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 Irreducible complexity
As with many aspects of science that creationists do not understand, the evolution of the flagellum is always on their "questions science cannot answer" lists, specifically with regards to irreducible complexity as Michael Behe postulates it: How could the flagellum have appeared? There is nothing smaller than a fully functioning flagellum, they would state. "Removing any of its parts makes it non-functional."
The flagellum became so famous a "body part", that it has appeared in Court, specifically Kitzmiller v. Dover, when Behe introduced the idea that
tides go in, tides go out, you can't explain that "The flagellum is so precisely constructed, no single part can be removed without the whole thing failing. Evolution cannot explain how that happens."
In The Flagellum Unspun Ken Miller recreates the argument he used against Behe in the Dover Courthouse.
Despite the fact that biologist Ken Miller and others have specifically shown exactly how a flagellum could have evolved, as distinct, critical, functional and useful steps, creationists continue to use the flagellum as one of their oft-repeated "self-evident" arguments. A video of Miller's arguments on the flagellum can be seen here.
 Bacterial flagellum
The filament is composed of the protein flagellin and is a hollow tube 20 nanometers thick. It is helical, and has a sharp bend just outside the outer membrane called the "hook" which allows the helix to point directly away from the cell. A shaft runs between the hook and the basal structure, passing through protein rings in the cell's membranes that act as bearings. Gram-positive organisms have 2 rings, one in the cell wall and one in the cell membrane. Gram-negative organisms have 4 rings, 2 in the cell wall and 2 in the cell membrane.
The bacterial flagellum is driven by a rotary engine composed of protein, located at the flagellum's anchor point on the inner cell membrane. The engine is powered by proton motive force, i.e., by the flow of protons across the bacterial cell membrane due to a concentration gradient set up by the cell's metabolism (in Vibrio species the motor is a sodium ion pump, rather than a proton pump). The rotor transports protons across the membrane, and is turned in the process. The rotor by itself can operate at 6,000 to 17,000 revolutions per minute (rpm), but with a filament attached usually only reaches 200 to 1000 rpm.
The components of the flagellum are capable of spontaneous assembly in bacterial membranes. Both the basal structure and the filament have a hollow core, through which the component proteins of the flagellum are able to move into their respective positions. The basal structure has many traits in common with some types of secretory pore which have a hollow rod-like "plug" in their centers extending out through the cell wall, and it is thought that bacterial flagella may have evolved from such pores.
Different species of bacteria have different numbers and arrangements of flagella. Monotrichous bacteria have a single flagellum. Lophotrichous bacteria have multiple flagella located at the same spot on the bacteria's surface which act in concert to drive the bacteria in a single direction. Amphitrichous bacteria have a single flagellum each on two opposite ends (only one end's flagellum operates at a time, allowing the bacteria to reverse course rapidly by switching which flagellum is active). Peritrichous bacteria have flagella projecting in all directions.
Some species of bacteria (those of Spirochete body form) have internal flagella that lie between their inner and outer membranes, the rotation of which causes the entire bacterium to corkscrew through its medium.
Anticlockwise rotation of monotrichous polar flagella thrusts the cell forward with the flagellum trailing behind. Periodically the direction of rotation is briefly reversed, causing what is known as a "tumble", and results in reorientation of the cell.
 Archaeal flagellum
The archaeal flagellum is another prokaryote flagellum that is found exclusively in the archaea (also known as archaeabacteria, depending on whether or not one believes that these prokaryotes constitute a fundamental domain of life (e.g., Woese), or a just a highly-derived bacterium with heavy adaptation to extremophily, particularly thermophily (e.g., Cavalier-Smith)).
The archaeal flagellum is superficially similar to the bacterial (or eubacterial) flagellum; in the 1980s they were thought to be homologous on the basis of gross morphology and behavior (Cavalier-Smith, 1987). Both flagella consist of filaments extending outside of the cell, and rotate to propel the cell.
However, discoveries in the 1990s have revealed numerous detailed differences between the archaeal and bacterial flagella; these include:
- Bacterial flagella are powered by a flow of H+ ions (or occasionally Na+ ions); archaeal flagella are almost certainly powered by ATP.
- Bacterial flagella grow by the addition of flagellin subunits at the tip; archaeal flagella grow by the addition of subunits at the base.
- Bacterial flagella are thicker than archaeal flagella, and the bacterial filament has a large enough hollow "tube" inside that the flagellin subunits can flow up the inside of the filament and get added at the tip; the archaeal flagellum is too thin to allow this.
- Many components of bacterial flagella share sequence similarity to components of the Type III secretion systems (TTSS); the components of bacterial and archaeal flagella share no sequence similarity, however, some components of archaeal flagella share sequence similarity with Type IV secretion systems, also known as Type IV pili.
These differences mean that the bacterial and archaeal flagella are a classic case of biological analogy, rather than homology; however, in comparison to the decades of well-publicized study of bacterial flagella (e.g. by Berg), archaeal flagella have only recently begun to get serious scientific attention. Therefore many assume erroneously that there is only one basic kind of prokaryotic flagellum, and that archaeal flagella are homologous to it (an example is Cavalier-Smith (2002), who is aware of the differences in archaeal and bacterial flagellins, but retains the misconception that the basal bodies are homologous).
 Eukaryotic flagellum (similar to the cilium)
The eukaryotic flagellum is completely different from the prokaryote flagella in structure and in evolutionary origin. The only thing that the bacterial, archaeal, and eukaryotic flagella have in common is that they stick outside of the cell and wiggle to produce propulsion.
A eukaryotic flagellum is a bundle of nine fused pairs of microtubules called "doublets" surrounding two central single microtubules (the so-called 9+2 structure; also called the "axoneme"). At the base of a eukaryotic flagellum is a microtubule organizing center about 500 nanometers long, called the basal body or kinetosome. The flagellum is encased within the cell's plasma membrane, so that the interior of the flagellum is accessible to the cell's cytoplasm. This is necessary because the flagellum's flexing is driven by the protein dynein bridging the microtubules all along its length and forcing them to slide relative to each other, and ATP must be transported to them for them to function.