Stochastic spatio-temporal dynamic model for gene/protein interaction network in early Drosophila development

Abstract

In order to investigate the possible mechanisms for eve stripe formation of Drosophila embryo, a spatio-temporal gene/protein interaction network model is proposed to mimic dynamic behaviors of protein synthesis, protein decay, mRNA decay, protein diffusion, transcription regulations and autoregulation to analyze the interplay of genes and proteins at different compartments in early embryogenesis. In this study, we use the maximum likelihood (ML) method to identify the stochastic 3-D Embryo Space-Time (3-DEST) dynamic model for gene/protein interaction network via 3-D mRNA and protein expression data and then use the Akaike Information Criterion (AIC) to prune the gene/protein interaction network. The identified gene/protein interaction network allows us not only to analyze the dynamic interplay of genes and proteins on the border of eve stripes but also to infer that eve stripes are established and maintained by network motifs built by the cooperation between transcription regulations and diffusion mechanisms in early embryogenesis. Literature reference with the wet experiments of gene mutations provides a clue for validating the identified network. The proposed spatio-temporal dynamic model can be extended to gene/protein network construction of different biological phenotypes, which depend on compartments, e.g. postnatal stem/progenitor cell differentiation.

Keywords: 3-D embryo space-time dynamic model; diffusion mechanism; drosophila embryo; eve stripe formation; gene/protein interaction network; transcription regulation.

Figure 1.

Determination of eve stripe boundaries at c14A8. A) Along the A-P axis and D-V axis, seven eve stripe boundaries {B1, B2, ..., B8} and three spatial region boundaries {bh1, bh2, bh3, bh4} are defined, respectively. B) The yellow square frame as shown in (a) is enlarged for the second eve stripe. Nine spatial regions with symbol R_stripe,lk are defined in each stripe.

Figure 2.

Normalized mRNA and protein expressions. Solid line and dashed line denote protein and mRNA expressions, respectively. The expressions of knirps (cyan line), krüppel (green line) and giant (black line) are plotted in time profiles.

Figure 3.

Original data and estimated results by our proposed dynamic model. The original eve mRNA and protein spatial data at c14A8 are shown in A) and C), respectively. After system identification, the estimated eve mRNA and protein spatial data generated by the dynamic model are shown in B) and D), respectively.

Figure 4.

3-DEST dynamic gene/protein interaction network for diffusion and transcriptional regulation mechanisms in different spatial regions in the whole embryo. The notations, R_1,11, R_1,12, R_1,13, R_1,21, ..., R_7,31, R_7,32, R_7,33, are the 63 spatial regions of the whole embryo which is specified by Figure 1(a). In each spatial region R_stripe,ij, the colors of the outer ring in the color circle are specified by the 14 gene names, which are given by the color bar below the figure, respectively. Each color of the outer ring is specified by each gene. The solid lines that connect color circles stand for transcription regulation between genes in each spatial region based on regulatory abilities β̂_ij of the identified 3-DEST dynamic model in Eq. (9). Positive and negative regulations are denoted by arrows and bars at the end of solid lines, respectively. Additionally, the colors of the inner circle, i.e. the black and white circle, inside the color circle stand for the TFs’ roles, i.e. donor or acceptor of the transcriptional regulation network, respectively. The bold color lines that connect the same genes in neighboring spatial regions with different roles stand for protein diffusions from donor (black inner circle) to acceptor (white inner circle) in neighboring spatial regions based on the diffusion coefficients γ̂_j of the identified 3-DEST dynamic model in Eq. (9). The specification of the colors in bold color lines is consistent with the colors in the outer ring of the color circle, which are specified by the color bar. For example (see also Fig. 5a), Caudal in R_4,11 with green color in outer ring and black color in inner circle found regulates ftz (yellow) and runt (navy blue) and plays as a donor, which can diffuse to the neighboring regions. A clearer figure is available online at the website, http://www.ee.nthu.edu.tw/bschen/Drosophila_Fig4.pdf.

Figure 5.

Coherence and incoherence feedforward loops of 3-DEST dynamic gene/protein interaction network. (A) According to the rule that each of the regulation relationships of FFLs must exist in at least four neighboring spatial regions, parts of gene/protein interaction network (left) in R_3,2, R_3,3, R_4,1 and R_4,2 are examples of feedforward loops, and can be redrawn as C15 (right). (B) From the above rule, we find the network motifs, i.e. 25 C-FFLs (C1∼C25) and 18 I-FFLs (I1∼I18), for the cooperation of transcription regulations with diffusions in early embryogenesis. The color bars denote diffusions, which are the same as those in Figure 4. A clearer figure is available online at the website, http://www.ee.nthu.edu.tw/bschen/Drosophila_Fig5.pdf.