Abstract
The spatial patterns of gene expression in early Drosophila melanogaster embryogenesis have been studied experimentally and theoretically to reveal the molecular basis of morphogenesis. In particular, the gene regulatory network (GRN) of gap genes has been investigated through mathematical modeling and simulation. Although these simulation-based approaches are useful for describing complex dynamics and have revealed several important regulations in spatial patterning, they are computationally intensive because they optimize GRN with iterative simulation. Recently, the advance of experimental technologies is enabling the acquisition of comprehensive spatial expression data, and an efficient algorithm will be necessary to analyze such large-scale data. In this research, we developed an efficient algorithm to infer the GRN based on a linear reaction-diffusion model. First, we qualitatively analyzed the GRNs of gap genes and pair-rule genes based on our algorithm and showed that two mutual repressions are fundamental regulations. Then, we inferred the GRN from gap gene data, and identified asymmetric regulations in addition to the two mutual repressions. We analyzed the effect of these asymmetric regulations on spatial patterns, and showed that they have the potential to adjust peak position. Our algorithm runs in sub-second time, which is significantly smaller than the runtime of simulation-based approaches (between 8 and 160 h, for exmaple). Neverthe-less, our inferred GRN was highly correlated with the simulation-based GRNs. We also analyzed the gap gene network of Clogmia albipunctata and showed that different mutual repression regulations might be important in comparison with those of Drosophila melanogaster. As our algorithm can infer GRNs efficiently and can be applied to several different network analysis, it will be a valuable approach for analyzing large-scale data.
