Analysis To Combinatorial Perturbation Of Bifurcation-based Theory And Its Applications

We present a bifurcation-based method of combinatorial perturbation to study some new issues relating to combinatorial regulations and combined drugs that arise from molecular networks, biological functions, development and treatment of diseases. The method can be used to analyze the influences of combinatorial regulations on dynam-ics of system. Compared with the known methods that are used to evaluate efficiency of combinatorial perturbation, our new method does not need the complicated computations and has a convenient analysis process, because this method does not revolve the transient dynamic that occurs as a response to stimulations. Moreover, the method has important applications on regulation of biological functions, cell fate decision, and treatment of combined drugs. Using the stability analysis and the bifurcation-based combinatori-al perturbation method, we investigate the dynamics evolution of HBV/HDV infection model during treatment with combined drugs of PEG IFN a and nucleos/tide analogues, and study the synergism of the combined drugs acting on treatment of HBV/HDV infec-tion. Moreover, by integrating with the known clinical and trail reports, we also analyze the potential reason why therapies with combined drugs of PEG IFN a and nucleos/tide analogues present the different efficacies to the different patients who has been infected by the HBV/HDV.Main works of the paper are sections 3 and 4. The details are shown in below:1) First, aiming at some issues of combinatorial perturbation arising from molec-ular networks and disease treatments with combined drugs, we analyze the realistic sig-nificance and rationality of the new bifurcation-based combinatorial perturbation method presented by us, and give the theoretical derivation and definition of the bifurcation-based combinatorial perturbation method by analyzing a multistable decision model. Second, we study the optimal strategy of combinatorial perturbation by investigating the relation-ship of objective function and combinatorial perturbation. Finally, using the bifurcation-based method we carry out the combinatorial perturbation analysis to a biologically real-istic CREB model to verify the efficiency and calculative simplicity of our method, and also to compare with the known method.2) We develop a new HBV/HDV infection model by integrating the immune response mechanism, and investigate the local stability of equilibria using the stability theory. We also study the dynamical evolutions of the model under treatments with single or combined drugs using the bifurcation theory. To investigate whether the synergistic action of the combinatorial drugs composed of PEG IFN a and nucleos/tide analogues on treatment of HBV/HDV co-infection or super-infection occurs, we perform a systematically analysis using the bifurcation-based method, and verify the synergistic regulation of the combined drugs acting on treating HDV infection. Moreover, based on the differences of immune responses of infected individuals, we preliminarily analyze the reason why the treatment with combined drug presents different efficiencies to different HDV infected patients.