Numerical scheme based on the spectral method for calculating nonlinear hyperbolic evolution equations

High-precision numerical scheme for nonlinear hyperbolic evolution equations is proposed based on the spectral method. The detail discretization processes are discussed in case of one-dimensional Klein-Gordon equations. In conclusion, a numerical scheme with the order of total calculation cost $O(N \log 2N)$ is proposed. As benchmark results, the relation between the numerical precision and the discretization unit size are demonstrated.Comment: To appear in the proceedings of ICCM2020. Figure is modified from the original versio

Simultaneous monitoring of independent gene expression patterns in two types of cocultured fibroblasts with different color-emitting luciferases

<p>Abstract</p> <p>Background</p> <p>Luciferase assay systems enable the real-time monitoring of gene expression in living cells. We have developed a dual-color luciferase assay system in which the expression of multiple genes can be tracked simultaneously using green- and red-emitting beetle luciferases. We have applied the system to monitoring independent gene expressions in two types of cocultured fibroblasts in real time.</p> <p>Results</p> <p>Two Rat-1 cell lines were established that stably express either green- or red-emitting luciferases under the control of the <it>mBmal1 </it>promoter, a canonical clock gene. We cocultured these cell lines, and gene expression profiles in both were monitored simultaneously. The circadian rhythms of these cell lines are independent, oscillating following their intrinsic circadian phases, even when cocultured. Furthermore, the independent rhythms were synchronized by medium change as an external stimulus.</p> <p>Conclusion</p> <p>Using this system, we successfully monitored independent gene expression patterns in two lines of cocultured fibroblasts.</p