From error bounds to the complexity of first-order descent methods for convex functions

This paper shows that error bounds can be used as effective tools for deriving complexity results for first-order descent methods in convex minimization. In a first stage, this objective led us to revisit the interplay between error bounds and the Kurdyka-\L ojasiewicz (KL) inequality. One can show the equivalence between the two concepts for convex functions having a moderately flat profile near the set of minimizers (as those of functions with H\"olderian growth). A counterexample shows that the equivalence is no longer true for extremely flat functions. This fact reveals the relevance of an approach based on KL inequality. In a second stage, we show how KL inequalities can in turn be employed to compute new complexity bounds for a wealth of descent methods for convex problems. Our approach is completely original and makes use of a one-dimensional worst-case proximal sequence in the spirit of the famous majorant method of Kantorovich. Our result applies to a very simple abstract scheme that covers a wide class of descent methods. As a byproduct of our study, we also provide new results for the globalization of KL inequalities in the convex framework. Our main results inaugurate a simple methodology: derive an error bound, compute the desingularizing function whenever possible, identify essential constants in the descent method and finally compute the complexity using the one-dimensional worst case proximal sequence. Our method is illustrated through projection methods for feasibility problems, and through the famous iterative shrinkage thresholding algorithm (ISTA), for which we show that the complexity bound is of the form $O(q^{k})$ where the constituents of the bound only depend on error bound constants obtained for an arbitrary least squares objective with $\ell^1$ regularization

Genomic Expansion of Magnetotactic Bacteria Reveals an Early Common Origin of Magnetotaxis with Lineage-specific Evolution

The origin and evolution of magnetoreception, which in diverse prokaryotes and protozoa is known as magnetotaxis and enables these microorganisms to detect Earth’s magnetic field for orientation and navigation, is not well understood in evolutionary biology. The only known prokaryotes capable of sensing the geomagnetic field are magnetotactic bacteria (MTB), motile microorganisms that biomineralize intracellular, membrane-bounded magnetic single-domain crystals of either magnetite (Fe3O4) or greigite (Fe3S4) called magnetosomes. Magnetosomes are responsible for magnetotaxis in MTB. Here we report the first large-scale metagenomic survey of MTB from both northern and southern hemispheres combined with 28 genomes from uncultivated MTB. These genomes expand greatly the coverage of MTB in the Proteobacteria, Nitrospirae, and Omnitrophica phyla, and provide the first genomic evidence of MTB belonging to the Zetaproteobacteria and “Candidatus Lambdaproteobacteria” classes. The gene content and organization of magnetosome gene clusters, which are physically grouped genes that encode proteins for magnetosome biosynthesis and organization, are more conserved within phylogenetically similar groups than between different taxonomic lineages. Moreover, the phylogenies of core magnetosome proteins form monophyletic clades. Together, these results suggest a common ancient origin of iron-based (Fe3O4 and Fe3S4) magnetotaxis in the domain Bacteria that underwent lineage-specific evolution, shedding new light on the origin and evolution of biomineralization and magnetotaxis, and expanding significantly the phylogenomic representation of MTB

Backbone rigidity and static presentation of guanidinium groups increases cellular uptake of arginine-rich cell-penetrating peptides

In addition to endocytosis-mediated cellular uptake, hydrophilic cell-penetrating peptides are able to traverse biological membranes in a non-endocytic mode termed transduction, resulting in immediate bioavailability. Here we analysed structural requirements for the non-endocytic uptake mode of arginine-rich cell-penetrating peptides, by a combination of live-cell microscopy, molecular dynamics simulations and analytical ultracentrifugation. We demonstrate that the transduction efficiency of arginine-rich peptides increases with higher peptide structural rigidity. Consequently, cyclic arginine-rich cell-penetrating peptides showed enhanced cellular uptake kinetics relative to their linear and more flexible counterpart. We propose that guanidinium groups are forced into maximally distant positions by cyclization. This orientation increases membrane contacts leading to enhanced cell penetration

Predictors of long-term outcome following high-dose chemotherapy in high-risk primary breast cancer

We report on a predictive model of long-term outcome in 114 high-risk breast cancer patients treated with high-dose chemotherapy between 1989 and 1994. Paraffin-blocks from 90 of the 114 primaries were assessed for the presence of five risk factors: grade, mitotic index, protein expression of p53, HER2/neu, and oestrogen/progesterone receptor status; we could analyse the effect of risk factors in 84 of these 90 tumours. Seven-year relapse-free and overall survival was 58% (95% confidence interval 44–74%) and 82% (95% confidence interval 71–94%) vs 33% (95% confidence interval 21–52%) and 41% (95% confidence interval 28–60%) for patients whose primary tumours displayed ⩾3 risk factors vs patients with ⩽2 risk factors. For the entire group of 168 high-risk breast cancer patients, inflammatory stage IIIB disease and involved post-mastectomy margins were associated with decreased relapse-free survival and overall survival; patients treated with non-doxorubicin containing standard adjuvant therapy experienced worse overall survival (RR, 2.08; 95% confidence interval 1.04 to 4.16; P=0.04), while adjuvant tamoxifen improved overall survival (RR, 0.65; 95% confidence interval 0.41–1.01; P=0.054). Future trial designs and patient selection for studies specific for high-risk breast cancer patients should include appropriate prognostic models. Validation of such models could come from recently completed randomised, prospective trials

Involvement of a Toxoplasma gondii Chromatin Remodeling Complex Ortholog in Developmental Regulation

The asexual cycle of the parasite Toxoplasma gondii has two developmental stages: a rapidly replicating form called a tachyzoite and a slow growing cyst form called a bradyzoite. While the importance of ATP-independent histone modifications for gene regulation in T. gondii have been demonstrated, ATP-dependent chromatin remodeling pathways have not been examined. In this study we characterized C9, an insertional mutant showing reduced expression of bradyzoite differentiation marker BAG1, in cultured human fibroblasts. This mutant contains an insertion in the gene encoding TgRSC8, which is homologous to the Saccharomyces cerevisiae proteins Rsc8p (remodel the structure of chromatin complex subunit 8) and Swi3p (switch/sucrose non-fermentable [SWI/SNF]) of ATP-dependent chromatin-remodeling complexes. In the C9 mutant, TgRSC8 is the downstream open reading frame on a dicistronic transcript. Though protein was expressed from the downstream gene of the dicistron, TgRSC8 levels were decreased in C9 from those of wild-type parasites, as determined by western immunoblot and flow cytometry. As TgRSC8 localized to the parasite nucleus, we postulated a role in gene regulation. Transcript levels of several markers were assessed by quantitative PCR to test this hypothesis. The C9 mutant displayed reduced steady state transcript levels of bradyzoite-induced genes BAG1, LDH2, SUSA1, and ENO1, all of which were significantly increased with addition of TgRSC8 to the mutant. Transcript levels of some bradyzoite markers were unaltered in C9, or unable to be increased by complementation with TgRSC8, indicating multiple pathways control bradyzoite-upregulated genes. Together, these data suggest a role for TgRSC8 in control of bradyzoite-upregulated gene expression. Thus chromatin remodeling, by both ATP-independent and dependent mechanisms, is an important mode of gene regulation during stage differentiation in parasites

The Bacterial Intimins and Invasins: A Large and Novel Family of Secreted Proteins

Gram-negative bacteria have developed a limited repertoire of solutions for secreting proteins from the cytoplasmic compartment to the exterior of the cell. Amongst the spectrum of secreted proteins are the intimins and invasins (the Int/Inv family; TC# 1.B.54) which are characterized by an N-terminal β-barrel domain and a C-terminal surface localized passenger domain. Despite the important role played by members of this family in diseases mediated by several species of the Enterobacteriaceae, there has been little appreciation for the distribution and diversity of these proteins amongst Gram-negative bacteria. Furthermore, there is little understanding of the molecular events governing secretion of these proteins to the extracellular milieu.In silico approaches were used to analyze the domain organization and diversity of members of this secretion family. Proteins belonging to this family are predominantly associated with organisms from the γ-proteobacteria. Whilst proteins from the Chlamydia, γ-, β- and ε-proteobacteria possess β-barrel domains and passenger domains of various sizes, Int/Inv proteins from the α-proteobacteria, cyanobacteria and chlorobi possess only the predicted β-barrel domains. Phylogenetic analyses revealed that with few exceptions these proteins cluster according to organismal type, indicating that divergence occurred contemporaneously with speciation, and that horizontal transfer was limited. Clustering patterns of the β-barrel domains correlate well with those of the full-length proteins although the passenger domains do so with much less consistency. The modular subdomain design of the passenger domains suggests that subdomain duplication and deletion have occurred with high frequency over evolutionary time. However, all repeated subdomains are found in tandem, suggesting that subdomain shuffling occurred rarely if at all. Topological predictions for the β-barrel domains are presented.Based on our in silico analyses we present a model for the biogenesis of these proteins. This study is the first of its kind to describe this unusual family of bacterial adhesins