Numerical Simulation And Theoretical Analysis Of Complex Spatiotemporal Self-Organization In Allosteric Enzyme Biochemical Reaction-Diffusion Systems

In the production processes of chemical engineering, interactions of nonlinear (bio)chemical reactions with a variety of physical processes including diffusion, adsorption and desorption, mass and heat exchange, global and local convective flows, and ionic migration in electric field form a typical nonequilibrium complex system. A typical characteristic of this system is the capacity to support abundant spatiotemporal self-organization phenomena.Through feedback adjustment, the allosteric enzymes control the biochemical reactions and induce the nonlinear feature of the reactions simultaneously. The coupling between the nonlinear biochemical reactions and species diffusion in the cells or biochemical reactors leads to the formation of static and dynamic spatiotemporal structures during the process of biochemical reactions. These spatiotemporal structures have very important significances for the formation of cytoskeleton, signal transduction, adjustment of metabolism, as well as the progress of the biochemical reactions in the reactors. The spatiotemporal self-organization process in the glycolysis-based single allosteric enzyme reaction-diffusion system and the coupling allosteric enzyme reaction-diffusion system are investigated in this dissertation. With the methods of numerical simulation and theoretical analysis, a lot of novel spatiotemporal structures have been discovered and some universal principles on the formation and evolution of spatiotemporal structures in chemical reaction-diffusion systems have been obtained.The conditions adopted by former researchers in the numerical simulations of the single allosteric enzyme reaction-diffusion model do not accord with the experimental conditions so that the simulation results can not reflect the validity of the model. The simulations in this dissertation, however, strictly mimic the experiments. With the research methods similar to the experiments of glycolytic extracts, the experimental phenomenon ? temporal target waves are first reproduced in numerical simulation, and irregular continuous target waves and spatiotemporal turbulences are observed by elevating the magnitude of the local perturbation which pioneers new directions for the experimental research of glycolytic reactions.Through the numerical simulation of the coupling allosteric reaction-diffusion system, three new kinds of complex spiral structures are discovered, which are spiral waves with superimposed target waves, novel tip spiral waves, and arm-splitting spiral waves, respectively. The superimposed target waves are formed due to the modulation on the spiral amplitude by the newly appearing modulation mode of the system. There are no evident changes occurring to the wavelength of the spiral waves during the evolution process of the spiral waves, which makes the breakup of the spiral waves with superimposed target waves happen via the rupture of the spiral arms rather than the collision of spiral arms in other modulated spiral waves. The concentration values of species in the conventional spiral tip all equal their steady state values, but the concentration value of one of the species in the novel spiral tip is larger than its steady state value. When the spiral tip begins to meander due to the modulation on the spiral waves, the value of the species in the tip begins to oscillate. When spiral meandering becomes irregular from regular, the spiral breakup will happen, but it can reintegrate soon. Some time later, it breaks up for the second time, but can not reintegrate again. Such phenomenon is also observed for the first time in the studies of spiral breakup. The spiral waves with mixed-mode oscillatory local dynamics are first studied using the coupling allosteric reaction-diffusion system, which gives rise to the observation of the arm-splitting phenomenon of the spiral waves. It is the first time to discover the complex sub-structure within the spiral arm. Moreover, it is observed that the breakup of the arm-splitting spiral waves is induced by the back-firing behavior: some small segment waves born in some parts of the spiral arm propagate in the direction opposite to that of the spiral waves and collide with the inner spiral arm so as to lead to the mutual annihilation and the subsequent spiral breakup in the collision sites. Unlike the usually studied spiral waves which tips are unstable focus, the tip of arm-splitting spiral waves is a saddle node. This should be the origin of the distinct dynamic behaviors supported by arm-splitting spiral waves.