Abstract
Large and complex biological networks are thought to be built from small functional modules called motifs. Currently there has been insufficient study of the fundamental understanding of these motifs which has resulted in a lack of consensus of their role and presence in biology. Here we investigate two networks that produce biologically important dynamics, an oscillation and a toggle switch. We couple these motifs and observe multiple sets of combined dynamic behaviour and evidence of gene connectivity preferences between the two networks. Such fundamental studies of networks can be performed computationally with detailed mathematical analysis that may not be possible from experimental data due to noise and experimental costs. Computational studies can also be used in conjunction with experimental data to analysis and interpret large scale data sets such as high-throughput data. Here we use such an approach to go beyond fundamental networks and model a system of particular interest in biology, the bacteria Streptomyces coelicolor, which produces a plethora of antibiotics and medicinal compounds. The regulatory network of genes in S. colicolor is vast and sub-networks can span hundreds, or even thousands of genes. Currently there is insufficient data to statistically reverse engineer regulatory networks for large networks, known as underdetermined problems. The complexity of real data due to noise is also a problem for inferring networks, and as a result much of the research community focus on small artificial data sets to benchmark their algorithms. Here we develop a novel algorithm which uses data integration and processing with a multi-objective set-up that enhances convergence through multiobjectivization. Additionally our algorithm uses a decoupled optimisation approach to improve the optimisation and parallel computation to significantly reduce computational run times. Our algorithm is general and can be applied to any network with time series data of any size. We compare various size biologically relevant sub-networks within S. colicolor with several optimisation arrangements and demonstrate our novel approach is the best over any network size. Furthermore, we apply our algorithm to the PhoP sub-network of 911 genes within S. colicolor, which is strongly linked to antibiotic production. All networks here are reconstructed from real experimental data. Our algorithm is able to build a regulatory model for 911 genes in the PhoP network for time series data sets of up to 32 points, both of which are far larger than current methods.