Related papers: Crystalizing the genetic code
This article introduces a novel binary representation of the canonical genetic code based on both the structural similarities of the nucleotides, as well as the physicochemical properties of the encoded amino acids. Each of the four mRNA…
The previously formulated model for the evolution of the genetic code was shown to clarify why base triplets of some precursor amino acids differ by a single base from product amino acid codons, while others show less homology. First, the…
We propose a (theoretical ;-) model for quantum computation where the result can be read out from the time average of the Hamiltonian dynamics of a 2-dimensional crystal on a cylinder. The Hamiltonian is a spatially local interaction among…
Many modified genetic codes are found in specific genomes in which one or more codons have been reassigned to a different amino acid from that in the canonical code. We present a model that unifies four possible mechanisms for reassignment,…
We introduce and numerically solve a mathematical model of the experimentally established mechanisms responsible for the symmetry breaking transition observed in the chiral crystallization experiments reported by I. Weissbuch, L. Addadi, L.…
Owing to their rich internal structure and significant long-range interactions, ultracold molecules have been widely explored as carriers of quantum information. Several different schemes for encoding qubits into molecular states, both bare…
The genesis of the stand genetic code is considered as a result of a fusion of two AU- and GC-codes distributed in two dominant and two recessive domains. The fusion of these codes is described with simple empirical rules. This formal…
A mathematical algorithm to describe DNA or RNA sequences of $N$ nucleotides by a string of $2N$ integers numbers is presented in the framework of the so called crystal basis model of the genetic code. The description allows to define a not…
We present a framework based on conditional entropy and the Dirichlet distribution for classifying chromosomes based on the degree to which they use synonymous codons uniformly or preferentially, that is, whether or not codons that code for…
Important aspects of the process of information storage and retrieval in DNA and RNA, and its evolution, are the role of the anticodons and associated $t$RNA's, and correlations between anticodons and amino acids; the degeneracy of the…
We develop theoretical methods for the implementation of creation and destruction operators in separate registers of a quantum computer, allowing for a transparent and dynamical creation and destruction of particle modes in second…
We derive the amino acid assignment to one codon representation (typical 64-dimensional irreducible representation) of the basic classical Lie superalgebra osp(5|2) from biochemical arguments. We motivate the approach of mathematical…
Surface codes describe quantum memory stored as a global property of interacting spins on a surface. The state space is fixed by a complete set of quasi-local stabilizer operators and the code dimension depends on the first homology group…
We give through pseudodifferential operator calculus a proof that the quantum dynamics of a class of infinite harmonic crystals becomes ergodic and mixing with respect to the quantum Gibbs measure if the classical infinite dynamics is…
The fields of structural biology and soft matter have independently sought out fundamental principles to rationalize protein crystallization. Yet the conceptual differences and the limited overlap between the two disciplines have thus far…
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…
DNA-coated colloids can self-assemble into an incredible diversity of crystal structures, but applications of this technology are limited by poor understanding and control over the dynamical crystallization pathways. To address this…
A one-dimensional long-range model of classical rotators with an extended degree of complexity, as compared to paradigmatic long-range systems, is introduced and studied. Working at constant density, in the thermodynamic limit one can prove…
Rich information on the prebiotic evolution is still stored in contemporary genomic data. The statistical mechanism at the sequence level may play a significant role in the prebiotic evolution. Based on statistical analysis of genome…
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…