Take a number, multiply it by itself and add the original number. The magic is on the Complex Plain. With these words, the French mathematician Benoit Mandelbrot described his findings about fractal structures design. A simple second- grade function, whose domain relies in the set of the complex numbers, could generate a self- similar and scale- dependent repetitive structure if plotted on the complex plane, a cartesian plain that confronts the real and imaginary part of a complex number. The geometry of disorder, the mathematics of Caos. For modelling complex systems such as biological systems, fractal geometry have always been an amazing tool, and it’s been applied several times.
In this application, an Indian team led by Serif Hassan, takes advantage from the fractal mathematics to describe the evolution of Olfactory Receptors between humans, mice and chimps. The subtle differences of genome organization found in these animals can be explained by fractals. The key- concept in this are two coefficients widely used in fractal mathematics: the fractal dimension D and the Hauss Exponent H. I won’t linger on the mathematical meaning of these two indicators, and I will limit to say that are numbers able to describe the topology of a fractal. The comparison of these two numbers is able to describe how genome organization of olfactive genes changes between mice, humans and greater apes.
For a more detailed dissertation, check this link on the Nature Precedings website.
Intriguingly, the same principles and laws of mathematics and topology are applied to genome organization. I always wonder if we will achieve a real set of mathematical laws to describe generic genome organization and forecast genome structures in unknown organisms. I started this blog mentioning the need of biology for the rise of a proper theoretical approach. This work really looks to go in this sense.