Fig. 4

Demonstration of 12 pairs of significant local differential networks. To demonstrate the effectiveness of the I-score scheme, 12 pairs of the most significant differential local networks are presented, i.e., local networks with dynamically significant change in I-scores around the identified critical time point (8 h). For each pair, the left network is the differential network in the normal state (4 h), while the right one is in the disease state (12 h). In terms of these networks, 55–80% nodes had turnover (from low expression to high expression with significance value P < 0.05, or vice versa) and 33–60% edges had turnover (from negative correlation value to positive, or vice versa) when the system progressed from the normal state to the disease state. The ratios of the turnover neighbours and edges overwhelm those of the background 28.6% (turnover neighbours) and 18.1% (turnover edges), i.e., the ratio of the turnover nodes/edges in the whole STRING molecular network. Among these significant local networks, some well-known genes that were involved in apoptosis or related to the inflammatory response were included: JUN (local network 8), NOTCH2 (local network 12), MYC (local network 1), IL1B (local network 7), and PTGS2 (local network 5). To analyse and illustrate the dynamical difference before and after the critical transition, graph-related information is shown in Table 1