## The structure of a pair of centrioles suggests their function as cellular eyes.

[See ref 9, ref 14, ref 16 ]

### Cellular eyes cannot use lenses to locate light sources.

Cellular eyes cannot resemble the eyes of familiar organisms in the macroscopic world. For example, cellular eyes cannot not use lenses, because the typical cell size of approximately 10 µm is too small. Obviously, such lenses would have to be much smaller than the cell itself. Therefore, let us assume that the lens diameter is 1 µm. Lenses can only focus light whose wavelength is smaller than about 1/1000th of their diameter. Otherwise, the light would simply diffract around the lens and ignore it. In other words, cellular lenses can only work with light whose wavelength is smaller than 1/1000 µm = 1 nm, i.e .with X-rays. This means that there are no materials from which to grind cellular lenses because no materials exist which are able to refract X-rays to any extent.

### Cellular eyes cannot compare signal intensities to locate light sources.

Many bacteria are fast swimmers. They can afford to do many trial-and-error runs in order to find the source of a chemoattractant. As long as the signal strength increases they continue their tack; whenever it decreases they tumble and change direction. Animal cells cannot use the same trick. Compared to bacteria they are extremely slow. By the time a cell has found a target in this way, the embryo would long be finished everywhere else.

There is a further problem. Due to the ubiquitous and violent thermal fluctuations the world of cells is extremely noisy in every respect. Whatever concentrations or intensities a cell on a trial-and-error run may wish to compare from place to place, they are all very unreliable. To be sure, a mathematical average over the signal strength could eliminate the fluctuations, however, in practical terms it would not work.Imagine yourself in a howling hurricane trying to average the strength of coffee aroma in the air order to find your cup!

### The ideal eye has no directional preference.

Consider a signal source (e.g.a source of light or anything else that propagates along straight lines, and let us design the ideal eye for it. (Of course, this is not how centrioles and their function evolved. In fact, we have no idea how they evolved. However, for didactic reasons I found it simpler to convince the reader that a structure may have a certain function, if the reader him-/herself, imagining to be an engineer with that particular function in mind, would have ended up constructing this very structure). Here is how we could proceed: Unlike our own eyes which can only see in the foreward direction, an ideal cellular eye would have no such directional bias. Consequently, it would be rotationally symmetrical like the circle on the figure below.

For the same reasons of symmetry the receptors for the particular kind of signal (depicted as blue spots on the figure) would have to be evenly spaced. As pointed out in the main text, the definition of an eye is a device that maps the directions of light sources in a one-to-one fashion. Therefore, the above structure would not work because it is not capable of mapping different source direction to different receptors.

### 'Blinds' can accomplish the one-to-one mapping of source directions

Considering that neither lenses nor intensity sensors can help us eliminate the ambiguity of the above source mapping device, we may try to attach blinds to each receptor that are able to block the signal. If we attach them radially as shown in the figure below we reduce much of the ambiguity, but not all.

Every source can still reach at least 2 receptors. (In anticipation of the result of all these considerations each blind is drawn similar to the blades of centrioles.) However, if we attach the blinds in a slanting fashion as shown in the figure below, each source direction can reach one and only one receptor.

In order to eliminate the ambiguity of the mapping process the blinds have to be attached at a special angle: The backward elongation of each blind intersects the foot of the previous one.

### Each 'blind' must be curved

In the previous figures the blinds were drawn slightly curved. It was necessary, because straight blinds could not prevent the ambiguity of the mapping for certain directions: Signals from a source in the very direction of the slanting blinds could still reach 2 receptors as shown on the left hand side of the figure below.

In contrast, curved blinds eliminate this last possibility of ambiguous mapping as shown on the right hand side of the figure: The blind's curvature casts a shadow on its own receptor if illuminated from this special direction.

### In order to work in 3 dimensions, the structure has to be a cylinder

The above structure can only work as long as the sources and the 'eye' are both located in the same plane. If the source rises above the plane of the 'eye' as shown below, the blinds can no longer protect the receptors, and the 'eye' fails to map the source direction.

Therefore, the structure of the 'eye' has to be extended into the third dimension while still complying with the condition of rotational symmetry. Only 2 structures can fulfill this condition: the circle with the slanting blinds has to be stretched into a cylinder or around a sphere. The extension into a cylinder poses no problem as shown in the figure below.

In contrast, stretching the blinds around the surface of a sphere is not possible: At the poles the directions of the slanting blinds would contradict each other unless we cap the sphere at its poles, as shown in the figure below.

In other words, the basic 3-dimensional structure of the 'eye' has to be either a cylinder with straight sides or with bulging sides, but a cylinder in any case.

### In order to map longitude and latitude of a source we need 2 cylinders perpendicular to each other.

Even the cylindrical structure of the 'eye' can only map the angle of the source in a plane perpendicular to its axis (e.g. the longitude). Therefore, we need a second cylinder at right angles to the first in order to determine the latitude of the source, too. The figure below illustrates how a pair of centrioles measures the longitude (yellow lines) and the latitude (green lines) of a source.

### Pitched blinds achieve continuous angular resolution.

So far the structure guarantees that each source direction can irradiate one and only one receptor. However, it does not guarantee that each receptor can detect only one source direction. In other words, the angular resolution of the structure is rather crude: If it has N blinds, then the angular resolution is 360°/N.

Unfortunately, one cannot increase the number N at will in order to achieve finer and finer resolution because each blind has to have a certain minimal thickness in order to absorb or reflect the signal. But there is a much more elegant way to refine the resolution to such a degree that it is practically continuous: One may pitch the blinds as shown in the figure below.

As the blinds run from the bottom of the cylinder to the top, they cross one sector of 360°/N. In order to assess the result, the figure below lets us take the position of the source and 'look' at the cylinder.

Whichever receptors we are able to see from our positions are the receptors that will be irradiated from our source direction. As shown by the animated figure, we can see receptors on the inside of 2 consecutive blinds.They are shown in red and yellow. And as we advance sector by sector around the cylinder, their relative lengths change in a well-defined way. In other words, the 'eye' can measure in a continuous fashion the location of a source within each sector by measuring how many receptors are irradiated on the base of consecutive blinds.

### Back to the drawing board?

Pitched blinds may offer continuous angular resolution, but can the 'eye' still map source directions in a one-to-one fashion? After all, each source can now reach the receptors of 2 consecutive blinds. Conversely, 2 sources in consecutive sectors should be able to reach receptors attached to the same pitched blind.

It is true, after adding a pitch to the blinds 2 sources can reach receptors on the same blind, but at different positions on the cylinder axis. Pitch or no pitch, any receptors at a specific position on the axis of the cylinder can still be reached by only one of the sources.

A problem arises, though, if the 2 sources are located in the same sector, and some of the receptors of the same blind are irradiated by both at the same time. Obviously, in this case the cell cannot tell the sources apart unless they differ in at least one characteristic. It would be rather simple to distinguish between different sources in the same sector if their emission would pulsate at specific frequencies. In this case the cell could compute the location of either source by (cross-)correlating only receptors that received signal pulses at the same time.

Pulsating source intensities would also offer a solution to the problem of increasing the signal-to-noise ratio that is particularly important in the thermally very noisy world of cells. Indeed, the experiments show, that cells are able to detect pulsating near-infrared light sources but not sources with constant intensity.

### Significance for cell intelligence:

All the geometric properties of the ideal cellular eye are found in actual centrioles.
The ideal cellular 'eye' looks remarkably like actual centrioles. Like the hypothetical 'eye' whose properties we described above
• Centrioles are built as a pair of cylinders perpendicular to each other.
• In cross-section they have slanting blades.
• The angle of the blades is such that the backward elongation of each blade intersects the foot of the previous one.
• Each blade is slightly curved.
• Each blade is pitched .
Furthermore, since the postulated properties of the 'eye' was based on necessary and optimized conditions of its intended function, there are not many other structures that would fulfil the same conditions. This feature seems to be matched by actual centrioles, as well. The geometric features of centrioles belong to the best conserved properties in nature. Independent of the place on the evolutionary tree, if a cell has centrioles, they have this particular structure. Their structure is, therefore, likely to point to an apparently universal function.