Spatiotemporal Pattern Formation

The evolution of spatiotemporal patterns of water footprint economic benefits (WFEB) in the 32 counties (cities and districts) of the Poyang Lake City Group in Jiangxi Province was evaluated based on panel data. Whereafter, the spatial spillover effects of the regional WFEB in the Poyang Lake City Group were investigated using the spatial Durbin model (SDM). The results showed a rising trend in the total water footprint (WF) and WFEB of the Poyang Lake City Group from 2010 to 2013, and the number of cities at the levels of high efficiency in the Poyang Lake City Group increased steadily. Clear local spatial autocorrelations were found in WFEB, the degree of spatial clustering of WFEB gradually strengthened during 2010–2013, and the spatial agglomeration of WFEB in the Poyang Lake City Group mainly showed Low-High and Low-Low types of trends, which accounted for 9.4% and 12.5%, respectively, of the four types of trends. Our SDM analysis further confirmed significant spatial dependence of WFEB in the Poyang Lake City Group in Jiangxi Province.

Keywords: water footprint economic benefits; spatiotemporal pattern; spillover effects; Poyang Lake City Group

It is hard to bridge the gap between mathematical formulations and biological implementations of Turing patterns, yet this is necessary for both understanding and engineering these networks with synthetic biology approaches. Here, we model a reaction−diffusion system with two morphogens in a monostable regime, inspired by components that we recently described in a synthetic biology study in mammalian cells. The model employs a single promoter to express both the activator and inhibitor genes and produces Turing patterns over large regions of parameter space, using biologically interpretable Hill function reactions. We applied a stability analysis and identified rules for choosing biologically tunable parameter relationships to increase the likelihood of successful patterning. We show how to control Turing pattern sizes and time evolution by manipulating the values for production and degradation relationships. More importantly, our analysis predicts that steep dose−response functions arising from cooperativity are mandatory for Turing patterns. Greater steepness increases parameter space and even reduces the requirement for differential diffusion between activator and inhibitor. These results demonstrate some of the limitations of linear scenarios for reaction−diffusion systems and will help to guide projects to engineer synthetic Turing patterns.