An Optimal Algorithm for the Maximum-Density Segment Problem

We address a fundamental problem arising from analysis of biomolecular sequences. The input consists of two numbers $w_{\min}$ and $w_{\max}$ and a sequence $S$ of $n$ number pairs $(a_i,w_i)$ with $w_i>0$. Let {\em segment} $S(i,j)$ of $S$ be the consecutive subsequence of $S$ between indices $i$ and $j$. The {\em density} of $S(i,j)$ is $d(i,j)=(a_i+a_{i+1}+...+a_j)/(w_i+w_{i+1}+...+w_j)$. The {\em maximum-density segment problem} is to find a maximum-density segment over all segments $S(i,j)$ with $w_{\min}\leq w_i+w_{i+1}+...+w_j \leq w_{\max}$. The best previously known algorithm for the problem, due to Goldwasser, Kao, and Lu, runs in $O(n\log(w_{\max}-w_{\min}+1))$ time. In the present paper, we solve the problem in O(n) time. Our approach bypasses the complicated {\em right-skew decomposition}, introduced by Lin, Jiang, and Chao. As a result, our algorithm has the capability to process the input sequence in an online manner, which is an important feature for dealing with genome-scale sequences. Moreover, for a type of input sequences $S$ representable in $O(m)$ space, we show how to exploit the sparsity of $S$ and solve the maximum-density segment problem for $S$ in $O(m)$ time.Comment: 15 pages, 12 figures, an early version of this paper was presented at 11th Annual European Symposium on Algorithms (ESA 2003), Budapest, Hungary, September 15-20, 200

The Mystery of Two Straight Lines in Bacterial Genome Statistics. Release 2007

In special coordinates (codon position--specific nucleotide frequencies) bacterial genomes form two straight lines in 9-dimensional space: one line for eubacterial genomes, another for archaeal genomes. All the 348 distinct bacterial genomes available in Genbank in April 2007, belong to these lines with high accuracy. The main challenge now is to explain the observed high accuracy. The new phenomenon of complementary symmetry for codon position--specific nucleotide frequencies is observed. The results of analysis of several codon usage models are presented. We demonstrate that the mean--field approximation, which is also known as context--free, or complete independence model, or Segre variety, can serve as a reasonable approximation to the real codon usage. The first two principal components of codon usage correlate strongly with genomic G+C content and the optimal growth temperature respectively. The variation of codon usage along the third component is related to the curvature of the mean-field approximation. First three eigenvalues in codon usage PCA explain 59.1%, 7.8% and 4.7% of variation. The eubacterial and archaeal genomes codon usage is clearly distributed along two third order curves with genomic G+C content as a parameter.Comment: Significantly extended version with new data for all the 348 distinct bacterial genomes available in Genbank in April 200

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.Comment: 16 page

Does codon bias have an evolutionary origin?

<p>Abstract</p> <p>Background</p> <p>There is a 3-fold redundancy in the Genetic Code; most amino acids are encoded by more than one codon. These synonymous codons are not used equally; there is a Codon Usage Bias (CUB). This article will provide novel information about the origin and evolution of this bias.</p> <p>Results</p> <p>Codon Usage Bias (CUB, defined here as deviation from equal usage of synonymous codons) was studied in 113 species. The average CUB was 29.3 ± 1.1% (S.E.M, n = 113) of the theoretical maximum and declined progressively with evolution and increasing genome complexity. A Pan-Genomic Codon Usage Frequency (CUF) Table was constructed to describe genome-wide relationships among codons. Significant correlations were found between the number of synonymous codons and (i) the frequency of the respective amino acids (ii) the size of CUB. Numerous, statistically highly significant, internal correlations were found among codons and the nucleic acids they comprise. These strong correlations made it possible to predict missing synonymous codons (wobble bases) reliably from the remaining codons or codon residues.</p> <p>Conclusion</p> <p>The results put the concept of "codon bias" into a novel perspective. The internal connectivity of codons indicates that all synonymous codons might be integrated parts of the Genetic Code with equal importance in maintaining its functional integrity.</p

Eustatic change modulates exhumation in the Japanese Alps

The exhumation of bedrock is controlled by the interplay between tectonics, surface processes, and climate. The highest exhumation rates of centimeters per year are recorded in zones of highly active tectonic convergence such as the Southern Alps of New Zealand or the Himalayan syntaxes, where high rock uplift rates combine with very active surface processes. Using a combination of different thermochronometric systems including trapped-charge thermochronometry, we show that such rates also occur in the Hida Mountain Range, Japanese Alps. Our results imply that centimeter per year rates of exhumation are more common than previously thought. Our thermochronometry data allow the development of time series of exhumation rate changes at the time scale of glacial-interglacial cycles, which show a fourfold increase in baseline rates to rates of ~10 mm/yr within the past ~65 k.y. This increase in exhumation rate is likely explained by knickpoint propagation due to a combination of very high precipitation rates, climatic change, sea-level fall, range-front faulting, and moderate rock uplift. Our data resolve centimeter-scale sub-Quaternary exhumation rate changes, which show that in regions with horizontal convergence, coupling between climate, surface processes, and tectonics can exert a significant and rapid effect on rates of exhumatio

Spin-dependent transport in metal/semiconductor tunnel junctions

This paper describes a model as well as experiments on spin-polarized tunnelling with the aid of optical spin orientation. This involves tunnel junctions between a magnetic material and gallium arsenide (GaAs), where the latter is optically excited with circularly polarized light in order to generate spin-polarized carriers. A transport model is presented that takes account of carrier capture in the semiconductor surface states, and describes the semiconductor surface in terms of a spin-dependent energy distribution function. The so-called surface spin-splitting can be calculated from the balance of the polarized electron and hole flow in the semiconductor subsurface region, the polarized tunnelling current across the tunnel barrier between the magnetic material and the semiconductor surface, and the spin relaxation at the semiconductor surface. Measurements are presented of the circular-polarization-dependent photocurrent (the so-called helicity asymmetry) in thin-film tunnel junctions of Co/Al2O3/GaAs. In the absence of a tunnel barrier, the helicity asymmetry is caused by magneto-optical effects (magnetic circular dichroism). In the case where a tunnel barrier is present, the data cannot be explained by magneto-optical effects alone; the deviations provide evidence that spin-polarized tunnelling due to optical spin orientation occurs. In Co/τ-MnAl/AlAs/GaAs junctions no deviations from the magneto-optical effects are observed, most probably due to the weak spin polarization of τ-MnAl along the tunnelling direction; the latter is corroborated by bandstructure calculations. Finally, the application of photoexcited GaAs for spin-polarized tunnelling in a scanning tunnelling microscope is discussed.