Modelling and Simulation of GeneRegulatory Networks: Segmentation genes of Honeybee (Apis mellifera) embryos

Abstract

The developmental process involves interactions between thousands and thousands genes. The reasons why, where, and when the genes are expressed can be revealed in the topology of a Gene Regulatory Network (GRN). In this study, we reconstruct a GRN which explains how the expression of gap-genes is initiated along the anterior-posterior axis of Honeybee embryos. We use gene-network-based methods to model these genes in four subdivisions of the anterior-posterior axis. Unlike Drosophila, few quantitative data are available for the segmentation genes of Honeybee embryos. However, we have enough qualitative data to start logically designing a network based on those data. Then, we extend the network considering the expression domain of genes, their functionality, and some assumptions. The generated network is tested using two ODE-based methods and taking into account the quantified form of the data. The methods are Hill-function-based method and gene-circuit method. Both methods create a set of ODEs that contains a number of unknown parameters. We run the simulated annealing optimisation to find the parameters including those that predict likely interactions occurring between the genes. Because the quantified data does not have enough number of time points, many possible solutions are obtained from the optimisation. This led us to reduce the number of unknown parameters considering genetic facts. In this way, the results derived from applying Hill-function-based method are not very encouraging as the results do not show consistency in several repeated experiments. However, the gene circuit method is successful and the results are more consistent after several repeats. The reason for this difference is that while the Hill-function-based method considers more biological details in its equations, the model also involves many parameters. However, applying two methods make the results strong enough to conclude the most likely interactions. Overall, our findings suggest a network whose interactions are testable. All the required data have been collected from the experiments done by Peter Dearden and his colleagues at the laboratory for Evolution and Development at the University of Otago.