Highlighting metabolic strategies using network analysis over strain optimization results

The field of Metabolic Engineering has been growing, sup- ported by the increase in the number of annotated genomes and genome- scale metabolic models. In silico strain optimization methods allow to create mutant strains able to overproduce certain metabolites of interest in Biotechnology. Thus, it is possible to reach (near-) optimal solutions, i.e. strains that provide the desired phenotype in computational pheno- type simulations. However, the validation of the results involves under- standing the strategies followed by these mutant strains to achieve the desired phenotype, studying the different use of reactions/ pathways by the mutants. This is quite complex given the size of the networks and the interactions between (sometimes distant) components. The manual verification and comparison of phenotypes is typically impossible. Here, automatic methods are proposed to analyse large sets of mutant strains, by taking the phenotypes of a large number of possible solutions and identifying shared patterns, using methods from network topology analysis. The topological comparison between the networks provided by the wild type and mutant strains highlights the major changes that lead to successful mutants. The methods are applied to a case study consider- ing E. coli and aiming at the production of succinate, optimizing the set of gene knockouts to apply to the wild type. Solutions provided by the use of Simulated Annealing and Evolutionary Algorithms are analyzed. The results show that these methods can help in the identification of the strategies leading to the overproduction of succinate.This work is supported by project PTDC/EIA-EIA/115176/2009, funded by Portuguese FCT and Programa COMPETE.José Pedro Pinto work is funded by a PhD grant from the Portuguese FCT (ref. SFRH/BD/41763/2007)

A software tool for network topology analysis under a Metabolic Engineering perspective

In this work, we present a software application that runs as a plug-in over the OptFlux Metabolic Engineering platform allowing the topological analysis of metabolic networks. The major aim of this tool is to allow the interconnection between phenotype simulation tasks (using algorithms such as Flux Balance Analysis) and topological analysis of the same networks. The provided methods include node degree and degree distributions, shortest path analysis, clustering coefficients and several node rankers (betweenness and closeness centrality, hubs and authorities, etc). Also, it allows the creation of sub-networks through severalfilters, including some based on the results of phenotype simulation.(undefined

Analysis of 140 published GSMs and identification of the most common representation problems

The number of publications related to GSMs is increasing exponentially, but as most of these models are scattered across the Internet there is a need to centralize these data in a way that users can easily access and load them into stoichiometric modelling tools. This work presents a web platform to collect scientific work related with the reconstruction of GSMs, providing links to the original publications and the available models (www.optflux.org/models). The platform also indicates which models are compatible with OptFlux, an open-source reference computational platform for the optimization of cellular factories by the application of in silico ME methods, designed for non-computational experts by providing a user-friendly interface. The compatible models can be automatically loaded into OptFlux via a repository manager. This work also presents a thorough analysis on more than 140 published GSMs available in the platform. This analysis highlights some common problems in published models, such as the lack of standards to represent them. The SBML format has been adopted as the main standard by the community, despite some limitations in representing all the information required for modelling purposes. As consequence, this format has been extended ad-hoc by several authors, thus making its automatic interpretation a non-trivial problem. This analysis provides some insight into the limitations of formats used and the recurrent problems in the representation of GSMs

An algorithm for SDV representation of 2D Behaviors

This paper deals with the characterization of 2D behaviors that are representable by means of special first order models, known as state/driving-variable (SDV) models. In previous work, [1], [2] we have shown how to identify SDV-representable behaviors using one of its full row rank representations. Here, we give a further refinement by showing that a 2D behavior is SDV-representable if and only if each of its kernel representations can be decomposed as a product of three 2D L-polynomial matrices: a zero right prime matrix, a cw-unital square matrix and a factor left prime matrix. Using that decomposition, we present a procedure to obtain SDV representations of a 2D behavior starting from any of its kernel representations

OptFlux3: an improved platform for in silico design of cellular factories

The rational design of cellular factories for industrial biotechnology aims to create optimized organisms for the production of bulk chemicals, pharmaceuticals, food ingredients and enzymes, among others. Metabolic engineering (ME) plays a key role in this process, supported by the latest advances in genetic engineering in combination with computational tools to define targets for strain improvement. OptFlux is an open-source reference computational platform for the optimization of cellular factories by the application of in silico ME methods, designed for non-computational experts by providing a user-friendly interface. It allows to load genome-scale models from several sources to be used in the prediction of cellular behavior and identification of metabolic targets for genetic engineering. Its latest version, OptFlux3, allows to perform the simulation of wild type and mutant strains (allowing the simulation of gene/ reaction deletion and over/under expression). Regarding strain optimization, the new architecture opts for a multi-objective framework, allowing users to easily add different goals as optimization targets in a flexible way. Specialized multi-objective algorithms, co-exist with traditional single objectives algorithms to be applied for each case. Also, OptFlux3 includes a new visualization framework for metabolic models and phenotype simulations and a new plug-in management interface that allows to install and remove plug-ins in execution time. Currently available plug-ins include the calculation and visualization of elementary modes, topological analysis and the ability to add reactions/ pathways to existing models. OptFlux is made freely available for all major operating systems, together with suitable documentation in www.optflux.org

Evaluating evolutionary algorithms and differential evolution for the online optimization of fermentation processes

Although important contributions have been made in recent years within the field of bioprocess model development and validation, in many cases the utility of even relatively good models for process optimization with current state-of-the-art algorithms (mostly offline approaches) is quite low. The main cause for this is that open-loop fermentations do not compensate for the differences observed between model predictions and real variables, whose consequences can lead to quite undesirable consequences. In this work, the performance of two different algorithms belonging to the main groups of Evolutionary Algorithms (EA) and Differential Evolution (DE) is compared in the task of online optimisation of fed-batch fermentation processes. The proposed approach enables to obtain results close to the ones predicted initially by the mathematical models of the process, deals well with the noise in state variables and exhibits properties of graceful degradation. When comparing the optimization algorithms, the DE seems the best alternative, but its superiority seems to decrease when noisier settings are considered.Fundo Europeu de Desenvolvimento Regional (FEDER)Fundação para a Ciência e a Tecnologia (FCT

TNA4OptFlux : a software tool for the analysis of strain optimization strategies

BACKGROUND:Rational approaches for Metabolic Engineering (ME) deal with the identification of modifications that improve the microbes' production capabilities of target compounds. One of the major challenges created by strain optimization algorithms used in these ME problems is the interpretation of the changes that lead to a given overproduction. Often, a single gene knockout induces changes in the fluxes of several reactions, as compared with the wild-type, and it is therefore difficult to evaluate the physiological differences of the in silico mutant. This is aggravated by the fact that genome-scale models per se are difficult to visualize, given the high number of reactions and metabolites involved.FINDINGS:We introduce a software tool, the Topological Network Analysis for OptFlux (TNA4OptFlux), a plug-in which adds to the open-source ME platform OptFlux the capability of creating and performing topological analysis over metabolic networks. One of the tool's major advantages is the possibility of using these tools in the analysis and comparison of simulated phenotypes, namely those coming from the results of strain optimization algorithms. We illustrate the capabilities of the tool by using it to aid the interpretation of two E. coli strains designed in OptFlux for the overproduction of succinate and glycine.CONCLUSIONS:Besides adding new functionalities to the OptFlux software tool regarding topological analysis, TNA4OptFlux methods greatly facilitate the interpretation of non-intuitive ME strategies by automating the comparison between perturbed and non-perturbed metabolic networks. The plug-in is available on the web site http://www.optflux.org webcite, together with extensive documentation.This work is funded by ERDF - European Regional Development Fund through the COMPETE Programme (operational programme for competitiveness) and by National Funds through the FCT (Portuguese Foundation for Science and Technology) within projects ref. COMPETE FCOMP-01-0124-FEDER-015079 and PEst-OE/EEI/UI0752/2011. JPP and RP work is funded by PhD grants from the Portuguese FCT (ref. SFRH/BD/41763/ 2007 and SFRH/BD/51111/2010)

Gravastars and Black Holes of Anisotropic Dark Energy

Dynamical models of prototype gravastars made of anisotropic dark energy are constructed, in which an infinitely thin spherical shell of a perfect fluid with the equation of state $p = (1-\gamma)\sigma$ divides the whole spacetime into two regions, the internal region filled with a dark energy fluid, and the external Schwarzschild region. The models represent "bounded excursion" stable gravastars, where the thin shell is oscillating between two finite radii, while in other cases they collapse until the formation of black holes. Here we show, for the first time in the literature, a model of gravastar and formation of black hole with both interior and thin shell constituted exclusively of dark energy. Besides, the sign of the parameter of anisotropy ($p_t - p_r$) seems to be relevant to the gravastar formation. The formation is favored when the tangential pressure is greater than the radial pressure, at least in the neighborhood of the isotropic case ($\omega=-1$).Comment: 16 pages, 8 figures. Accepted for publication in Gen. Rel. Gra

Revisiting Clifford algebras and spinors III: conformal structures and twistors in the paravector model of spacetime

This paper is the third of a series of three, and it is the continuation of math-ph/0412074 and math-ph/0412075. After reviewing the conformal spacetime structure, conformal maps are described in Minkowski spacetime as the twisted adjoint representation of the group Spin_+(2,4), acting on paravectors. Twistors are then presented via the paravector model of Clifford algebras and related to conformal maps in the Clifford algebra over the lorentzian R{4,1}$ spacetime. We construct twistors in Minkowski spacetime as algebraic spinors associated with the Dirac-Clifford algebra Cl(1,3)(C) using one lower spacetime dimension than standard Clifford algebra formulations, since for this purpose the Clifford algebra over R{4,1} is also used to describe conformal maps, instead of R{2,4}. Although some papers have already described twistors using the algebra Cl(1,3)(C), isomorphic to Cl(4,1), the present formulation sheds some new light on the use of the paravector model and generalizations.Comment: 17 page