Pedro Miramontes

On the evolution of the single-subunit RNA polymerases

Abstract. Many eukaryotic nuclear genomes as well as mitochondrial plasmids contain genes displaying evident sequence similarity to those encoding the single-subunit RNA polymerase (ssRNAP) of bacteriophage T7 and its relatives. We have collected and aligned these ssRNAP sequences and have constructed unrooted phylogenetic trees that demonstrate the separation of ssRNAPs into three well-defined and nonoverlapping clusters (phage-encoded, nucleus-encoded, and plasmid-encoded). Our analyses indicate that these three subfamiles of T7-like RNAPs shared a common ancestor; however, the order in which the groups diverged cannot be inferred from available data. On the basis of structural similarities and mutational data, we suggest that the ancestral ssRNAP gene may have arisen via duplication and divergence of a DNA polymerase or reverse transcriptase gene. Considering the current phylogenetic distribution of ssRNAP sequences, we further suggest that the origin of the ancestral ssRNAP gene closely paralleled in time the introduction of mitochondria into eukaryotic cells through a eubacterial endosymbiosis.

Universality of Rank-Ordering Distributions in the Arts and Sciences

Searching for generic behaviors has been one of the driving forces leading to a deep understanding and classification of diverse phenomena. Usually a starting point is the development of a phenomenology based on observations. Such is the case for power law distributions encountered in a wealth of situations coming from physics, geophysics, biology, lexicography as well as social and financial networks. This finding is however restricted to a range of values outside of which finite size corrections are often invoked. Here we uncover a universal behavior of the way in which elements of a system are distributed according to their rank with respect to a given property, valid for the full range of values, regardless of whether or not a power law has previously been suggested. We propose a two parameter functional form for these rank-ordered distributions that gives excellent fits to an impressive amount of very diverse phenomena, coming from the arts, social and natural sciences. It is a discrete version of a generalized beta distribution, given by f(r) = A(N+1-r)b/ra, where r is the rank, N its maximum value, A the normalization constant and (a, b) two fitting exponents. Prompted by our genetic sequence observations we present a growth probabilistic model incorporating mutation-duplication features that generates data complying with this distribution. The competition between permanence and change appears to be a relevant, though not necessary feature. Additionally, our observations mainly of social phenomena suggest that a multifactorial quality resulting from the convergence of several heterogeneous underlying processes is an important feature. We also explore the significance of the distribution parameters and their classifying potential. The ubiquity of our findings suggests that there must be a fundamental underlying explanation, most probably of a statistical nature, such as an appropriate central limit theorem formulation.

On the behavior of journal impact factor rank-order distribution

An empirical law for the rank-order behavior of journal impact factors is found. Using an extensive data base on impact factors including journals on education, agrosciences, geosciences, mathematics, chemistry, medicine, engineering, physics, biosciences and environmental, computer and material sciences, we have found extremely good fittings outperforming other rank-order models. Based in our results, we propose a two-exponent Lotkaian Informetrics. Some extensions to other areas of knowledge are discussed.

Fitting Ranked Linguistic Data with Two-Parameter Functions

It is well known that many ranked linguistic data can fit well with one-parameter models such as Zipf’s law for ranked word frequencies. However, in cases where discrepancies from the one-parameter model occur (these will come at the two extremes of the rank), it is natural to use one more parameter in the fitting model. In this paper, we compare several two-parameter models, including Beta function, Yule function, Weibull function—all can be framed as a multiple regression in the logarithmic scale—in their fitting performance of several ranked linguistic data, such as letter frequencies, word-spacings, and word frequencies. We observed that Beta function fits the ranked letter frequency the best, Yule function fits the ranked word-spacing distribution the best, and Altmann, Beta, Yule functions all slightly outperform the Zipf’s power-law function in word ranked- frequency distribution.

Diminishing return for increased Mappability with longer sequencing reads: implications of the k-mer distributions in the human genome

BackgroundThe amount of non-unique sequence (non-singletons) in a genome directly affects the difficulty of read alignment to a reference assembly for high throughput-sequencing data. Although a longer read is more likely to be uniquely mapped to the reference genome, a quantitative analysis of the influence of read lengths on mappability has been lacking. To address this question, we evaluate the k-mer distribution of the human reference genome. The k-mer frequency is determined for k ranging from 20 bp to 1000 bp.ResultsWe observe that the proportion of non-singletons k-mers decreases slowly with increasing k, and can be fitted by piecewise power-law functions with different exponents at different ranges of k. A slower decay at greater values for k indicates more limited gains in mappability for read lengths between 200 bp and 1000 bp. The frequency distributions of k-mers exhibit long tails with a power-law-like trend, and rank frequency plots exhibit a concave Zipf’s curve. The most frequent 1000-mers comprise 172 regions, which include four large stretches on chromosomes 1 and X, containing genes of biomedical relevance. Comparison with other databases indicates that the 172 regions can be broadly classified into two types: those containing LINE transposable elements and those containing segmental duplications.ConclusionRead mappability as measured by the proportion of singletons increases steadily up to the length scale around 200 bp. When read length increases above 200 bp, smaller gains in mappability are expected. Moreover, the proportion of non-singletons decreases with read lengths much slower than linear. Even a read length of 1000 bp would not allow the unique alignment of reads for many coding regions of human genes. A mix of techniques will be needed for efficiently producing high-quality data that cover the complete human genome.

Fitting Ranked English and Spanish Letter Frequency Distribution in US and Mexican Presidential Speeches

Abstract The limited range in the abscissa of ranked letter frequency distributions causes multiple functions to fit the observed distribution reasonably well. In order to critically compare various functions, we apply the statistical model selections on ten functions, using the texts of US and Mexican presidential speeches of the last few centuries. Despite minor switching of ranking order of certain letters during the temporal evolution for both datasets, the letter usage is generally stable. The best fitting function, judged by either least-square-error or by AIC/BIC model selection, is the Cocho/Beta function. We also use a novel method to discover clusters of letters by their observed-over-expected frequency ratios.

The puzzling origin of the genetic code

Recent results add to the mystery of the origin of the genetic code. In spite of early doubts, RNA can discriminate between hydrophobic amino acids under certain contexts. Moreover, codon reassignment, which has taken place in several organisms and mitochondria, is not a random process. Finally, phylogenies of some aminoacyl-tRNA synthetases suggest that the entire code was not completely assigned at the time of the divergence of bacteria from nucleated cells.

Structural and Thermodynamic Properties of DNA Uncover Different Evolutionary Histories

We propose an index of DNA homogeneity (IDH) based on a binary distribution model that quantifies structural and thermodynamic aggregates present in DNA primary structures. Extensive analysis of sequence databases with the IDH uncovers significant constraints on DNA sequence other than those derived from codon usage or protein function. This index clearly distinguishes between organisms of different evolutive origins and places them in disjoint domains of DNA sequence space.

Bacterial genomes lacking long-range correlations may not be modeled by low-order Markov chains

We examine the relationship between exponential correlation functions and Markov models in a bacterial genome in detail. Despite the well known fact that Markov models generate sequences with correlation function that decays exponentially, simply constructed Markov models based on nearest-neighbor dimer (first-order), trimer (second-order), up to hexamer (fifth-order), and treating the DNA sequence as being homogeneous all fail to predict the value of exponential decay rate. Even reading-frame-specific Markov models (both first- and fifth-order) could not explain the fact that the exponential decay is very slow. Starting with the in-phase coding-DNA-sequence (CDS), we investigated correlation within a fixed-codon-position subsequence, and in artificially constructed sequences by packing CDSs with out-of-phase spacers, as well as altering CDS length distribution by imposing an upper limit. From these targeted analyses, we conclude that the correlation in the bacterial genomic sequence is mainly due to a mixing of heterogeneous statistics at different codon positions, and the decay of correlation is due to the possible out-of-phase between neighboring CDSs. There are also small contributions to the correlation from bases at the same codon position, as well as by non-coding sequences. These show that the seemingly simple exponential correlation functions in bacterial genome hide a complexity in correlation structure which is not suitable for a modeling by Markov chain in a homogeneous sequence. Other results include: use of the (absolute value) second largest eigenvalue to represent the 16 correlation functions and the prediction of a 10-11 base periodicity from the hexamer frequencies.

Beyond Zipf’s Law: The Lavalette Rank Function and Its Properties

Although Zipf’s law is widespread in natural and social data, one often encounters situations where one or both ends of the ranked data deviate from the power-law function. Previously we proposed the Beta rank function to improve the fitting of data which does not follow a perfect Zipf’s law. Here we show that when the two parameters in the Beta rank function have the same value, the Lavalette rank function, the probability density function can be derived analytically. We also show both computationally and analytically that Lavalette distribution is approximately equal, though not identical, to the lognormal distribution. We illustrate the utility of Lavalette rank function in several datasets. We also address three analysis issues on the statistical testing of Lavalette fitting function, comparison between Zipf’s law and lognormal distribution through Lavalette function, and comparison between lognormal distribution and Lavalette distribution.