Markov Chains In Biological Networks

Complex networks exist in every aspect of nature and society. After being created, it has become one of the most powerful tools in the study of complex systems. Most system in the life sciences can be described by the various biological networks, whose topology is the current study mainly focuses on. The paper is organized as follows.In chapter 1, we have a description about the history of the complex networks'development, the categories of the biological networks, and some existing models.In chapter 2, we introduce the basic conception and theories of the Markov Chains and Martingale, also the Laplace method of the differential equations is mentioned at the same time.In chapter 3, the growing pro tome network which is put forward by Romualdo et al is recommended, then we make some improvement on the way of the evolutionary, and propose the improved R model. At last of this chapter, with the use of the Markov Chains and the Laplace method, we prove that the degree distribution of this model obeys a power law, that is, it's a scale-free network.In chapter 4, we bring forward a more accurate model which named evolving protome networks, and demonstrate the existence of the degree distribution in this model. Further more, we have the explicit expressions of it. The result shows that the degree distribution of this model obeys a power law, which means, it's a scale-free network. The result has some reference values on the application of the Markov chains in PPI networks.In the last chapter, we summarized the advantages and the shortcomings of the model we put forward, and propose the improving areas.