Time-varying gene expression network analysis for evolution 1 of the human prefrontal cortex

9 Background: The prefrontal cortex (PFC) constitutes a large part of the human central nervous 10 system and is essential for the normal social affection and executive function of humans and other 11 primates. Despite ongoing research in this region, the evolution of interactions between PFC genes 12 is still unknown, and there is a need to better understand changes in expression of age-related genes 13 over the lifespan. To investigate the evolution of PFC gene interaction networks and further 14 identify hub genes, we obtained time-series gene expression data of human PFC tissues from the 15 Gene Expression Omnibus (GEO) database. A statistical model, loggle , was used to construct 16 time-varying networks and explore the evolution of PFC gene networks over time. Several 17 common network attributes were used to explore the evolution of PFC gene networks over time. 18 The hub genes of different evolutionary stages were identified. At the same time, we explored 19 several known KEGG pathways in PFC and the corresponding development patterns of central 20 genes. 21 Results: Network similarity analysis showed that the development of human PFC is divided into 22 three stages, namely, fast development period, deceleration to stationary period, and destructive 23 recession period. We identified some genes related to PFC evolution at these different stages, 24 including genes involved in neuronal differentiation or synapse formation, genes involved in nerve 25 impulse transmission, and genes involved in the development of myelin around neurons. Some of 26 these genes are consistent with findings in previous reports. Pathway evolution analysis suggests 27 that the axon guidance pathway has been most responsive during the evolution of PFC. 28 Conclusions: This study clarified the evolutionary trajectory of the interaction between PFC genes, 29 and proposed a set of candidate genes related to PFC development, which helps further study of 30 human brain development at the genomic level supplemental to regular anatomical analyses. The 31 analytical process used in this study, involving the loggle model, similarity analysis, and central 32 analysis, provides a comprehensive strategy to gain novel insights into the evolution and 33 development of brain networks in other organisms.

shows the cross-validation results of the three models. We can see that loggle has a 131 smaller CV score than kernel and invar. In addition, loggle and kernel have fewer average edges, 132 while invar has more edges. Furthermore, from Fig. 2, we can see that the PFC time-varying graph 133 constructed by the invar model does not change throughout the lifespan. In contrast, the PFC time-    We further analyzed the similarity between the networks of the nine age periods using the CNSI periods into one category. A closer look at this bubble chart also reveals that the similarity between 181 the 20s and the 30s is also very high (0.6), and the tree diagram puts them in the same cluster. The 182 similarity among the 40s, 50s, and 60s is also high, and their distances in the tree are also short. In 183 contrast, the similarity between the 10s and other networks is low, and the dendrogram places 10s 184 in separate clusters.

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Based on these results, we divided the evolution of PFC into three stages, namely, fast 186 development period (fetus, infant, child), deceleration to stationary period (10s, 20s, 30s), and 187 destructive recession period (40s, 50s, 60s). Central analysis was performed separately to identify Here, we selected five pathways related to brain function (see Table 2 for details) to see the  From Fig. 6 we can see that, as age increases, the number of network edges in these five 215 pathways gradually decreases. From the fetus to the child stage, the network size of these pathways 216 remains largely stable, meaning that most genes involved in these pathways are mostly active in 217 the PFC region during this time period. Then, from the child stage to the 30s, the numbers of edges 218 and genes in all pathways gradually decrease; thus, development gradually slows down and 219 eventually remains relatively stable after the 30s. Among the pathways, the pathway hsa04360 220 (Axon guidance pathway) has the most nodes and edges, with the fastest change from child to 30s.

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Among the five pathways, the Axon guidance pathway is most sensitive to age changes, followed shows that the evolution of PFC gradually declined to a stable period, that is, 10s, 20s, and 30s; (C) demonstrates the destructive recession period in PFC evolution, namely, 40s, 50s, and 60s. A larger node size in the graph corresponds to a higher node degree. Nodes with the highest degree are considered to be hubs and are placed in the network center. We also performed a central analysis of the other two developmental stages, the declining stage 239 (10s, 20s, and 30s) and the stable stage (40s, 50s, and 60s). Owing to limits of space, we placed 240 Fig. 6 The evolution of the time-varying networks over different age periods. The y-axis shows the optimal number of edges at each developmental stage.
the results in the Supplemental File. Please see Fig. S1 and S2 for more details.

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Although the macro-level PFC evolution model has been widely accepted, owing to 258 technological limitations, the trend of evolution at the gene interaction level has not been clearly 259 described. To fill this gap, in our study, we used time-series gene expression data to construct the 260 evolutionary pattern of PFC at the molecular level by estimating the time-varying network graphs. 261 We found that, from the fetus to child stages, PFC experiences fast development and most genes 262 are active during this period. A review by Teffer et al. [26] described that, as the brain size increases   278 We attempted to elucidate the mechanism driving the evolution of PFC by performing a central 279 analysis in three stages based on evolutionary trends; as a result, we identified several hub genes. mainly through the LRRC4C and PARD6G genes (Fig. 7). The gene LRRC4C has been reported to 339 be involved in the regulation of axon development and synaptic development, and its deficit can 340 cause neurodevelopmental disorders [50]. In the case of the gene PARD6G, it was found to be from a cohort study. In addition, we hope to integrate other omics data such as miRNA, DNA methylation, and proteomics data into the network analysis, to obtain a more comprehensive 377 picture of PFC evolution and development. We plan to pursue these issues in future work. represents the sample size. For simplicity, we centered the observations by subtracting the 398 estimated mean ( ) from so that each is drawn independently from (0, ∑( )). 399 We next estimated the precision matrix ( ) ( ( ) = Σ −1 ( )) to construct the graph edge set.

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The loggle model assumes the smoothness of the graphical topology, that is, the edge set of the  high-degree node is called a "hub," and removing such a node affects the network topology and 486 Fig. 9 Detailed procedure for investigating the evolutionary pattern of human PFC gene interaction networks and hub genes