You wonder how many forms of shells exist in nature? How many options for coloring? Surprisingly, it turned out that all this diversity is described by a single equation with nine variables. Elegant discovery has made at the junction of mathematics, biology, and (surprise) neurophysiology, will help scientists better understand how the brain works … and even — as it stores memories.
An unusual approach to the disclosure of the puzzle picture on shellfish used Bittayger graduate student Alistair (Alistair Boettiger) from the University of California at Berkeley (UC Berkeley), his colleague at the university biophysicist George Oster (George Oster), and neuroscientist Baird Irmentraut (Bard Ermentrout) from Pittsburgh ( University of Pittsburgh).
They argue that the creation of specific color patterns of shells, as well as for the choice of forms, including small details like hills and furrows, meet the neural network embedded in the mantle of a mollusk.
Mantle remembers growing and distribution of substances (such as calcium carbonate) in the layer, laid before, and builds a new layer according to a common plan. "Drawing on the sink — a memory clam" — says Oster. Well, not quite real memory, as, for example, in humans. Still, the similarity here is deeper than it seems at first glance.
The researchers tested their theory on a computer model. Here, only one virtual clam (right) of many series "grown" in the car according to the regularities found. It is exactly coincided with the pattern and the shape of the actually existing shellfish Conus vicweei (Left). More details about the model we describe below (photo Alistair Boettiger / UC Berkeley).
"The shell is composed of layers. The mantle is probing the history of 'thoughts' clam and extrapolates them to the next level, just like our brain thinks about the future, "- adds the researcher.
Here it is necessary to clarify that marine molluscs record in early philosophers. We are talking about close analogies. For what is thought of in terms of physiology? Simply put, it's the wave of excitation and inhibition in neural circuits.
But it is precisely such waves and direct the growth of shells, "according to plan", explains our heroes. And what determines the plan itself? It helps to understand step aside … visual illusions.
Back in 1865 the Austrian physicist Ernst Mach (Ernst Mach) has suggested that for some of the illusions of vision corresponds to the so-called lateral inhibition (lateral inhibition). In fact, it has been discovered and proved much later — in the XX century.
The effect is as follows: receptor (stick) that is experiencing the strongest stimulus (light), not only sends a corresponding signal to the brain, but also suppresses the response to light in several neighboring cells (ie, surrounding himself with a zone inhibition).
This will automatically increase the contrast of the observed image and improves the perception of faces and boundaries of objects, especially in low light conditions. The same effect, note also work in case of the tactile sensor and the skin.
An example of Mach bands. This pattern consists of three sections: a uniform light field and dark field light strip therebetween, where there is a smooth gradient from a luminance to the other. But the more you look into the image, the more clearly see another two thin stripes — very light, on the border between the region and the gradient of light and very dark, on the border between the gradient and a "just" a dark area. These two thin strips do not really have — we are tricks of the retina (illustration from the site wikipedia.org).
In particular, the visual illusion of "Mach Bands» (Mach bands) is explained by the lateral inhibition of rows of photoreceptors, which are then certain vertical lines in the image.
As the network of cells evaluates not just the brightness of each point "in the absolute," and compares the brightness of adjacent pixels, boosted lateral contrast effect leads to a curious error in perception (see picture left). This is our (and wider — mammals) fees for decent clarity of vision in twilight.
What's the connection with the shells of mollusks? The most direct — that lateral inhibition controls the patterning of a growing shell of sea creatures. Back in the 1970s and Oster Irmentraut published their model of early neural mechanism for managing the growth of the shell. But they did not have the opportunity to check it. But now they (along with Bittaygerom) performed a masterful job.
Olivia porphyria. Left — the real clam, right — the virtual model, who grew up just like a real (photo Alistair Boettiger / UC Berkeley).
First, with the electron microscope, scientists have studied the example of several shellfish as a network of receptors in the mantle is associated with secretory cells that produce calcium carbonate and proteins (some of them — are pigments). During the building of a new layer level synthesis of certain substances and determines the shape and color (pattern) of the shell.
Then, the idea of simulated size of the areas around the inhibition of excited neurons growing in the sink — or rather, around the secretory cells controlled by neurons and assessed the likely effect of the lateral thresholds.
It was found that all the nine combinations are physiological parameters. This is the coefficients of the variables in a single equation (compiled by the authors of the work), the solution of which determines — how many connections which will be "posted on the wall" at each point as the construction of shells.
Check numerical model failed as follows: varying the original 9 parameters, the authors were able to get the program in the computer almost all major types of shellfish! And how open rules worked in certain cases — we now explain.
Bittayger and his colleagues found that all the pictures on the shells can be divided into three classes: stripes running parallel to the growing edge, stripes running perpendicular to the growing edge, and complex patterns that form recurring spots, shevronchiki and so on, as the authors explain — by traveling waves pigment and calcium.
The manifestation of a pattern type depends on the nature of the lateral inhibition of neurons in the mantle of the mollusk.
In each pair of clam on the left — the present, to the right — the computer. The resemblance is striking. So, scientists have been able to catch the tail of mathematical harmony shells (photo Alistair Boettiger / UC Berkeley).
If the cells outstanding pigment, inhibit the secretion of pigment in the neighboring cells, but not at one and the same scheme of distribution of "mortar" is repeated day after day, generating a strip perpendicular to the growing edge of the sink. If the same effect secretory cells which produce calcium carbonate — appear combs.
Scientists point out that as the size of the band shell combs and divide (branching), remaining one (th) of the same width as before. This is a purely mathematical — physical size of inhibiting neuronal regions anywhere identical.
Strip parallel to the edge of the sink, the authors of the model explained by inhibition of cell secretory activity in the future (deferred). The pigment obtained in one day can inhibit operation of the secretory cells in the next few days, resulting in creating an on / off paint, leading to a series of bands.
However, the most interesting, according to a press release from the university, the models that generate zigzags, diamonds, chevrons, arrowheads, and so on. This occurs when the present pigment inhibits secretion at the same location, but in the future, but turned secretion in surrounding cells. Pigment spots, thus "moving" sideways day-to-day with the growth of shellfish, producing a sort of traveling wave. But the interference of the waves and gives rise to complex patterns.
Two more computer shells grown algorithm Bittaygera, Oster and Irmentrauta, were identical to the real toxic shellfish: the marble cone (Conus marmoreus, top) and Conus gloriamaris (Bottom). These shells are shown in the insets (illustrations Alistair Boettiger, George Oster / UC Berkeley; Bard Emmentrout / Pittsburgh).
The work of American scientists should prove useful for several areas of biological research. After all, the same lateral inhibition is an important principle of the neural networks in general, and not just a system of visual perception. In particular, it is involved in regulation of higher nervous activity, the mechanism of the memory, and even development of the embryo and growing organism cell specialization.
So it turns out that the simple principles, open Mach almost half a century ago, were used to describe the complex mechanisms such, it seems different from each other, from visual illusions to the brain and "drawing" all the same "art" on the sides of shellfish .
The researchers themselves intend to apply their laws to open a further task of marine animals. Processes similar to the display of the picture on the sink, only reaching far faster, are responsible for the color changes of cuttlefish, sometimes playing colors, like a stroboscope — says Oster.
Such is the breadth of applications of the algorithm. But is it any wonder? In all the beautiful things there is a certain harmony, which may be described by the general formulas. The beauty of nature comes through the device in a variety of images. Shellfish — just an example. No wonder one of the authors of this work — Bittayger — said that the only reward it had an aesthetic sense, the sense of beauty of the whole project.
Thank you very much Yuri for a link to an interesting article