Related papers: Nonlinear Dynamics in the Binary DNA/RNA Coding Pr…
Designing RNA molecules has garnered recent interest in medicine, synthetic biology, biotechnology and bioinformatics since many functional RNA molecules were shown to be involved in regulatory processes for transcription, epigenetics and…
Proteins have regular tertiary structures but irregular amino acid sequences. This made it very difficult to decode the structural information in the protein sequences. Here we demonstrate that many small alpha protein domains have hidden…
The complexity of the primary structure of human DNA is explored using methods from nonequilibrium statistical mechanics, dynamical systems theory and information theory. The use of chi-square tests shows that DNA cannot be described as a…
Motivation: DNA data is transcribed into single-stranded RNA, which folds into specific molecular structures. In this paper we pose the question to what extent sequence- and structure-information correlate. We view this correlation as…
A two-dimensional string is simply a two-dimensional array. We continue the study of the combinatorial properties of repetitions in such strings over the binary alphabet, namely the number of distinct tandems, distinct quartics, and runs.…
Most binary superlattices created using DNA functionalization or other approaches rely on particle size differences to achieve compositional order and structural diversity. Here we study two-dimensional (2D) assembly of DNA-functionalized…
Motif finding in DNA, RNA and proteins plays an important role in life science research. Recent patents concerning motif finding in the biomolecular data are recorded in the DNA Patent Database which serves as a resource for policy makers…
In this paper we characterize the algebraic structure of two-dimensional $(\alpha,\beta )$-constacyclic codes of arbitrary length $s.\ell$ and of their duals. For $\alpha,\beta \in \{1,-1\}$, we give necessary and sufficient conditions for…
Combinatorial analysis of a certain abstract of RNA structures has been studied to investigate their statistics. Our approach regards the backbone of secondary structures as an alternate sequence of paired and unpaired sets of nucleotides,…
We calculate the spectrum of torsional vibrations of a double-stranded structure that models the double helix of the DNA. We come to the conclusion that within the framework of the model elementary excitations may display an asymmetry as…
The tertiary structures of functional RNA molecules remain difficult to decipher. A new generation of automated RNA structure prediction methods may help address these challenges but have not yet been experimentally validated. Here we apply…
The in vivo free energy of looping double-stranded DNA by the lac repressor has a remarkable behavior whose origins are not fully understood. In addition to the intrinsic periodicity of the DNA double helix, the in vivo free energy has an…
The intricate three-dimensional geometries of protein tertiary structures underlie protein function and emerge through a folding process from one-dimensional chains of amino acids. The exact spatial sequence and configuration of amino…
Most living systems rely on double-stranded DNA (dsDNA) to store their genetic information and perpetuate themselves. This biological information has been considered the main target of evolution. However, here we show that symmetries and…
The equilibrium three dimensional shape of relatively short loops of DNA is studied using an elastic model that takes into account anisotropy in bending rigidities. Using a reasonable estimate for the anisotropy, it is found that cyclized…
Enumerative studies of RNA secondary structures were initiated four decades ago by Waterman and his coworkers. Since then, RNA secondary structures have been explored according to many different structural characteristics, for instance,…
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…
We examine the conformations of a model for a short segment of closed DNA. The molecule is represented as a cylindrically symmetric elastic rod with a constraint corresponding to a specification of the linking number. We obtain analytic…
A representation of the genetic code as a six-dimensional Boolean hypercube is proposed. It is assumed here that this structure is the result of the hierarchical order of the interaction energies of the bases in codon-anticodon recognition.…
A non-linear Penner type interaction is introduced and studied in the random matrix model of homo-RNA. The asymptotics in length of the partition function is discussed for small and large $N$ (size of matrix). The interaction doubles the…