Revisiting the Training of Logic Models of Protein Signaling Networks with a Formal Approach based on Answer Set Programming

A fundamental question in systems biology is the construction and training to data of mathematical models. Logic formalisms have become very popular to model signaling networks because their simplicity allows us to model large systems encompassing hundreds of proteins. An approach to train (Boolean) logic models to high-throughput phospho-proteomics data was recently introduced and solved using optimization heuristics based on stochastic methods. Here we demonstrate how this problem can be solved using Answer Set Programming (ASP), a declarative problem solving paradigm, in which a problem is encoded as a logical program such that its answer sets represent solutions to the problem. ASP has significant improvements over heuristic methods in terms of efficiency and scalability, it guarantees global optimality of solutions as well as provides a complete set of solutions. We illustrate the application of ASP with in silico cases based on realistic networks and data

Exploiting the pathway structure of metabolism to reveal high-order epistasis

<p>Abstract</p> <p>Background</p> <p>Biological robustness results from redundant pathways that achieve an essential objective, e.g. the production of biomass. As a consequence, the biological roles of many genes can only be revealed through multiple knockouts that identify a <it>set </it>of genes as essential for a given function. The identification of such "epistatic" essential relationships between network components is critical for the understanding and eventual manipulation of robust systems-level phenotypes.</p> <p>Results</p> <p>We introduce and apply a network-based approach for genome-scale metabolic knockout design. We apply this method to uncover over 11,000 minimal knockouts for biomass production in an <it>in silico </it>genome-scale model of <it>E. coli</it>. A large majority of these "essential sets" contain 5 or more reactions, and thus represent complex epistatic relationships between components of the <it>E. coli </it>metabolic network.</p> <p>Conclusion</p> <p>The complex minimal biomass knockouts discovered with our approach illuminate robust essential systems-level roles for reactions in the <it>E. coli </it>metabolic network. Unlike previous approaches, our method yields results regarding high-order epistatic relationships and is applicable at the genome-scale.</p

Computing paths and cycles in biological interaction graphs

<p>Abstract</p> <p>Background</p> <p>Interaction graphs (signed directed graphs) provide an important qualitative modeling approach for Systems Biology. They enable the analysis of causal relationships in cellular networks and can even be useful for predicting qualitative aspects of systems dynamics. Fundamental issues in the analysis of interaction graphs are the enumeration of paths and cycles (feedback loops) and the calculation of shortest positive/negative paths. These computational problems have been discussed only to a minor extent in the context of Systems Biology and in particular the shortest signed paths problem requires algorithmic developments.</p> <p>Results</p> <p>We first review algorithms for the enumeration of paths and cycles and show that these algorithms are superior to a recently proposed enumeration approach based on elementary-modes computation. The main part of this work deals with the computation of shortest positive/negative paths, an NP-complete problem for which only very few algorithms are described in the literature. We propose extensions and several new algorithm variants for computing either exact results or approximations. Benchmarks with various concrete biological networks show that exact results can sometimes be obtained in networks with several hundred nodes. A class of even larger graphs can still be treated exactly by a new algorithm combining exhaustive and simple search strategies. For graphs, where the computation of exact solutions becomes time-consuming or infeasible, we devised an approximative algorithm with polynomial complexity. Strikingly, in realistic networks (where a comparison with exact results was possible) this algorithm delivered results that are very close or equal to the exact values. This phenomenon can probably be attributed to the particular topology of cellular signaling and regulatory networks which contain a relatively low number of negative feedback loops.</p> <p>Conclusion</p> <p>The calculation of shortest positive/negative paths and cycles in interaction graphs is an important method for network analysis in Systems Biology. This contribution draws the attention of the community to this important computational problem and provides a number of new algorithms, partially specifically tailored for biological interaction graphs. All algorithms have been implemented in the <it>CellNetAnalyzer </it>framework which can be downloaded for academic use at <url>http://www.mpi-magdeburg.mpg.de/projects/cna/cna.html</url>.</p

Origem do adensamento em solos do tabuleiro sertanejo do estado de Pernambuco: pedogenetica e/ou deposicional.

O presente trabalho foi desenvolvido para identificar e caracterizar horizontes adensados em podzólico amarelo e solonetz solodizado no semi-árido pernambucano, visando testar a hipótese de que estes apresentam descontinuidade textural

A Taxonomy of Causality-Based Biological Properties

We formally characterize a set of causality-based properties of metabolic networks. This set of properties aims at making precise several notions on the production of metabolites, which are familiar in the biologists' terminology. From a theoretical point of view, biochemical reactions are abstractly represented as causal implications and the produced metabolites as causal consequences of the implication representing the corresponding reaction. The fact that a reactant is produced is represented by means of the chain of reactions that have made it exist. Such representation abstracts away from quantities, stoichiometric and thermodynamic parameters and constitutes the basis for the characterization of our properties. Moreover, we propose an effective method for verifying our properties based on an abstract model of system dynamics. This consists of a new abstract semantics for the system seen as a concurrent network and expressed using the Chemical Ground Form calculus. We illustrate an application of this framework to a portion of a real metabolic pathway

Adensamento subsuperficial em solos do semi-árido: processos geológicos e / ou pedogenéticos.

Nos tabuleiros setanejos do Estado de Pernambuco encontram-se solos com adensamento subsuperficial, que provoca limitações no seu uso e, conseqüentemente diminuição da produtividade agrícola. Com o objetivo de identificar a ocorrência de processos geológicos (discontinuidade litológica) e/ou pedogenéticos envolvidos na gênese desse adensamento, selecionaram-se três perfis de solo distribuidos numa seqüência topográfica, localizados nos tabuleiros sertanejos, município de Petrolina, zona semi-árida do Estado de Pernambuco, nos quais foram determinados distribuição granulométrica, morfoscopia da fração areia, parâmetros sedimentológicos, densidade e porosidade, e calculadas as frações areia e silte livres de argila e as relações areia fina, areia média e areia muito fina/areia total e argila fina/argila total. Os resultados indicam que o adensamento subsuperficial não é resultado de processos deposicionais, ou seja, devido a descontinuidade litológica, uma vez que os parâmetros estudados não apresentaram variações em profundidade que indicassem a sua ocorrência

Caracterização micromorfológica e considerações sobre a gênese de solos de tabuleiro do semi-árido do Brasil.

Detalhadas investigações macro e, especialmente, micromorfológicas foram realizadas em dois perfis de Agrissolo Amarelo e um Planossolo de uma superfície geomorfológica tabular, pertencentes aos Tabuleiros Sertanejos (Interioranos) na bacia hidrográfica do médio São Francisco em Petrolina, Pernambuco. O objetivo do estudo foi caracterizar micromorfologicamente os solos, procurando fornecer subsídios para o entendimento da pedogênese, como uma forma de entender a diversidade dos solos na paisagem. Os resultados indicam que os três perfis foram derivados de sedimentos pós-cretáceos, em intensa mistura com resíduos de rochas cristalinas do Pré-Cambriano, provavelmente, ainda, influenciados por materiais de antigos terraços fluviais do rio São Francisco. As diferenciações entre os três perfis estão relacionadas com a heterogeneidade resultante da mistura desses materiais de origem, mas, principalmente, com o posicionamento dos solos do relevo, gerando condições diferenciadas de drenagem. Concreções de ferro herdadas do material de origem, sofreram degradações e se transformaram em mosqueamentos plínticos, e, posteriormente, foram dissipadas no solo, eluviação, ou perdas do sistema, parece ser um dos processos envolvidos na pedogênese

A new computational method to split large biochemical networks into coherent subnets

<p>Abstract</p> <p>Background</p> <p>Compared to more general networks, biochemical networks have some special features: while generally sparse, there are a small number of highly connected metabolite nodes; and metabolite nodes can also be divided into two classes: internal nodes with associated mass balance constraints and external ones without. Based on these features, reclassifying selected internal nodes (separators) to external ones can be used to divide a large complex metabolic network into simpler subnetworks. Selection of separators based on node connectivity is commonly used but affords little detailed control and tends to produce excessive fragmentation.</p> <p>The method proposed here (Netsplitter) allows the user to control separator selection. It combines local connection degree partitioning with global connectivity derived from random walks on the network, to produce a more even distribution of subnetwork sizes. Partitioning is performed progressively and the interactive visual matrix presentation used allows the user considerable control over the process, while incorporating special strategies to maintain the network integrity and minimise the information loss due to partitioning.</p> <p>Results</p> <p>Partitioning of a genome scale network of 1348 metabolites and 1468 reactions for <it>Arabidopsis thaliana </it>encapsulates 66% of the network into 10 medium sized subnets. Applied to the flavonoid subnetwork extracted in this way, it is shown that Netsplitter separates this naturally into four subnets with recognisable functionality, namely synthesis of lignin precursors, flavonoids, coumarin and benzenoids. A quantitative quality measure called <it>efficacy </it>is constructed and shows that the new method gives improved partitioning for several metabolic networks, including bacterial, plant and mammal species.</p> <p>Conclusions</p> <p>For the examples studied the Netsplitter method is a considerable improvement on the performance of connection degree partitioning, giving a better balance of subnet sizes with the removal of fewer mass balance constraints. In addition, the user can interactively control which metabolite nodes are selected for cutting and when to stop further partitioning as the desired granularity has been reached. Finally, the blocking transformation at the heart of the procedure provides a powerful visual display of network structure that may be useful for its exploration independent of whether partitioning is required.</p