Locating Depots for Capacitated Vehicle Routing

We study a location-routing problem in the context of capacitated vehicle routing. The input is a set of demand locations in a metric space and a fleet of k vehicles each of capacity Q. The objective is to locate k depots, one for each vehicle, and compute routes for the vehicles so that all demands are satisfied and the total cost is minimized. Our main result is a constant-factor approximation algorithm for this problem. To achieve this result, we reduce to the k-median-forest problem, which generalizes both k-median and minimum spanning tree, and which might be of independent interest. We give a (3+c)-approximation algorithm for k-median-forest, which leads to a (12+c)-approximation algorithm for the above location-routing problem, for any constant c>0. The algorithm for k-median-forest is just t-swap local search, and we prove that it has locality gap 3+2/t; this generalizes the corresponding result known for k-median. Finally we consider the "non-uniform" k-median-forest problem which has different cost functions for the MST and k-median parts. We show that the locality gap for this problem is unbounded even under multi-swaps, which contrasts with the uniform case. Nevertheless, we obtain a constant-factor approximation algorithm, using an LP based approach.Comment: 12 pages, 1 figur

Approximating k-Forest with Resource Augmentation: A Primal-Dual Approach

In this paper, we study the $k$-forest problem in the model of resource augmentation. In the $k$-forest problem, given an edge-weighted graph $G(V,E)$, a parameter $k$, and a set of $m$ demand pairs $\subseteq V \times V$, the objective is to construct a minimum-cost subgraph that connects at least $k$ demands. The problem is hard to approximate---the best-known approximation ratio is $O(\min\{\sqrt{n}, \sqrt{k}\})$. Furthermore, $k$-forest is as hard to approximate as the notoriously-hard densest $k$-subgraph problem. While the $k$-forest problem is hard to approximate in the worst-case, we show that with the use of resource augmentation, we can efficiently approximate it up to a constant factor. First, we restate the problem in terms of the number of demands that are {\em not} connected. In particular, the objective of the $k$-forest problem can be viewed as to remove at most $m-k$ demands and find a minimum-cost subgraph that connects the remaining demands. We use this perspective of the problem to explain the performance of our algorithm (in terms of the augmentation) in a more intuitive way. Specifically, we present a polynomial-time algorithm for the $k$-forest problem that, for every $\epsilon>0$, removes at most $m-k$ demands and has cost no more than $O(1/\epsilon^{2})$ times the cost of an optimal algorithm that removes at most $(1-\epsilon)(m-k)$ demands

RNA-controlled nucleocytoplasmic shuttling of mRNA decay factors regulates mRNA synthesis and a novel mRNA decay pathway

mRNA level is controlled by factors that mediate both mRNA synthesis and decay, including the 5' to 3' exonuclease Xrn1. Here we show that nucleocytoplasmic shuttling of several yeast mRNA decay factors plays a key role in determining both mRNA synthesis and decay. Shuttling is regulated by RNAcontrolled binding of the karyopherin Kap120 to two nuclear localization sequences (NLSs) in Xrn1, location of one ofwhich is conserved fromyeast to human. The decaying RNA binds and masks NLS1, establishing a link between mRNA decay and Xrn1 shuttling. Preventing Xrn1 import, either by deleting KAP120 or mutating the two Xrn1 NLSs, compromises transcription and, unexpectedly, also cytoplasmic decay, uncovering a cytoplasmic decay pathway that initiates in the nucleus.MostmRNAs are degraded by both pathways - the ratio between them represents a full spectrum. Importantly, Xrn1 shuttling is required for proper responses to environmental changes, e.g., fluctuating temperatures, involving proper changes in mRNA abundance and in cell proliferation rate

The 3-Hydroxy-2-Butanone Pathway Is Required for Pectobacterium carotovorum Pathogenesis

Pectobacterium species are necrotrophic bacterial pathogens that cause soft rot diseases in potatoes and several other crops worldwide. Gene expression data identified Pectobacterium carotovorum subsp. carotovorum budB, which encodes the α-acetolactate synthase enzyme in the 2,3-butanediol pathway, as more highly expressed in potato tubers than potato stems. This pathway is of interest because volatiles produced by the 2,3-butanediol pathway have been shown to act as plant growth promoting molecules, insect attractants, and, in other bacterial species, affect virulence and fitness. Disruption of the 2,3-butanediol pathway reduced virulence of P. c. subsp. carotovorum WPP14 on potato tubers and impaired alkalinization of growth medium and potato tubers under anaerobic conditions. Alkalinization of the milieu via this pathway may aid in plant cell maceration since Pectobacterium pectate lyases are most active at alkaline pH

Global Self-Organization of the Cellular Metabolic Structure

Background: Over many years, it has been assumed that enzymes work either in an isolated way, or organized in small catalytic groups. Several studies performed using "metabolic networks models'' are helping to understand the degree of functional complexity that characterizes enzymatic dynamic systems. In a previous work, we used "dissipative metabolic networks'' (DMNs) to show that enzymes can present a self-organized global functional structure, in which several sets of enzymes are always in an active state, whereas the rest of molecular catalytic sets exhibit dynamics of on-off changing states. We suggested that this kind of global metabolic dynamics might be a genuine and universal functional configuration of the cellular metabolic structure, common to all living cells. Later, a different group has shown experimentally that this kind of functional structure does, indeed, exist in several microorganisms. Methodology/Principal Findings: Here we have analyzed around 2.500.000 different DMNs in order to investigate the underlying mechanism of this dynamic global configuration. The numerical analyses that we have performed show that this global configuration is an emergent property inherent to the cellular metabolic dynamics. Concretely, we have found that the existence of a high number of enzymatic subsystems belonging to the DMNs is the fundamental element for the spontaneous emergence of a functional reactive structure characterized by a metabolic core formed by several sets of enzymes always in an active state. Conclusions/Significance: This self-organized dynamic structure seems to be an intrinsic characteristic of metabolism, common to all living cellular organisms. To better understand cellular functionality, it will be crucial to structurally characterize these enzymatic self-organized global structures.Supported by the Spanish Ministry of Science and Education Grants MTM2005-01504, MTM2004-04665, partly with FEDER funds, and by the Basque Government, Grant IT252-07

The Lsm1-7/Pat1 complex binds to stress-activated mRNAs and modulates the response to hyperosmotic shock

RNA-binding proteins (RBPs) establish the cellular fate of a transcript, but an understanding of these processes has been limited by a lack of identified specific interactions between RNA and protein molecules. Using MS2 RNA tagging, we have purified proteins associated with individual mRNA species induced by osmotic stress, STL1 and GPD1. We found members of the Lsm1-7/Pat1 RBP complex to preferentially bind these mRNAs, relative to the non-stress induced mRNAs, HYP2 and ASH1. To assess the functional importance, we mutated components of the Lsm1-7/Pat1 RBP complex and analyzed the impact on expression of osmostress gene products. We observed a defect in global translation inhibition under osmotic stress in pat1 and lsm1 mutants, which correlated with an abnormally high association of both non-stress and stress-induced mRNAs to translationally active polysomes. Additionally, for stress-induced proteins normally triggered only by moderate or high osmostress, in the mutants the protein levels rose high already at weak hyperosmosis. Analysis of ribosome passage on mRNAs through co-translational decay from the 5' end (5P-Seq) showed increased ribosome accumulation in lsm1 and pat1 mutants upstream of the start codon. This effect was particularly strong for mRNAs induced under osmostress. Thus, our results indicate that, in addition to its role in degradation, the Lsm1-7/Pat1 complex acts as a selective translational repressor, having stronger effect over the translation initiation of heavily expressed mRNAs. Binding of the Lsm1-7/Pat1p complex to osmostress-induced mRNAs mitigates their translation, suppressing it in conditions of weak or no stress, and avoiding a hyperresponse when triggered

On the dynamics of the adenylate energy system: homeorhesis vs homeostasis.

Biochemical energy is the fundamental element that maintains both the adequate turnover of the biomolecular structures and the functional metabolic viability of unicellular organisms. The levels of ATP, ADP and AMP reflect roughly the energetic status of the cell, and a precise ratio relating them was proposed by Atkinson as the adenylate energy charge (AEC). Under growth-phase conditions, cells maintain the AEC within narrow physiological values, despite extremely large fluctuations in the adenine nucleotides concentration. Intensive experimental studies have shown that these AEC values are preserved in a wide variety of organisms, both eukaryotes and prokaryotes. Here, to understand some of the functional elements involved in the cellular energy status, we present a computational model conformed by some key essential parts of the adenylate energy system. Specifically, we have considered (I) the main synthesis process of ATP from ADP, (II) the main catalyzed phosphotransfer reaction for interconversion of ATP, ADP and AMP, (III) the enzymatic hydrolysis of ATP yielding ADP, and (IV) the enzymatic hydrolysis of ATP providing AMP. This leads to a dynamic metabolic model (with the form of a delayed differential system) in which the enzymatic rate equations and all the physiological kinetic parameters have been explicitly considered and experimentally tested in vitro. Our central hypothesis is that cells are characterized by changing energy dynamics (homeorhesis). The results show that the AEC presents stable transitions between steady states and periodic oscillations and, in agreement with experimental data these oscillations range within the narrow AEC window. Furthermore, the model shows sustained oscillations in the Gibbs free energy and in the total nucleotide pool. The present study provides a step forward towards the understanding of the fundamental principles and quantitative laws governing the adenylate energy system, which is a fundamental element for unveiling the dynamics of cellular life

RNA delivery by extracellular vesicles in mammalian cells and its applications.

The term 'extracellular vesicles' refers to a heterogeneous population of vesicular bodies of cellular origin that derive either from the endosomal compartment (exosomes) or as a result of shedding from the plasma membrane (microvesicles, oncosomes and apoptotic bodies). Extracellular vesicles carry a variety of cargo, including RNAs, proteins, lipids and DNA, which can be taken up by other cells, both in the direct vicinity of the source cell and at distant sites in the body via biofluids, and elicit a variety of phenotypic responses. Owing to their unique biology and roles in cell-cell communication, extracellular vesicles have attracted strong interest, which is further enhanced by their potential clinical utility. Because extracellular vesicles derive their cargo from the contents of the cells that produce them, they are attractive sources of biomarkers for a variety of diseases. Furthermore, studies demonstrating phenotypic effects of specific extracellular vesicle-associated cargo on target cells have stoked interest in extracellular vesicles as therapeutic vehicles. There is particularly strong evidence that the RNA cargo of extracellular vesicles can alter recipient cell gene expression and function. During the past decade, extracellular vesicles and their RNA cargo have become better defined, but many aspects of extracellular vesicle biology remain to be elucidated. These include selective cargo loading resulting in substantial differences between the composition of extracellular vesicles and source cells; heterogeneity in extracellular vesicle size and composition; and undefined mechanisms for the uptake of extracellular vesicles into recipient cells and the fates of their cargo. Further progress in unravelling the basic mechanisms of extracellular vesicle biogenesis, transport, and cargo delivery and function is needed for successful clinical implementation. This Review focuses on the current state of knowledge pertaining to packaging, transport and function of RNAs in extracellular vesicles and outlines the progress made thus far towards their clinical applications