Related papers: Symmetry Scheme for Amino Acid Codons
Modeling potential alloys requires the exploration of all possible configurations of atoms. Additionally, modeling the thermal properties of materials requires knowledge of the possible ways of displacing the atoms. One solution to finding…
The concepts of alpha- and beta-packets of the periodic table of chemical elements and chemical compounds are defined. The first of the 47 minerals alpha-packets is composed. In it all minerals are arranged in increasing Iav index of…
In an effort to further our interest in understanding basic chemistry of interstellar molecules, we carry out here an extensive investigation of the stabilities of interstellar carbon chains; Cn, H2Cn, HCnN and CnX (X=N, O, Si, S, H, P, H-,…
We prove that for every nonempty set $\Sigma$ of integers bigger than $1$, which has at most three elements, there exists a numerical semigroup $T$ and an element $x$ of $T$ such that a natural number $n$ is the number of atoms in a…
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…
We introduce the simple parametrization for the space of codons (triples of nucleotides) by 8\times 8 table. This table (which we call the dyadic plane) possesses the natural 2-adic ultrametric. We show that after this parametrization the…
The values of molecular polarizabilities and softnesses of the twenty amino acids were computed ab initio (MP2). By using the iterative Hirshfeld scheme to partition the molecular electronic properties, we demonstrate that the values of the…
Biologists have long sought a way to explain how statistical properties of genetic sequences emerged and are maintained through evolution. On the one hand, non-random structures at different scales indicate a complex genome organisation. On…
Erd\"os conjectured the existence of an infinite Sidon sequence of positive integers which is also an asymptotic basis of order 3. We make progress towards this conjecture in several directions. First we prove the conjecture for all cyclic…
The numbers of natural chemical elements, minerals, inorganic and organic chemical compounds are determined by 1, 2, 3 and 4-combinations of a set 95 and are respectively equal to 95, 4,465, 138,415 and 3,183,545. To explain these relations…
Using a fast tree-searching algorithm and a Pentium cluster, we enumerated all the sequences and compact conformations (structures) for a protein folding model on a cubic lattice of size $4\times3\times3$. We used two types of amino acids…
We present a structural data set of the 20 proteinogenic amino acids and their amino-methylated and acetylated (capped) dipeptides. Different protonation states of the backbone (uncharged and zwitterionic) were considered for the amino…
New developments are presented in the framework of the model introduced by the authors in refs. [1,2] and in which nucleotides as well as codons are classified in crystal bases of the quantum group U_q(sl(2)+sl(2)) in the limit q -> 0. An…
The importance of the notion of symmetry in physics is well established: could it also be the case for the genetic code? In this spirit, a model for the Genetic Code based on continuous symmetries and entitled the "Crystal Basis Model" has…
We give recurrence relations for the enumeration of symmetric elements within four classes of arc diagrams corresponding to certain involutions and set partitions whose blocks contain no consecutive integers. These arc diagrams are…
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…
The search for possible mixing patterns of charged leptons and neutrinos is important to get clues of the origin of nearly maximal mixings, since there are some preferred bases of the lepton mass matrices given by underlying theories. We…
In a similar way in which the folding of single--domain proteins provide an important test in the study of self--organization, the folding of homodimers constitute a basic challenge in the quest for the mechanisms which are at the basis of…
Acid-base reactions are ubiquitous in nature. Understanding their mechanisms is crucial in many fields, from biochemistry to industrial catalysis. Unfortunately, experiments only give limited information without much insight into the…
Proteins have evolved through mutations, amino acid substitutions, since life appeared on Earth, some 109 years ago. The study of these phenomena has been of particular significance because of their impact on protein stability, function,…