How to make a centriole or basal body (Iris Diaphragm Model).

[See ref 12, ref 14, ]

The microtubular skeleton of centrioles and basal bodies is characterized by the following features: Their formation has frequently been associated with the following observations The main feature of the model is its reduction of the universal and quite complex geometry of centrioles and basal bodies to only four basic numbers. It is described in much greater detail and with the pertinant references in ref 12: For example, the bud structure results from the microtubular radius and the ninefold symmetry. The blade curvature is a consequence of the radius and the 13-fold symmetry of the microtubules. The arm structure and location of the hinges follows from the microtubular radius, the ninefold symmetry, and the number 4 of the segments covered by the arm, and so forth.

Bud formation.

We assume that the formation of a centriole (basal body) begins with a ring of nine short microtubules or precursors to microtubules spaced in a wall-to-wall configuration in the densest possible packing. The second and third row conists of incomplete microtubules as in actual centrioles. This structure will be called the bud.

Based on a microtubular radius of = 12 nm, the bud diameter D = 94nm. The bud is likely to resemble a coil of fibers that hold the structure together.

Fig.1. Bud formation by adding in the form of densest packing 2 rows of Incomplete microtubules (precursors)to an initial ring of 9 microtubules (precursor)

Blade curvature.

Assuming that centriolar microtubules and basal body microtubules are composed of 13 protofilaments, like ordinary microtubules, important constraints on the shape of the future blades result. For example, the B tubule must share two of the protofilaments with the A tubule. Since the number 13 of protofilaments is odd, the C tubules cannot be attached along the straight line that connects the centers of A and B. It must turn aside in order to share the protofilaments. The resulting triplet is curved similar to the shape of blades of actual centrioles and basal bodies. The blade curvature can be described by the angle τ, which measures how much the center C of the C tubules is shifted away from the midline connecting the A and B tubules.

There is a second possibility to attach the C tubule.In this case, the angle of the blade curvature is 3τ.

In addition to these two possibilities, the blade curvatures could assume values of -τ and -3τ, which correspond to the mirror images of the blade structures described above. Ultimately, these blade curvatures would require to mirror image every other structure of the bud, hence the entire centriole structure. However, mirror image centrioles have never been observed.

Fig.2. Two possible ways of connecting 3 microtubules with shared protofilaments (black dots. )

Formation of the swivel arms.

A major postulate of the model is the formation of fibrous arms that extend around the perimeter of the bud along 4 microtubular diameters. One of the nine arms is drawn in red as a polygon of 4 segments that stretch from center to center of five consecutive microtubular precursors. The number of segments covered by each arm is essential for the model. If one changes it to three or five, the resulting structures are markedly different from actual centrioles and basal bodies.

The model assumes that each of the nine arms is rigidly connected to the three specific microtubular precursors drawn in red ('blade') Thus, it divides the bud into nine identical structures, called swivel arms, one of which is drawn in red. The free end of each arm is assumed to be able to swivel around a hinge. It should be noted that each hinge coincides with the center of one of the microtubular precursors of the bud.

The main idea of the iris diaphragm model of centriole (and basal body) formation is expressed in the following two postulates: