The Effect On Polymer In Biological Clock Oscillation

The biological clock is an intrinsic mechanism for the physiological and behavioral changes of the organism to adapt to the periodic changes of the environmental factors.These physiological phenomena,which change periodically for 24 hours,are essentially the result of periodic changes in the concentration of some proteins in the cells.So we can describe the changes in the concentration of these proteins by establishing differential equations,and then study the problem of the biological clock.This paper,based on polymeric mathematical model of the mammalian clock,uses a cross study method to explore the role of polymer in the biological clock oscillation.The research methods include:(1)mathematical modeling;(2)Hopf bifurcation analysis of delay differential equations;(3)numerical simulation experiments.The work of this article is mainly concentrated in the following three parts:(1)The establishment of a polymeric mathematical model for the transcription regulation of the mammalian clock systemThe biological clock system is essentially composed of clock genes and self-regulated loops.Based on the regulation of the mammalian circadian clock gene diagram simplification,we set up a delay differential equation to describe the negative feedback regulation mechanism of biological clock gene composition,and study the dynamical behavior of biological clock system from the mathematical level.(2)To explore the effect on polymer in biological clock oscillator based on the bifurcation theory of delay differential equationsThe biological clock system with time delay,the negative feedback regulation loop is an important mechanism of system oscillation,based on polymeric mathematical model of the mammalian biological clock,using the method of analysis of delay differential equations Hopf branch,combined with the mathematical theory to prove that the unimer cannot make the system clock oscillation;And further,according to the mathematical knowledge,the more polymerization of the polymer in the biological clock system,the more robust the oscillation of the system is.(3)Numerical simulation combined with biological phenomena to illustrate the correctness of the above conclusionsFinally,using Matlab software to verify the relevant conclusions of this paper in the exploration of the role of the polymer in the biological clock oscillator,the correctness of the conclusion is further explained,and the relevant results are given a reasonable explanation on the biological level.This paper studies the effect on polymer in the biological clock oscillator,is essentially the influence of parameter variation on the stability of the system,to a certain extent,illustrates a mechanism of biological clock oscillation robustness,and provides a new idea for synthetic biology oscillator.