Bacterial Flagella

A flagellum is a lash-like appendage that protrudes from the cell body of certain prokaryotic and eukaryotic cells. The word flagellum in Latin means whip. The primary role of the flagellum is locomotionbut it also often has function as a sensory organelle, being sensitive to chemicals and temperatures outside the cell. Flagella are organelles defined by function rather than structure. There are large differences between different types of flagella; the prokaryotic and eukaryotic flagella differ greatly in protein composition, structure, and mechanism of propulsion. However, both are used for swimming.

The Flagellum and Bacterial Motility
Bacterial flagella are helically shaped structures containing the protein flagellin. The base of the flagellum (the hook) near the cell surface is attached to the basal body enclosed in the cell envelope. The flagellum rotates in a clockwise or counterclockwise direction, in a motion similar to that of a propeller.
The most common mechanism used by bacteria to swim through liquid media is the flagellum. The bacterial flagellum consists of 3 major domains: an ion driven motor, which can provide a torque in either direction; the hook, a universal joint which transmits motor torque even if it is curved; and the filament, a very long structure which acts as a propeller, and behaves differently depending on which way the motor turns.
When the bacterial flagellum is rotated by the motor, the filament forms a supercoil, giving it an overall corkscrew-like shape. Flagellated bacteria are able to undergo directed movement through changes in the rotary behavior of the flagellum. When the flagellum rotates clockwise, the filament forms a long pitch supercoil, allowing several flagella on a single cell to form a large bundle, which propels the bacterium along a straight line in a single direction. When the filament is rotated in the opposite direction, it forms a shorter pitch supercoil; this causes the flagellar bundle to disassemble, and the independent motion of several flagella on the cell cause it to tumble randomly. Using these two modes of motion, bacteria can move up or down a stimulus gradient by decreasing their tumbling frequency (if they are moving in the preferred direction) or increasing their tumbling frequency (if they are moving against the desired direction), allowing them to undergo a biased random walk
The movement of eukaryotic flagella depends on adenosine triphosphate (ATP) for energy, while that of the prokaryotes derives its energy from the proton-motive force, or ion gradient, across the cellmembrane.

Arrangement

There are basically four different types of flagellar arrangements:
1. A single flagellum can extend from one end of the cell - if so, the bacterium is said to be monotrichous.
2. A single flagellum (or multiple flagella; see below) can extend from both ends of the cell - amphitrichous.
3. Several flagella (tuft) can extend from one end or both ends of the cell - lophotrichous; or,
4. Multiple flagella may be randomly distributed over the entire bacterial cell - peritrichous.

Which will cause faster motility? Why? 

Among all four, monotrichous & lophotrichous gives good motility because they are at one side & don't need to change their direction. While amphitrichous & peritrichous firstly arrange, all flagella with respect to their site of movement & now all works with each other in bacterial specific site movement.

Difference between gram positive and gram negative bacterial flagella
 Gram-positive organisms have two of these basal body rings, one in the peptidoglycan layer and one in the plasma membrane. Gram-negative organisms have four such rings: the L ring associates with the lipopolysaccharides, the P ring associates with peptidoglycan layer, the M ring is embedded in the plasma membrane, and the S ring is directly attached to the plasma membrane. The filament ends with a capping protein.