Calcium Ions And Coupled Calcium System Dynamic Behavior And The Regulatory Mechanism Of Transcription Factors

Nonlinear dynamics is an interdisciplinary science which studies non-equilibrium processes , mechanism and the law of mutual transformation of nonlinear dynamic behaviors.Stochastic resonance(SR) is a counterintuitive and nonlinear phenomenon of nonlinear systems.It shows that the input signal can be amplified and the signal-to-noise can be maximized under the certain noise intensity as the nonlinearity of a system matches with its input signal and its input noise.It is applied in many fields like Physics,Chemistry,Biology,Mathematics,Sociology and etc.In later research,it reveals that when the system is inherently oscillatory and the periodic force is absent,the similar phenomenon is observed and is termed as coherent resonance(CR).Cell is the basic structural and functional unit of organism.Calcium ion is one of the most important messengers in the cells and it plays an important role in the information transmission among and inter-cells. As it has a high degree of nonlinear and abundant nonlinear dynamic behaviors,it has been attracting considerable attention and at the same time it is also becoming a hotspot because of its controlling of transcription factors.In order to explain the Ca²⁺ oscillation behavior and its influence to transcription factors,scholars have developed many relevant Ca²⁺ dynamic models and dynamic models of transcription factors. In this thesis,we made some new attempts and researches based on those models.The main contents of my dissertation are as follows:1.The positive effects of noise recycling on calcium ion system was investigated by using numerical simulation methods.It shows that under noise recycling,with re-injection of a fractionε=1 of (?) (t),the multiple calcium coherence resonance phenomenon appears as the noise-recycling prolongs.Whether the re-injected fractionεof ? (t) is positive or negative can only change the extremes of the coherence resonance but not the intensity of coherence resonance,but the amplitude of coherence resonance can be influenced by the size of the value ofε.When the external signal is injected into the system,the intensity of coherence resonance can be strengthened with the increasing of signal amplitude,and the number of peaks can not be changed;when the signal amplitude is fixed,the coherence resonance becomes complicated with the changes of signal frequency.The first peak value of coherence resonance can be strengthened with the changes of external signal amplitude and frequency,which leads to the conclusion that more noise energy can be converted into signal energy when the first peak is formed.2.Dynamics of calcium oscillation in one-dimensional linear two-way coupling cell system is discussed by recycled noise. it shows that when one end of the cell chain is perturbed by recycled noise,the calcium ion signal can propagate along a linearly coupled cell chain with considerable enhancement and periodic calcium ion oscillation produces with the time-delayed increases of the recycled noise.The closer to the H?pf bifurcation point,the coherence resonance is more likely to be amplified. When the re-injected fraction of recycled noise is negative,system can also oscillate with different phases of periodic Ca²⁺ oscillation and the first resonance peak splits into two smaller peaks when noise intensity is small.Furthermore,the size of the re-injected fraction of recycled noise can also act as a control way of coupled calcium ion.3.It is found that oscillation area of the H?pf bifurcation point is increased by the calcium ion model joined time delayed.Further studies shows that comparing time delayed to time delayedτ=0,under the internal or external noises,time delayed can produce the coherent resonance of coupling Ca²⁺ system when steady-state distance of the H?pf bifurcation point is the same.the maximum value with time delayed is the same as the maximum CM value without time delayed,but coherent resonance of system can be suppressed by the existence of time delayed,i.e. noise intensity which is correspond to the maximum CM value with time delayed is much larger than noise intensity when time delayed does not exist.4.The noise-induced Ca²⁺ oscillations is studied how to control the activation of transcription factors for the four configuration of the connected cells.It is found that the coherence resonance (CR) phenomenon can occur in transcription factors with the increment of noise intensity,implying the noise-induced Ca²⁺ oscillations can effectively control the activation of the transcription factors.When only one noise source is injected to the system, the effect of configuration of the connected cells plays a key role for the activation of the transcription factors,the smaller the average distance between the noise-induced cell and other cells is,the larger the oscillatory frequency and the better the regularity of the transcription factors is,and the signals are more favorable for the propagation among the cells.However,if different noise sources are introduced into the system,the effect of noise on the activation of the transcription factor is more remarkable than that of the configuration of the connected cells.