What Are Numerators and Denominators? In math, there are times we have to divide something whole into pieces.
Say, for instance, your family has one whole pizza to eat for dinner. If the pizza isn't cut into pieces, does that mean only one person gets to eat the whole pizza? Of course not! We would need to cut the pizza into equal pieces.
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Let's say your dad cuts the pizza into 4 equal pieces. Because we have 4 equal pieces in our whole pizza, now your pizza becomes a fraction with a denominator of 4. The denominator shows us how many equal pieces something has been divided into. It is the bottom number in a fraction.
A fraction has a top number and a bottom number. If the bottom number is the denominator, that means the top number must have a name also, right? The top number in a fraction is the numerator.
The numerator shows us how many pieces we are counting or working with. The numerator is the top number, and the denominator is the bottom number in fractions. Pizza Fractions Back to the pizza! If your family eats 3 pieces of the pizza, how many pieces are left?
There would only be 1 piece (out of 4) left. This means 1/4 of the pizza is left. If we eat 3 pieces out of 4 total, we have 1 left, or 1/4. 1 is the numerator, and 4 is the denominator. Since we are counting only the leftover piece, this is numerator, and it goes on the top of our fraction.
There were 4 equal pieces in our whole pizza, which means our denominator is 4. Remember the denominator is the number of equal pieces in our whole pizza.
Puppy Fractions But, it's not just pizza that we can turn into fractions. We can turn almost anything into parts and wholes. Here's another example: a group of 8 puppies, some are girls and some are boys. Let's make some fractions.
If there are 5 boy puppies and 3 girl puppies, how can we use fractions with numerators and denominators to represent these numbers? If there are 5 boy puppies, this means 5/8 of the puppies are boys. If there are 3 girls, this means 3/8 of the puppies are girls. Remember, the numbers on top are the numerators. These are the parts that we are counting. If there are 8 puppies total, this is your denominator for both fractions. We have a group of 8 equal pieces (or puppies) in our whole group.
In this example, 3/8 of the puppies are girls and 5/8 are boys. The numbers 3 and 5 are the numerators (parts we are counting), and 8 is the denominator (whole group). Let's Practice Can you find the numerator and denominator in the fraction 2/3? In this example, the numerator is 2 and the denominator is 3. This means we are talking about something whole that is split up into 3 equal parts.
Because of this, 3 is the denominator. The number 2 is the numerator, or the number of parts we are counting or working with out of the total equal parts. Lesson Summary A fraction has a top number and a bottom number. The top number is the numerator, which represents the parts we are counting or working with. The bottom number is the denominator, which is the total number of equal parts.
Contents • • • • • • • • • • • • • • • • • Introduction [ ] Multicellular are made of two fundamental cell types. Germ cells produce gametes and are the only cells that can undergo as well as.
These cells are sometimes said to be immortal because they are the link between generations. Are all the other cells that form the building blocks of the body and they only divide by mitosis. The lineage of germ cells is called germ line.
Germ cell specification begins during in many animals or in the during in and. After transport, involving passive movements and active migration, germ cells arrive at the developing gonads. In humans, sexual differentiation starts approximately 6 weeks after conception.
The end-products of the germ cell cycle are the egg or sperm. Under special conditions germ cells can acquire properties similar to those of embryonic (ES). The underlying mechanism of that change is still unknown. These changed cells are then called embryonic germ cells (EG). Both EG and ES are in vitro, but only ES has proven pluripotency in vivo. Recent studies have demonstrated that it is possible to give rise to primordial germ cells from ES. Specification [ ] There are two mechanisms to establish the germ cell lineage in the.
The first way is called preformistic and involves that the cells destined to become germ cells inherit the specific germ cell determinants present in the germ plasm (specific area of the cytoplasm) of the egg (ovum). The unfertilized egg of most animals is asymmetrical: different regions of the cytoplasm contain different amounts of and proteins.
The second way is found in birds and mammals, where germ cells are not specified by such determinants but by signals controlled by zygotic genes. In mammals, a few cells of the early embryo are induced by signals of neighboring cells to become. Mammalian eggs are somewhat symmetrical and after the first divisions of the fertilized egg, the produced cells are all. This means that they can differentiate in any cell type in the body and thus germ cells. Specification of primordial germ cells in the laboratory mouse is initiated by high levels of bone morphogenetic protein (BMP) signaling, which activates expression of the transcription factors Blimp-1/ and Prdm14.
Migration [ ] Primordial germ cells, germ cells that still have to reach the gonads, also known as PGCs, precursor germ cells or gonocytes, divide repeatedly on their migratory route through the gut and into the developing gonads. [ ] Invertebrates [ ] In the, pole cells passively move from the end of the embryo to the posterior midgut because of the infolding of the blastoderm. Then they actively move through the gut into the.
Cells differentiate and together with Wunen proteins they induce the migration through the gut. Wunen proteins are that lead the germ cells away from the endoderm and into the mesoderm. After splitting into two populations, the germ cells continue migrating laterally and in parallel until they reach the gonads.
Columbus proteins,, stimulate the migration in the gonadal mesoderm. [ ] Vertebrates [ ] In the egg, the germ cell determinants are found in the most. These presumptive PGCs are brought to the endoderm of the. They are determined as germ cells when gastrulation is completed. Migration from the hindgut along the gut and across the dorsal then takes place. The germ cells split into two populations and move to the paired gonadal ridges. Migration starts with 3-4 cells that undergo three rounds of cell division so that about 30 PGCs arrive at the gonads.
On the migratory path of the PGCs, the orientation of underlying cells and their secreted molecules such as play an important role. [ ] Mammals have a migratory path comparable to that in Xenopus. Migration begins with 50 gonocytes and about 5,000 PGCs arrive at the gonads. Proliferation occurs also during migration and lasts for 3–4 weeks in humans. [ ] PGCs come from the and migrate subsequently into the mesoderm, the endoderm and the posterior of the.
Migration then takes place from the along the gut and across the dorsal mesentery to reach the gonads (4.5 weeks in human beings). Maps here also a polarized network together with other molecules. The somatic cells on the path of germ cells provide them attractive, repulsive, and survival signals.
But germ cells also send signals to each other. [ ] In and, germ cells use another path. PGCs come from the epiblast and move to the to form the germinal crescent ( extraembryonic structure). The then squeeze into and use the for transport. They squeeze out of the vessels when they are at height of the. On the of the blood vessels and molecules such as are probably involved in helping PGCs migrate. [ ] The Sry gene of the Y chromosome [ ] The ( Sex-determining Region of the ) directs male development in mammals by inducing the somatic cells of the gonadal ridge to develop into a testis, rather than an ovary.
Sry is expressed in a small group of of the gonads and influences these cells to become (supporting cells in testis). Sertoli cells are responsible for sexual development along a male pathway in many ways. One of these ways involves stimulation of the arriving primordial cells to differentiate into. In the absence of the Sry gene, primordial germ cells differentiate into. Removing genital ridges before they start to develop into or results in the development of a female, independent of the carried. Gametogenesis [ ], the development of germ cells into either eggs or sperm (respectively oogenesis and spermatogenesis) is different for each but the general stages are similar. And have many features in common, they both involve: • • Extensive differentiation • Incapacity of surviving for very long if fertilization does not occur Despite their homologies they also have major differences: [ ] • Spermatogenesis has equivalent meiotic divisions resulting in four equivalent while oogenic meiosis is: only one egg is formed together with three.
• Different timing of maturation: oogenic meiosis is interrupted at one or more stages (for a long time) while spermatogenic meiosis is rapid and uninterrupted. Oogenesis [ ] After migration primordial germ cells will become oogonia in the forming gonad (ovary). The oogonia proliferate extensively by mitotic divisions, up to 5-7 million cells in humans. But then many of these oogonia die and about 50,000 remain. These cells differentiate into primary oocytes.
In week 11-12 post coitus the first meiotic division begins (before birth for most mammals) and remains arrested in prophase I from a few days to many years depending on the species. It is in this period or in some cases at the beginning of sexual maturity that the primary oocytes secrete proteins to form a coat called and they also produce containing enzymes and proteins needed for fertilization. Meiosis stands by because of the that send inhibitory signals through and the zona pellucida.
Sexual maturation is the beginning of periodic ovulation. Is the regular release of one oocyte from the ovary into the reproductive tract and is preceded by follicular growth. A few follicle cells are stimulated to grow but only one oocyte is ovulated. A primordial follicle consists of an epithelial layer of follicular granulosa cells enclosing an oocyte. The secrete (FSHs) that stimulate follicular growth and oocyte maturation. The around each follicle secrete.
This hormone stimulates the production of FSH receptors on the follicular granulosa cells and has at the same time a negative feedback on FSH secretion. This results in a competition between the follicles and only the follicle with the most FSH receptors survives and is ovulated.
Meiotic division I goes on in the ovulated oocyte stimulated by (LHs) produced by the. FSH and LH block the gap junctions between follicle cells and the oocyte therefore inhibiting communication between them. Most follicular granulosa cells stay around the oocyte and so form the cumulus layer. Large non-mammalian oocytes accumulate,,,, and the needed for protein synthesis during early embryonic growth. These intensive RNA biosynthese are mirrored in the structure of the, which decondense and form lateral loops giving them a lampbrush appearance (see ).
Oocyte maturation is the following phase of oocyte development. It occurs at sexual maturity when hormones stimulate the oocyte to complete meiotic division I.
The meiotic division I produces 2 cells differing in size: a small polar body and a large secondary oocyte. The secondary oocyte undergoes meiotic division II and that results in the formation of a second small polar body and a large mature egg, both being cells. The polar bodies degenerate.
Oocyte maturation stands by at metaphase II in most vertebrates. During ovulation, the arrested secondary oocyte leaves the ovary and matures rapidly into an egg ready for fertilization. Fertilization will cause the egg to complete meiosis II.
In human females there is proliferation of the oogonia in the fetus, meiosis starts then before birth and stands by at meiotic division I up to 50 years, ovulation begins. [ ] Egg growth [ ] A 10 - 20 μm large somatic cell generally needs 24 hours to double its for mitosis.
By this way it would take a very long time for that cell to reach the size of a mammalian egg with a diameter of 100 μm (some insects have eggs of about 1,000 μm or greater). Eggs have therefore special mechanisms to grow to their large size. One of these mechanisms is to have extra copies of: meiotic division I is paused so that the oocyte grows while it contains two diploid chromosome sets. Some species produce many extra copies of genes, such as amphibians, which may have up to 1 or 2 million copies. A complementary mechanism is partly dependent on syntheses of other cells.
In amphibians, birds, and insects, yolk is made by the liver (or its equivalent) and secreted into the. Neighboring in the ovary can also provide nutritive help of two types. In some invertebrates some oogonia become.
These cells are connected by cytoplasmic bridges with oocytes. The nurse cells of insects provide oocytes macromolecules such as proteins and mRNA. Follicular granulosa cells are the second type of accessory cells in the ovary in both invertebrates and vertebrates.
They form a layer around the oocyte and nourish them with small molecules, no macromolecules, but eventually their smaller precursor molecules,. [ ] Mutation and DNA repair [ ] The frequency of female cells is about 5-fold lower than that of. The mouse in the (prolonged diplotene) stage of actively repairs, whereas was not detected in the pre-dictyate (, and ) stages of meiosis. The long period of meiotic arrest at the four dictyate stage of meiosis may facilitate repair of DNA damages. Spermatogenesis [ ] is representative for most animals. In human males, spermatogenesis begins at puberty in in the testicles and go on continuously. Spermatogonia are immature germ cells.
They proliferate continuously by mitotic divisions around the outer edge of the, next to the. Some of these cells stop proliferation and differentiate into primary spermatocytes. After they proceed through the first meiotic division, two secondary spermatocytes are produced. The two secondary spermatocytes undergo the second meiotic division to form four haploid spermatids.
These spermatids differentiate morphologically into sperm by nuclear condensation, ejection of the cytoplasm and formation of the and. [ ] The developing male germ cells do not complete during spermatogenesis. Consequently, cytoplasmic bridges assure connection between the clones of differentiating daughter cells to form a. In this way the haploid cells are supplied with all the products of a complete diploid. Sperm that carry a, for example, is supplied with essential molecules that are encoded by genes on the.
[ ] Mutation and DNA repair [ ] The mutation frequencies for cells throughout the different stages of in mice is similar to that in female germline cells, that is 5 to 10-fold lower than the mutation frequency in somatic cells Thus low mutation frequency is a feature of germline cells in both sexes. Homologous recombinational repair of double-strand breaks occurs in mouse during sequential stages of spermatogenesis, but is most prominent in. The lower frequencies of mutation in germ cells compared to somatic cells appears to be due to more efficient removal of DNA damages by repair processes including homologous recombination repair during meiosis. Mutation frequency during spermatogenesis increases with age. The mutations in spermatogenic cells of old mice include an increased prevalence of mutations compared to young and middle-aged mice. Diseases [ ] is a rare that can affect people at all ages.
2.4 children out of 1 million are affected, and it counts for 4% of all cancers in children and adolescents younger than 20 years old. [ ] Germ cell tumors are generally located in the but can also appear in the,,,. Germ cells migrating to the gonads may not reach that intended destination and a tumor can grow wherever they end up, but the exact cause is still unknown. These tumors can be. Induced differentiation [ ] Inducing differentiation of certain cells to germ cells has many applications. One implication of induced differentiation is that it may allow for the eradication of male and female factor infertility. Furthermore, it would allow same-sex couples to have biological children if sperm could be produced from female cells or if eggs could be produced from male cells.
Efforts to create sperm and eggs from skin and embryonic stem cells were pioneered by Hayashi and Saitou's research group at Kyoto University. These researchers produced primordial germ cell-like cells (PGCs) from embryonic stem cells (ESCs) and skin cells in vitro. Hayashi and Saitou's group was able to promote the differentiation of embryonic stem cells into PGCs with the use of precise timing and bone morphogenetic protein 4 (Bmp4). Upon succeeding with embryonic stem cells, the group was able to successfully promote the differentiation of induced pluripotent stem cells (iPSCs) into PGCs.
These primordial germ cell-like cells were then used to create spermatozoa and oocytes. Efforts for human cells are less advanced due to the fact that the PGCs formed by these experiments are not always viable. In fact Hayashi and Saitou's method is only one third as effective as current in vitro fertilization methods, and the produced PGCs are not always functional. Furthermore, not only are the induced PGCs not as effective as naturally occurring PGCs, but they are also less effective at erasing their epigenetic markers when they differentiate from iPSCs or ESCs to PGCs. There are also other applications of induced differentiation of germ cells. Another study showed that culture of in mitotically inactivated (POF) causes differentiation into germ cells, as evidenced by analysis.
See also [ ] • • References [ ]. • Alberts B.; Johnson A.; Lewis J.; Raff M.; Roberts K.; Walter P.
Molecular biology of the cell. New York, Garland Science, 1463 p.
• Twyman R.M. Developmental biology.
Oxford, Bios Scientific Publishers, 451p. • Cinalli R.M.; Rangan P.; Lehmann R. 'Germ cells are forever'. Cell 132:559-562. • Kunwar P.S.; Lehmann R. 'Germ-cell attraction'. Nature 421:226-227.
• Turnpenny L.; Spalluto C.M.; Perrett R.M.; O’Shea M.; Hanley K.P.; Cameron I.T.; Wilson D.I.; Hanley N.A. 'Evaluating human embryonic germ cells: concord and conflict as pluripotent stem cells'. Stem Cells 24:212-220. 24 (2): 212–20... • Saitou M, Yamaji M (November 1, 2012). 'Primordial Germ Cells in Mice'. Cold Spring Harbor Perspectives in Biology.
4 (11): 1–19... • ^ Alberts B, Johnson A, Lewis J, et al. 'Primordial Germ Cells and Sex Determination in Mammals'.. Garland Science. • De Felici M.; Scaldaferri M.L.; Lobascio M.; Iona S.; Nazzicone V.; Klinger F.G.; Farini D. Human Reproduction Update.
Human reproduction update 10:197-206. 10 (3): 197–206... • ^ Murphey P, McLean DJ, McMahan CA, Walter CA, McCarrey JR (2013).. 88 (1): 6.... • Guli CL, Smyth DR (1988). 'UV-induced DNA repair is not detectable in pre-dictyate oocytes of the mouse'. 208 (2): 115–9..
• ^ Mira A (1998). 'Why is meiosis arrested?' 194 (2): 275–87... • ^ Walter CA, Intano GW, McCarrey JR, McMahan CA, Walter RB (1998).. 95 (17): 10015–9... • Bernstein H and Bernstein C (2013).
Evolutionary Origin and Adaptive Function of Meiosis. In Meiosis: Bernstein C and Bernstein H, editors., InTech, • Walter CA, Intano GW, McMahan CA, Kelner K, McCarrey JR, Walter RB (2004). 'Mutation spectral changes in spermatogenic cells obtained from old mice'. DNA Repair (Amst.). 3 (5): 495–504... CureSearch.org Medical Editorial Board.
• Hayashi K, Ogushi S, Kurimoto K, Shimamoto S, Ohta H, Saitou M (November 2012). 'Offspring from Oocytes Derived from in Vitro Primordial Germ Cell–like Cells in Mice'. 338 (6109): 971–975... • Cyranoski, David (August 2013). 'Egg Engineers'. 500 (7463): 392–94..
• Richards M, Fong CY, Bongso A (December 2008). 'Comparative evaluation of different in vitro systems that stimulate germ cell differentiation in human embryonic stem cells'. 93 (3): 986–94... External links [ ] • at the US National Library of Medicine (MeSH) •.
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