Chaos Game Representation Of Functional Protein Sequences And Their Recurrent Iterated Function Systems Simulation

Investigating the biological function of proteins is one key aspect of protein studies. With the development of bioinformatics , bioinformatics methods become important methods to study the biological function of proteins. In this thesis, first we give the chaos game representation of functional protein sequences, then we propose to use recurrent iterated function systems to simulate their chaos game representations, this method can help us to analyze some features of functional protein sequences, furthermore to get the biological function of these proteins. We randomly concatenate the protein sequences with the same function one by one to get a long linked protein sequence. We call these linked protein sequences as linked functional protein sequences. According to the chaos game representation of the linked functional protein sequences and their iterated function systems simulation, we get some conclusions: first, the Chaos Game Representation (CGR) of randomly- linked protein sequences have clear fractal patterns ; second, we find that the recurrent iterated function systems model can simulate the CGR of randomly-linked protein sequences very well; third, when we use recurrent iterated function systems to simulate the CGR of linked functional protein sequences, the relative standard error and the probability matrix are independent on the order to link the functional protein sequences randomly; fourth, the estimated probability matrices in the recurrent iterated function systems model for linked functional protein sequences with different biological functions have evidently difference, this conclusion can tell us that the CGR and estimated probability matrices in the recurrent iterated function systems model for linked functional protein sequences can be used to characterize the difference among linked functional protein sequences with different biological functions.