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Abstract Background Due to the huge amount of information at genomic level made recently available by high-throughput experimental technologies, networks of regulatory interactions between genes and gene products, the so-called gene-regulatory networks, can be uncovered. Most networks of interest are quite intricate because of both the high dimension of interacting elements and the complexity of the kinds of interactions between them. Then, mathematical and computational modeling frameworks are a must to predict the network behavior in response to environmental stimuli. A specific class of Ordinary Differential Equations (ODE) has shown to be adequate to describe the essential features of the dynamics of gene-regulatory networks. But, deriving quantitative predictions of the network dynamics through the numerical simulation of such models is mostly impracticable as they are currently characterized by incomplete knowledge of biochemical reactions underlying regulatory interactions, and of numeric values of kinetic parameters. Results This paper presents a computational framework for qualitative simulation of a class of ODE models, based on the assumption that gene regulation is threshold-dependent, i.e. only effective above or below a certain threshold. The simulation algorithm we propose assumes that threshold-dependent regulation mechanisms are modeled by continuous steep sigmoid functions, unlike other simulation tools that considerably simplifies the problem by approximating threshold-regulated response functions by step functions discontinuous in the thresholds. The algorithm results from the interplay between methods to deal with incomplete knowledge and to study phenomena that occur at different time-scales. Conclusion The work herein presented establishes the computational groundwork for a sound and a complete algorithm capable to capture the dynamical properties that depend only on the network structure and are invariant for ranges of values of kinetic parameters. At the current state of knowledge, the exploitation of such a tool is rather appropriate and useful to understand how specific activity patterns derive from given network structures, and what different types of dynamical behaviors are possible.

Computational and mathematical models are a must for the in silico analysis or design of Gene Regulatory Networks (GRN)as they offer a theoretical context to deeply address biological regulation. We have proposed a framework where models of network dynamics are expressed through a class of nonlinear and temporal multiscale Ordinary Differential Equations (ODE). To find out models that disclose network structures underlying an observed or desired network behavior, and parameter values that enable the candidate models to reproduce such behavior, we follow a reasoning cycle that alternates procedures for model selection and parameter refinement. Plausible network models are first selected via qualitative simulation, and next their parameters are given quantitative values such that the ODE model solution reproduces the specified behavior. This paper gives algorithms to tackle the parameter refinement problem formulated as an optimization problem. We search, within the parameter space symbolically expressed, for the largest hypersphere whose points correspond to parameter values such that the ODE solution gives an instance of the given qualitative trajectory. Our approach overcomes the limitation of a previously proposed stochastic approach, namely computational load and very reduced scalability. Its applicability and effectiveness are demonstrated through two benchmark synthetic networks with different complexity. [ABSTRACT FROM AUTHOR]

Presents information as it relates to the 1997 International Workshop on Qualitative Reasoning, which was held between 3rd June and 6th, June 1997. Where the workshop was held; Focus of the workshop; Impact of qualitative reasoning to system identification; Importance of qualitative simulation.