Dictyostelium Cell Populations In The Spiral-wave Numerical Simulation

The past decades witness the golden age of molecular genetics by understanding several model organisms such as Dictyostelium discoideum.Howerver,we still learn little about pattern formation in living systems,neither at the subcellular level such as ca²⁺waves in a single living cell,nor at the supracellular level such as electrical waves in heart tissue.Dictyostelium cell populations provide one of the best investigation tools for probing spatiotemporal pattern formation at the supracellular level in living media.We have much knowledge about molecular details of Dictyostelium.The behavior of cAMP waves in Dictyostelium cell populations can be well described within the classical reaction-diffusion equations.In this paper we numerically study the local control problem of spatiotemporal turbulence of spiral cAMP waves in Dictyostelium cell populations.Simple models can always capture the nature of systems.Generally speaking,Dictyostelium cell populations are classical excitable media.Under some conditions,it can be shifted to oscillatory media.In the second part of this paper,we adopt two different simple models to model the universal behavior of spiral cAMP waves in Dictyostelium cell populations.One is the Complex Ginzburg-Landau equation,which is a generic equation describing spatially extended systems in the vicinity of a Hopf bifurcation. The other is the FitzHugh-Nagumo type equation,which describes classical excitable media.Our results reveal that in the classical oscillatory and excitable media:(1)local stimulation with specific frequencies and amplitudes,located in the very vicinity of a spiral tip,can significantly change the oscillating period of a little spiral in the spatiotemporal turbulence,and then remove turbulence by developing the spiral;(2) local stimulation with appropriate frequencies and amplitudes can directly generate target waves to remove turbulence.The study of controlling spiral cAMP waves in Dictyostelium cell populations has peculiar value for the problem that how to terminate spiral electrical waves in hearts.Today we know little about the real behavior of spiral electrical waves in vivo. On the one hand it is mostly because the minimally invasive,genetically targeted and temporally precise control of cell activity in vivo in large spatial domains of hearts is definitely impossible currently.One the other hand we could not directly image the electrical patterns in deep hearts of three dimensions.