In the biological world, a phase transition can be defined as the transformation of a biological system from one phenotype or state to another, where different phenotypes can be mapped to distinct states. For example, cell cycle is known to have four distinct phases: G1, S, G2 and M phases; cell differentiation contains different stages like cell proliferation, growth arrest and mature differentiation; and cancer development mainly involves three steps as mutation, promotion and invasion. Obviously, analysing those biological phase transitions will offer valuable clues for understanding life and its dynamics. Therefore, a fundamental but important question is how to trace the temporal characteristics or dynamics of a biological system during a particular phase transition process.
The study on molecular mechanism of biological phase transition has attracted much attention [1
]. For instance, by modulating the intracellular redox state and measuring cell cycle progression, the redox cycle within the (mammalian) mouse embryonic fibroblast cell cycle was found to maintain the metabolic processes early in G1 and activate G1-regulatory proteins ahead of entry into S phase [1
]. For a well known agricultural pest as migratory locust with a phase transition from the solitary to the gregarious, many down-regulated and some up-regulated genes were found in various organs when arriving to gregarious phase [2
], which provides molecular indicators and recovers genetic mechanisms of phase transition in locusts. To determine the dormancy status of raspberry buds whose developmental regulation is helpful to promote the economic values of fruit and horticultural industries, a few significant dormancy-related candidate genes for raspberry buds had been identified by principal component analysis on clones' expressions [5
]. Generally speaking, these research works are mainly on the different genotypes or expression variations at the level of individual genes under specific phases. Despite of those progresses, however, there is much less of focus on studying cascade changes or sequential dynamics of genes' or modules' functions at the level of networks during phase transition process.
As well known to us, one gene generally has multiple roles in biological processes but what role at a specific time is still unclear. Thus, identifying a gene functional group or module, which is composed of cooperative genes in biological processes or pathways, can reveal the functional specificity of individual genes or network modules. On the other hand, nowadays, there is rich information on biological processes [6
], but the information on biological processes generally lacks dynamic features even compared with pathways [8
]. Hence, in this paper we intend to identify the sequential structure or cascade dynamics of biological processes during phase transitions by developing a general framework for gene-specific segmentation and temporal block network (or network module), in particular on when and what a biological process or function will be cooperatively facilitated by network modules (or gene modules) during a phase transition. Note that, in the previous studies, the term "dynamic biological process" was usually used to refer to the dynamics of some general biological functional work-flow rather than sequential dynamics of biological processes or pathways [10
]. In contrast, our work focuses on studying conditional and time-dependent behaviours or sequential dynamics of network modules, which are functionally enriched on specific biological processes [13
The rapid accumulation of temporal gene expression data provides us the opportunity to unveil mechanisms of dynamic processes behind phenotype changes. In particular, a recent work shows that temporal dynamical model has ability to detect the presence and absence of stage/phase specific biological processes in Yeast
cell cycle and metabolic cycle [13
]. But, this model is limited to the analysis on the time segmentation for all genes, by simply using the replicated observations to infer biological processes' temporal coordination. To overcome this problem, a new bicluster-based temporal segmentation method in this paper is developed to build a causal process model (CPM) for identifying the temporal features of biological processes during genotype or system reorganizations. In addition to biological processes and pathways, network modules or protein complexes [14
] are used to further illustrate the sequential dynamics of biological systems as the molecular basis of those functional temporal features. Actually, protein modules or protein complexes have been found to play many important roles in biological phase changes, such as, indicator of genetic effect during mammary gland oncogenesis [15
], marker of cancer diagnosis and prognosis [16
], predictor of genotype-phenotype associations [17
], and responser of dynamic cues from the environment [19
In summary, the construction of our causal process model (CPM) includes three steps. First, we identify specific biclusters with linear patterns, and assemble them into temporal blocks representing a group of genes and their time segmentations. Then, each temporal block is refined by conducting functional enrichment analysis. Finally, we infer the sequential or cascade (causal) relations between temporal blocks by a graphical model (e.g., partial correlation) among two groups of genes. Through various experiments, we demonstrate the effect of our method on gene-specific temporal segmentation. In particular, on Yeast
cell cycle data, we show that the phase division based on CPM is more efficient and effective than the segmentation based on traditional CCC-biclustering method [20
]; and in the analysis of phase/cell cycle related biological processes, we found that the group of genes actually displays conditional functional enrichment and protein interaction network rewiring. All those results show that CPM is indeed able to unveil the biological mechanism behind complicated phase transitions.