Review on computational methods for Lyapunov functions

Lyapunov functions are an essential tool in the stability analysis of dynamical systems, both in theory and applications. They provide sufficient conditions for the stability of equilibria or more general invariant sets, as well as for their basin of attraction. The necessity, i.e. the existence of Lyapunov functions, has been studied in converse theorems, however, they do not provide a general method to compute them. Because of their importance in stability analysis, numerous computational construction methods have been developed within the Engineering, Informatics, and Mathematics community. They cover different types of systems such as ordinary differential equations, switched systems, non-smooth systems, discrete-time systems etc., and employ di_erent methods such as series expansion, linear programming, linear matrix inequalities, collocation methods, algebraic methods, set-theoretic methods, and many others. This review brings these different methods together. First, the different types of systems, where Lyapunov functions are used, are briefly discussed. In the main part, the computational methods are presented, ordered by the type of method used to construct a Lyapunov function

Molecular Characterization of a 21.4 Kilobase Antibiotic Resistance Plasmid from an α-Hemolytic Escherichia coli O108:H- Human Clinical Isolate

This study characterizes the 21.4 kilobase plasmid pECTm80 isolated from Escherichia coli strain 80, an α hemolytic human clinical diarrhoeal isolate (serotype O108:H-). DNA sequence analysis of pECTm80 revealed it belonged to incompatibility group X1, and contained plasmid partition and toxin-antitoxin systems, an R6K-like triple origin (ori) replication system, genes required for replication regulation, insertion sequences IS1R, ISEc37 and a truncated transposase gene (Tn3-like ΔtnpA) of the Tn3 family, and carried a class 2 integron. The class 2 integron of pECTm80 contains an intact cassette array dfrA1-sat2, encoding resistance to trimethoprim and streptothricin, and an aadA1 gene cassette truncated by the insertion of IS1R. The complex plasmid replication system includes α, β and γ origins of replication. Pairwise BLASTn comparison of pECTm80 with plasmid pE001 reveals a conserved plasmid backbone suggestive of a common ancestral lineage. Plasmid pECTm80 is of potential clinical importance, as it carries multiple genes to ensure its stable maintenance through successive bacterial cell divisions and multiple antibiotic resistance genes

Influence of DNA topology on expression of the tdc operon in Escherichia coli K-12

TdcB activity expressed from the chromosomal gene and LacZ expression from single-copy tdc-lacZ transcriptional and translational fusions were measured in Escherichia coli strains harboring mutations in the genes encoding DNA gyrase, topoisomerase I and the HU protein. The pattern of tdc operon expression in these mutants suggests that relaxation of supercoiled DNA enhances tdc transcription in vivo.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47585/1/438_2004_Article_BF00290409.pd

Imaging of Bubonic Plague Dynamics by In Vivo Tracking of Bioluminescent Yersinia pestis

Yersinia pestis dissemination in a host is usually studied by enumerating bacteria in the tissues of animals sacrificed at different times. This laborious methodology gives only snapshots of the infection, as the infectious process is not synchronized. In this work we used in vivo bioluminescence imaging (BLI) to follow Y. pestis dissemination during bubonic plague. We first demonstrated that Y. pestis CO92 transformed with pGEN-luxCDABE stably emitted bioluminescence in vitro and in vivo, while retaining full virulence. The light produced from live animals allowed to delineate the infected organs and correlated with bacterial loads, thus validating the BLI tool. We then showed that the first step of the infectious process is a bacterial multiplication at the injection site (linea alba), followed by a colonization of the draining inguinal lymph node(s), and subsequently of the ipsilateral axillary lymph node through a direct connection between the two nodes. A mild bacteremia and an effective filtering of the blood stream by the liver and spleen probably accounted for the early bacterial blood clearance and the simultaneous development of bacterial foci within these organs. The saturation of the filtering capacity of the spleen and liver subsequently led to terminal septicemia. Our results also indicate that secondary lymphoid tissues are the main targets of Y. pestis multiplication and that colonization of other organs occurs essentially at the terminal phase of the disease. Finally, our analysis reveals that the high variability in the kinetics of infection is attributable to the time the bacteria remain confined at the injection site. However, once Y. pestis has reached the draining lymph nodes, the disease progresses extremely rapidly, leading to the invasion of the entire body within two days and to death of the animals. This highlights the extraordinary capacity of Y. pestis to annihilate the host innate immune response

The NlpD Lipoprotein Is a Novel Yersinia pestis Virulence Factor Essential for the Development of Plague

Yersinia pestis is the causative agent of plague. Previously we have isolated an attenuated Y. pestis transposon insertion mutant in which the pcm gene was disrupted. In the present study, we investigated the expression and the role of pcm locus genes in Y. pestis pathogenesis using a set of isogenic surE, pcm, nlpD and rpoS mutants of the fully virulent Kimberley53 strain. We show that in Y. pestis, nlpD expression is controlled from elements residing within the upstream genes surE and pcm. The NlpD lipoprotein is the only factor encoded from the pcm locus that is essential for Y. pestis virulence. A chromosomal deletion of the nlpD gene sequence resulted in a drastic reduction in virulence to an LD50 of at least 107 cfu for subcutaneous and airway routes of infection. The mutant was unable to colonize mouse organs following infection. The filamented morphology of the nlpD mutant indicates that NlpD is involved in cell separation; however, deletion of nlpD did not affect in vitro growth rate. Trans-complementation experiments with the Y. pestis nlpD gene restored virulence and all other phenotypic defects. Finally, we demonstrated that subcutaneous administration of the nlpD mutant could protect animals against bubonic and primary pneumonic plague. Taken together, these results demonstrate that Y. pestis NlpD is a novel virulence factor essential for the development of bubonic and pneumonic plague. Further, the nlpD mutant is superior to the EV76 prototype live vaccine strain in immunogenicity and in conferring effective protective immunity. Thus it could serve as a basis for a very potent live vaccine against bubonic and pneumonic plague

Concentration-dependent organization of DNA by the dinoflagellate histone-like protein HCc3

The liquid crystalline chromosomes of dinoflagellates are the alternative to the nucleosome-based organization of chromosomes in the eukaryotes. These nucleosome-less chromosomes have to devise novel ways to maintain active parts of the genome. The dinoflagellate histone-like protein HCc3 has significant sequence identity with the bacterial DNA-binding protein HU. HCc3 also has a secondary structure resembling HU in silico. We have examined HCc3 in its recombinant form. Experiments on DNA-cellulose revealed its DNA-binding activity is on the C-terminal domain. The N-terminal domain is responsible for intermolecular oligomerization as demonstrated by cross-linking studies. However, HCc3 could not complement Escherichia coli HU-deficient mutants, suggesting functional differences. In ligation assays, HCc3-induced DNA concatenation but not ring closure as the DNA-bending HU does. The basic HCc3 was an efficient DNA condensing agent, but it did not behave like an ordinary polycationic compound. HCc3 also induced specific structures with DNA in a concentration-dependent manner, as demonstrated by atomic force microscopy (AFM). At moderate concentration of HCc3, DNA bridging and bundling were observed; at high concentrations, the complexes were even more condensed. These results are consistent with a biophysical role for HCc3 in maintaining extended DNA loops at the periphery of liquid crystalline chromosomes

Concentration-dependent organization of DNA by the dinoflagellate histone-like protein HCc3

The liquid crystalline chromosomes of dinoflagellates are the alternative to the nucleosome-based organization of chromosomes in the eukaryotes. These nucleosome-less chromosomes have to devise novel ways to maintain active parts of the genome. The dinoflagellate histone-like protein HCc3 has significant sequence identity with the bacterial DNA-binding protein HU. HCc3 also has a secondary structure resembling HU in silico. We have examined HCc3 in its recombinant form. Experiments on DNA-cellulose revealed its DNA-binding activity is on the C-terminal domain. The N-terminal domain is responsible for intermolecular oligomerization as demonstrated by cross-linking studies. However, HCc3 could not complement Escherichia coli HU-deficient mutants, suggesting functional differences. In ligation assays, HCc3-induced DNA concatenation but not ring closure as the DNA-bending HU does. The basic HCc3 was an efficient DNA condensing agent, but it did not behave like an ordinary polycationic compound. HCc3 also induced specific structures with DNA in a concentration-dependent manner, as demonstrated by atomic force microscopy (AFM). At moderate concentration of HCc3, DNA bridging and bundling were observed; at high concentrations, the complexes were even more condensed. These results are consistent with a biophysical role for HCc3 in maintaining extended DNA loops at the periphery of liquid crystalline chromosomes

Analysis of In-Vivo LacR-Mediated Gene Repression Based on the Mechanics of DNA Looping

Interactions of E. coli lac repressor (LacR) with a pair of operator sites on the same DNA molecule can lead to the formation of looped nucleoprotein complexes both in vitro and in vivo. As a major paradigm for loop-mediated gene regulation, parameters such as operator affinity and spacing, repressor concentration, and DNA bending induced by specific or non-specific DNA-binding proteins (e.g., HU), have been examined extensively. However, a complete and rigorous model that integrates all of these aspects in a systematic and quantitative treatment of experimental data has not been available. Applying our recent statistical-mechanical theory for DNA looping, we calculated repression as a function of operator spacing (58–156 bp) from first principles and obtained excellent agreement with independent sets of in-vivo data. The results suggest that a linear extended, as opposed to a closed v-shaped, LacR conformation is the dominant form of the tetramer in vivo. Moreover, loop-mediated repression in wild-type E. coli strains is facilitated by decreased DNA rigidity and high levels of flexibility in the LacR tetramer. In contrast, repression data for strains lacking HU gave a near-normal value of the DNA persistence length. These findings underscore the importance of both protein conformation and elasticity in the formation of small DNA loops widely observed in vivo, and demonstrate the utility of quantitatively analyzing gene regulation based on the mechanics of nucleoprotein complexes

Identification of Chromosomal Genes in Yersinia pestis that Influence Type III Secretion and Delivery of Yops into Target Cells

Pathogenic Yersinia species possess a type III secretion system, which is required for the delivery of effector Yop proteins into target cells during infection. Genes encoding the type III secretion machinery, its substrates, and several regulatory proteins all reside on a 70-Kb virulence plasmid. Genes encoded in the chromosome of yersiniae are thought to play important roles in bacterial perception of host environments and in the coordinated activation of the type III secretion pathway. Here, we investigate the contribution of chromosomal genes to the complex regulatory process controlling type III secretion in Yersinia pestis. Using transposon mutagenesis, we identified five chromosomal genes required for expression or secretion of Yops in laboratory media. Four out of the five chromosomal mutants were defective to various extents at injecting Yops into tissue culture cells. Interestingly, we found one mutant that was not able to secrete in vitro but was fully competent for injecting Yops into host cells, suggesting independent mechanisms for activation of the secretion apparatus. When tested in a mouse model of plague disease, three mutants were avirulent, whereas two strains were severely attenuated. Together these results demonstrate the importance of Y. pestis chromosomal genes in the proper function of type III secretion and in the pathogenesis of plague