Related papers: Genus Distributions For Extended Matrix Models Of …
A quantitative characterization of the relationship between molecular sequence and structure is essential to improve our understanding of how function emerges. This particular genotype-phenotype map has been often studied in the context of…
The branching of an RNA molecule is an important structural characteristic yet difficult to predict correctly, especially for longer sequences. Using plane trees as a combinatorial model for RNA folding, we consider the thermodynamic cost,…
The ability to detect whether a species (or dimension) is zero in Chemical Reaction Networks (CRN), Vector Addition Systems, or Petri Nets is known to increase the power of these models -- making them capable of universal computation. While…
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 mechanical model based on beads and springs, which we recently proposed to study non-specific DNA-protein interactions [J. Chem. Phys. 130, 015103 (2009)], was improved by describing proteins as sets of interconnected beads instead of…
We provide a perturbative expansion for the empirical spectral distribution of a Hermitian matrix with large size perturbed by a random matrix with small operator norm whose entries in the eigenvector basis of the first one are independent…
In this article, we study branching random walks on graphs modeling division-mutation processes inspired by adaptive immunity. We apply the theory of expander graphs on mutation rules in evolutionary processes and obtain estimates for the…
RNA viruses form genetically diverse populations structured as mutant spectra, or quasispecies, whose internal organization influences their evolutionary and adaptive dynamics. While genetic diversity has been extensively characterized, the…
Dual graphs have been applied to model RNA secondary structures with pseudoknots, or intertwined base pairs. In previous works, a linear-time algorithm was introduced to partition dual graphs into maximally connected components called…
Computational RNA secondary structure prediction is rather well established. However, such prediction algorithms always depend on a large number of experimentally measured parameters. Here, we study how sensitive structure prediction…
An RNA molecule is structured on several layers. The primary and most obvious structure is its sequence of bases, i.e. a word over the alphabet {A,C,G,U}. The higher structure is a set of one-to-one base-pairings resulting in a…
The problem of RNA secondary structure design (also called inverse folding) is the following: given a target secondary structure, one aims to create a sequence that folds into, or is compatible with, a given structure. In several practical…
A double stranded DNA molecule when pulled with a force acting on one end of the molecule can become either partially or completely unzipped depending on the magnitude of the force F. For a random DNA sequence, the number M of unzipped base…
Nucleic acids are highly deformable helical molecules constantly stretched, twisted and bent in their biological functioning. Single molecule experiments have shown that double stranded (ds)-RNA and standard ds-DNA have opposite…
Motivated by empirical observations of algebraic duplicated sequence length distributions in a broad range of natural genomes, we analytically formulate and solve a class of simple discrete duplication/substitution models that generate…
The Gram matrix is a classical object formed from the pairwise inner products of a collection of vectors, with fundamental roles in functional analysis, statistics, combinatorics, and coding theory. In the realm of sequence design,…
Background: Duplication of genes is important for evolution of molecular networks. Many authors have therefore considered gene duplication as a driving force in shaping the topology of molecular networks. In particular it has been noted…
Secondary structure formation of nucleic acids strongly depends on salt concentration and temperature. We develop a theory for RNA folding that correctly accounts for sequence effects, the entropic contributions associated with loop…
Proposing beneficial amino acid substitutions, whether for mutational effect prediction or protein engineering, remains a central challenge in structural biology. Recent inverse folding models, trained to reconstruct sequences from…
We propose a simple nonlinear scaler displacement model to calculate the distribution of effect created by a shear stress on a double stranded DNA (dsDNA) molecule and the value of shear force $F_c$ which is required to separate the two…