Effect Of Biochemical Parameters On Population Behavior

There are many factors for influence the population behavior of cells. Except for the ways of cellular communication and the cellular environment, which have been considered in the previous studies, transcription cooperativity(or Hill coefficient) that has been little considered before is also an important factor. This article investigates the effects of Hill coefficient on dynamical behavior in a synthetic multicellular system, where individual oscillators are an integration of repressilator and hysteresis-based oscillators and are coupled through a quorum-sensing mechanism.By bifurcation analysis and numerical simulation, we find that because of the variety of Hill coefficient the system can show five kinds of typical dynamical structures on cell density, which suggests that Hill coefficient has great influences not only on the system’s ability to oscillate and the modes of oscillation but also on the occurrence of multistability. Properly increasing Hill coefficient, the system evolve along the route from monostability to switches among monostability, bistability and multistability,from non-oscillation to simple oscillation, from a single oscillating mode to switches among a variety of oscillating modes. Our results may be the foundation for understanding complicated collective behaviors of cells.On the basis of the above study, we change the structure of a single system, in the suppression of vibrator applying a feedback loop, based on the topology of the knowledge, such coupling feedback loop has a total of 12 cases, in order to consider the effect on biochemical parameters of the coupled system is more convenient, only consider 12 kinds of 2 kinds of coupling feedback loop here, composed of loop interaction of biological networks can exhibit complex dynamic behavior. Typically,the biological function of the loop is composed of some simple feedback circuit. In the second part of this paper studies the coupling loop consisting of simple circuit,through the modeling and dynamic behavior of mathematical analysis. By changing a parameter value, found the coupled system to show the dynamic behavior of a richer.By plotting the bifurcation diagram, shown between 2 coupled loop in the dynamic aspects of the mutual influence and role, find out the interval of Hill coefficients of Hopf bifurcation occurs when the coupling system, and the interval of pressing parameters produce of bistable.