Influence Of Spatial Heterogeneity On Bistable Biochemical Reaction System

Mesoscopic level description methods have been widely used to study practical biochemical reaction systems.Many studies have shown that there are many unavoidable noises in the biochemical reaction process in the cell.The system noise on the mesoscopic scale will make the cells with the same gene show complicated variety,and then play an active role in the process of life.Therefore,it is an important scientific question to reconsider the systematic behavior on this kind of mesoscopic level.Experimental and theoretical studies have shown that the bistable behavior of mesoscopic and macro level systems is significantly different.However,the work has focused on a single whole system and has not specifically discussed the effect of spatial heterogeneity of biochemical reaction system on its behavior.It has been shown that the randomness of the biochemical reaction and the population structure of the reaction system,including the volume,shape and spatial distribution of the system,are the main sources of noise in the biological processes within the cells.The actual intracellular biological processes we are facing are more closely related to their spatial structure.Therefore,in this paper,the spatial structure of the system is introduced,and the influence of spatial structure factors on the self-organizing behavior of the biochemical reaction system at mesoscopic level and the change of self-organized critical characteristics are discussed in detail.First,we define the distance function,and discuss the influence of space factors such as volume,dimension and diffusion coefficient on system stability.The experimental results show that,for the system without spatial heterogeneity,with the increase of the system volume,the bistability is becoming clearer and the system state gradually tends to the result of the macro deterministic equation.When the system has a non-uniform spatial structure,there is a most suitable volume range due to the fluctuation of the space points,which makes the system emerge a remarkable bistability phenomenon,and the volume range is closely related to the factors such as the system dimension and diffusion coefficient.Then,we study the behavior characteristics and statistical laws of the typical systems of the double negative feedback loop,which can be used to measure the critical behavior of the mesoscopic system.Our statistical results show that the size distribution of the molecular clusters in the bistable system generated by the bidirectional negative feedback loop is exponential distribution.