A Universal Approximation Result for Difference of Log-Sum-Exp Neural Networks.

We show that a neural network whose output is obtained as the difference of the outputs of two feedforward networks with exponential activation function in the hidden layer and logarithmic activation function in the output node, referred to as log-sum-exp (LSE) network, is a smooth universal approximator of continuous functions over convex, compact sets. By using a logarithmic transform, this class of network maps to a family of subtraction-free ratios of generalized posynomials (GPOS), which we also show to be universal approximators of positive functions over log-convex, compact subsets of the positive orthant. The main advantage of difference-LSE networks with respect to classical feedforward neural networks is that, after a standard training phase, they provide surrogate models for a design that possesses a specific difference-of-convex-functions form, which makes them optimizable via relatively efficient numerical methods. In particular, by adapting an existing difference-of-convex algorithm to these models, we obtain an algorithm for performing an effective optimization-based design. We illustrate the proposed approach by applying it to the data-driven design of a diet for a patient with type-2 diabetes and to a nonconvex optimization problem.

Log-Sum-Exp Neural Networks and Posynomial Models for Convex and Log-Log-Convex Data.

In this paper, we show that a one-layer feedforward neural network with exponential activation functions in the inner layer and logarithmic activation in the output neuron is a universal approximator of convex functions. Such a network represents a family of scaled log-sum exponential functions, here named log-sum-exp ( LSET ). Under a suitable exponential transformation, the class of LSET functions maps to a family of generalized posynomials GPOST , which we similarly show to be universal approximators for log-log-convex functions. A key feature of an LSET network is that, once it is trained on data, the resulting model is convex in the variables, which makes it readily amenable to efficient design based on convex optimization. Similarly, once a GPOST model is trained on data, it yields a posynomial model that can be efficiently optimized with respect to its variables by using geometric programming (GP). The proposed methodology is illustrated by two numerical examples, in which, first, models are constructed from simulation data of the two physical processes (namely, the level of vibration in a vehicle suspension system, and the peak power generated by the combustion of propane), and then optimization-based design is performed on these models.

Exploration of the role of the virulence factor ElrA during Enterococcus faecalis cell infection.

Enterococcus faecalis, an organism generally not pathogenic for healthy humans, has the potential to cause disease in susceptible hosts. While it seems to be equipped to interact with and circumvent host immune defense, most of the molecular and cellular mechanisms underlying the enterococcal infectious process remain elusive. Here, we investigated the role of the Enterococcal Leucine Rich protein A (ElrA), an internalin-like protein of E. faecalis also known as a virulence factor. ElrA was previously shown to prevent adhesion to macrophages. We show that ElrA does not inhibit the basic phagocytic process, but is able to prevent sensing and migration of macrophages toward E. faecalis. Presence or absence of FHL2, a eukaryotic partner of ElrA, does not affect the ElrA-dependent mechanism preventing macrophage migration. However, we highlight a partial contribution of FHL2 in ElrA-mediated virulence in vivo. Our results indicate that ElrA plays at least a dual role of which anti-phagocytic activity may contribute to dissemination of extracellular E. faecalis during infection.

Overexpression of Enterococcus faecalis elr operon protects from phagocytosis.

BACKGROUND: Mechanisms underlying the transition from commensalism to virulence in Enterococcus faecalis are not fully understood. We previously identified the enterococcal leucine-rich protein A (ElrA) as a virulence factor of E. faecalis. The elrA gene is part of an operon that comprises four other ORFs encoding putative surface proteins of unknown function. RESULTS: In this work, we compared the susceptibility to phagocytosis of three E. faecalis strains, including a wild-type (WT), a ΔelrA strain, and a strain overexpressing the whole elr operon in order to understand the role of this operon in E. faecalis virulence. While both WT and ΔelrA strains were efficiently phagocytized by RAW 264.7 mouse macrophages, the elr operon-overexpressing strain showed a decreased capability to be internalized by the phagocytic cells. Consistently, the strain overexpressing elr operon was less adherent to macrophages than the WT strain, suggesting that overexpression of the elr operon could confer E. faecalis with additional anti-adhesion properties. In addition, increased virulence of the elr operon-overexpressing strain was shown in a mouse peritonitis model. CONCLUSIONS: Altogether, our results indicate that overexpression of the elr operon facilitates the E. faecalis escape from host immune defenses.

Discrete limit and monotonicity properties of the Floquet eigenvalue in an age structured cell division cycle model.

We consider a cell population described by an age-structured partial differential equation with time periodic coefficients. We assume that division only occurs within certain time intervals at a rate [Formula: see text] for cells who have reached minimal positive age (maturation). We study the asymptotic behavior of the dominant Floquet eigenvalue, or Perron-Frobenius eigenvalue, representing the growth rate, as a function of the maturation age, when the division rate [Formula: see text] tends to infinity (divisions become instantaneous). We show that the dominant Floquet eigenvalue converges to a staircase function with an infinite number of steps, determined by a discrete dynamical system. This indicates that, in the limit, the growth rate is governed by synchronization phenomena between the maturation age and the length of the time intervals in which division may occur. As an intermediate result, we give a sufficient condition which guarantees that the dominant Floquet eigenvalue is a nondecreasing function of the division rate. We also give a counter example showing that the latter monotonicity property does not hold in general.

Enterococcal Rgg-like regulator ElrR activates expression of the elrA operon.

The Enterococcus faecalis leucine-rich protein ElrA promotes virulence by stimulating bacterial persistence in macrophages and production of the interleukin-6 (IL-6) cytokine. The ElrA protein is encoded within an operon that is poorly expressed under laboratory conditions but induced in vivo. In this study, we identify ef2687 (renamed elrR), which encodes a member of the Rgg (regulator gene for glucosyltransferase) family of putative regulatory proteins. Using quantitative reverse transcription-PCR, translational lacZ fusions, and electrophoretic mobility shift assays, we demonstrate that ElrR positively regulates expression of elrA. These results correlate with the attenuated virulence of the ΔelrR strain in a mouse peritonitis model. Virulence of simple and double elrR and elrA deletion mutants also suggests a remaining ElrR-independent expression of elrA in vivo and additional virulence-related genes controlled by ElrR.

Mutational analysis of a predicted double ß-propeller domain of the DspA/E effector of Erwinia amylovora.

The bacterium Erwinia amylovora causes fire blight, an invasive disease that threatens apple trees, pear trees and other plants of the Rosaceae family. Erwinia amylovora pathogenicity relies on a type III secretion system and on a single effector DspA/E. This effector belongs to the widespread AvrE family of effectors whose biological function is unknown. In this manuscript, we performed a bioinformatic analysis of DspA/E- and AvrE-related effectors. Motif search identified nuclear localization signals, peroxisome targeting signals, endoplasmic reticulum membrane retention signals and leucine zipper motifs, but none of these motifs were present in all the AvrE-related effectors analysed. Protein threading analysis, however, predicted a conserved double ß-propeller domain in the N-terminal part of all the analysed effector sequences. We then performed a random pentapeptide mutagenesis of DspA/E, which led to the characterization of 13 new altered proteins with a five amino acids insertion. Eight harboured the insertion inside the predicted ß-propeller domain and six of these eight insertions impaired DspA/E stability or function. Conversely, the two remaining insertions generated proteins that were functional and abundantly secreted in the supernatant suggesting that these two insertions stabilized the protein.

PecS is an important player in the regulatory network governing the coordinated expression of virulence genes during the interaction between Dickeya dadantii 3937 and plants.

Successful infection of a pathogen relies on the coordinated expression of numerous virulence factor-encoding genes. In plant-bacteria interactions, this control is very often achieved through the integration of several regulatory circuits controlling cell-cell communication or sensing environmental conditions. Dickeya dadantii (formerly Erwinia chrysanthemi), the causal agent of soft rot on many crops and ornamentals, provokes maceration of infected plants mainly by producing and secreting a battery of plant cell wall-degrading enzymes. However, several other virulence factors have also been characterized. During Arabidopsis infection, most D. dadantii virulence gene transcripts accumulated in a coordinated manner during infection. This activation requires a functional GacA-GacS two-component regulatory system but the Gac system is not involved in the growth phase dependence of virulence gene expression. Here we show that, contrary to Pectobacterium, the AHL-mediated ExpIR quorum-sensing system does not play a major role in the growth phase-dependent control of D. dadantii virulence genes. On the other hand, the global regulator PecS participates in this coordinated expression since, in a pecS mutant, an early activation of virulence genes is observed both in vitro and in planta. This correlated with the known hypervirulence phenotype of the pecS mutant. Analysis of the relationship between the regulatory circuits governed by the PecS and GacA global regulators indicates that these two regulators act independently. PecS prevents a premature expression of virulence genes in the first stages of colonization whereas GacA, presumably in conjunction with other regulators, is required for the activation of virulence genes at the onset of symptom occurrence.

The HrpN effector of Erwinia amylovora, which is involved in type III translocation, contributes directly or indirectly to callose elicitation on apple leaves.

Erwinia amylovora is responsible for fire blight of apple and pear trees. Its pathogenicity depends on a type III secretion system (T3SS) mediating the translocation of effectors into the plant cell. The DspA/E effector suppresses callose deposition on apple leaves. We found that E. amylovora and Pseudomonas syringae DC3000 tts mutants or peptide flg22 do not trigger callose deposition as strongly as the dspA/E mutant on apple leaves. This suggests that, on apple leaves, callose deposition is poorly elicited by pathogen-associated molecular patterns (PAMPs) such as flg22 or other PAMPs harbored by tts mutants and is mainly elicited by injected effectors or by the T3SS itself. Callose elicitation partly depends on HrpW because an hrpW-dspA/E mutant elicits lower callose deposition than a dspA/E mutant. Furthermore, an hrpN-dspA/E mutant does not trigger callose deposition, indicating that HrpN is required to trigger this plant defense reaction. We showed that HrpN plays a general role in the translocation process. Thus, the HrpN requirement for callose deposition may be explained by its role in translocation: HrpN could be involved in the translocation of other effectors inducing callose deposition. Furthermore, HrpN may also directly contribute to the elicitation process because we showed that purified HrpN induces callose deposition.

The GacA global regulator is required for the appropriate expression of Erwinia chrysanthemi 3937 pathogenicity genes during plant infection.

Pathogenicity of the phytopathogenic enterobacterium Erwinia chrysanthemi, the causal agent of soft rot disease on many plants, is a complex process involving several factors whose production is regulated by a complex, intertwined regulatory network. In this work we characterized the GacA regulator, member of the GacS-GacA two-component system, as a global regulator which is required for disease expression but not for bacterial multiplication in planta during the first stages of the plant infection. GacA was shown to control the expression of plant cell wall-degrading enzymes and hrp genes in vitro. Analysis of virulence gene expression during infection of Arabidopsis thaliana revealed a coordinated expression of these virulence genes at 12 h post infection and showed that GacA is required for the appropriate production of virulence factors in planta. GacA might partly act by negatively controlling the expression of the pecT gene encoding the global repressor PecT, indicating a hierarchy in the pathways involved in the E. chrysanthemi regulatory network.

Evaluation of potential risks associated with recombination in transgenic plants expressing viral sequences.

Virus-resistant transgenic plants have been created primarily through the expression of viral sequences. It has been hypothesized that recombination between the viral transgene mRNA and the RNA of an infecting virus could generate novel viruses. As mRNA/viral RNA recombination can occur in virus-resistant transgenic plants, the key to testing this risk hypothesis is to compare the populations of recombinant viruses generated in transgenic and non-transgenic plants. This has been done with two cucumoviral systems, involving either two strains of cucumber mosaic virus (CMV), or CMV and the related tomato aspermy virus (TAV). Although the distribution of the sites of recombination in the CMV/CMV and TAV/CMV systems was quite different, equivalent populations of recombinant viruses were observed in both cases. These results constitute the first comparison of the populations of recombinants in transgenic and non-transgenic plants, and suggest that there is little risk of emergence of recombinant viruses in these plants, other than those that could emerge in non-transgenic plants.

A map of the diversity of RNA3 recombinants appearing in plants infected with Cucumber mosaic virus and Tomato aspermy virus.

In order to better understand the role of recombination in creating the diversity of viral genomes that is acted on by selection, we have studied in detail the population of recombinant RNA3 molecules occurring in tobacco plants coinfected with wild-type strains of cucumber mosaic virus (CMV) and tomato aspermy virus (TAV) under conditions of minimal selection pressure. Recombinant RNA3s were observed in 9.6% of the samples. Precise homologous recombination predominated since it was observed at 28 different sites, primarily in six hot spots. Imprecise homologous recombination was observed at two sites, particularly within a GU repeat in the 5' noncoding region. Seven of the eight aberrant homologous recombination sites observed were clustered in the 3' noncoding region. These results have implications on the role of recombination in host adaptation and virus evolution. They also provide essential baseline information for understanding the potential epidemiological impact of recombination in transgenic plants expressing viral sequences.

Transient expression in mammalian cells of transgenes transcribed from the Cauliflower mosaic virus 35S promoter.

Gene constructs containing the Cauliflower mosaic virus (CaMV) 35S promoter and a sequence coding either for a green fluorescent protein (GFP) or for firefly luciferase were transfected into Chinese hamster ovary (CHO) cells. Both reporter genes were expressed to significant levels. The 35S promoter was 40 times less active than the human eF1 alpha promoter, which is known to be one of the most potent promoters in mammalian cells. The 35S promoter must therefore be considered to be a promoter of significant potency in mammalian cells. RT-PCR analysis suggested that transcription initiation in CHO cells occurred between the TATA box and the transcription start site of the 35S promoter that function in plant cells. Further analysis by 5'RACE confirmed that transcription was initiated in CHO cells at different sites located essentially between the TATA box and the plant transcription start site, showing that 35S promoter activity in animal cells is due to the presence of promoter elements that are functional in mammalian cells, but that are not those used in plants. The data reported here raise the possibility that genes controlled by the 35S promoter, which is commonly used in transgenic plants, have the potential for expression in animal cells.

A novel strategy for creating recombinant infectious RNA virus genomes.

Reverse transcriptases with RNase H activity are particularly apt to switch templates and generate recombinant molecules in vitro. This property has been exploited for the first time to create a library of recombinant RNAs 3 between two strains of Cucumber mosaic virus (CMV) or between CMV and Tomato aspermy virus (TAV), which share 75 and 63% sequence identity, respectively. The recombination events were almost entirely of the precise homologous type, and occurred at the same sites as those previously identified in co-infected plants, making it possible to use this strategy to create numerous cDNA fragments with crossovers similar to those occurring in vivo. Sub-cloning of recombinant fragments into an infectious full-length clone was accomplished by homologous recombination in yeast, alleviating the need for in vitro ligation at common restriction sites. Most of the recombinant genomes were infectious. Association of these two methods constitutes an efficient and practical means for generating numerous infectious viral genomes equivalent to ones that might arise by precise homologous recombination between two parental viral genomes in nature.