Andrew Hart

The λ-classification of continuous-time birth-and-death processes

We study the λ-classification of absorbing birth-and-death processes, giving necessary and sufficient conditions for such processes to be λ-transient, λ-null recurrent and λ-positive recurrent.

A Gibbs Approach to Chargaff’s Second Parity Rule

Chargaff’s second parity rule (CSPR) asserts that the frequencies of short polynucleotide chains are the same as those of the complementary reversed chains. Up to now, this hypothesis has only been observed empirically and there is currently no explanation for its presence in DNA strands. Here we argue that CSPR is a probabilistic consequence of the reverse complementarity between paired strands, because the Gibbs distribution associated with the chemical energy between the bonds satisfies CSPR. We develop a statistical test to study the validity of CSPR under the Gibbsian assumption and we apply it to a large set of bacterial genomes taken from the GenBank repository.

A model capturing novel strand symmetries in bacterial DNA.

Chargaffs second parity rule for short oligonucleotides states that the frequency of any short nucleotide sequence on a strand is approximately equal to the frequency of its reverse complement on the same strand. Recent studies have shown that, with the exception of organellar DNA, this parity rule generally holds for double-stranded DNA genomes and fails to hold for single-stranded genomes. While Chargaffs first parity rule is fully explained by the Watson-Crick pairing in the DNA double helix, a definitive explanation for the second parity rule has not yet been determined. In this work, we propose a model based on a hidden Markov process for approximating the distributional structure of primitive DNA sequences. Then, we use the model to provide another possible theoretical explanation for Chargaffs second parity rule, and to predict novel distributional aspects of bacterial DNA sequences.

Statistical Testing of Chargaff's Second Parity Rule in Bacterial Genome Sequences

Chargaffs first parity rule is a property of double-stranded DNA which states that the number of A and T nucleotides, and the number of C and G nucleotides, are the same within the duplex. It arises as a result of the chemistry of nucleic acids which only permits A to bond with T and C to bond with G. In contrast, Chargaffs second parity rule asserts that the same is also true within a single strand, not only for mononucleotide chains, but also for short polynucleotide chains. Unlike the first parity rule, the second is not exact[ 12 ]. Several explanations for the origins of this intrastrand symmetry have been proposed, but the relative contribution of these mechanisms to the symmetry are still not clear[ 19 ]. This work aims to scrutinise Chargaffs second parity rule by developing tests of statistical significance for the rule and then applying them to a large set of bacterial genomes taken from the GenBank repository. We also consider the vector of mononucleotide frequencies (π a : a ∈ {A, C, G, T}), together with the stochastic matrix of conditional nucleotide frequencies P = (P a, b : a, b ∈ {A, C, G, T}), where P a, b is the observed frequency of b-type nucleotides given that they are preceded by an a-type nucleotide, and prove that Chargaffs second parity rule for mononucleotides and dinucleotides is equivalent to P possessing a particular structure. The proposed tests make a uniform assumption either on the set of all 4 × 4 stochastic matrices or on the set of 4-element probability vectors and compare this with the structure induced by Chargaffs second parity rule. When applied to real bacterial genome sequences, the tests generally confirm Chargaffs second parity rule.

Markovianness and conditional independence in annotated bacterial DNA

Abstract We explore the probabilistic structure of DNA in a number of bacterial genomes and conclude that a form of Markovianness is present at the boundaries between coding and non-coding regions, that is, the sequence of START and STOP codons annotated for the bacterial genome. This sequence is shown to satisfy a conditional independence property which allows its governing Markov chain to be uniquely identified from the abundances of START and STOP codons. Furthermore, we show that the annotated sequence of STARTs and STOPs complies with Chargaff’s second parity rule.

Global gene expression analysis provides insight into local adaptation to geothermal streams in tadpoles of the Andean toad Rhinella spinulosa

The anuran Rhinella spinulosa is distributed along the Andes Range at altitudes that undergo wide daily and seasonal variation in temperature. One of the populations inhabits geothermal streams, a stable environment that influences life history traits such as the timing of metamorphosis. To investigate whether this population has undergone local adaptation to this unique habitat, we carried out transcriptome analyses in animals from two localities in two developmental stages (prometamorphic and metamorphic) and exposed them to two temperatures (20 and 25 °C). RNA-Seq, de novo assembly and annotation defined a transcriptome revealing 194,469 high quality SNPs, with 1,507 genes under positive selection. Comparisons among the experimental conditions yielded 1,593 differentially expressed genes. A bioinformatics search for candidates revealed a total of 70 genes that are highly likely to be implicated in the adaptive response of the population living in a stable environment, compared to those living in an environment with variable temperatures. Most importantly, the population inhabiting the geothermal environment showed decreased transcriptional plasticity and reduced genetic variation compared to its counterpart from the non-stable environment. This analysis will help to advance the understanding of the molecular mechanisms that account for the local adaptation to geothermal streams in anurans.

Codon usage bias reveals genomic adaptations to environmental conditions in an acidophilic consortium

The analysis of codon usage bias has been widely used to characterize different communities of microorganisms. In this context, the aim of this work was to study the codon usage bias in a natural consortium of five acidophilic bacteria used for biomining. The codon usage bias of the consortium was contrasted with genes from an alternative collection of acidophilic reference strains and metagenome samples. Results indicate that acidophilic bacteria preferentially have low codon usage bias, consistent with both their capacity to live in a wide range of habitats and their slow growth rate, a characteristic probably acquired independently from their phylogenetic relationships. In addition, the analysis showed significant differences in the unique sets of genes from the autotrophic species of the consortium in relation to other acidophilic organisms, principally in genes which code for proteins involved in metal and oxidative stress resistance. The lower values of codon usage bias obtained in this unique set of genes suggest higher transcriptional adaptation to living in extreme conditions, which was probably acquired as a measure for resisting the elevated metal conditions present in the mine.

An entropy-based technique for classifying bacterial chromosomes according to synonymous codon usage

We present a framework based on information theoretic concepts and the Dirichlet distribution for classifying chromosomes based on the degree to which they use synonymous codons uniformly or preferentially, that is, whether or not codons that code for an amino acid appear with the same relative frequency. At its core is a measure of codon usage bias we call the Kullback–Leibler codon information bias (KL-CIB or CIB for short). Being defined in terms of conditional entropy makes KL-CIB an ideal and natural quantity for expressing a chromosome’s degree of departure from uniform synonymous codon usage. Applying the approach to a large collection of annotated bacterial chromosomes reveals three distinct groups of bacteria.

Sequential dynamics of high order polynomial automata networks: an application to the Erlang fixed-point equations

We present results concerning the sequential evolution of p-order polynomial, symmetric automata networks with monotone transition functions. In particular, any such network has a Lyapunov functional, that may, depending on the transition function of the network, be strictly Lyapunov, resulting in all limit cycles of its dynamical evolution in the sequential mode being fixed points. As an application, we use our results to show that it is always possible to solve, via sequential iteration, the Erlang fixed-point equations, an important fixed point problem which appears in the theory of teletraffic networks.