Related papers: A model capturing novel strand symmetries in bacte…
We study the convergence rate to stationarity for a class of exchangeable partition-valued Markov chains called cut-and-paste chains. The law governing the transitions of a cut-and-paste chain are determined by products of i.i.d. stochastic…
The expression of genes usually follows a two-step procedure. First, a gene (encoded in the genome) is transcribed resulting in a strand of (messenger) RNA. Afterwards, the RNA is translated into protein. Classically, this gene expression…
Double stranded DNA chain is known to have nontrivial elasticity. We study the effect of this elasticity on the denaturation profile of DNA oligomer by constraining one base pair at one end of the oligomer to remain in unstretched (or…
DNA is an attractive candidate for data storage. Its millennial durability and nanometer scale offer exceptional data density and longevity. Its relevance to medical applications also drives advances in DNA-related biotechnology. To protect…
The key finding in the DNA double helix model is the specific pairing or binding between nucleotides A-T and C-G, and the pairing rules are the molecule basis of genetic code. Unfortunately, no such rules have been discovered for proteins.…
Sequencing by synthesis is the underlying technology for many next-generation DNA sequencing platforms. We developed a new model, the fixed flow cycle model, to derive the distributions of sequence length for a given number of flow cycles…
We prove exponential decay of pair correlations for 1D stationary point processes when spacings satisfy a Markov condition, geometric ergodicity, and a condition on exponential moments. The conditions are phrased for stationary sequences of…
The relationship between sequences and secondary structures or shapes in RNA exhibits robust statistical properties summarized by three notions: (1) the notion of a typical shape (that among all sequences of fixed length certain shapes are…
RNA polymerase (RNAP) elongates RNA by walking along a DNA template and selectively incorporating ribonucleoside triphosphates (rNTPs). Rather than mechanically replicating the base sequence, RNAP conditions binding and chemistry on the…
We study numerically the mechanical stability and elasticity properties of duplex DNA molecules within the frame of a network model incorporating microscopic degrees of freedom related with the arrangement of the base pairs. We pay special…
The bacterial genome is organized in a structure called the nucleoid by a variety of associated proteins. These proteins can form complexes on DNA that play a central role in various biological processes, including chromosome segregation. A…
This paper studies two problems that are motivated by the novel recent approach of composite DNA that takes advantage of the DNA synthesis property which generates a huge number of copies for every synthesized strand. Under this paradigm,…
A nucleotides sequence is identified, in the two (four) letters alphabet, by the the labels of a vector state of an irreducible representation of U_q(sl(2)) (U_q(sl(2) + sl(2))), in the limit q -> 0. A master equation for the distribution…
In computational biology, tandem duplication is an important biological phenomenon which can occur either at the genome or at the DNA level. A tandem duplication takes a copy of a genome segment and inserts it right after the segment - this…
We consider DNA codes based on the nearest-neighbor (stem) similarity model which adequately reflects the "hybridization potential" of two DNA sequences. Our aim is to present a survey of bounds on the rate of DNA codes with respect to a…
Synthetic DNA approaches 227.5 exabytes per gram of storage density with stability over millennial timescales. Realising this capacity requires error-correction codes that recover data from substantial synthesis and sequencing errors.…
Replication of genetic material is an important process for all living organisms. Origins of replication initiate the copying of DNA at many points on a chromosome, and it is the distribution of these points that is relevant here, as it…
DNA segments and sequences have been studied thoroughly during the past decades. One of the main problems in computational biology is the identification of exon-intron structures inside genes using mathematical techniques. Previous studies…
We identify the ballistically and diffusively rescaled limit distribution of the second class particle position in a wide range of asymmetric and symmetric interacting particle systems with established hydrodynamic behavior, respectively…
In this paper, we consider convergence properties of a second order Markov chain. Similar to a column stochastic matrix is associated to a Markov chain, a so called {\em transition probability tensor} $P$ of order 3 and dimension $n$ is…