[Circular dirigida a todos los corregidores y gobernadores del Reino, para que según reales ordenes cobren de los comerciantes y envien al tesorero de la Junta de Comercio D. Fernando Galán la tercera parte de un prestamo... [Texto impreso]

Hay un ejemplar encuadernado con: La Real Compañia formada por S.M. para llevar a efecto el canal de navegación y riego del reyno de Murcia, las... experiencias de que informa D. Domingo Aguirre... le han confirmado en los abusos y fraudes que hacen muchos... (XVIII/4279).

[Circular enviada por Xavier Elío informando sobre la necesidad de usas pasaporte para circular por España] [Texto impreso]

Hay un ejemplar encuadernado con: La Real Compañia formada por S.M. para llevar a efecto el canal de navegación y riego del reyno de Murcia, las... experiencias de que informa D. Domingo Aguirre... le han confirmado en los abusos y fraudes que hacen muchos... (XVIII/4279).

Geometry of circular vectors and pattern recognition of shape of a boundary

This paper deals with pattern recognition of the shape of the boundary of closed figures on the basis of a circular sequence of measurements taken on the boundary at equal intervals of a suitably chosen argument with an arbitrary starting point. A distance measure between two boundaries is defined in such a way that it has zero value when the associated sequences of measurements coincide by shifting the starting point of one of the sequences. Such a distance measure, which is invariant to the starting point of the sequence of measurements, is used in identification or discrimination by the shape of the boundary of a closed figure. The mean shape of a given set of closed figures is defined, and tests of significance of differences in mean shape between populations are proposed.

Equilibrium distributions of topological states in circular DNA: Interplay of supercoiling and knotting

Two variables define the topological state of closed double-stranded DNA: the knot type, K, and ΔLk, the linking number difference from relaxed DNA. The equilibrium distribution of probabilities of these states, P(ΔLk, K), is related to two conditional distributions: P(ΔLk|K), the distribution of ΔLk for a particular K, and P(K|ΔLk) and also to two simple distributions: P(ΔLk), the distribution of ΔLk irrespective of K, and P(K). We explored the relationships between these distributions. P(ΔLk, K), P(ΔLk), and P(K|ΔLk) were calculated from the simulated distributions of P(ΔLk|K) and of P(K). The calculated distributions agreed with previous experimental and theoretical results and greatly advanced on them. Our major focus was on P(K|ΔLk), the distribution of knot types for a particular value of ΔLk, which had not been evaluated previously. We found that unknotted circular DNA is not the most probable state beyond small values of ΔLk. Highly chiral knotted DNA has a lower free energy because it has less torsional deformation. Surprisingly, even at |ΔLk| > 12, only one or two knot types dominate the P(K|ΔLk) distribution despite the huge number of knots of comparable complexity. A large fraction of the knots found belong to the small family of torus knots. The relationship between supercoiling and knotting in vivo is discussed.

The Vibrio cholerae genome contains two unique circular chromosomes

Vibrio cholerae, the etiologic agent of the diarrheal disease cholera, is a Gram-negative bacterium that belongs to the γ subdivision of the family Proteobacteriaceae. The physical map of the genome has been reported, and the genome has been described as a single 3.2-Mb chromosome [Majumder, R., et al. (1996) J. Bacteriol. 178, 1105–1112]. By using pulsed-field gel electrophoresis of genomic DNA immobilized in agarose plugs and digested with the restriction enzymes I-CeuI, SfiI, and NotI, we have also constructed the physical map of V. cholerae. Our analysis estimates the size of the genome at 4.0 Mb, 25% larger than the physical map reported by others. Our most notable finding is, however, that the V. cholerae chromosome appears to be not the single chromosome reported but two unique and separate circular megareplicons.

BAliBASE (Benchmark Alignment dataBASE): enhancements for repeats, transmembrane sequences and circular permutations

BAliBASE is specifically designed to serve as an evaluation resource to address all the problems encountered when aligning complete sequences. The database contains high quality, manually constructed multiple sequence alignments together with detailed annotations. The alignments are all based on three-dimensional structural superpositions, with the exception of the transmembrane sequences. The first release provided sets of reference alignments dealing with the problems of high variability, unequal repartition and large N/C-terminal extensions and internal insertions. Here we describe version 2.0 of the database, which incorporates three new reference sets of alignments containing structural repeats, trans­membrane sequences and circular permutations to evaluate the accuracy of detection/prediction and alignment of these complex sequences. BAliBASE can be viewed at the web site http://www-igbmc.u-strasbg.fr/BioInfo/BAliBASE2/index.html or can be downloaded from ftp://ftp-igbmc.u-strasbg.fr/pub/BAliBASE2/.

Random circular permutation of genes and expressed polypeptide chains: application of the method to the catalytic chains of aspartate transcarbamoylase.

Recent studies on proteins whose N and C termini are in close proximity have demonstrated that folding of polypeptide chains and assembly of oligomers can be accomplished with circularly permuted chains. As yet no methodical study has been conducted to determine how extensively new termini can be introduced and where such termini cannot be tolerated. We have devised a procedure to generate random circular permutations of the catalytic chains of Escherichia coli aspartate transcarbamoylase (ATCase; EC 2.1.3.2) and to select clones that produce active or stable holoenzyme containing permuted chains. A tandem gene construct was made, based on the desired linkage between amino acid residues in the C- and N-terminal regions of the polypeptide chain, and this DNA was treated with a suitable restriction enzyme to yield a fragment containing the rearranged coding sequence for the chain. Circularization achieved with DNA ligase, followed by linearization at random with DNase I, and incorporation of the linearized, repaired, blunt-ended, rearranged genes into a suitable plasmid permitted the expression of randomly permuted polypeptide chains. The plasmid with appropriate stop codons also contained pyrI, the gene encoding the regulatory chain of ATCase. Colonies expressing detectable amounts of ATCase-like molecules containing permuted catalytic chains were identified by an immunoblot technique or by their ability to grow in the absence of pyrimidines in the growth medium. Sequencing of positive clones revealed a variety of novel circular permutations. Some had N and C termini within helices of the wild-type enzyme as well as deletions and insertions. Permutations were concentrated in the C-terminal domain and only few were detected in the N-terminal domain. The technique, which is adaptable generally to proteins whose N and C termini are near each other, can be of value in relating in vivo folding of nascent, growing polypeptide chains to in vitro renaturation of complete chains and determining the role of protein sequence in folding kinetics.

Circular RNAs from transcripts of the rat cytochrome P450 2C24 gene: correlation with exon skipping.

The cytochrome P450 2C24 gene is characterized by the capability to generate, in rat kidney, a transcript containing exons 2 and 4 spliced at correct sites but having the donor site of exon 4 directly joined to the acceptor site of exon 2 (exon scrambling). By reverse transcriptase-PCR analysis, it is now shown that the only exons present in the scrambled transcript are exons 2, 3, and 4 and that this molecule lacks a poly(A)+ tail. Furthermore, the use of PCR primers in both orientations of either exon 2 or exon 4 revealed that the orders of the exons in the scrambled transcript are 2-3-4-2 and 4-2-3-4, respectively. These results, combined with the observation that P450 2C24 is a single-copy gene, with no duplication of the exon 2 to exon 4 segment, suggest that the scrambled transcript has properties consistent with that of a circular molecule. In line with this is the observation of an increased resistance of the transcript to phosphodiesterase I, a 3'-exonuclease. Moreover, an alternatively processed cytochrome P450 2C24 mRNA, lacking the three scrambled exons and having exon 1 directly joined to exon 5, has been identified in kidney and liver, tissues that express the scrambled transcript. This complete identity of the exons that are absent in the alternatively processed mRNA but present in the scrambled transcript is interpreted as indicative of the possibility that exon scrambling and exon skipping might be interrelated phenomena. It is therefore proposed that alternative pre-mRNA processing has the potential to generate not only mRNAs lacking one or more exons but also circular RNA molecules.

Origin and evolution of circular waves and spirals in Dictyostelium discoideum territories.

Randomly distributed Dictyostelium discoideum cells form cooperative territories by signaling to each other with cAMP. Cells initiate the process by sending out pulsatile signals, which propagate as waves. With time, circular and spiral patterns form. We show that by adding spatial and temporal noise to the levels of an important regulator of external cAMP levels, the cAMP phosphodiesterase inhibitor, we can explain the natural progression of the system from randomly firing cells to circular waves whose symmetries break to form double- and single- or multi-armed spirals. When phosphodiesterase inhibitor is increased with time, mimicking experimental data, the wavelength of the spirals shortens, and a proportion of them evolve into pairs of connected spirals. We compare these results to recent experiments, finding that the temporal and spatial correspondence between experiment and model is very close.

Data analysis using circular causality in networks

Complex systems in causal relationships are known to be circular rather than linear; this means that a particular result is not produced by a single cause, but rather that both positive and negative feedback processes are involved. However, although interpreting systemic interrelationships requires a language formed by circles, this has only been developed at the diagram level, and not from an axiomatic point of view. The first difficulty encountered when analysing any complex system is that usually the only data available relate to the various variables, so the first objective was to transform these data into cause-and-effect relationships. Once this initial step was taken, our discrete chaos theory could be applied by finding the causal circles that will form part of the system attractor and allow their behavior to be interpreted. As an application of the technique presented, we analyzed the system associated with the transcription factors of inflammatory diseases.