The development of multi-cellular organisms relies on the coordinated spatiotemporal regulation of gene expressions. To unravel the organizing principles of developmental gene regulatory networks, it is crucial to understand the relationship between the structure and function of spatiotemporal subnetworks. However, thus far, such spatiotemporal networks have not been investigated. Hence, we proposed a new concept called a “spatiotemporal network motif,” which is a sequence of network motifs in time and space, and we applied this concept to analyze the developmental gene regulatory network of D. melanogaster. We found that the results of our approach coincide with spatially specific processes in early, middle, and late embryogenesis.
We also identified patterns of spatiotemporal network motifs and analyzed the relationship between network structures and their biological functions (Figure ). We found that the most frequently observed structure in the spatiotemporal network motif pattern was the feed-forward loop structure (Motif 4) (79% for 19 sub-networks). This finding is also well supported by recent studies: Motif 4 is found ubiquitously in the D. melanogaster
gene regulatory network [6
]; Motif 4 is the core structure of the D. melanogaster
gene regulatory network [30
]; Motif 4 plays an essential role in the D. melanogaster
central nervous system [31
]. This structure, with various regulation types, has several important functions in a biological network, such as detecting persistent signals, generating pulse, and accelerating response [5
]. For example, in the feed-forward loop consisting of the three genes eve, en
, and hb,
the genes are related to specifying cell fate (GO: 0001708) and commitment (GO: 0045165). These triple genes form a coherent type-1 of Motif 4, such that eve
are activated by hb
, and en
is activated by eve
in ectoderm tissue at stages 4–6. In this developmental process, the dynamics of the coherent type-1 [32
] of Motif 4 can be used as a persistent signal detector, which enables the system to respond only to persistent signals while neglecting short-term signals. This means that developmental processes related to cell fate must be robust in relation to noises, and explains how the developmental network deals with noises via the structure of the coherent type-1 of Motif 4.
Interestingly, we found that nested feedback loops were frequently observed in the gap gene network and most of the nested feedback loops contain mutual inhibition structures. Based on Boolean simulations, we showed that the gap gene network has a significantly large number of attractors (eight attractors) and such many attractors in the network are attributable to mutual inhibition. Hence we infer that the gap gene network might have evolved to induce a large number of attractors (by increasing the number of mutual inhibitions) which correspond to various developmental states.
The interlinked incoherent feed-forward loop structure is a key regulatory structure for stripe formation at 4–6 stages in the maternal region [7
] and we identified this network motif (ID 6) at the same spatiotemporal developmental stages. The triple genes (gt, Kr
) of the network motif ID 6 are also consistent with the previous study [6
]. In addition, it is well-known that the feed-forward loop is a crucial structure to DV (Droso-Ventral) axis formation at 4–6 stages in the maternal region [33
] and we also identified this network motif (ID 4) at the same spatiotemporal stages. From these, we conclude we could infer the design principles of Drosophila
development in a holistic manner using our approach.
Network motifs cannot uniquely determine the whole dynamical properties of a regulatory network. In general, the dynamics of a regulatory network depends on multiple factors such as initial conditions, cellular environments, and randomness [34
]. However, some particular dynamical properties can be determined by certain network structures [36
]. For instance, bistable switching cannot be realized without a positive feedback loop in the regulatory network. So, understanding the relationship between network structures and dynamics may still be useful as we can infer some possible dynamical characteristics of a network from its structure. The proposed approach guides us to find specific network motifs (e.g., positive feedback) at a specific spatiotemporal stage and therefore we can estimate possible dynamical properties (e.g., bistable switch) related to the identified network motifs. Taken together, our approach is useful to infer developmental functions of spatiotemporally varying cells based on identification of network motifs.
Most of the previous studies identified network motifs of the whole regulatory networks integrated from various literatures without considering particular biological contexts (e.g., environmental conditions, developmental stages, etc.). The key difference of our study from the previous ones is the identification of network motifs depending on active sub-network assuming that only part of genes may express under some particular spatiotemporal condition. Such a concept has not been proposed so far. This concept provides us (time- and space-) varying patterns of network motifs in terms of time and region simultaneously. For instance, we can find out many types of network motifs at the 4–8 stages, while there is no network motif at the 9–16 stages in the maternal region (Figure ). From this, we can infer that the maternal region requires more complex regulation through several types of network motifs at the former stages compared to the latter stages.
The topological structures of the network motifs that we discovered in this study are not new by themselves. However, the sequence of time- and space-varying network motifs is new. Furthermore, we could associate the dynamical properties of identified network motifs and spatiotemporal developmental processes of Drosophila. For instance, it is well known that the major developmental process at 4–6 stages is differentiation, but there is no differentiation at 1–3 stages in the maternal region. Interestingly, we found the mutual inhibition network motif (ID 8), a key network motif for the differentiation process, at 4–6 stages but not at 1–3 stages. Together, we can infer a specific developmental process at a specific developmental stage from the dynamical properties of the identified network motifs. Furthermore, the presented approach provides us with a useful and single framework in which we can investigate the whole developmental process in a comprehensive view.