Applications of a formal approach to decipher discrete genetic networks

Abstract

Background: A growing demand for tools to assist the building and analysis of biological networks exists in systems biology. We argue that the use of a formal approach is relevant and applicable to address questions raised by biologists about such networks. The behaviour of these systems being complex, it is essential to exploit efficiently every bit of experimental information. In our approach, both the evolution rules and the partial knowledge about the structure and the behaviour of the network are formalized using a common constraint-based language.

Results: In this article our formal and declarative approach is applied to three biological applications. The software environment that we developed allows to specifically address each application through a new class of biologically relevant queries. We show that we can describe easily and in a formal manner the partial knowledge about a genetic network. Moreover we show that this environment, based on a constraint algorithmic approach, offers a wide variety of functionalities, going beyond simple simulations, such as proof of consistency, model revision, prediction of properties, search for minimal models relatively to specified criteria.

Conclusions: The formal approach proposed here deeply changes the way to proceed in the exploration of genetic and biochemical networks, first by avoiding the usual trial-and-error procedure, and second by placing the emphasis on sets of solutions, rather than a single solution arbitrarily chosen among many others. Last, the constraint approach promotes an integration of model and experimental data in a single framework.

Figure 1

Illustration of main notions defining a model M from an example of interaction graph .

Figure 2

Examples of interaction compositions and resulting compositions of cellular contexts over example in Figure 1.

Figure 3

Example of interaction compositions and resulting compositions of cellular contexts for a given order of thresholds.

Figure 4

Graphical representation of relative to example in Figure 3.

Figure 5

Interaction graph for the model about immunity control by the λ phage.

Figure 6

Set of possible transitions for the instantiation of parameters in Example 8 of the model about immunity control by the λ phage.

Figure 7

Interaction graph for the model about carbon nutritional stress in E. coli.

Figure 8

Interaction graph for the model about gap-gene module of the segmentation of the D. melanogaster embryo.