Abstract
Pattern formation is ubiquitously seen in nature, while the underlying mechanisms are not clear in most cases. We described a synthetic system by simply coupling cell density and motility, which enabled the programmed cells to form autonomous sequential periodic stripes. To characterize the stripe pattern, several novel techniques have been developed to quantify the key parameters, such as cell growth, cell density profile and the relationship between the cell density and motility, besides the standard molecular biological measurements. To better understand the underlying principle of the stripe pattern formation, a quantitative model is developed based on the experimental system and the quantitative measurements. The detailed dynamic process is studied by computer simulation, which helps us to understand the mechanism of the system. Besides, the model predicts that the number of stripes can be tuned by varying the parameters in the system. This has been tested by quantitatively modulation of the basal expression level of a single gene in the genetic circuit. Moreover, theoretical analysis of a simplified model provides us a clear picture of the stripe formation process. The steady state solution in the traveling wave coordinate is calculated, which lead to an analytic ansatz that can determine the phase boundary between the stripe and the no-stripe phases.
This study does not only provide a quantitative understanding to the novel mechanism of forming stripe patterns formation, but also sets an example for quantitative biology studies. The techniques, methods and knowledge glean here may be applied in various fields in the future interdisciplinary studies.