The Studies On Dynamic Behaviors In Biological Gene Regulatory Systems And Calcium Ion System

The research of nonlinear science covers mathematics, physics, biology, medicine, geology, engineering, economics, and sociology, and other spheres. Nonlinear dynamics is interdisciplinary science which studies non-equilibrium processes, mechanism and the law of mutual transformation of those nonlinear dynamic behaviors. The study of nonlinear dynamics in the different field has very important significance.Organism is a typical nonlinear and non-equilibrium system. The organisms exchange the matter, energy and information with the environment all the time in order to survive. All the living actions run under the transformation and modulation of the cell information, such as growth, development, reproduction, metabolism, irritability. Organisms live in environments filled with a variety of noise and signal, so we can be sure that the impact of various noise and signal on the information exchange and transmission in the cells is inevitable. The investigation of those influences is very important in nonlinear science. In this dissertation, we have studied nonlinear dynamic behaviors of the synthetic gene network system and calcium ion system affected by noise and signal in the biological cell. The results are believed to make contributions for getting a better understanding in dynamic mechanism in the synthetic gene network system and calcium ion systerns.The main contents of my dissertation are as follows:First, the influence of external disturbances on synthetic gene network was studied. The dynamics behavior of a synthetic gene network is investigated by numerical simulation. The results show that when the additive noise and multiplicative noise is injected into system at the same time, without the external signal, noise can take active part in the system, noise induced switch, explicit internal signal stochastic resonance, implicit internal signal stochastic resonance and internal signal stochastic bi-resonance can be exhibited. If a periodic signal is considered, the intensity of the internal signal stochastic resonance can be enhanced or suppressed by adjusting the periodic signal amplitude or frequency, which indicates that if the amplitude or frequency of the external periodic signal is tuned, the intensity of internal signal stochastic resonance can be adjusted. Second, the dynamics behavior of the synthetic gene network which is proposed by Hasty et al was investigated in four kinds of noise disturbance means, inspired by the above-mentioned research. The results show that the explicit internal signal stochastic resonance and implicit internal signal stochastic resonance which is induced by noise can occur, under the different kinds of noise disturbance means. The dependency of the correlation time on control parameter is studied under different kinds of noise disturbance means. It is found that internal signal stochastic bi-resonance (ISBR) can take place in the systems, and we find the best way of noise disturbance that internal signal stochastic resonance (ISSR) and ISBR can occur. Then, we propose a new program which can be used to adjust ISSR and ISBR.Then, the vibrational resonance in the synthetic gene network system was studied. The results show that the system which lies in the stable state can take place vibrational resonance under the in?uence of both low- and high-frequency forces without noise, different amplitude or frequency of the low-frequency signals can be amplified by vibrational resonance.We find that the ratio of the best high-frequency signal amplitude and the corresponding high-frequency signal frequency is a different constant under the different control parameters, we believe that discovery can provide theoretical guidance for looking for the optimum amplitude of high frequency signal under which vibrational resonance can take place. Moreover, the effect of noise on the vibrational resonance was studied.Finally, the vibrational bioresonance (VBR) and its control in a calcium ion oscillation system under the influence of low-and high-frequency signals were studied. Results show that calcium ion oscillations consist of two peaks (VBR) under the influence of both low-frequency and high-frequency signal. The weak signal with lower frequency and higher amplitude is more likely to be amplified during VBR. Close to the Hopf bifurcation point (small control parameter threshold), VBR is weak and the maximum amplitude of the high-frequency signal gradually shifts to higher values. The feedback mechanism plays an important role in the amplification and suppression of VBR during the formation of calcium waves in cells. A positive feedback mechanism, therefore, enhances the VBR while a negative feedback mechanism decreases the VBR. Furthermore, when noise is introduced into the system, the stochastic resonance (SR) suppressed the VBR and influences the number of vibrational resonance (VR) peaks. A critical level of noise exists for different resonant behaviors and when the noise intensity is below a critical level VBR occurs, while above the critical level a single VR peak appears.