An octopus can count; some birds can count; you can count; but is it possible that your DNA can also count? Can this ability be related to the origin of life on earth? Recent studies I have performed with Diego L. Gonzalez (Institute for Microelectronics and Microsystems, Italian National Research Council) and with Rodolfo Rosa (Statistics Department, University of Bologna), show that this apparently innocent question might lead to a significant advance in our understanding of how life manages genetic information. In brief, this management consists of three main steps, 1) replication: the DNA molecule (where all our genetic information is stored, like the hard disk of a PC) is duplicated just before cell division; 2) transcription: one strand of the double helix of DNA is copied forming a single strand RNA; 3) translation: the mRNA (messenger RNA) is translated into proteins. This latter step is performed using the translation table known as the genetic code. In this way, each codon, a piece of mRNA consisting of three consecutive bases, is translated into one of the 20 amino acids that constitute the building blocks of proteins. There are four such bases in RNA, Uracil, Cytosine, Adenine, and Guanine (U, C, A, G).

At this point a first answer to our question can be given. In fact, DNA replication is performed one base at a time. Moreover, in the transcription step, when an error is produced, the machinery stops and goes back five bases. Finally, protein translation implies counting bases exactly in multiples of three. Thus, the complex genetic machinery requires an intrinsic counting capability. Furthermore, as the studies report, also the genetic code is closely linked to counting. In fact, counting is at the basis of numeration systems, and is, consequently, at the basis of mathematics. For representing integer numbers, usual numeration systems adopt the powers of a base, for instance, 10 in our standard decimal system, or 2 in the binary one mainly used by computers. But these numeration systems are univocal, that is, any integer number has one and only one representation. In contrast, the genetic code is redundant (not univocal). Specifically, a given amino acid can be represented by more than one codon, therefore, the usual numeration systems are of little relevance for dealing with the genetic code.

Fortunately, there are numeration systems that are not univocal. One outstanding example is the Fibonacci numeration system. In the Fibonacci system, the powers of two of the binary system (1,2,4,8,16, …), are replaced by the well-known Fibonacci numbers, (1,1,2,3,5,8, …). The surprising result is that a modification of the Fibonacci system allows us to describe mathematically the genetic code including many of its symmetries. Such a description uncovers the existence of a hidden language based on redundancy and embedded into DNA sequences. These theoretical findings are supported by advanced statistical methods applied to real data. In a metaphorical sense, it is as if life used redundant numeration systems for counting! But what could be the biological advantage of such an arithmetic capability? The studies suggest that a method for error detection and correction could be implemented on this basis. In fact, the main problem in managing binary information is to avoid the propagation of errors which are unavoidably produced through the transmission channels. For instance, when playing a CD, error detection/correction techniques are activated for correcting errors that would degrade the recorded information. To this end, the binary information contained in the CD is made redundant and coded in such a way that, when decoded, errors are minimised. The research indicates that the integrity of genetic information is preserved by means of analogous mechanisms. Without them, Information Theory proves that it would be impossible to find in extant organisms ancient genes that originated billions of years ago in primordial forms of life.

The understanding of how genetic information is organised and processed can greatly contribute to the development of techniques such as genetic therapies for tackling serious diseases, or the creation of secure and fully controllable genetically modified organisms. Indeed, the main challenge for achieving these goals is related to our relative ignorance about the true language in which the book of life is written. We cannot correct or modify a Chinese philosophy book if we have only a philosophical background; we need to know the meaning of the Chinese ideograms. These studies contribute to the understanding of the structure of the genetic information from a new perspective and also prompt fundamental inquiries on the hot problem of the origin and evolution of life.