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Evolution consists of distinct stages: cosmological, biological, linguistic. Since biology verges on natural sciences and linguistics, we expect that it shares structures and features from both forms of knowledge. Indeed, in DNA we…
Matrix forms of the representation of the multi-level system of molecular-genetic alphabets have revealed algebraic properties of this system. Families of genetic (4*4)- and (8*8)-matrices show unexpected connections of the genetic system…
Degeneracy of the genetic code is a biological way to minimize effects of the undesirable mutation changes. Degeneration has a natural description on the 5-adic space of 64 codons $\mathcal{C}_5 (64) = \{n_0 + n_1 5 + n_2 5^2 : n_i = 1, 2,…
The protein folding problem must ultimately be solved on all length scales from the atomic up through a hierarchy of complicated structures. By analyzing the stability of the folding process using physics and mathematics, this paper shows…
Predicting how genetic variation affects phenotypic outcomes at the organismal, cellular, and molecular levels requires deciphering the cis-regulatory code, the sequence rules by which non-coding regions regulate genes. In this perspective,…
The number of atoms in the four ribonucleotides uridine monophosphate, cytidine monophosphate, adenine monophosphate and guanine monophosphate is taken as a key parameter. A mathematical relation describing the condensation of the three…
The article is devoted to phenomena of symmetries and algebras in matrix presentations of the genetic code. The Kronecker family of the genetic matrices is investigated, which is based on the alphabetical matrix [C A; U G], where C, A, U, G…
Evolution of genetic code is studied as the change in the choice of enzymes that are used to synthesize amino acids from the genetic information of nucleic acids. We propose the following theory: the differentiation of physiological states…
We introduce a lattice model of protein conformations which is able to reproduce second structures of proteins (alpha--helices and beta--sheets). This model is based on the following two main ideas. First, we model backbone parts of amino…
This article is interested in the origin of the genetic code, it puts forward a scenario of a simultaneous selection of the bases and amino acids and setting up of a correlation between them. Each amino acid is associated with a pair of its…
A codon table is a useful tool for mapping codons to amino acids as they have been assigned by nature. It has become a scientific icon because of the way it embodies our understanding of this natural process and the way it immediately…
A heuristic diagram of the evolution of the standard genetic code is presented. It incorporates, in a way that resembles the energy levels of an atom, the physical notion of broken symmetry and it is consistent with original ideas by Crick…
Proteins are the common constituents of all living cells. They are molecular machines that interact with each other as well as with other cell products and carry out a dizzying array of functions with distinction. These interactions follow…
Gene regulation is a complex process involving the role of several genomic elements which work in concert to drive spatio-temporal expression. The experimental characterization of gene regulatory elements is a very complex and…
The genetic code is profoundly shaped by an origin in ancient RNA-mediated interactions, needing an extended development to reach the Standard Genetic Code (SGC). That development can serially use RNA specificities, a ribonucleopeptide…
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…
The GC-content is very variable in different genome regions and species but although many hypothesis we still do not know the reason why. Here we show that a relationship exists with the mutation rate, in particular we noticed a new…
The coding space of protein sequences is shaped by evolutionary constraints set by requirements of function and stability. We show that the coding space of a given protein family--the total number of sequences in that family--can be…
Generating molecules, both in a directed and undirected fashion, is a huge part of the drug discovery pipeline. Genetic algorithms (GAs) generate molecules by randomly modifying known molecules. In this paper we show that GAs are very…
The article represents a new class of hidden symmetries in long sequences of oligonucleotides of single stranded DNA from their representative set. These symmetries are an addition to symmetries described by the second parity rule of…