Qualitative methods for the analysis of forcings of biological networks

Leaders: Anne Siegel and Michel Le Borgne

[ Research area | Publications | Communication talks | Collaborations | Software ]

Research area

Activity report

• Introduction to system biology
  

Modelling equilibrium shifts of genetically regulated biological networks

Qualitative modeling is used to infer functioning of complex systems from their graphical structural representations without detailed quantitative parameter knowledge. In molecular biology, several different approaches can be designated as qualitative. Boolean and multi-valued logical approaches (Thomas, 2001) use synchronous or asynchronous cellular automata on graphs. These approaches were successfully applied to identify attractors of gene networks and study their dynamics (de Jong, 2002).
Our qualitative approach is different from these approaches in several ways: to adapt to the kind of observations which are possible, at present, with the biological techniques at hand, we concentrate of the interaction graph of a biological network. Biologists we collaborate with are located in Rennes; they work on liver biological processes, namely the regulation of the synthesis of fatty acids (collaboration with Agrocampus Rennes) and the implication of TGF-beta signalling in the development of fibrosis, often leading to liver cancer (collaboration with Inserm U456, Rennes). Because of these collaborations, the methods we develop must have two caracteristics: a). Biological applications we are interested in lead to build models that integrate simulnateously a biochemical (metabolic or signalling) component and a genetic component. Our goal is to understand better the relations between these two components. b). The lack of quantitative measurements about these applications enforces the need for a qualitative modelling approach, either discrete event networks or qualitative differential models.

Main contributions

• Qualitative methods for the construction and correction of graphical methods
  We do not classify attractors, instead we provide a simplified mathematical formalism to study the displacements of attractors under forcings. This makes our method well adapted to compare heterogeneous perturbation data sets to a unique graphical model (interaction graph), which is a signed oriented graph. Another difference with respect to previous approaches is the mathematical framework: the relation between model and data is described as a system of qualitative equations in sign algebra (Siegel et al, Biosystems, 2006). We have shown theoretically and tested for a model of genetic regulation of lipogenesis (Radulescu et al., Royal Society Interface, 2006) how one can distinguish in these equations between forcings (direct action on nodes of the network  or various RNA induced perturbations) and observed variations (such as expression profiles in microarrays). The complete set of solutions of the qualitative equations is obtained automatically with an algorithm using polynomial coding on Z/3Z. The system can be undetermined (many solutions), determined (unique solution) or incompatible (no solution). We have designed efficient methods to solve these systems implemented by ternary decision diagrams (Veber et al, Complex Us, 2006). Our qualitative methods can be used for various purposes: correct errors or detect incompleteness in incorrect or incomplete graphical models produced by network inferrence, propose optimal experiment design, provide hints to functioning of complex networks by a study of balances among pathways.
  The qualitative approach formalizes the biologist's intuition in a simple mathematical way; it has the great advantage of being automatized and thus applicable to large networks (concerning scalability, networks of hundreds of nodes are solved within minutes). Nevertheless the method does not distinguish between a) small and large displacements b) direct and indirect interactions. These difficulties are not crucial because they do not generate contradictions.

• Qualitative analysis and decomposition of the functionning of network
  We have designed several qualitative tools to understand the functioning of networks. Many of the signaling pathways have context dependent response. A possible model for this is that various modules of the same or of different pathways have competing actions on some common nodes. Once a graphical model is built we would like to identify such competitions and balances. We have designed an automated way to do this, based on a theoretical work (Siegel et al, Biosystems, 2006).
  Alternatively, we have designed a modular, qualitative approach to the functioning of networks (Radulescu et al., submitted, 2006). Within this approach, modules will be separated by using a global univalence criterion (Gale-Nikaido theorem) that ensures an univoque input/output response of the module. Coupling between modules uses elasticities, similar to those used in metabolism control. Although this idea is close to similar approaches by Kholodenko and Sontag (2002) our criterion for defining modules is different and our analysis is entirely qualitative. For instance, different functioning modes will be distinguished by qualitative conditions that are inequalities among elasticities. We have succesfully tested this approach for a model of regulated lipid metabolism in hepatocytes (Radulescu et al., submitted, 2006). The goal is to provide qualitative conditions that have as much biological significance as possible and to help biological interpretation. These modular methods are different from the sign algebra calculations and they involve symbolic calculations that are not yet automatized. 
  The main advantage of this approach is the qualitative nature of the reasonings. There are nevertheless limits of these techniques. At the present stage, the modular analysis is limited by dimension (we have worked with systems of tens of variables). With increasing number of variables and modules, the complexity of the qualitative conditions increases and their biological significance is less obvious. We intend to improve our approach by using an hierarchical model reduction procedure that regroups elasticities in a biologically significant way. The balance analysis methods has good scalability but also limited predictive power. This is why we shall develop these two methods in complementarity. Balance analysis will be used to identify those modules that contain interesting competitions. The detailed functioning of these will be further investigated by using the qualitative modular analysis.

Software

Publications

Conference with proceedings

• A Siegel, M Le Borgne, O Radulescu, C Guziolowski, P Veber
  Qualitative response of interaction networks: application to the validation of biological models
  Contribution to minisymposium New research in bioinformatics.
  6th International Congress on Industrial and Applied Mathematics. ICIAM 07
  Zurich, 2007 (preprint.pdf)
  

• C Guziolowski, P Veber, M Le Borgne, O Radulescu, and A Siegel
  Checking Consistency Between Expression Data and Large Scale Regulatory Networks: A Case Study
  Réseaux d'interaction : analyse, modélisation et simulation. RIAMS'06, Lyon, France.
  2006 (slides) (preprint.pdf)
  

• P. Veber, M. Le Borgne, A. Siegel, S. Lagarrique, O. Radulescu
  Complex Qualitative Models in Biology: a new approach
  Proceedings of ECCS, Paris, November 2005. To appear in Complex Us.(abstract)(preprint.pdf)(slides)

Miscellaneous

_Preprints

• O. Radulescu, A. Siegel, S. Laguarrigue, E. Pecou
  A model for regulated fatty acid metabolism in liver; equilibria and their changes
  Arxiv q-bio.CB/0603021, (abstract)(file.pdf)

Communication Talks

• Données qualitatives sur un réseau biologique: règle de cohérence, applications au diagnostic et à la prédiction [A. Siegel] [slides]
• Qualitative modeling of biological networks, combinatorial optimization, PhD Thesis [Ph.Veber] (slides)
  
• Cinquièmes Rencontres autour de la plate-forme Bio-informatique Genouest, Rennes, France 2007. 'Bioquali : tool for analyzing regulatory networks'  [C. Guziolowski] (slides) (video)
• Qualitative response of interaction networks: application to the validation of biological models, ICIAM'07 [A. Siegel] (preprint.pdf)
  
• Modèles mathématiques de la complexité en biologie moléculaire et en mécanique des fluides  [O. Radulescu]
  Habilitation à diriger des recherches soutenue le 11/12/2006 (document de synthèse)(slides)(live)

• New qualitative approaches in molecular biology, Bangalore meeting 2006 (in English) [O. Radulescu] (slides)

• Modélisations (étendue et abstraite) de la régulation génétique du métabolisme des lipides : problèmes et méthodes (Journée Inra-Inria, Lyon, 12/2006) [A. Siegel/ S. Lagariggue] [Slides]
• Abstract model for the regulation of lipid metabolism (VicAnne Workshop, Paris, 01-2006) [A. Siegel] [[slides]
  
• Complex Qualitative Models in Biology: a new approach (ECCS, Paris, 11-2005) [P. Veber] [slides]

Participants

Paper abstracts

Inferring the role of transcription factors in regulatory networks

Expression profiles obtained from multiple perturbation experiments are increasingly used to reconstruct transcriptional regulatory networks, from well studied, simple organisms up to higher eukaryotes. Admittedly, a key ingredient in developing a reconstruction method is its ability to integrate heterogeneous sources of information, as well as to comply with practical observability issues: measurements can be scarce or noisy. In this work, we show how to combine a network of genetic regulations with a set of expression profiles, in order to infer the functional effect of the regulations, as inducer or repressor. Our approach is based on a consistency rule between a network and the signs of variation given by expression arrays.
We evaluate our approach in several settings of increasing complexity. First, we generate artificial expression data on a transcriptional network of \emph{E.~coli} extracted from the literature (1529 nodes and 3802 edges), and we estimate that 30\% of the regulations can be annotated with about 30 profiles. We additionally prove that at most 40.8\% of the network can be inferred using our approach. Second, we use this network in order to validate the predictions obtained with a compendium of real expression profiles. We describe a filtering algorithm that generates particularly reliable predictions. Finally, we apply our inference approach to {\em S.~cerevisiae } transcriptional network (2419 nodes and 4344 interactions), by combining ChIP-chip data and 15 expression profiles . We are able to detect and isolate inconsistencies between the expression profiles and a significant portion of the model (15\% of all the interactions). In addition, we report predictions for 14.5\% of all interactions.
Our approach does not require accurate expression levels nor times series. Nevertheless, we show on both data, real and artificial, that a relatively small  number of perturbation experiments are enough to determine a significant portion of regulatory effects. This is a key practical asset compared to statistical methods for network reconstruction. We demonstrate that our approach is able to provide accurate predictions, even when the network is incomplete and the data is noisy.

Optimiser un plan d'expérience à partir de modèles qualitatifs?

A. Siegel, C. Guziolowski, P. Veber, O. Radulescu, M. Le Borgne 

Un biologiste modifie la concentration d'une entrée d’un système initialement stable, et attend qu’il se stabilise à nouveau. On observe un déplacement d'équilibre sous l'effet d'une perturbation. Les techniques de production de données en masse renseignent sur ces déplacements d'équilibre mais des observations se révèlent plus utiles que d'autres. Nous discutons et évaluons l'intérêt que présente l'observation d'un composant par rapport à un autre.

Checking Consistency Between Expression Data and Large Scale Regulatory Networks: A Case Study

C Guziolowski, P Veber, M Le Borgne, O Radulescu, and A Siegel

We proposed in previous articles a qualitative approach to check the compatibility between a model of interactions and gene expression data. The purpose of the present work is to validate this methodology on a real-size setting. We study the response of \emph{E.coli} regulatory network to nutritional stress, and compare it to publicly available DNA microarray experiments. We show how the incompatibilities we found reveal missing interactions in the network, as well as observations in contradiction with available literature.

Complex Qualitative Models in Biology: a new approach

P. Veber, M. Le Borgne, A. Siegel, S. Lagarrique, O. Radulescu

We advocate the use of qualitative models in the analysis of large biological systems. We show how qualitative
models are linked to theoretical differential models and practical graphical models of biological networks. A new technique for analyzing qualitative models is introduced, which is based on an efficient representation of
qualitative systems. As shown through several applications, this representation is a relevant tool for the understanding and testing of large and complex biological networks.

Une méthodologie pour l'analyse qualitative des réseaux biologiques: de la base de données à la vérification formelle

Topology and linear response of interaction networks in molecular biology

Qualitative analysis of the relation between DNA microarray data and behavioral models of regulation networks

Equilibria and their changes for genetically regulated lipid metabolism in liver