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Reconstruction of regulatory networks is one of the most challenging tasks of systems biology. A limited amount of experimental data and little prior knowledge make the problem difficult to solve. Although models that are currently used for inferring regulatory networks are sometimes able to make useful predictions about the structures and mechanisms of molecular interactions, there is still a strong demand to develop increasingly universal and accurate approaches for network reconstruction.
Time series data are an important source of information for regulatory network reconstruction. A widely used approach to reconstruct regulatory networks from time-series data is based on the first-order, linear ordinary differential equations. This approach is justified only if it is applied to system relaxations after weak perturbations. However, weak perturbations may not be informative enough to reveal unambiguously network structures. Other approaches are based on specific models of gene regulation and therefore are of limited applicability.
We have developed a generalized approach for the reconstruction of regulatory networks from time-series data. This approach uses elements of control theory and the space-state formalism to approximate interactions between two observable nodes (e.g. measured genes). This leads to a reconstruction model formulated in terms of integral equations with flexible kernel functions. The kernel functions can be derived from priory knowledge or identified from experimental data. A library of empirical kernel functions can be used for the first insights into network structures.
The appropriate kernel function can significantly increase the accuracy of network reconstruction. The best kernel can be selected using prior information on a few nodes’ interactions. Even with as small as two known interactions it may be already possible to select models ensuring reasonable performance.
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