An Empirical Study of Immune System Based On Bipartite Network

Many complex systems use networks as their backbone. Complex Network is a more effective method to describe complex systems. In particular, in biological systems studies, it is increasingly recognized the role played by the topology of cellular networks, the intricate web of interaction among genes, proteins and other molecules regulating cell activity, in unveiling the function and the evolution of living organisms (Jeong et al., 2000; Wagner and Fell, 2001; Jeong et al., 2001; Maslov and Sneppen, 2002; Milo et al., 2002) [1][2][3][4][5] . It is interesting to investigate the network descriptions on immune system (IS). IS is the most important defense system to resist human pathogens. This system consists of immune organs, immune cells and immune molecules. Each cell plays an important role in immune system. The function of many cells in immune system mediated by a group of protein is called cytokines. Cytokines are rapidly produced by immune cells in response to tissue injury, infection, or inflammation. The overproduction of cytokines mediates tissue damage and physiological and molecular mechanisms have evolved to control their production and to prevent the injury during the host response. In addition to regulate cellular interactions, cytokines are the molecular players that signal the brain to respond to the danger of viruses, bacteria, fungi and parasites through an elaborated coordination [6,7] . So we have necessary to find some important immune cells and cytokines .

Although many details of cytokine interactions have been elucidated and the effects of cytokines on a myriad of cellular functions have been described [8] , practically nothing is known about the network topological structure of the system as a whole. All cytokine interaction exhibit nonlinear behaviors [9] . In fact, they act in a complex, intermingled network where one cytokine can influence the production of, and response to, many other cytokines. So we believe that IS should be more effectively described by complex network.

In this paper we suggest an immune model with complex network theory [10,11] . The paper is organized as follows. In section two we shall present our model and method. In section three we shall present some results. In the last section, we make a conclusion.

Other authors have modeled the immune system, with a variety of approaches and areas of emphasis [7,12] . But many essential features of this complex system are still not understood. P.Tieri has presented a method to quantifying the relevance of different mediators in the human immune cell network. He draw the cumulative relevance distribution of the immune weighted network , which followed power-law with index of 2.8 [?] . We collect immune data through COPE database and built an immune cytokine network [?] .

Here we use bipartite graphs to built our network. Bipartite network is a graph which connects two distinct sets (or partitions) of nodes, which we will refer to as the top and the bottom set. An edge in the network runs between a pair of a top and a bottom node but never between a pair of top or a pair of bottom nodes [13] (see Fig. 1). Typical examples of this type of networks include collaboration networks [14]. Such as the movie-actor, article-author, and board-director network. In the movie-actor network, for instance, the movies and actors are the elements of the top and the bottom set respectively, and an edge between an actor “a” and a movie “m” indicates that “a” has acted in “m”. The actors “a “and “a′” are collaborators if both have participated in the same movie ,i.e., if both are connected to the same node “m ′” [13] . The concept of collaboration can be extended to include so diverse phenomena represented by bipartite networks as the city people network, in which an edge between a person and a city indicates that the person has visited that particular city, the word-sentence [15,16] , bank-company [17] or donor-acceptor network, which accounts for injection and merging of magnetic field lines [18,19] .

As described above is the bipartite network on the knowledge . Next, we used the method of bipartite network to build our immune system. Because the immune system we discuss in this paper have two distinct sets of nodes, the edges between the top nodes and the bottom nodes in our immune system indicates secretion relation.

The immune bipartite network we consider is constituted by two kinds of nodes, one is immune cell types, the other is mediators . In this view, the mediators’s role is uniquely one element in a network of mediators interaction. We consider these immune cells mediated by soluble molecules such as cytokines, chemokines, hormones. In the immune system model we construct with 44 top nodes, 1640 bottom nodes, 5391 links. We can also considered top nodes and bottom nodes respectively as act and actor. These data are small compared to other bipartite networks such as the Hollywood actors collaboration network and scienti

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