In the pre-genome era, traditional molecular biology provides very informative knowledge on how individual bio-molecule, i.e. DNA, RNA and protein, perform biological functions. Networks of interactions among bio-molecules are fundamental to all biological processes; for example, the Gene Regulatory Network (GRN) can be described as a complex network of genes regulated by protein binding. Cellular processes are controlled by various types of biochemical networks; such as (i) metabolic networks, (ii) Protein-Protein Interaction (PPI) networks, (iii) GRN, and (iv) signal transduction networks. Biochemical networks are complex in nature; they consist of a large number of bio-molecules, interacting with each other give rise to biological responses and stabilities.
In the post-genome era, it is more productive to investigate how bio-molecules regulate or cooperate on a system level. The graph theory approach is a powerful tool for investigating the underlying topological structures of different molecular networks. A great diversity of graph theoretical notions is discussed to characterize biological networks.
The theory of complex networks plays an important role, ranging from computer science, sociology, engineering and physics, to bioinformatics etc. Within the fields of bioinformatics, potential applications of network analysis include drug target identification, determining biomolecules’ pathways and function, and designing effective strategies for treating various diseases. Molecular networks are the basis of biological processes. Such networks can be decomposed into smaller modules, also known as network motifs. These motifs show interesting dynamical behaviors, in which co-operatively effects between the motif components play a critical role in human diseases. Some of the network motifs are interconnected which can be merged together and form more complex structures, the so-called Coupled Motif Structures (CMS). These structures exhibit mixed dynamical behavior, which may lead biological organisms to perform specific functions.
On the other hand, the ability of a network to perform its intended function depends on how it responds to pressures - both internal and external, Maslov and Sneppen claimed that one could take into account experimental artifacts or mutations by doing an error tolerance study. Therefore, quantifying the robustness of a network is vital in a number of disciplines. Albert et al. proposed four traditional four conventional perturbations: (i) network edges are deleted randomly, during which the process of the total number of nodes are not changed; (ii) network nodes are removed randomly (failure); (iii) the most connected nodes are successively removed (attack) and (iv) nodes are rewired randomly, which is known as the local rewiring algorithm, in which the node degree of each node remains unchanged.
Protein complexes play an essential role in many biological processes. Complexes can interact with other complexes to form Protein Complex Interaction Network (PCIN) that involves in important cellular processes. On the other hand, Cardio Vascular Diseases (CVDs) affect tens of millions of human beings each year. Abnormal proliferation of Vascular Smooth Muscle Cell (VSMC) is a major cause of CVDs. In this study, we examine how VSMC responses when subject to mechanical stress. Time course microarray experiments were used to identify stress-induced Differentially Expressed Genes (DEGs). The gene association network among the DEGs was inferred by using the Gaussian Graphical Model. Besides, Lung cancer is the leading cause of death in Taiwan. By using the microarray data downloaded from GEO, we built the up-regulated and downregulated PPI (Protein-Protein Interaction) network. By comparing early- and late-stage cancer, we can identify stage-specific lung cancer-associated genes. Although many studies are related to biological networks, but there are relatively few studies on examining the above three kinds of biological networks, and little is known about the stability of biological networks. We will employ graph theoretical approach to reveal hidden properties and features of biological networks. A great diversity of graph theoretical notions is employed to characterize many species’ PCINs. Three main issues are addressed; (i) the global and local network topological properties and network structures, (ii) propose 9 new types of network robustness measurements and (iii) derive the key genes and clusters on network topologies.
There are many tasks are undergoing by our research teams to examine the graph theory and robustness analysis of biological networks:
In conclusion, graph theory approach is a useful tool for studying biological networks at a system level and provides insights on topology properties usage. It is very likely that graph theory analysis can supply very specific information for further study; it is an indispensable tool for network biology research.
Huang CH. Graph Theory: A Powerful Research Tool for Biological Network Analysis. SM J Biol. 2015; 1(1): 1001.