polycomb Repressive Complex 2 and trimethylated lysine 27 on histone 3 during germline epigenetic programming that we speculate is required to repress target sequences while DNA methylation is removed. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s13072-017-0113-9) contains supplementary material, which is available to authorized users