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

Age-dependent loss of cohesion protection in human oocytes

Aneuploid human eggs (oocytes) are a major cause of infertility, miscarriage, and chromosomal disorders. Such aneuploidies increase greatly as women age, with defective linkages between sister chromatids (cohesion) in meiosis as a common cause. We found that loss of a specific pool of the cohesin protector protein, shugoshin 2 (SGO2), may contribute to this phenomenon. Our data indicate that SGO2 preserves sister chromatid cohesion in meiosis by protecting a ‘‘cohesin bridge’’ between sister chromatids. In human oocytes, SGO2 localizes to both sub-centromere cups and the pericentromeric bridge, which spans the sister chromatid junction. SGO2 normally colocalizes with cohesin; however, in meiosis II oocytes from older women, SGO2 is frequently lost from the pericentromeric bridge and sister chromatid cohesion is weakened. MPS1 and BUB1 kinase activities maintain SGO2 at sub-centromeres and the pericentromeric bridge. Removal of SGO2 throughout meiosis I by MPS1 inhibition reduces cohesion protection, increasing the incidence of single chromatids at meiosis II. Therefore, SGO2 deficiency in human oocytes can exacerbate the effects of maternal age by rendering residual cohesin at pericentromeres vulnerable to loss in anaphase I. Our data show that impaired SGO2 localization weakens cohesion integrity and may contribute to the increased incidence of aneuploidy observed in human oocytes with advanced maternal age

The first mitotic division of human embryos is highly error prone

Human beings are made of ~50 trillion cells which arise from serial mitotic divisions of a single cell - the fertilised egg. Remarkably, the early human embryo is often chromosomally abnormal, and many are mosaic, with the karyotype differing from one cell to another. Mosaicism presumably arises from chromosome segregation errors during the early mitotic divisions, although these events have never been visualised in living human embryos. Here, we establish live cell imaging of chromosome segregation using normally fertilised embryos from an egg-share-to-research programme, as well as embryos deselected during fertility treatment. We reveal that the first mitotic division has an extended prometaphase/metaphase and exhibits phenotypes that can cause nondisjunction. These included multipolar chromosome segregations and lagging chromosomes that lead to formation of micronuclei. Analysis of nuclear number and size provides evidence of equivalent phenotypes in 2-cell human embryos that gave rise to live births. Together this shows that errors in the first mitotic division can be tolerated in human embryos and uncovers cell biological events that contribute to preimplantation mosaicism

Chronic testicular Chlamydia muridarum infection impairs mouse fertility and offspring development

With approximately 131 million new genital tract infections occurring each year, Chlamydia is the most common sexually transmitted bacterial pathogen worldwide. Male and female infections occur at similar rates and both cause serious pathological sequelae. Despite this, the impact of chlamydial infection on male fertility has long been debated, and the effects of paternal chlamydial infection on offspring development are unknown. Using a male mouse chronic infection model, we show that chlamydial infection persists in the testes, adversely affecting the testicular environment. Infection increased leukocyte infiltration, disrupted the blood:testis barrier and reduced spermiogenic cell numbers and seminiferous tubule volume. Sperm from infected mice had decreased motility, increased abnormal morphology, decreased zona-binding capacity, and increased DNA damage. Serum anti-sperm antibodies were also increased. When both acutely and chronically infected male mice were bred with healthy female mice, 16.7% of pups displayed developmental abnormalities. Female offspring of chronically infected sires had smaller reproductive tracts than offspring of noninfected sires. The male pups of infected sires displayed delayed testicular development, with abnormalities in sperm vitality, motility, and sperm-oocyte binding evident at sexual maturity. These data suggest that chronic testicular Chlamydia infection can contribute to male infertility, which may have an intergenerational impact on sperm quality

The lipid peroxidation product 4-hydroxynonenal contributes to oxidative stress-mediated deterioration of the ageing oocyte

An increase in intraovarian reactive oxygen species (ROS) has long been implicated in the decline in oocyte quality associated with maternal ageing. Oxidative stress (OS)-induced lipid peroxidation and the consequent generation of highly electrophilic aldehydes, such as 4-hydroxynonenal (4-HNE), represents a potential mechanism by which ROS can inflict damage in the ageing oocyte. In this study, we have established that aged oocytes are vulnerable to damage by 4-HNE resulting from increased cytosolic ROS production within the oocyte itself. Further, we demonstrated that the age-related induction of OS can be recapitulated by exposure of germinal vesicle (GV) oocytes to exogenous H2 O2 . Such treatments stimulated an increase in 4-HNE generation, which remained elevated during in vitro oocyte maturation to metaphase II. Additionally, exposure of GV oocytes to either H2 O2 or 4-HNE resulted in decreased meiotic completion, increased spindle abnormalities, chromosome misalignments and aneuploidy. In seeking to account for these data, we revealed that proteins essential for oocyte health and meiotic development, namely α-, β-, and γ-tubulin are vulnerable to adduction via 4-HNE. Importantly, 4-HNE-tubulin adduction, as well as increased aneuploidy rates, were resolved by co-treatment with the antioxidant penicillamine, demonstrating a possible therapeutic mechanism to improve oocyte quality in older females

Molecular Mechanisms Responsible for Increased Vulnerability of the Ageing Oocyte to Oxidative Damage

In their midthirties, women experience a decline in fertility, coupled to a pronounced increase in the risk of aneuploidy, miscarriage, and birth defects. Although the aetiology of such pathologies are complex, a causative relationship between the age-related decline in oocyte quality and oxidative stress (OS) is now well established. What remains less certain are the molecular mechanisms governing the increased vulnerability of the aged oocyte to oxidative damage. In this review, we explore the reduced capacity of the ageing oocyte to mitigate macromolecular damage arising from oxidative insults and highlight the dramatic consequences for oocyte quality and female fertility. Indeed, while oocytes are typically endowed with a comprehensive suite of molecular mechanisms to moderate oxidative damage and thus ensure the fidelity of the germline, there is increasing recognition that the efficacy of such protective mechanisms undergoes an age-related decline. For instance, impaired reactive oxygen species metabolism, decreased DNA repair, reduced sensitivity of the spindle assembly checkpoint, and decreased capacity for protein repair and degradation collectively render the aged oocyte acutely vulnerable to OS and limits their capacity to recover from exposure to such insults. We also highlight the inadequacies of our current armoury of assisted reproductive technologies to combat age-related female infertility, emphasising the need for further research into mechanisms underpinning the functional deterioration of the ageing oocyte

Assessment of microRNA expression in mouse epididymal epithelial cells and spermatozoa by next generation sequencing

The mammalian epididymis is a highly specialized region of the male reproductive tract that is lined with a continuous layer of epithelial cells that display a remarkable level of regionalized secretory and absorptive activity. The luminal environment created by this combined secretory and absorptive activity is directly responsible for promoting the functional maturation of spermatozoa and their maintenance in a quiescent and viable state prior to ejaculation. This study was designed to identify the complement of microRNAs (miRNAs) that are expressed within the mouse epididymal epithelial cells and the maturing populations of spermatozoa. Through the use of Next Generation Sequencing technology we have demonstrated that both epididymal epithelial cells and spermatozoa harbour a complex repertoire of miRNAs that have substantially different expression profiles along the length of the tract. These data, deposited in the Gene Expression Omnibus (GEO) with the accession numbers GSE70197 and GSE70198, afford valuable insight into the post-transcriptional control of gene expression within the epididymis and provide the first evidence for the dynamic transformation of the miRNA content of maturing sperm cells. Ultimately such information promises to inform our understanding of the aetiology of male infertility. Herein we provide a detailed description of the methodology used to generate these important data

Next generation sequencing analysis reveals segmental patterns of microRNA expression in mouse epididymal epithelial cells

The functional maturation of mammalian spermatozoa is accomplished as the cells descend through the highly specialized microenvironment of the epididymis. This dynamic environment is, in turn, created by the combined secretory and absorptive activity of the surrounding epithelium and displays an extraordinary level of regionalization. Although the regulatory network responsible for spatial coordination of epididymal function remains unclear, recent evidence has highlighted a novel role for the RNA interference pathway. Indeed, as noncanonical regulators of gene expression, small noncoding RNAs have emerged as key elements of the circuitry involved in regulating epididymal function and hence sperm maturation. Herein we have employed next generation sequencing technology to profile the genome-wide miRNA signatures of mouse epididymal cells and characterize segmental patterns of expression. An impressive profile of some 370 miRNAs were detected in the mouse epididymis, with a subset of these specifically identified within the epithelial cells that line the tubule (218). A majority of the latter miRNAs (75%) were detected at equivalent levels along the entire length of the mouse epididymis. We did however identify a small cohort of miRNAs that displayed highly regionalized patterns of expression, including miR-204-5p and miR-196b-5p, which were down- and up-regulated by approximately 39- and 45-fold between the caput/caudal regions, respectively. In addition we identified 79 miRNAs (representing ∼ 21% of all miRNAs) as displaying conserved expression within all regions of the mouse, rat and human epididymal tissue. These included 8/14 members of let-7 family of miRNAs that have been widely implicated in the control of androgen signaling and the repression of cell proliferation and oncogenic pathways. Overall these data provide novel insights into the sophistication of the miRNA network that regulates the function of the male reproductive tract

Dynamin 2 is essential for mammalian spermatogenesis

The dynamin family of proteins play important regulatory roles in membrane remodelling and endocytosis, especially within brain and neuronal tissues. In the context of reproduction, dynamin 1 (DNM1) and dynamin 2 (DNM2) have recently been shown to act as key mediators of sperm acrosome formation and function. However, little is known about the roles that these proteins play in the developing testicular germ cells. In this study, we employed a DNM2 germ cell-specific knockout model to investigate the role of DNM2 in spermatogenesis. We demonstrate that ablation of DNM2 in early spermatogenesis results in germ cell arrest during prophase I of meiosis, subsequent loss of all post-meiotic germ cells and concomitant sterility. These effects become exacerbated with age, and ultimately result in the demise of the spermatogonial stem cells and a Sertoli cell only phenotype. We also demonstrate that DNM2 activity may be temporally regulated by phosphorylation of DNM2 via the kinase CDK1 in spermatogonia, and dephosphorylation by phosphatase PPP3CA during meiotic and post-meiotic spermatogenesis