Model selection in the reconstruction of regulatory networks from time-series data

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 if it is applied to system relaxations after weak perturbations. However, weak perturbations may not be informative enough to reveal 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 state-space 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. We propose a library of kernel functions that can be used for the first insights into network structures.

We have found that the appropriate kernel function significantly increases the accuracy of network reconstruction. The best kernel can be selected using prior information on a few nodes' interactions. We have shown that it may be already possible to select models ensuring reasonable performance even with as small as two known interactions. The developed approaches have been tested with simulated and experimental data.