A simple maximization model inspired by algorithms for the organization of genetic candidates in bacterial DNA

Abstract

We propose a simple model for interaction between gene candidates in the two strands of bacterial DNA (deoxyribonucleic acid). Our model assumes that 'final' genes appear in one of the two strands, that they do not overlap (in bacteria there is only a small percentage of overlap), and that the final genes maximize the occupancy rate, which is defined to be the proportion of the genome occupied by coding zones. We are more concerned with describing the organization and distribution of genes in bacterial DNA than with the very hard problem of identifying genes. To this end, an algorithm for selecting the final genes according to the previously outlined maximization criterion is proposed. We study the graphical and probabilistic properties of the model resulting from applying the maximization procedure to a Markovian representation of the genic and intergenic zones within the DNA strands, develop theoretical bounds on the occupancy rate (which, in our view, is a rather intractable quantity), and use the model to compute quantities of relevance to the Escherichia coli genome and compare these to annotation data. Although this work focuses on genomic modelling, we point out that the proposed model is not restricted to applications in this setting. It also serves to model other resource allocation problems.

A Note on the Asymptotic Behavior of the Height for a Birth-and-Death Process

“…The process {X t , t ≥ 0} has been studied in statistical physics as a special mean-field model on a complete graph (see [4][5][6][7][8][9]13]), which gives the rate of convergence to a stationary distribution, and as the Anick-Mitra-Sondhi model (see [1,10]) which is related to the data-handling system with multiple sources. When N = 2 and N = 3, {X t , t ≥ 0} is also considered as a genomic model in [8].…”

A note on the asymptotic behavior of the height for a birth-and-death process

“…The process {X t , t ≥ 0} has been studied in statistical physics as a meanfield model (see [3]), and as the Anick-Mitra-Sondhi model [1] which is related to data-handling system with multiple sources. When N = 2 and N = 3, {X t , t ≥ 0} is also considered as a genomic model in [4].…”

A Markovian genomic concatenation model guided by persymmetric matrices

“…For example, in [3], a maximum likelihood approach was used to perform analyses of DNA sequences in order to estimate evolutionary trees, while in [22], a measure of the long-range correlation between the nucleotide bases of DNA sequences was used to classify bacteria. In addition, strand compositional asymmetry (SCA) was used to detect replication origins in bacteria [5], while [19] used interpolated Markov models to identify genes in bacteria, [9] proposed a maximization model to describe the organization and distribution of genes in bacterial DNA and [13] presented a stationary stochastic process for modeling the placement of coding and noncoding regions within a genome that incorporates the phenomenon of start codons appearing within coding regions.…”