Abstract
BackgroundModeling a dynamical biological system is often a difficult task since the a priori unknown parameters of such models are not always directly given by the experiments. Despite the lack of experimental quantitative knowledge, one can see a dynamical biological system as (i) the combined evolution tendencies (increase or decrease) of the biological compound concentrations, and: (ii) the temporal features, such as delays between two concentration peaks (i.e. the times when one of the components completes an increase (resp. decrease) phase and starts a decrease (resp. increase) phase).ResultsWe propose herein a new hybrid modeling framework that follows such biological assumptions. This hybrid approach deals with both a qualitative structure of the system and a quantitative structure. From a theoretical viewpoint, temporal specifications are expressed as equality or inequality constraints between delay parameters, while the qualitative specifications are expressed as an ordered pattern of the concentrations peaks of the components. Using this new hybrid framework, the temporal specifications of a biological system can be obtained from incomplete experimental data. The model may be processed by a hybrid model-checker (e.g. Phaver) which is able to give some new constraints on the delay parameters (e.g. the delay for a given transition is exactly 5 hours after the later peak of a gene product concentration). Furthermore, by using a constraint solver on the previous results, it becomes possible to get the set of parameters settings which are consistent with given specifications. Such a modeling approach is particularly accurate for modeling oscillatory biological behaviors like those observed in the Drosophila circadian cycles. The achieved results concerning the parameters of this oscillatory system formally confirm the several previous studies made by numerical simulations. Moreover, our analysis makes it possible to propose an automatic investigation of the respective impact of per and tim on the circadian cycle.ConclusionsA new hybrid technique for an automatic formal analysis of biological systems is developed with a special emphasis on their oscillatory behaviors. It allows the use of incomplete and empirical biological data.
Highlights
Modeling a dynamical biological system is often a difficult task since the a priori unknown parameters of such models are not always directly given by the experiments
These components interact together within a network. The set of these interactions can be abstracted in a gene regulatory network (GRN), which is the major biological framework for investigating dynamical biological behaviors
The time delay represents a unique opportunity to refine existing qualitative models by showing qualitative properties that verify experimental temporal constraints. It emphasizes a need for a modeling that includes both qualitative properties, arisen from the biological network structure, and delays associated with the dynamics of genes or gene products
Summary
We propose a new hybrid modeling framework that follows such biological assumptions. Temporal specifications are expressed as equality or inequality constraints between delay parameters, while the qualitative specifications are expressed as an ordered pattern of the concentrations peaks of the components. Using this new hybrid framework, the temporal specifications of a biological system can be obtained from incomplete experimental data. By using a constraint solver on the previous results, it becomes possible to get the set of parameters settings which are consistent with given specifications Such a modeling approach is accurate for modeling oscillatory biological behaviors like those observed in the Drosophila circadian cycles. Our analysis makes it possible to propose an automatic investigation of the respective impact of per and tim on the circadian cycle
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