Related papers: Waiting for regulatory sequences to appear
Transcription factors are short stretches of DNA (or $k$-mers) mainly located in promoters sequences that enhance or repress gene expression. With respect to an initial distribution of letters on the DNA alphabet, Behrens and Vingron…
We consider a model of a population of fixed size N in which each individual gets replaced at rate one and each individual experiences a mutation at rate \mu. We calculate the asymptotic distribution of the time that it takes before there…
An approach for approximately calculating the number of genes in a genome is presented, which takes into account the average protein length expected for the species. A number of virus, bacterial and eukaryotic genomes are scrutinized.…
In a recent article, Behrens and Vingron (JCB 17, 12, 2010) compute waiting times for k-mers to appear during DNA evolution under the assumption that the considered k-mers do not occur in the initial DNA sequence, an issue arising when…
We show that textual analysis of microbial genomes reveal telling footprints of the early evolution of the genomes. The frequencies of word occurrence of random DNA sequences considered as texts in their four nucleotides are expected to…
We investigate the behavior of the periods and border lengths of random words over a fixed alphabet. We show that the asymptotic probability that a random word has a given maximal border length $k$ is a constant, depending only on $k$ and…
Various approaches to alignment-free sequence comparison are based on the length of exact or inexact word matches between two input sequences. Haubold {\em et al.} (2009) showed how the average number of substitutions between two DNA…
Evolution of gene regulation is crucial for our understanding of the phenotypic differences between species, populations and individuals. Sequence-specific binding of transcription factors to the regulatory regions on the DNA is a key…
Cancer prognosis can be regarded as estimating the risk of future outcomes from multiple variables. In prognostic signatures, these variables represent expressions of genes that are summed up to calculate a risk score. However, it is a…
Eukaryotic transcription generally occurs in bursts of activity lasting minutes to hours; however, state-of-the-art measurements have revealed that many of the molecular processes that underlie bursting, such as transcription factor binding…
We compare an efficiency of a deterministic "lawnmower" and random search strategies for finding a prescribed sequence of letters (a password) of length M in which all letters are taken from the same Q-ary alphabet. We show that at best a…
We consider the population genetics problem: how long does it take before some member of the population has $m$ specified mutations? The case $m=2$ is relevant to onset of cancer due to the inactivation of both copies of a tumor suppressor…
This paper presents a novel method to segment/decode DNA sequences based on n-grams statistical language model. Firstly, we find the length of most DNA 'words' is 12 to 15 bps by analyzing the genomes of 12 model species. Then we design an…
This paper focuses on the problem of modeling the correspondence pattern for ordinary people. Suppose that letters arrive at a rate $\lambda$ and are answered at a rate $\mu$. Furthermore, we assume that, for a constant $T$, a letter is…
For a beneficial allele which enters a large unstructured population and eventually goes to fixation, it is known that the time to fixation is approximately $2\log(\alpha)/\alpha$ for a large selection coefficient $\alpha$. For a population…
A fundamental result in psycholinguistics is that less predictable words take a longer time to process. One theoretical explanation for this finding is Surprisal Theory (Hale, 2001; Levy, 2008), which quantifies a word's predictability as…
Transcription factor proteins bind specific DNA sequences to control the expression of genes. They contain DNA binding domains which belong to several super-families, each with a specific mechanism of DNA binding. The total number of…
Objections to Darwinian evolution are often based on the time required to carry out the necessary mutations. Seemingly, exponential numbers of mutations are needed. We show that such estimates ignore the effects of natural selection, and…
When considering binary strings, it's natural to wonder how many distinct subsequences might exist in a given string. Given that there is an existing algorithm which provides a straightforward way to compute the number of distinct…
This paper describes the probabilistic behaviour of a random Sturmian word. It performs the probabilistic analysis of the recurrence function which can be viewed as a waiting time to discover all the factors of length $n$ of the Sturmian…