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I'm sure by the nature of this question you will come to know my amateurish knowledge in biology. During mitosis, they simply state that the organelles just replicate… while we are provided somewhat detailed information regarding the division of the cell. How do the nucleus and the other organelles divide? Mitochondria used to be prokaryotes apparently so do they divide by binary fission? while we're on that what exactly are the organelles composed of? There is a spike in protein production during interphase… so how do the organelles even go about dividing?
Well, the nucleus does not divide per se. Remember, the nuclear membrane dissolves during mitosis. It starts reforming after metaphase. Here is a review detailing the process and the mechanisms which are known. By extension, the Endoplasmic reticulum gets portioned as it is derived from the nuclear membrane.
Organelles also rely on the cytoskeleton and associated motor proteins for distribution between the daughters. A debated aspect in this regard is whether the organelles are distributed at random or is there an active process that ensures similar distribution between the daughters.
Finally, on to mitochondria. Till this point we have assumed symmetric cell division i.e. both daughters get almost equal amounts of maternal material. But in stem cell divisions, the non-stem daughter is smaller in size. Interestingly, this paper shows that the stem like daughter gets younger mitochondria (less damaged mitochondrial DNA).
As you can see, it is impossible to cover all the organelles in a single answer. And we are not even considering physiological differences between different cell types. Cheers!
How do organelles divide? - Biology
An excellent question. Mitochondria divide by simple fission, splitting in two just as bacterial cells do, and although the DNA replication strategies are a little different, forming displacement or D-loop structures, they partition their circular DNA in much the same way as do bacteria. Mitochondrial reproduction is not autonomous (self-governed), however, as is bacterial reproduction. Most of the components required for mitochondrial division are encoded as genes within the eukaryotic (host) nucleus and translated into proteins by the cytoplasmic ribosomes of the host cell. Mitochondrial replication is thus impossible without nuclear participation, and mitochondria cannot be grown in a cell-free culture. A tight control over mitochondrial division is essential to prevent uncontrolled mitochondrial replication, which could easily lead to destruction of the host cell. This provides an elegant illustration of the co-evolution between the mitochondria and their hosts in the evolution of the eukaryota.
Mitochondria and chloroplasts divide by fission, much like bacteria. When the cell divides, the mito and chloro are distributed to the daughter cells.
Most of the proteins in the mito and chloro are encoded by the nuclear genome and they are imported. They are translated on ribosomes in the cytoplasm. The newly formed protein has a sequence of amino acids at the N-terminus that acts as an import signal - it is recognized and bound by the import machinery on the membrane of the mito or chloro and the protein is pulled inside.
Wow, what a good question! I never thought to ask about that when I took my biology classes in college. Doing some research, I found that this is an area scientists don't know much about. I'm not at all knowledgeable on the subject, so I got a friend of mine to help me out (Ed Lowry, a graduate student in the Department of Ecology, Evolution and Marine Biology at UC Santa Barbara). Remember that chloroplasts and mitochondria are known as organelles (another word for membrane-bound bodies within a cell), and the cytosol is the liquid within the cytoplasm, or the interior of the cell. Here's what Ed had to say:
Some old texts of mine bring a few interesting bits to light. 3&4 are the most pertinent ones. All quotes are from Ch. 7 of Molecular Biology of the Cell, by Alberts and his buddies:
1) Mitochondria in the cell are not strictly individuals. They are "remarkably plastic organelles, constantly changing their shape, even fusing with one another and then separating again."
2) Mitochondria and chloroplasts are dependent for the most part on proteins synthesized from nuclear DNA and imported into the organelle. Some proteins are encoded by organelle DNA and synthesized in the organelle. Interestingly, "no protein is known to be exported from mitochondria or chloroplasts to the cytosol."
3) A class of yeast mutants called "cytoplasmic petite mutants" entirely lack DNA in their mitochondria. "Although petite mutants cannot synthesize proteins in their mitochondria, and therefore cannot make mitochondria that produce ATP, they nevertheless contain mitochondria that have a normal outer and an inner membrane with poorly developed cristae [the folds in the membrane]. Such mutants dramatically demonstrate the overwhelming importance of the nucleus in biogenesis. They also show that an organelle that [here's the important part!] divides by fission can replicate indefinitely in the cytoplasm of proliferating eukaryotic cells even in the complete absence of its own genome."
4) "Overall control [of organelle replication] clearly resides in the nucleus. the nucleus must regulate the number of mitochondria and chloroplasts in the cell according to need. Although these regulatory aspects are crucial to our understanding of eukaryotic cells, we know relatively little about them." Well, shoot.
For most cell types there is what is called a "restriction point" in the cell cycle. Prior to this point the cells might maintain a sort of status quo if, for example, the environment is unfavorable for growth. Past this point, an internal change takes place which commits the cell to replicate its DNA and divide.
A signaler called "S-phase activator" (I guess people with lots of imagination become screenwriters or clothing designers) appears in the cytoplasm prior to DNA replication. (the book says it may be a group of molecules and not a single one, but it doesn't specify their identities). The major control molecules have been related to a class of genes termed "cdc" genes, for "cell-division cycle", of which there are more than twenty.
How do organelles divide? - Biology
The processes in and around mitotic division in eukaryotes are very interesting. The short answer is their organelles do not replicate when the cell does. Some of these organelles have lost their own distinctive cycles however mitochondria (and chloroplasts in plants) have retained some independence. They still have their own DNA.This DNA is one long circular strand much like you would see in a prokaryotic cell. The mitochondrion has its own replication cycle, completely separate from the cell in which it resides. The mitochondria are dispersed throughout the cell so that when the cell divides some mitochondria wind up in one daughter cell and some in the other. This process to the best of our knowledge is not regulated so that a very unlucky cell could actually wind up with no mitochondria at all. (As an aside: This is one of the reasons scientists think that eukaryotic cells evolved from prokaryotic cells.)
Many of the other organelles do divide at the same time as the cell divides (especially organelles that do not have their own DNA). One example is illustrated in the endoplasmic reticulum. This structure divides into many pieces contained in vesicles which are then separated into the two daughter cells. This is a common way for organelles which only have one copy in the cell to segregate into the two daughter cells. These organelles do not appear to replicate before cell division the way DNA does.
During the gap phases (G1 and G2) the cell increases the amount of protein and organelles it contains in preparation for cytokinesis. How exactly the cell partitions its organelles during division is not well understood. It might be a stochastic process or perhaps there is some direction to it (via microtubules. ) It is important to note that some organelles (i.e. mitochondria and chloroplast) have their own DNA and replicate themselves under the control of the cell cycle. Mitochondria divide by binary fission like bacteria.
It seems that detailed information about organelle divisions during mitosis is elusive. I was able to find the following cellbiology
"During the cell division process there is a reorganization of nearly all cell organelles and the cell cytoskeleton.
Interestingly, of the cell organelles, mitochondria appear to undergo there own cycles of division (similar to bacterial division) independent of the cell."
Mitochondrial division is in fact closely associated with cell division and is regulated at "distinct checkpoints" during mitosis, while mitochondrial morphology and segregation is controlled by microtubules in the cell.
A basic college biology textbook, "Life -- The Science of Biology" (Purves, Sadava, Orians, and Heller, 6th edition) states on page 164 "Followingcytokineses, both daughter cells contain all the components of a complete cell. Organelles such as ribosome, mitochondria, and chloroplasts need not be distributed equally between daughter cells as long as some of each are present in both cells accordingly, there is no mechanism with a precision comparable to that of mitosis to provide for their equal allocation to daughter cells."
Another website suggested that organelle division and synthesis occurred primarily during cytokineses cohmetrix
This is not an "edu" website so I can't vouch for its accuracy:
"Cytokineses, the second stage of cell division, begins to occur before mitosisis complete (usually during telophase) and continues after the nuclei of the daughter cells are completely formed. The preliminary steps of cytokineses occur during the growth interphases (called the G phases) of the cell cycle.In the G phases, various membrane structures and organelles, such as the endoplasmic reticulum and Golgi bodies, are produced out of components in the cytoplasm. Therefore, before cytokineses begins, there is growth in the size of the cytoplasm and in the number of its organelles. During the G phases there is also reproduction of the mitochondria and chloroplasts. These organelles contain their own DNA, called organelle DNA, and the organelles' reproduction includes the replication of the organelle DNA.
During cytokineses, the cytoplasm and its contents divide. In animal cells, the cytoplasm divides by pinching inward, whereas in plant cells, a partition, called the cell plate, begins to grow and divide the cytoplasm.Cytokineses is not as precise a process as mitosis because the amount of cytoplasm in a daughter cell will be about half, but not exactly half, the amount of cytoplasm in the parent cell. In addition, each daughter cell will have about half of the organelles from the cytoplasm of the parent cell. In contrast to mitosis, there is no precise mechanism working during cytokinesesto guarantee that each daughter cell receives exactly half of the parent cell's cytoplasm and its organelles.
Cytokineses does not always occur when mitosis occurs because in some cells (such as those found in certain molds) mitosis occurs repeatedly without cytokineses taking place. In this case, each repeated replication of genetic material with no division of cytoplasm (or final separation into new daughter cells) results in cells with two nuclei."
(technically not part of mitosis, but it is included in the cell cycle)
Cell is in a resting phase, performing cell functions
Organelles double in number, to prepare for division
1. chromosomes visible (chromatids)
2. centrioles migrate to the poles
3. nuclear membrane disappears
4. nucleolus disappears
5. spindle form
Chromosomes line up along the equator
Chromatids separate and move to opposite poles
1. chromosomes disappear (becoming chromatin)
2. nuclear membrane reforms
- division of the cytoplasm to form 2 new daughter cells
- daughter cells are genetically identical
- cells return to interphase
. cytokinesis takes two forms, depending on the cell.
Animal Cells - cell pinches inward and then splits into two
Plants - a new cell wall (called the cell plate) forms between the two new cells
Figure 4. Ribosomes are made up of a large subunit (top) and a small subunit (bottom). During protein synthesis, ribosomes assemble amino acids into proteins.
Ribosomes are the cellular structures responsible for protein synthesis. When viewed through an electron microscope, free ribosomes appear as either clusters or single tiny dots floating freely in the cytoplasm. Ribosomes may be attached to either the cytoplasmic side of the plasma membrane or the cytoplasmic side of the endoplasmic reticulum (Figure 4).
Electron microscopy has shown that ribosomes consist of large and small subunits. Ribosomes are enzyme complexes that are responsible for protein synthesis and are composed of both proteins and RNA.
Because protein synthesis is essential for all cells, ribosomes are found in practically every cell, although they are smaller in prokaryotic cells. They are particularly abundant in immature red blood cells for the synthesis of hemoglobin, which functions in the transport of oxygen throughout the body.
Organelles are specialized structures that perform various tasks inside cells.
Just as organs are separate body parts that perform certain functions in the human body, organelles are microscopic sub-units that perform specific functions within individual cells.
Photograph by Science Source
Organelles are specialized structures that perform various jobs inside cells. The term literally means &ldquolittle organs.&rdquo In the same way organs, such as the heart, liver, stomach, and kidneys, serve specific functions to keep an organism alive, organelles serve specific functions to keep a cell alive.
Cells are grouped into two different categories, prokaryotic cells and eukaryotic cells, which are primarily differentiated by the presence of one organelle, the nucleus. Prokaryotic cells do not have a nucleus, whereas eukaryotic cells do. A nucleus is a large organelle that stores DNA and serves as the cell&rsquos command center. Single-cell organisms are usually prokaryotic, while multi-cell organisms are usually made of eukaryotic cells.
Another large organelle found in eukaryotic cells is the mitochondrion, an organelle responsible for making ATP, a chemical that organisms use for energy. Cells often contain hundreds of mitochondria. These mitochondria have an outer membrane, which encases the organelle, and an inner membrane, which folds over several times to create a multi-layered structure known as cristae. The fluid inside the mitochondria is called the matrix, which is filled with proteins and mitochondrial DNA.
Chloroplasts are another organelle that contain a double membrane and retain their own DNA. Unlike mitochondria, however, the inner membrane of chloroplasts is not folded. They do, however have a third, internal membrane called the thylakoid membrane, which is folded. In addition, unlike mitochondria, chloroplasts are only present in plant cells. They are responsible for converting sunlight into energy through a process called photosynthesis.
Other organelles like lysosomes are responsible for digesting and recycling toxic substances and waste. They are embedded with proteins called enzymes, which break down macromolecules, including amino acids, carbohydrates, and phospholipids. Lysosomes are produced by a larger organelle called the Golgi complex, which manufactures other cellular machinery as well. Whenever a cell dies, it self-destructs using its own lysosomes.
Just as organs are separate body parts that perform certain functions in the human body, organelles are microscopic sub-units that perform specific functions within individual cells.
The endomembrane system
Camillo Golgi, an Italian physician working in the late 1800s, is said to have discovered the Golgi apparatus when he was looking at cells from the body's central nervous system. The internal reticular apparatus, as he called it, appeared to be an individual structure when viewed through his microscope, which was the cutting edge technology of the day (Figure 8). Today, we know that the Golgi apparatus is connected to a larger endomembrane system.
Figure 8: The Golgi apparatus is part of a larger system of organelles called the endomembrane system. image © Julian Thorpe
The endomembrane system divides the cell's cytoplasm into separate compartments, or organelles, that each performs specialized tasks within the cell. The separate compartments, however, aren't entirely separate. Some are actually connected by shared membranes, as is the case with the rough endoplasmic reticulum and the nuclear membrane. This particular network forms a pathway for large molecules and signals to pass between the nucleus and the environment outside the cell.
Compartments that don't share a direct physical connection pass signals, proteins, and waste via tiny membrane-bound sacs called vesicles. Vesicles form when part of an organelle's membrane pinches off, forms a lipid-bound sac, and floats through the cytoplasm to deliver its cargo between organelles. The vesicles, being formed of the same plasma membrane that surrounds the cell and all the organelles, easily merges with the membranes surrounding each compartment. Vesicles containing basic proteins synthesized in the rough endoplasmic reticulum travel to the Golgi apparatus for final processing via vesicles. Vesicles containing the finished protein leave the Golgi apparatus and deliver the final product out to another organelle (Figure 9).
Figure 9: Depiction of vesicles containing newly synthesized protein leaving the Golgi apparatus. image © University of Dundee/Wellcome Images
Our current understanding of the membranes surrounding organelles has come from new techniques in biochemistry that give researchers greater access to the inner workings of cells than the scientists of Margulis's day had. Researchers today can sift through cell samples using centrifuges and isolate individual organelles for closer scrutiny. They can also track the movement of specific chemicals and proteins through a cell's system and witness first-hand the flow of chemicals and signals from one organelle to another. The result has been a greater understanding of the true spirit of cooperation that was the basis of the evolution of the eukaryotic cell in the first place. As Lynn Margulis and her son wrote in one of their many books, “Life did not take over the globe by combat, but by networking."
Evolution isn't always about competition. It can also be about cooperation, as is the case with the development of chloroplasts and mitochondria from free-living bacteria. This module explains the theory of endosymbiosis along with its origins. Convincing evidence in support of the theory is presented. The evolution of the nucleus and other organelles through invagination of the cell membrane is also discussed.
One of the main differences between eukaryotic cells and prokaryotic cells is the presence of a nucleus and other membrane-bound organelles.
Chloroplasts and mitochondria have specialized roles in producing energy for the cell and have several unique features including some of their own DNA. Because of this, scientists believe that both of these organelles originated through endosymbiosis when one small cell began to live inside a larger one.
Membrane-bound organelles evolved as folds of the plasma membrane this allowed these cells to establish compartments with different environments appropriate for the specific function that the organelle performs.
2. Temporary organelles for specific tasks
- is a temporary organelle for autophagy.
- Autophagy (aka “self-eating”) is a process that cells recycle some of their existed proteins and organelles due to the shortage of nutrient supply.
- Damaged proteins or organelles will be put on a “garbage tags”. The cell recognizes the tags and packs these recycle materials into autophagosomes.
- Autophagosomes carry the cellular garbage to lysosomes for degradation.
- Special autophagy to degrade bad mitochondria is named “mitophagy.”
[In this figure] The process of autophagy.
- is a membrane-bound temporary organelle for engulfing the stuff outside of the cell.
- Endosomes are formed by the invagination of the cell membrane, a process called “endocytosis.”
- After endocytosis, the endosome can carry its cargo to different places in the cell.
[In this figure] Phagocytosis vs. Endocytosis.
- When the cells prepare for the cell division, each DNA thread is organized into a much compact structure, called “chromosome”.
- Every human cell has 23 pairs of chromosomes (1-22, and X or Y).
- A chromosome is formed by wrapping DNA around histone proteins into a core complex, called a nucleosome.
[In this figure] In order to handle the long DNA molecules, our cells pack DNA threads into many compact structures, called “chromosome”.
- are X-shaped chromosomes that remain attached at a centromeric region (centromere) after DNA duplication.
- Sister chromatids will be split into two identical chromosomes during mitosis.
[In this figure] Chromosome replication forms sister chromatids.
- are organelles that only appear during mitosis and serve as the main microtubule organizing center (MTOC).
- Each cell has two centrosomes. They move toward the opposite positions of the cells when the mitosis starts.
- The microtubules extend from the centrosome and attach to the centromeres of sister chromatids. Both centromeres retrieve their microtubule at the same time to split the sister chromatids apart and move into new cells.
[In this figure] Illustration and electron micrography of the centrosome.
Bacterial cell division happens through binary fission or budding. The divisome is a protein complex in bacteria that is responsible for cell division, constriction of inner and outer membranes during division, and peptidoglycan (PG) synthesis at the division site. A tubulin-like protein, FtsZ plays a critical role in formation of a contractile ring for the cell division. 
Cell division in eukaryote is much more complicated than prokaryote. Depending upon chromosomal number reduced or not Eukaryotic cell divisions can be classified as Mitosis (equational division) and Meiosis (reductional division). A primitive form of cell division is also found which is called amitosis. The amitotic or mitotic cell division is more atypical and diverse in the various groups of organisms such as protists (namely diatoms, dinoflagellates etc) and fungi.
In mitotic metaphase (see below), typically the chromosomes (each with 2 sister chromatid that they developed due to replication in the S phase of interphase) arranged and sister chromatids split and distributed towards daughter cells.
In meiosis, typically in Meiosis-I the homologous chromosomes are paired and then separated and distributed into daughter cells. Meiosis-II is like mitosis where the chromatids are separated. In human and other higher animals and many other organisms, the meiosis is called gametic meiosis, that is the meiosis gives rise to gametes. Whereas in many groups of organisms, especially in plants (observable in lower plants but vestigial stage in higher plants), the meiosis gives rise to the kind of spores that germinate into haploid vegetative phase (gametophyte). This kind of meiosis is called sporic meiosis.
Interphase is the process through which a cell must go before mitosis, meiosis, and cytokinesis.  Interphase consists of three main phases: G1, S, and G2. G1 is a time of growth for the cell where specialized cellular functions occur in order to prepare the cell for DNA Replication.  There are checkpoints during interphase that allow the cell to either advance or halt further development. One of the checkpoint is between G1 and S, the purpose for this checkpoint is to check for appropriate cell size and any DNA damage. The second check point is in the G2 phase, this checkpoint also checks for cell size but also the DNA replication. The last check point is located at the site of metaphase, where it checks that the chromosomes are correctly connected to the mitotic spindles.  In S phase, the chromosomes are replicated in order for the genetic content to be maintained.  During G2, the cell undergoes the final stages of growth before it enters the M phase, where spindles are synthesized. The M phase can be either mitosis or meiosis depending on the type of cell. Germ cells, or gametes, undergo meiosis, while somatic cells will undergo mitosis. After the cell proceeds successfully through the M phase, it may then undergo cell division through cytokinesis. The control of each checkpoint is controlled by cyclin and cyclin-dependent kinases. The progression of interphase is the result of the increased amount of cyclin. As the amount of cyclin increases, more and more cyclin dependent kinases attach to cyclin signaling the cell further into interphase. At the peak of the cyclin, attached to the cyclin dependent kinases this system pushes the cell out of interphase and into the M phase, where mitosis, meiosis, and cytokinesis occur.  There are three transition checkpoints the cell has to go through before entering the M phase. The most important being the G1-S transition checkpoint. If the cell does not pass this checkpoint, it results in the cell exiting the cell cycle. 
Prophase is the first stage of division. The nuclear envelope is broken down in this stage, long strands of chromatin condense to form shorter more visible strands called chromosomes, the nucleolus disappears, and microtubules attach to the chromosomes at the disc-shaped kinetochores present in the centromere.  Microtubules associated with the alignment and separation of chromosomes are referred to as the spindle and spindle fibers. Chromosomes will also be visible under a microscope and will be connected at the centromere. During this condensation and alignment period in meiosis, the homologous chromosomes undergo a break in their double-stranded DNA at the same locations, followed by a recombination of the now fragmented parental DNA strands into non-parental combinations, known as crossing over.  This process is evidenced to be caused in a large part by the highly conserved Spo11 protein through a mechanism similar to that seen with toposomerase in DNA replication and transcription. 
In metaphase, the centromeres of the chromosomes convene themselves on the metaphase plate (or equatorial plate), an imaginary line that is at equal distances from the two centrosome poles and held together by complex complexes known as cohesins. Chromosomes line up in the middle of the cell by microtubule organizing centers (MTOCs) pushing and pulling on centromeres of both chromatids thereby causing the chromosome to move to the center. At this point the chromosomes are still condensing and are currently one step away from being the most coiled and condensed they will be, and the spindle fibers have already connected to the kinetochores.  During this phase all the microtubules, with the exception of the kinetochores, are in a state of instability promoting their progression towards anaphase.  At this point, the chromosomes are ready to split into opposite poles of the cell towards the spindle to which they are connected. 
Anaphase is a very short stage of the cell cycle and it occurs after the chromosomes align at the mitotic plate. Kinetochores emit anaphase-inhibition signals until their attachment to the mitotic spindle. Once the final chromosome is properly aligned and attached the final signal dissipates and triggers the abrupt shift to anaphase.  This abrupt shift is caused by the activation of the anaphase-promoting complex and its function of tagging degradation of proteins important towards the metaphase-anaphase transition. One of these proteins that is broken down is securin which through its breakdown releases the enzyme separase that cleaves the cohesin rings holding together the sister chromatids thereby leading to the chromosomes separating.  After the chromosomes line up in the middle of the cell, the spindle fibers will pull them apart. The chromosomes are split apart while the sister chromatids move to opposite sides of the cell.  As the sister chromatids are being pulled apart, the cell and plasma are elongated by non-kinetochore microtubules. 
Telophase is the last stage of the cell cycle in which a cleavage furrow splits the cells cytoplasm (cytokinesis) and chromatin. This occurs through the synthesis of a new nuclear envelopes that forms around the chromatin which is gathered at each pole and the reformation of the nucleolus as the chromosomes decidedness their chromatin back to the loose state it possessed during interphase.   The division of the cellular contents is not always equal and can vary by cell type as seen with oocyte formation where one of the four daughter cells possess the majority of the cytoplasm. 
The last stage of the cell division process is cytokinesis. In this stage there is a cytoplasmic division that occurs at the end of either mitosis or meiosis. At this stage there is a resulting irreversible separation leading to two daughter cells. Cell division plays an important role in determining the fate of the cell. This is due to there being the possibility of an asymmetric division. This as a result leads to cytokinesis producing unequal daughter cells containing completely different amounts or concentrations of fate-determining molecules. 
In animals the cytokinesis ends with formation of a contractile ring and thereafter a cleavage. But in plants it happen differently. At first a cell plate is formed and then a cell wall develops between the 2 daughter cells.
In Fission yeast (S. pombe) the cytokinesis happens in G1 phase 
Cells are broadly classified into two main categories: simple non-nucleated prokaryotic cells and complex nucleated eukaryotic cells. Due to their structural differences, eukaryotic and prokaryotic cells do not divide in the same way. Also, the pattern of cell division that transforms eukaryotic stem cells into gametes (sperm cells in males or egg cells in females), termed meiosis, is different from that of the division of somatic cells in the body. Image of the mitotic spindle in a human cell showing microtubules in green, chromosomes (DNA) in blue, and kinetochores in red.
Multicellular organisms replace worn-out cells through cell division. In some animals, however, cell division eventually halts. In humans this occurs, on average, after 52 divisions, known as the Hayflick limit. The cell is then referred to as senescent. With each division the cells telomeres, protective sequences of DNA on the end of a chromosome that prevent degradation of the chromosomal DNA, shorten. This shortening has been correlated to negative effects such as age related diseases and shortened lifespans in humans.   Cancer cells, on the other hand, are not thought to degrade in this way, if at all. An enzyme complex called telomerase, present in large quantities in cancerous cells, rebuilds the telomeres through synthesis of telomeric DNA repeats, allowing division to continue indefinitely. 
A cell division under microscope was first discovered by German botanist Hugo von Mohl in 1835 as he worked over the green alga Cladophora glomerata. 
In 1943, cell division was filmed for the first time  by Kurt Michel using a phase-contrast microscope. 
- 1. Is it green or does it have green parts?
- Yes - go to 2
- No - go to 3
- Single-celled? go to 6
- Multicellular? Plantae. Look for cell walls, internal structure. In the compound microscope you might be able to see chloroplasts.
- Single-celled - go to 4
- Multicellular (Look for complex or branching structure, appendages) - go to 5
- Yes - Protista. You should be able to see at least a nucleus and/or contractile vacuole, and a definite shape. Movement should be present, using cilia, flagella, or amoeboid motion. Cilia or flagella may be difficult to see.
- No - Monera. Should be quite small. May be shaped like short dashes (rods), small dots (cocci), or curved or spiral shaped. The largest them that is commonly found in freshwater is called Spirillum volutans. It is spiral shaped, and can be nearly a millimeter long. Except for Spirillum, it is very difficult to see Monerans except in a compound microscope with special lighting.
- Yes - Animalia. Movement can be by cilia, flagella, or complex, involving parts that contract. Structure should be complex. Feeding activity may be obvious.
- No - Fungus. Should be branched, colorless filaments. May have some kind of fruiting body (mushrooms are a fungus, don't forget). Usually attached to some piece of decaying matter - may form a fuzzy coating on or around an object. In water, some bacterial infections of fish and other animals may be mistaken for a fungus.
Remember, the more you observe the organism, the more sure you can be. Many living things have stages that make them resemble members of another kingdom.
How do organelles replicate in eukaryotes?
I know how DNA replicates during mitosis and meiosis, but I'm just wondering about how things like the Golgi apparatus reproduce.
I know that mitochondria have their own DNA and reproduce by themselves, but an explanation for this would also be highly appreciated.
I keep thinking that maybe proteins synthesize them somehow, but I'm not sure.
Man, this is a complicated topic! The most direct answer is "we aren't done figuring that out, and it depends on the organelle".
For starters, I found two reviews: 1 and 2. These guys may be paywalled. I have the pdfs.
Anyway, I guess we can try to go through some of the organelles:
Golgi: The Golgi apparatus changes shape really drastically at the onset of mitosis, and basically seems to fracture into a much of much smaller vesicles, which either get distributed between the daughter cells passively (since there are a bunch of these little vesicles, they can diffuse and roughly get split evenly) or maybe actively (travel along the mitotic spindle, or with other organelle fragments). As I'm sure you'll notice, this passive/active question sort of sticks around for all of these.
ER: The endoplasmic reticulum ends up absorbing the fragments of the nuclear envelope (and maybe these golgi fragments too, wow that's complicated). The ER may then be actively pulled to the different poles of the dividing cell.
Endosomes: Leave it to endosomes to make it complicated. Early endosomes don't appear to be actively segregated, but lysosomes and late endosomes appear to maybe interact with the mitotic spindle, and move along that way.
Keep in mind that these organelles that we are talking about are lipid-bound, and thus eventually require lipid synthesis to grow back to size.