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The RNA inverse folding problem, a key challenge in RNA design, involves identifying nucleotide sequences that can fold into desired secondary structures, which are critical for ensuring molecular stability and function. The inherent…
The assembly and maturation of viruses with icosahedral capsids must be coordinated with icosahedral symmetry. The icosahedral symmetry imposes also the restrictions on the cooperative specific interactions between genomic RNA/DNA and coat…
Coding information is the main source of heterogeneity (non-randomness) in the sequences of bacterial genomes. This information can be naturally modeled by analysing cluster structures in the "in-phase" triplet distributions of relatively…
We show the expected order of RNA saturated secondary structures of size $n$ is $\log_4n(1+O(\frac{\log_2n}{n}))$, if we select the saturated secondary structure uniformly at random. Furthermore, the order of saturated secondary structures…
We study genetic networks that produce many species of non-coding RNA molecules that are present at a moderate density, as typically exists in the cell. The associations of the many species of these RNA are modeled physically, taking into…
Viruses can amplify their genomes following different replication modes (RMs) ranging from the stamping machine replication (SMR) model to the geometric replication (GR) model. Different RMs are expected to produce different evolutionary…
Transcriptional activity has been shown to relate to the organization of chromosomes in the eukaryotic nucleus and in the bacterial nucleoid. In particular, highly transcribed genes, RNA polymerases and transcription factors gather into…
In this paper we compute the loop homology of bi-secondary structures. Bi-secondary structures were introduced by Haslinger and Stadler and are pairs of RNA secondary structures, i.e. diagrams having non-crossing arcs in the upper…
Is protein secondary structure primarily determined by local interactions between residues closely spaced along the amino acid backbone, or by non-local tertiary interactions? To answer this question we have measured the entropy densities…
A DNA palindrome is a segment of double-stranded DNA sequence with inver- sion symmetry which may form secondary structures conferring significant biolog- ical functions ranging from RNA transcription to DNA replication. To test if the…
This paper proposes a new mathematical approach to characterize native protein structures based on the discrete differential geometry of tetrahedron tiles. In the approach, local structure of proteins is classified into finite types…
A model of self-avoiding walk with suitable constraints on self-attraction is developed to describe the conformational behavior of a short RNA or a single stranded DNA molecule that forms hairpin structure and calculate the properties…
Non-coding RNA molecules fold into precise base pairing patterns to carry out critical roles in genetic regulation and protein synthesis. We show here that coupling systematic mutagenesis with high-throughput SHAPE chemical mapping enables…
RNA is a fundamental class of biomolecules that mediate a large variety of molecular processes within the cell. Computational algorithms can be of great help in the understanding of RNA structure-function relationship. One of the main…
In this paper, we propose an end-to-end deep learning model, called E2Efold, for RNA secondary structure prediction which can effectively take into account the inherent constraints in the problem. The key idea of E2Efold is to directly…
Specific elements of viral genomes regulate interactions within host cells. Here, we calculated the secondary structure content of >2500 coronaviruses and computed >100000 human protein interactions with severe acute respiratory syndrome…
This work describes the implementation of a genetic algorithm-based strategy combined with first-principles computations for identifying the structure of the most stable boron 1D structures. We focus our attention on the structure of…
A growing number of RNA sequences are now known to have distributions of multiple stable sequences. Recent algorithms use the list of nucleotides in a sequence and auxiliary experimental data to predict such distributions. Although the…
The information capacity of double-crossover (DX) tiles was successfully increased beyond a binary representation to higher base representations. By controlling the length and the position of DNA hairpins on the DX tile, ternary and senary…
We discuss the physics of RNA as described by its secondary structure. We examine the static properties of a homogeneous RNA-model that includes pairing and base stacking energies as well as entropic costs for internal loops. For large…