Systems approaches to modelling pathways and networks.

Peer reviewedPreprin

Enumeration of minimal stoichiometric precursor sets in metabolic networks

Background: What an organism needs at least from its environment to produce a set of metabolites, e.g. target(s) of interest and/or biomass, has been called a minimal precursor set. Early approaches to enumerate all minimal precursor sets took into account only the topology of the metabolic network (topological precursor sets). Due to cycles and the stoichiometric values of the reactions, it is often not possible to produce the target(s) from a topological precursor set in the sense that there is no feasible flux. Although considering the stoichiometry makes the problem harder, it enables to obtain biologically reasonable precursor sets that we call stoichiometric. Recently a method to enumerate all minimal stoichiometric precursor sets was proposed in the literature. The relationship between topological and stoichiometric precursor sets had however not yet been studied. Results: Such relationship between topological and stoichiometric precursor sets is highlighted. We also present two algorithms that enumerate all minimal stoichiometric precursor sets. The first one is of theoretical interest only and is based on the above mentioned relationship. The second approach solves a series of mixed integer linear programming problems. We compared the computed minimal precursor sets to experimentally obtained growth media of several Escherichia coli strains using genome-scale metabolic networks. Conclusions: The results show that the second approach efficiently enumerates minimal precursor sets taking stoichiometry into account, and allows for broad in silico studies of strains or species interactions that may help to understand e.g. pathotype and niche-specific metabolic capabilities. sasita is written in Java, uses cplex as LP solver and can be downloaded together with all networks and input files used in this paper at http://www.sasita.gforge.inria.fr

Computational approaches to complex biological networks

The need of understanding and modeling the biological networks is one of the raisons d'\ueatre and of the driving forces behind the emergence of Systems Biology. Because of its holistic approach and because of the widely different level of complexity of the networks, different mathematical methods have been developed during the years. Some of these computational methods are used in this thesis in order to investigate various properties of different biological systems. The first part deals with the prediction of the perturbation of cellular metabolism induced by drugs. Using Flux Balance Analysis to describe the reconstructed genome-wide metabolic networks, we consider the problem of identifying the most selective drug synergisms for given therapeutic targets. The second part of this thesis considers gene regulatory and large social networks as signed graphs (activation/deactivation or friendship/hostility are rephrased as positive/negative coupling between spins). Using the analogy with an Ising spin glass an analysis of the energy landscape and of the content of \u201cdisorder\u201d 'is carried out. Finally, the last part concerns the study of the spatial heterogeneity of the signaling pathway of rod photoreceptors. The electrophysiological data produced by our collaborators in the Neurobiology laboratory have been analyzed with various dynamical systems giving an insight into the process of ageing of photoreceptors and into the role diffusion in the pathway

Inferring Gene Regulatory Networks from Time Series Microarray Data

The innovations and improvements in high-throughput genomic technologies, such as DNA microarray, make it possible for biologists to simultaneously measure dependencies and regulations among genes on a genome-wide scale and provide us genetic information. An important objective of the functional genomics is to understand the controlling mechanism of the expression of these genes and encode the knowledge into gene regulatory network (GRN). To achieve this, computational and statistical algorithms are especially needed. Inference of GRN is a very challenging task for computational biologists because the degree of freedom of the parameters is redundant. Various computational approaches have been proposed for modeling gene regulatory networks, such as Boolean network, differential equations and Bayesian network. There is no so called golden method which can generally give us the best performance for any data set. The research goal is to improve inference accuracy and reduce computational complexity. One of the problems in reconstructing GRN is how to deal with the high dimensionality and short time course gene expression data. In this work, some existing inference algorithms are compared and the limitations lie in that they either suffer from low inference accuracy or computational complexity. To overcome such difficulties, a new approach based on state space model and Expectation-Maximization (EM) algorithms is proposed to model the dynamic system of gene regulation and infer gene regulatory networks. In our model, GRN is represented by a state space model that incorporates noises and has the ability to capture more various biological aspects, such as hidden or missing variables. An EM algorithm is used to estimate the parameters based on the given state space functions and the gene interaction matrix is derived by decomposing the observation matrix using singular value decomposition, and then it is used to infer GRN. The new model is validated using synthetic data sets before applying it to real biological data sets. The results reveal that the developed model can infer the gene regulatory networks from large scale gene expression data and significantly reduce the computational time complexity without losing much inference accuracy compared to dynamic Bayesian network

Monotonicity, frustration, and ordered response: an analysis of the energy landscape of perturbed large-scale biological networks

<p>Abstract</p> <p>Background</p> <p>For large-scale biological networks represented as signed graphs, the index of frustration measures how far a network is from a monotone system, i.e., how incoherently the system responds to perturbations.</p> <p>Results</p> <p>In this paper we find that the frustration is systematically lower in transcriptional networks (modeled at functional level) than in signaling and metabolic networks (modeled at stoichiometric level). A possible interpretation of this result is in terms of energetic cost of an interaction: an erroneous or contradictory transcriptional action costs much more than a signaling/metabolic error, and therefore must be avoided as much as possible. Averaging over all possible perturbations, however, we also find that unlike for transcriptional networks, in the signaling/metabolic networks the probability of finding the system in its least frustrated configuration tends to be high also in correspondence of a moderate energetic regime, meaning that, in spite of the higher frustration, these networks can achieve a globally ordered response to perturbations even for moderate values of the strength of the interactions. Furthermore, an analysis of the energy landscape shows that signaling and metabolic networks lack energetic barriers around their global optima, a property also favouring global order.</p> <p>Conclusion</p> <p>In conclusion, transcriptional and signaling/metabolic networks appear to have systematic differences in both the index of frustration and the transition to global order. These differences are interpretable in terms of the different functions of the various classes of networks.</p

Road planning with slime mould: If Physarum built motorways it would route M6/M74 through Newcastle

Plasmodium of Physarum polycephalum is a single cell visible by unaided eye. During its foraging behaviour the cell spans spatially distributed sources of nutrients with a protoplasmic network. Geometrical structure of the protoplasmic networks allows the plasmodium to optimize transfer of nutrients between remote parts of its body, to distributively sense its environment, and make a decentralized decision about further routes of migration. We consider the ten most populated urban areas in United Kingdom and study what would be an optimal layout of transport links between these urban areas from the "plasmodium's point of view". We represent geographical locations of urban areas by oat flakes, inoculate the plasmodium in Greater London area and analyse the plasmodium's foraging behaviour. We simulate the behaviour of the plasmodium using a particle collective which responds to the environmental conditions to construct and minimise transport networks. Results of our scoping experiments show that during its colonization of the experimental space the plasmodium forms a protoplasmic network isomorphic to a network of major motorways except the motorway linking England with Scotland. We also imitate the reaction of transport network to disastrous events and show how the transport network can be reconfigured during natural or artificial cataclysms. The results of the present research lay a basis for future science of bio-inspired urban and road planning.Comment: Submitted November (2009

Machine learning methods for detecting structure in metabolic flow networks

Metabolic flow networks are large scale, mechanistic biological models with good predictive power. However, even when they provide good predictions, interpreting the meaning of their structure can be very difficult, especially for large networks which model entire organisms. This is an underaddressed problem in general, and the analytic techniques that exist currently are difficult to combine with experimental data. The central hypothesis of this thesis is that statistical analysis of large datasets of simulated metabolic fluxes is an effective way to gain insight into the structure of metabolic networks. These datasets can be either simulated or experimental, allowing insight on real world data while retaining the large sample sizes only easily possible via simulation. This work demonstrates that this approach can yield results in detecting structure in both a population of solutions and in the network itself. This work begins with a taxonomy of sampling methods over metabolic networks, before introducing three case studies, of different sampling strategies. Two of these case studies represent, to my knowledge, the largest datasets of their kind, at around half a million points each. This required the creation of custom software to achieve this in a reasonable time frame, and is necessary due to the high dimensionality of the sample space. Next, a number of techniques are described which operate on smaller datasets. These techniques, focused on pairwise comparison, show what can be achieved with these smaller datasets, and how in these cases, visualisation techniques are applicable which do not have simple analogues with larger datasets. In the next chapter, Similarity Network Fusion is used for the first time to cluster organisms across several levels of biological organisation, resulting in the detection of discrete, quantised biological states in the underlying datasets. This quantisation effect was maintained across both real biological data and Monte-Carlo simulated data, with related underlying biological correlates, implying that this behaviour stems from the network structure itself, rather than from the genetic or regulatory mechanisms that would normally be assumed. Finally, Hierarchical Block Matrices are used as a model of multi-level network structure, by clustering reactions using a variety of distance metrics: first standard network distance measures, then by Local Network Learning, a novel approach of measuring connection strength via the gain in predictive power of each node on its neighbourhood. The clusters uncovered using this approach are validated against pre-existing subsystem labels and found to outperform alternative techniques. Overall this thesis represents a significant new approach to metabolic network structure detection, as both a theoretical framework and as technological tools, which can readily be expanded to cover other classes of multilayer network, an under explored datatype across a wide variety of contexts. In addition to the new techniques for metabolic network structure detection introduced, this research has proved fruitful both in its use in applied biological research and in terms of the software developed, which is experiencing substantial usage.EPSR