Modes and cuts in metabolic networks: complexity and algorithms

Constraint-based approaches recently brought new insight into our understanding of metabolism. By making very simple assumptions such as that the system is at steady-state and some reactions are irreversible, and without requiring kinetic parameters, general properties of the system can be derived. A central concept in this methodology is the notion of an elementary mode (EM for short) which represents a minimal functional subsystem. The computation of EMs still forms a limiting step in metabolic studies and several algorithms have been proposed to address this problem leading to increasingly faster methods. However, although a theoretical upper bound on the number of elementary modes that a network may possess has been established, surprisingly, the complexity of this problem has never been systematically studied. In this paper, we give a systematic overview of the complexity of optimisation problems related to modes. We first establish results regarding network consistency. Most consistency problems are easy, i.e., they can be solved in polynomial time. We then establish the complexity of finding and counting elementary modes. We show in particular that finding one elementary mode is easy but that this task becomes hard when a specific EM (i.e. an EM containing some specified reactions) is sought. We then show that counting the number of elementary modes is musical sharpP-complete. We emphasize that the easy problems can be solved using currently existing software packages. We then analyse the complexity of a closely related task which is the computation of so-called minimum reaction cut sets and we show that this problem is hard. We then present two positive results which both allow to avoid computing EMs as a prior to the computation of reaction cuts. The first one is a polynomial approximation algorithm for finding a minimum reaction cut set. The second one is a test for verifying whether a set of reactions constitutes a reaction cut; this test can be readily included in existing algorithms to improve their performance. Finally, we discuss the complexity of other cut-related problems.     

Lossless filter for multiple repeats with bounded edit distance

Background  

Identifying local similarity between two or more sequences, or identifying repeats occurring at least twice in a sequence, is an essential part in the analysis of biological sequences and of their phylogenetic relationship. Finding such fragments while allowing for a certain number of insertions, deletions, and substitutions, is however known to be a computationally expensive task, and consequently exact methods can usually not be applied in practice.     

Vinculin Is a Dually Regulated Actin Filament Barbed End-capping and Side-binding Protein

The focal adhesion protein vinculin is an actin-binding protein involved in the mechanical coupling between the actin cytoskeleton and the extracellular matrix. An autoinhibitory interaction between the N-terminal head (Vh) and the C-terminal tail (Vt) of vinculin masks an actin filament side-binding domain in Vt. The binding of several proteins to Vh disrupts this intramolecular interaction and exposes the actin filament side-binding domain. Here, by combining kinetic assays and microscopy observations, we show that Vt inhibits actin polymerization by blocking the barbed ends of actin filaments. In low salt conditions, Vt nucleates actin filaments capped at their barbed ends. We determined that the interaction between vinculin and the barbed end is characterized by slow association and dissociation rate constants. This barbed end capping activity requires C-terminal amino acids of Vt that are dispensable for actin filament side binding. Like the side-binding domain, the capping domain of vinculin is masked by an autoinhibitory interaction between Vh and Vt. In contrast to the side-binding domain, the capping domain is not unmasked by the binding of a talin domain to Vh and requires the dissociation of an additional autoinhibitory interaction. Finally, we show that vinculin and the formin mDia1, which is involved in the processive elongation of actin filaments in focal adhesions, compete for actin filament barbed ends.     

Quick and Simple Detection Technique to Assess the Binding of Antimicrotubule Agents to the Colchicine-Binding Site

Development of antimitotic binding to the colchicine-binding site for the treatment of cancer is rapidly expanding. Numerous antimicrotubule agents are prepared every year, and the determination of their binding affinity to tubulin requires the use of purified tubulins and radiolabeled ligands. Such a procedure is costly and time-consuming and therefore is limited to the most promising candidates. Here, we report a quick and inexpensive method that requires only usual laboratory resources to assess the binding of antimicrotubules to colchicine-binding site. The method is based on the ability of N,N'-ethylene-bis(iodoacetamide) (EBI) to crosslink in living cells the cysteine residues at position 239 and 354 of β-tubulin, residues which are involved in the colchicine-binding site. The β-tubulin adduct formed by EBI is easily detectable by Western blot as a second immunoreacting band of β-tubulin that migrates faster than β-tubulin. The occupancy of colchicine-binding site by pertinent antimitotics inhibits the formation of the EBI: β-tubulin adduct, resulting in an assay that allows the screening of new molecules targeting this binding site.     

Molecular Basis for the Dual Function of Eps8 on Actin Dynamics: Bundling and Capping

Actin capping and cross-linking proteins regulate the dynamics and architectures of different cellular protrusions. Eps8 is the founding member of a unique family of capping proteins capable of side-binding and bundling actin filaments. However, the structural basis through which Eps8 exerts these functions remains elusive. Here, we combined biochemical, molecular, and genetic approaches with electron microscopy and image analysis to dissect the molecular mechanism responsible for the distinct activities of Eps8. We propose that bundling activity of Eps8 is mainly mediated by a compact four helix bundle, which is contacting three actin subunits along the filament. The capping activity is mainly mediated by a amphipathic helix that binds within the hydrophobic pocket at the barbed ends of actin blocking further addition of actin monomers. Single-point mutagenesis validated these modes of binding, permitting us to dissect Eps8 capping from bundling activity in vitro. We further showed that the capping and bundling activities of Eps8 can be fully dissected in vivo, demonstrating the physiological relevance of the identified Eps8 structural/functional modules. Eps8 controls actin-based motility through its capping activity, while, as a bundler, is essential for proper intestinal morphogenesis of developing Caenorhabditis elegans.     

Concerted action of two formins in gliding motility and host cell invasion by Toxoplasma gondii

The invasive forms of apicomplexan parasites share a conserved form of gliding motility that powers parasite migration across biological barriers, host cell invasion and egress from infected cells. Previous studies have established that the duration and direction of gliding motility are determined by actin polymerization; however, regulators of actin dynamics in apicomplexans remain poorly characterized. In the absence of a complete ARP2/3 complex, the formin homology 2 domain containing proteins and the accessory protein profilin are presumed to orchestrate actin polymerization during host cell invasion. Here, we have undertaken the biochemical and functional characterization of two Toxoplasma gondii formins and established that they act in concert as actin nucleators during invasion. The importance of TgFRM1 for parasite motility has been assessed by conditional gene disruption. The contribution of each formin individually and jointly was revealed by an approach based upon the expression of dominant mutants with modified FH2 domains impaired in actin binding but still able to dimerize with their respective endogenous formin. These mutated FH2 domains were fused to the ligand-controlled destabilization domain (DD-FKBP) to achieve conditional expression. This strategy proved unique in identifying the non-redundant and critical roles of both formins in invasion. These findings provide new insights into how controlled actin polymerization drives the directional movement required for productive penetration of parasites into host cells.     

Mature-onset obesity and insulin resistance in mice deficient in the signaling adapter p62

Signaling cascades that control adipogenesis are essential in the regulation of body weight and obesity. The adaptor p62 controls pathways that modulate cell differentiation. We report here that p62(-/-) mice develop mature-onset obesity, leptin resistance, as well as impaired glucose and insulin intolerance. The metabolic rate was significantly reduced in p62(-/-) nonobese mice, which displayed increased mRNA levels of PPAR-gamma and reduced levels of UCP-1 in adipose tissue. Basal activity of ERK was enhanced in fat from nonobese mutant mice. Embryo fibroblasts from p62(-/-) mice differentiated better than the wild-type controls into adipocytes, which was abrogated by pharmacological inhibition of the ERK pathway. p62 is induced during adipocyte differentiation and inhibits ERK activation by direct interaction. We propose that p62 normally antagonizes basal ERK activity and adipocyte differentiation and that its loss leads to the hyperactivation of ERK that favors adipogenesis and obesity.