06 May 2010

MeioSIS 1

Meiosis Tutorial

Meiosis I 

What is meiosis I?
In meiosis I, chromosomes in a diploid cell resegregate, producing four haploid daughter cells. It is this step in meiosis that generates genetic diversity.
The phases of meiosis I & II
Prophase I
Prophase I

DNA replication precedes the start of meiosis I. During prophase I, homologous chromosomes pair and form synapses, a step unique to meiosis. The paired chromosomes are called bivalents, and the formation of chiasmata caused by genetic recombination becomes apparent. Chromosomal condensation allows these to be viewed in the microscope. Note that the bivalent has two chromosomes and four chromatids, with one chromosome coming from each parent.
Prometaphase I
Prometaphase I

The nuclear membrane disappears. One kinetochore forms per chromosome rather than one per chromatid, and the chromosomes attached to spindle fibers begin to move.
Metaphase I
Metaphase I

Bivalents, each composed of two chromosomes (four chromatids) align at the metaphase plate. The orientation is random, with either parental homologue on a side. This means that there is a 50-50 chance for the daughter cells to get either the mother's or father's homologue for each chromosome.
Anaphase I
Anaphase I

Chiasmata separate. Chromosomes, each with two chromatids, move to separate poles. Each of the daughter cells is now haploid (23 chromosomes), but each chromosome has two chromatids.
Telophase I
Telophase I

Nuclear envelopes may reform, or the cell may quickly start meiosis II.

Analogous to mitosis where two complete daughter cells form.



What is (and is not) mitosis?
Mitosis is nuclear division plus cytokinesis, and produces two identical daughter cells during prophase, prometaphase, metaphase, anaphase, and telophase. Interphase is often included in discussions of mitosis, but interphase is technically not part of mitosis, but rather encompasses stages G1, S, and G2 of the cell cycle.
Interphase & mitosis

The cell is engaged in metabolic activity and performing its prepare for mitosis (the next four phases that lead up to and include nuclear division). Chromosomes are not clearly discerned in the nucleus, although a dark spot called the nucleolus may be visible. The cell may contain a pair of centrioles (or microtubule organizing centers in plants) both of which are organizational sites for microtubules.

Chromatin in the nucleus begins to condense and becomes visible in the light microscope as chromosomes. The nucleolus disappears. Centrioles begin moving to opposite ends of the cell and fibers extend from the centromeres. Some fibers cross the cell to form the mitotic spindle.

The nuclear membrane dissolves, marking the beginning of prometaphase. Proteins attach to the centromeres creating the kinetochores. Microtubules attach at the kinetochores and the chromosomes begin moving.

Spindle fibers align the chromosomes along the middle of the cell nucleus. This line is referred to as the metaphase plate. This organization helps to ensure that in the next phase, when the chromosomes are separated, each new nucleus will receive one copy of each chromosome.

The paired chromosomes separate at the kinetochores and move to opposite sides of the cell. Motion results from a combination of kinetochore movement along the spindle microtubules and through the physical interaction of polar microtubules.

Chromatids arrive at opposite poles of cell, and new membranes form around the daughter nuclei. The chromosomes disperse and are no longer visible under the light microscope. The spindle fibers disperse, and cytokinesis or the partitioning of the cell may also begin during this stage.

In animal cells, cytokinesis results when a fiber ring composed of a protein called actin around the center of the cell contracts pinching the cell into two daughter cells, each with one nucleus. In plant cells, the rigid wall requires that a cell plate be synthesized between the two daughter cells.


Covalent bonds

Covalent bonds create molecules, which can be represented by a molecular formula. For chemicals such as a basic sugar (C6H12O6), the ratios of atoms have a common multiple, and thus the empirical formula is CH2O. Note that a molecule with a certain empirical formula is not necessarily the same as one with the same molecular formula.


Formation of Covalent Bonds

Covalent bonds form between two atoms which have incomplete octets — that is, their outermost shells have fewer than eight electrons. They can share their electrons in a covalent bond. The simplest example is water (H2O). Oxygen has six valence electrons (and needs eight) and the hydrogens have one electron each (and need two). The oxygen shares two of its electrons with the hydrogens, and the hydrogens share their electrons with the oxygen. The result is a covalent bond between the oxygen and each hydrogen. The oxygen has a complete octet and the hydrogens have the two electrons they each need.
When atoms move closer, their orbitals change shape, letting off energy. However, there is a limit to how close the atoms get to each other—too close, and the nuclei repel each other.

Argon dimer potential.png

One way to think of this is a ball rolling down into a valley.It will settle at the lowest point. As a result of this potential energy "valley", there is a specific bond length for each type of bond. Also, there is a specific amount of energy, measured in kilojoules per mole (kJ/mol) that is required to break the bonds in one mole of the substance. Stronger bonds have a shorter bond length and a greater bond energy.

The Valence Bond Model

One useful model of covalent bonding is called the Valence Bond model. It states that covalent bonds form when atoms share electrons with each other in order to complete their valence (outer) electron shells. They are mainly formed between non-metals.
An example of a covalently bonded substance is hydrogen gas (H2). A hydrogen atom on its own has one electron—it needs two to complete its valence shell. When two hydrogen atoms bond, each one shares its electron with the other so that the electrons move about both atoms instead of just one. Both atoms now have access to two electrons: they become a stable H2 molecule joined by a single covalent bond.

Diagram of a covalent bond between hydrogen atoms


Double and Triple Bonds

Covalent bonds can also form between other non-metals, for example chlorine. A chlorine atom has 7 electrons in its valence shell—it needs 8 to complete it. Two chlorine atoms can share 1 electron each to form a single covalent bond. They become a Cl2 molecule.
Oxygen can also form covalent bonds, however, it needs a further 2 electrons to complete its valence shell (it has 6). Two oxygen atoms must share 2 electrons each to complete each other's shells, making a total of 4 shared electrons. Because twice as many electrons are shared, this is called a double covalent bond. Double bonds are much stronger than single bonds, so the bond length is shorter and the bond energy is higher.
Furthermore, nitrogen has 5 valence electrons (it needs a further 3). Two nitrogen atoms can share 3 electrons each to make a N2 molecule joined by a triple covalent bond. Triple bonds are stronger than double bonds. They have the shortest bond lengths and highest bond energies.


Electron Sharing and Orbitals

Carbon, contrary to the trend, does not share four electrons to make a quadruple bond. The reason for this is that the fourth pair of electrons in carbon cannot physically move close enough to be shared. The valence bond model explains this by considering the orbitals involved.
Recall that electrons orbit the nucleus within a cloud of electron density (orbitals). The valence bond model works on the principle that orbitals on different atoms must overlap to form a bond. There are several different ways that the orbitals can overlap, forming several distinct kinds of covalent bonds.


The Sigma Bond

The first and simplest kind of overlap is when two s orbitals come together. It is called a sigma bond (sigma, or σ, is the greek equivalent of 's'). Sigma bonds can also form between two p orbitals that lie pointing towards each other. Whenever you see a single covalent bond, it exists as a sigma bond. When two atoms are joined by a sigma bond, they are held close to each other, but they are free to rotate like beads on a string.

The electron density is in between the two atoms in an σ bond.


The Pi Bond

The second, and equally important kind of overlap is between two parallel p orbitals. Instead of overlapping head-to-head (as in the sigma bond), they join side-to-side, forming two areas of electron density above and below the molecule. This type of overlap is referred to as a pi (π, from the greek equivalent of p) bond. Whenever you see a double or triple covalent bond, it exists as one sigma bond and one or two pi bonds. Due to the side-by-side overlap of a pi bond, there is no way the atoms can twist around each other as in a sigma bond. Pi bonds give the molecule a rigid shape.

The electron density lies above and below the atoms in a π bond.



Consider a molecule of methane: a carbon atom attached to four
hydrogen atoms. Each atom is satisfying the octet rule, and each bond is a single covalent bond.
Now look at the electron configuration of carbon: 1s22s22p2. In its valence shell, it has two s electrons and two p electrons. It would not be possible for the four electrons to make equal bonds with the four hydrogen atoms (each of which has one s electron). We know, by measuring bond length and bond energy, that the four bonds in methane are equal, yet carbon has two different types of electrons.
To solve the problem, hybridization occurs. One of the s electrons "jumps up" to an empty p orbital. Then, the s electron and 3 p electrons hybridize into four sp3 electrons. Observe:
C\quad   \frac{\uparrow\downarrow}{1s}\;\;   \frac{\uparrow\downarrow}{2s}\;   \frac{\uparrow\,}{2p_x}\;   \frac{\uparrow\,}{2p_y}\;   \frac{\,\,}{2p_z}
C^{*}\quad \frac{\uparrow\downarrow}{1s}\;\;   \frac{\uparrow\,}{2s}\;   \frac{\uparrow\,}{2p_x}\;   \frac{\uparrow\,}{2p_y}\;   \frac{\uparrow\,}{2p_z}
C^{*}\quad \frac{\uparrow\downarrow}{1s}\;\;   \frac{\uparrow\,}{sp^3} \frac{\uparrow\,}{sp^3} \frac{\uparrow\,}{sp^3} \frac{\uparrow\,}{sp^3}
Now carbon can form four equal bonds with four hydrogen atoms. Hybridization may involve d orbitals in the atoms that have them, allowing up to a sp3d2 hybridization.

Exercise for the reader
Predict the hybridized electron configuration of carbon in ethene. How many sigma bonds are there? How many pi bonds?
Hint: Hybridized electrons form only sigma bonds. Pi bonds form only between p electrons.