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.

Chiral molecular self-assembly of phospholipid tubules: A circular dichroism study

We report on spectroscopic studies of the chiral structure in phospholipid tubules formed in mixtures of alcohol and water. Synthetic phospholipids containing diacetylenic moieties in the acyl chains self-assemble into hollow, cylindrical tubules in appropriate conditions. Circular dichroism provides a direct measure of chirality of the molecular structure. We find that the CD spectra of tubules formed in mixtures of alcohol and water depends strongly on the alcohol used and the lipid concentration. The relative spectral intensity of different circular dichroism bands correlates with the number of bilayers observed using microscopy. The results provide experimental evidence that tubule formation is based on chiral packing of the lipid molecules and that interbilayer interactions are important to the tubule structure.

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.

Site-specific conformational determination in thermal unfolding studies of helical peptides using vibrational circular dichroism with isotopic substitution

Understanding the detailed mechanism of protein folding requires dynamic, site-specific stereochemical information. The short time response of vibrational spectroscopies allows evaluation of the distribution of populations in rapid equilibrium as the peptide unfolds. Spectral shifts associated with isotopic labels along with local stereochemical sensitivity of vibrational circular dichroism (VCD) allow determination of the segment sequence of unfolding. For a series of alanine-rich peptides that form α-helices in aqueous solution, we used isotopic labeling and VCD to demonstrate that the α-helix noncooperatively unwinds from the ends with increasing temperature. For these blocked peptides, the C-terminal is frayed at 5°C. Ab initio level theoretical simulations of the IR and VCD band shapes are used to analyze the spectra and to confirm the conformation of the labeled components. The VCD signals associated with the labeled residues are amplified by coupling to the nonlabeled parts of the molecule. Thus small labeled segments are detectable and stereochemically defined in moderately large peptides in this report of site-specific peptide VCD conformational analysis.

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.

Least activation path for protein folding: investigation of staphylococcal nuclease folding by stopped-flow circular dichroism.

Is the pathway of protein folding determined by the relative stability of folding intermediates, or by the relative height of the activation barriers leading to these intermediates? This is a fundamental question for resolving the Levinthal paradox, which stated that protein folding by a random search mechanism would require a time too long to be plausible. To answer this question, we have studied the guanidinium chloride (GdmCl)-induced folding/unfolding of staphylococcal nuclease [(SNase, formerly EC 3.1.4.7; now called microbial nuclease or endonuclease, EC 3.1.31.1] by stopped-flow circular dichroism (CD) and differential scanning microcalorimetry (DSC). The data show that while the equilibrium transition is a quasi-two-state process, kinetics in the 2-ms to 500-s time range are triphasic. Data support the sequential mechanism for SNase folding: U3 <--> U2 <--> U1 <--> N0, where U1, U2, and U3 are substates of the unfolded protein and N0 is the native state. Analysis of the relative population of the U1, U2, and U3 species in 2.0 M GdmCl gives delta-G values for the U3 --> U2 reaction of +0.1 kcal/mol and for the U2 --> U1 reaction of -0.49 kcal/mol. The delta-G value for the U1 --> N0 reaction is calculated to be -4.5 kcal/mol from DSC data. The activation energy, enthalpy, and entropy for each kinetic step are also determined. These results allow us to make the following four conclusions. (i) Although the U1, U2, and U3 states are nearly isoenergetic, no random walk occurs among them during the folding. The pathway of folding is unique and sequential. In other words, the relative stability of the folding intermediates does not dictate the folding pathway. Instead, the folding is a descent toward the global free-energy minimum of the native state via the least activation path in the vast energy landscape. Barrier avoidance leads the way, and barrier height limits the rate. Thus, the Levinthal paradox is not applicable to the protein-folding problem. (ii) The main folding reaction (U1 --> N0), in which the peptide chain acquires most of its free energy (via van der Waals' contacts, hydrogen bonding, and electrostatic interactions), is a highly concerted process. These energy-acquiring events take place in a single kinetic phase. (iii) U1 appears to be a compact unfolded species; the rate of conversion of U2 to U1 depends on the viscosity of solution. (iv) All four relaxation times reported here depend on GdmCl concentrations: it is likely that none involve the cis/trans isomerization of prolines. Finally, a mechanism is presented in which formation of sheet-like chain conformations and a hydrophobic condensation event precede the main-chain folding reaction.

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.