Imprimir Republish


The dynamic rules of evolution

A mathematical model describes how the genetic code was formed and assists the unveiling of the origin of human beings

Almost 150 years ago, Charles Darwin revolutionized biology with the book The Origin of the Species, in which he put forward the idea that living beings are subject to changes and described how they arose, evolved and disappeared throughout the course of history. For 40 years now it has been suspected that there had been, too, an evolution in genetic code, present in each cell in deoxyribonucleic acid (DNA), which transmits the genetic information from one generation to another. However, there was no way of proving the theory.

Today there is a key that helps us understand this. A group, coordinated by José Eduardo Martinho Hornos, of the Physics Institute of São Carlos of the São Paulo University (USP), has concluded a mathematical model that helps us to understand how life came about some 4 billion years ago and describes each phase in the changes of the code in the process of evolution.

The discovery of a genetic code is relatively recent. Since the beginning of the decade of the 50s, it has been known that is the molecule of DNA that transmits genetic information. Ten years later, it was discovered that a code present in DNA organized the assembling of the proteins that differentiate tissue and the different forms of organisms. It became clear that the information contained in the DNA is transmitted by 64 combinations, each one formed by three of the four nitrogenous bases, adenine (A), cytosine (C), thymine (T) e guanine (G). It is these combinations, called codons, which are the units of the genetic code.

Presented in December of 1993 in the Physical Review Letters, and commented upon in an editorial two weeks later in the magazine Nature, the work of the group of Hornos suggests that at the beginning of the evolutionary process, the 64 codons allowed the organisms to make use of less amino acids, the molecules that form the proteins, than today. The differentiation took place in four stages: first, only six amino acids were used, afterwards 14, then 16 and finally the present 21 amino acids that form any and all living organism. The results point in the direction of studies into primordialamino acids, that it is believed were six in total.

What is missing is how to explain the differentiation. “We have to cooperate. Each area has its own pieces of evidence.” says the German mathematician and physicist Frank Michael Forger, of the Mathematics and Statistics Institute (IME) of USP, who has been an full-time member of the team since 1994. The group intends to incorporate other researchers, in order to test to what extent the mathematical rules that they propose were actually carried out.

Two ballerinas
The researchers used complex mathematical theories in order to put forward their ideas in a 90-page article published in 1999 in the International Journal of Modern Physics, – but explain the formation of the genetic code based on a very simple concept, that of symmetry. Nothing goes beyond one or more transformations, of a point, of a line or of an object, about an axis.However, it is a dynamic symmetry as produced by two ballerinas on stage, exemplifies Hornos: both executing symmetrical movements, mirrored, based on an imaginary central line. “Order and symmetry don’t signify stationary situations, rather the contrary, which is movement.” he says. If one of the ballerinas moves slower than the other, or stumbles, the symmetry is broken. It was exactly this breach of harmony or breaking of symmetry that was capable of undoing only a little the initial order, that the researchers detected as the origin of the changes in the genetic code.

Moment zero
To combine the 64 codons with the 21 amino acids and to demonstrate the breaking of symmetry, they made use of Group Theory, a part of mathematics that shows how to carry out consecutive operations with a finite or infinite grouping of elements. Shortly afterwards they verified that the genetic code could not be formed in that manner, since the possibilities of the random combination of the 64 codons with the 21 amino acids are in the order of 10 raised to the power of 70, or the number 1 followed by 70 zeros. “The universe doesn’t have time to experiment all of these possibilities and it is highly unlikely that it would get things right in the first few attempts.” concluded Forger.

According to the model at which they had arrived, four billion years ago the codons were in volcanic vents or in the ocean, mixed with amino acids formed by accident. It was the zero moment of live, when the codons had not differentiated yet: they didn’t make amino acids and didn’t have biological functions. The only began to differentiate and to direct themselves towards the assembling of amino acids after the first break in symmetry. From that point onwards, they no longer functioned, or danced, in the same way and the DNA began to synthesize proteins. When the pre-biotic phase had finished, when there were only the rocks, the oceans and a primitive atmosphere – a combination of mechanisms that allowed the codons to pass forward the information about the production of proteins. As a result, the first cells appeared.

The codons, that were initially one only group, began to form into six, corresponding to the amino acids with which they could deal. The differentiation progressed. Another break in symmetry originated in 14 groupings of codons. Two more were produced in the third phase and five in the fourth and final, when the 64 codons organized themselves into 21 groupings of the current genetic code. “The differentiation of the codons occurred four billion years ago during a relatively short period of time, that mustn’t have been more than 400 million years”, says Forger.

The break of symmetry appears in theories that describe the formation of the Universe by the differentiation of forces or interactions between sub atomic particles, all of them initially unified. But why think on symmetry in the organization and in the functioning of the trios of bases of DNA? For Dr. Forger, “the principle of symmetry is one of the methodologies that can establish a little order into the process of evolution in general.” Today there are at least two distinct similarities between the models of the breaking of symmetry that explain the organization of atomic particles and the genetic code: both have a defined final point in that they cannot create other things beyond what already exists, and the difficulty of regressing to previous stages.

However, only a few years ago, what appeared obvious to the physicists disturbed the biologists, even though some of them believed that the genetic code had formed itself from simpler structures until, for some reason, the differentiation had ceased with the congealing of the code as it is now characterized. “Nobody believed that there could be symmetry in living systems.” recalls Hornos, whose initial study was successively sent back by magazines on biochemistry and evolution until it was accepted for publication in the Physical Review Letters.

A recent study, in which participated Lígia Braggion and Márcio Magini, also from USP in São Carlos, shows that the genetic code standard, of the nucleus of practically all cells, has had an exact symmetry from the moment that it was formed, close to 3.8 billion years ago. The same type of symmetry has been verified in the majority of mitochondrial codes, contained in the cellular compartments called mitochondria. The DNA mitochondrial uses less than ten amino acids. We are speaking of a group of genetic codes called deviants. There are at least a dozen of them, found in small variations in the mitochondria of bacteria, fungi, animals and plants, and the genetic code in the nucleus of the cells of each of them is generally identical.

But which came first, the standard genetic code or the mitochondrials? In search of an answer, which would be a just another small piece in putting together the jig-saw puzzle of the origin of life, the USP researchers used the mathematical arsenal available to them to see if it would be possible to generate the genetic mitochondrial codes in parallel with the standard. Naturally the attempt didn’t work out. There would have to be distinct evolutionary paths for each case. The second approach paid dividends: “We looked at the differences with more concern and perceived that it was more coherent to interpret the changes in the genetic mitochondrial codes by beginning with the genetic standard.” tells Hornos. “Sometimes, the changes even incline towards retroactivity, which looks to re-establish part of the lost symmetry.”

The mathematical conclusion that the genetic code deviants were formed from the standard code coincides with other recent biological studies. Syuozo Osawa, of the Nagoya University in Japan and author of Evolution of the Genetic Code, estimates that the oldest deviation occurred approximately 1 billion years ago, well after the formation of the standard code. At this point, the mathematical model and the biological model come together. Both represent the tendency towards change and at the same time towards conservation. “In the line that led to the vertebrates, evolution preserved the symmetry of the standard code and at times even looked to restore a broader and older symmetry”, states Hornos.

Universal principle
This type of symmetry is not exclusive to genetic coding. It is very similar to that of tautomerism, a phenomena which makes two molecules of the same formula that have different properties depending on the spatial arrangement of the specific groups of atoms. The comparisons go further. “The notion of symmetry” explains Hornos, “is as old as human culture itself. The Mayas never saw anything of the Egyptians but they adopted the same concept of symmetry when constructing their pyramids.” Sumerian art, Thai or Arabic architecture, in the arts of all the peoples in all of the times symmetry is present, a universal principal.

The work brings up the prospect of the application to the extent that it represents each codon by a series of numbers, corresponding to their coordinates in a 3-dimensional geometric figure that describes the differentiation of the genetic coding. This is a type of identity card which, in Hornos’ view, could help in the quest for biological consequences of the model, measured, for example in a yet purely speculative manner, by the production of abnormal proteins that cause diseases.

As with every model, this one supplies some answers but doesn’t say everything. An essential doubt persists: what provokes the breaking of symmetry, and what makes the genetic coding become different? The answer will perhaps take some time.

The unraveling of the code

In 1953 the Englishman Francis Harry Compton Crick (1916-) and the North American James Dewey Watson (1928-) discovered that it is the molecule of DNA that transmits genetic information, a discovery that won them the Nobel Prize for Medicine in 1962. Shortly afterwards the question was raised to how this information is dealt with and translated into biological structures in such a way as to form tissue, from plants leaves to human skin. What makes the difference between one tissue and another are the proteins of which it is composed.

Crick himself and the South African Sidney Brenner (1927-) solved the puzzle in 1961 by discovering the genetic code present in DNA, which organizes the assembling of the proteins. In the end it became clear: the genetic information contained in DNA is transmitted by way of groupings of three to four nitrogenous bases – adenine (A), cytosine (C), thymine (T) e guanine (G) -, called codons, and that they are the units of the genetic code.

Combined three by three, the four bases form 64 codons, which guide the assembling of amino acids in the protein. The genetic code is the grouping of the codons and respective amino acids, united in a table as important to the biochemists as the periodic table to the chemists. They are the actors of a process that occurs all of the time in the cells: specific enzymes identify stretches of a molecule of ribonucleic acid, the RNA messenger, formed from one to the two strips of DNA, and put together the corresponding amino acid. The amino acids fit into each other one by one until the protein is completed, sometimes with thousands of amino acids.

The 64 codons, as has been proven experimentally, correspond to only 21 amino acids, including the so called termination signal, which informs on the exact moment to close the reading of the messenger RNA. The same amino acid, nonetheless, is associated with more than one codon, a phenomenon known as degeneration of the genetic code. The combination is peculiar. Three amino acids are derived from six codons, five are formed from four, two are provided by three and nine can be produced starting from two. Only two amino acids, methionine and tryptophan, depend on only one codon.

The Group Theory, created by three mathematicians, the Frenchman Evariste Galois (1811-1832), the Norwegian Marius Sophus Lie (1842-1899) and another Frenchman Joseph Cartan (1869-1951), opened up thousands of possibilities of organizing the 64 codons into the 21 amino acids, without getting away from the experimental data. Each response had to be examined one by one. An arduous piece of work, only concluded this month, shows that there are at least ten models based on the principle of the breaking of symmetry that reproduce the genetic coding standard.

The reply which stands out is exactly that originally proposed by Hornos and launched in 1993, constructed beginning with the simplistic group Sp(6), thus baptized by the German mathematician Hermann Klaus Hugo Weyl (1885-1955). The Sp(6) is made up of transformations of objects in six dimensions, which are pure abstractions, but can be compared to the three dimensions of physical space, length, breadth and depth. It can also be applied to objects in 64 dimensions, namely the codons.

Based on the ideas of Weyl, which added to those of the German mathematician Felix Christian Klein (1849-1925), who emphasized the connections between geometry and Group Theory, the researchers constructed a 3-dimensional model with 64 points, or small balls, each one corresponding to a codon. The result is a solid of 14 sides, eight hexagons and six squares, with a regular octahedron which allows one to visualize the breaking of symmetry: the small balls painted different colors represent the differentiation of the codons in each phase.

The Project
The Breaking of Symmetry and the Evolution of the Genetic Code (nº 96/01501-6); Modality Thematic project; Coordinator Dr. José Eduardo Martinho Hornos – Physics Institute of São Carlos, USP; Investment R$ 115,696.93