GINML
Introduction
Regulatory networks are involved in most biological processes. They allow the cell or the organism to control development processes and to adjust their biochemical behaviour to internal and environmental changes. Understanding how regulatory networks are structured and how their structures affect the dynamical behaviour of the cell is clearly crucial. In this perspective, we present a flexible and rigorous logical formalism enabling the qualitative dynamical modelling of biological regulatory networks. This logical approach has been implemented in the form of a Java software, GINsim, itself integrated in a more general suite dedicated to the integration and the analysis of genetic regulatory data.
In this context, we addressed the question of adopting a format to stock and exchange regulatory graphs as well as state transition graphs which represent possible dynamical behaviour of the modelled system. Thus, we worked on a preliminary proposal for an exchange format for these graphs. For this purpose, we have extended GXL (Graph eXchange Language) which has been designed to be a standard exchange format for graphs (see also [2,3])
In this document, we provide a short description of regulatory networks and state transition graphs (details can be find in [1]).
Note : Systems Biology Markup Language (SBML) has been proposed as a common representation language for storing biochemical models. SBML is based on XML, and contains structures for representing compartments, species and reactions, as well as optional unit definitions, parameters and rules (constraints). In this representation, the graph structure of the model has to be reconstructed. Indeed, given a network of biochemical reactions, it can be broken down into its constituents. Then, its corresponding SBML model definition consists of lists of these components: beginning of model definition, list of unit definitions, list of compartments, list of species, list of parameters, list of rules, list of reactions, end of model definition.
As our modelling approach deeply relies on the graph structure of the regulatory networks and of their dynamical behaviour (state transition graphs), we have made the choice of the extension of existing format for graphs.
Introduction
Regulatory graphs
State transition graphs
GINML format
An example
References
Regulatory graphs
Logical regulatory graphs are defined as follow:
1. The nodes (or vertices): G={G1, G2,… Gn} representing n components (regulatory products, genes, proteins, …) labelled by their names;
2. The labelled oriented graph R: Vertices are G’s elements, and arcs represent interactions between regulatory products, labelled with a sign when the interaction corresponds to an activation or an inhibition.
3. The products levels: For each node, a specific variable represents the level of expression (or of activity) of the corresponding node. This level (me g) is related to the threshold above which an outgoing interaction becomes functional. It is represented by an integer in {0,...,max}, where max equals, at most, the number of outgoing interactions from this particular component. By default, two extreme values are considered, 0 (none outgoing interaction functional) and max=1 (all interactions functional). The user can then define additional values to represent functional intermediate levels for the activity of the corresponding node.
4. The logical parameters: They allow the qualitative specification of the effects of combinations of interactions controlling a given element. A parameter is named by the set of incoming interactions which are functional. At present, a null value is assign to all parameters by default.
State transition graphs
Logical state transition graphs represent the dynamical behaviour of systems described by regulatory graphs, given a set of initial states. They are defined as follows,
1. The graph defined by a set of nodes (vertices) and a set of arcs connecting pairs of nodes.
2. The nodes represent states of the system, defined by a word resulting of ogique temporelle et model checking pour les rthe concatenation of the actual level of each regulatory product.
3. The arcs represent spontaneous transitions between pairs of states.
In addition, we have to define an updating method to specify the temporal ordering of the transitions. Under the synchronous assumption, all orders of commutation are executed simultaneously at each time step. From a biological point of view, this assumption implies that all macromolecular processes are realised in identical amounts of time, which is clearly unrealistic and often at the origin of simulation artefacts. Under the asynchronous assumption, when multiple orders of commutations occur at a given state, additional information is needed to select specific transitions. As we have no such information, all possible transitions are considered. Introduction
GINML format
Note that we are testing the <Oxygen/> XML editor under a trial license.
We have choosen to extend the GXL (Graph eXchange Language). This extension comprises new attributes and subelements for elements node and edge, and an additional element called parameter. We briefly describe these extensions
• element node :
1. a new attribute basevalue corresponds to the "based level of expression" of the corresponding component (default value 0). In other words, it is the value of the logical parameter corresponding to the case where none of the incoming interactions if functional.
2. new subelements within a node:
▪ a list of elements parameter corresponding to the user defined logical parameters for this node
▪ an element intdefining the maximum level of expression of this node
• element edge :
1. a new attribute sign which gives the sign of the interaction (positive for an activation, negative for a repression, otherwise unknown)
2. one or two subelements int (level or interval letting the interaction functional)
• element parameter, is empty and has two attributes :
1. attribute idActiveInteractions gives the "name" of the parameter. It is the list of the functional interactions exerted upon the considered node,
2. attribute val is the value of the logical parameter.
See the GINML's dtd or in pdf format
See also the GINML description of the gap-gene network case A, or in pdf format. Introduction
An example
This example is taken from [4], and is also listed in the model repository and in the documentation.
The gene regulation network bellow, described in this ginml file, controls the decision between lysis and lysogenisation in bacteriophage lambda.
References
[1]
C. Chaouiya, E. Remy, B. Mossé and D. Thieffry . Qualitative analysis of regulatory graphs: a computational tool based on a discrete formal framework. "First Multidisciplinary International Symposium on Positive Systems: Theory and Applications" (POSTA 2003); Farina (Eds), Springer-Verlag, LNCIS 294:119-126 doi >
[2]
R. C. Holt, A. Winter, A. Schürr . GXL: Towards a Standard Exchange Format. Proceedings 7th Working Conference on Reverse Engineering (WCRE 2000)
[3]
A. Winter . GXL: Graph Exchange Language. Dagstuhl Seminar Interoperability of Reengineering Tools January, 2001, Dagstuhl, Saarland, Germany
[4]
Thieffry, D., Thomas, R. . Dynamical behaviour of biological regulatory networks--II. Immunity control in bacteriophage lambda. Bull. Math. Biol. 57 277-295