Mathematic principles underlying genetic structures

Shannon's mathematical theory of communication defines fundamental limits on how much information can be transmitted between the different components of any man-made or biological system. This paper is an informal but rigorous introduction to the main ideas implicit in Shannon's theory. An annotated reading list is provided for further reading.

At the 2023 Les Houches Summer School on Theoretical Biological Physics, several students asked for some background on information theory, and so we added a tutorial to the scheduled lectures. This is largely a transcript of that tutorial, lightly edited. It covers basic definitions and context rather than detailed calculations. We hope to have maintained the informality of the presentation, including exchanges with the students, while still being useful.

This article introduces the physics of information in the context of molecular biology and genomics. Entropy and information, the two central concepts of Shannon's theory of information and communication, are often confused with each other but play transparent roles when applied to statistical ensembles (i.e., identically prepared sets) of symbolic sequences. Such an approach can distinguish between entropy and information in genes, predict the secondary structure of ribozyme...

Molecular Communication (MC) is a communication strategy that uses molecules as carriers of information, and is widely used by biological cells. As an interdisciplinary topic, it has been studied by biologists, communication theorists and a growing number of information theorists. This paper aims to specifically bring MC to the attention of information theorists. To do this, we first highlight the unique mathematical challenges of studying the capacity of molecular channels. ...

The genetic code is connection between 64 codons, which are building blocks of the genes, and 20 amino acids, which are building blocks of the proteins. In addition to coding amino acids, a few codons code stop signal, which is at the end of genes, i.e. it terminates process of protein synthesis. This article is a review of simple modelling of the genetic code and related subjects by concept of p-adic distance. It also contains some new results. In particular, the article pre...

We present a theoretical as well as experimental investigation of a population of self-replicating segments of code subject to random mutation and survival of the fittest. Under the assumption that such a system constitutes a minimal system with characteristics of life, we obtain a number of statements on the evolution of complexity and the trade-off between entropy and information.

Codes have been used for centuries to convey secret information.To a cryptanalyst, the interception of a code is only the first step in recovering a secret message.Deoxyribonucleic acid (DNA) is a biological and molecular code.Through the work of Marshall Nirenberg and others, DNA is now understood to specify for amino acids in triplet codes of bases.The possibilty of DNA encoding secret information in a natural language is explored, since a code is expected to have a distinc...

Information is a key concept in evolutionary biology. Information is stored in biological organism's genomes, and used to generate the organism as well as to maintain and control it. Information is also "that which evolves". When a population adapts to a local environment, information about this environment is fixed in a representative genome. However, when an environment changes, information can be lost. At the same time, information is processed by animal brains to survive ...

This article is devoted to applications of projection operators to simulate phenomenological properties of the molecular-genetic code system. Oblique projection operators are under consideration, which are connected with matrix representations of the genetic coding system in forms of the Rademacher and Hadamard matrices. Evidences are shown that sums of such projectors give abilities for adequate simulations of ensembles of inherited biological phenomena including ensembles o...

DNA, with remarkable properties of high density, durability, and replicability, is one of the most appealing storage media. Emerging DNA storage technologies use composite DNA letters, where information is represented by probability vectors, leading to higher information density and lower synthesizing costs than regular DNA letters. However, it faces the problem of inevitable noise and information corruption. This paper explores the channel of composite DNA letters in DNA-bas...