Stability Analysis of the Explicit Difference Scheme for Richards Equation.

A stable explicit difference scheme, which is based on forward Euler format, is proposed for the Richards equation. To avoid the degeneracy of the Richards equation, we add a perturbation to the functional coefficient of the parabolic term. In addition, we introduce an extra term in the difference scheme which is used to relax the time step restriction for improving the stability condition. With the augmented terms, we prove the stability using the induction method. Numerical experiments show the validity and the accuracy of the scheme, along with its efficiency.

Molecular cloning, characterization, mRNA expression changes and nucleocytoplasmic shuttling during kidney embryonic development of SOX9 in Alligator sinensis.

SOX9 plays a crucial, extensive and conservative role in the process of somatic tissue development and adult regeneration through the positive self-regulation mediated by SOM across all vertebrates. In this study, we have cloned SOX9 from the kidney of hatchling Alligator sinensis. The full-length of SOX9 cDNA is 3878 bp with an open reading frame encoding 494 amino acids. Amino acid alignment analyses indicated that the SOX9 exhibit highly conserved functional domains. Using the droplet digital PCR, the mRNA abundances of SOX9 during nephrogenesis in A. sinensis showed prominent changes in the embryonic development, suggesting that SOX9 might combines a vital role in the regulation of complex renal development. Interestingly, we detected the nucleocytoplasmic shuttling of SOX9 protein using immunofluorescence, implying that nucleocytoplasmic shuttling is critical to the regulation of SOX9 in the renal embryonic development. Collectively, these data provide an important foundation for further studies on renal developmental biology and molecular biology of non-mammalian SOX9. Furthermore, it provides new insights into the phenomenon of SOX9 nucleocytoplasmic shuttling in Alligator sinensis, which is probably of great significance to the development of kidney metanephros embryo.

Aprotinin Encapsulated Gold Nanoclusters: A Fluorescent Bioprobe with Dynamic Nuclear Targeting and Selective Detection of Trypsin and Heavy Metal.

Fluorescence imaging has currently emerged as one of the most frequently used noninvasive imaging technologies to selectively monitor biological processes in living systems. In past decades, gold nanoclusters (Au NCs) has received increasing attraction because of their intrinsic fluorescence and their inherent biocompatibility. As a stabilizing and reducing agent, an abundant, sustainable, and widely used polypeptide derived drug molecule, aprotinin (Ap), is selected for the synthesis of Au nanoclusters (Ap-Au NCs) due to characteristic bioactivity, excellent biocompatibility, biodegradability, and non-allergenic character. Herein, Ap encapsulated Au NCs with desirable red fluorescence was facilely produced for the first time, which were subsequently used for cell imaging and detection of various analytes. Much interestingly, dynamically subcellular targeting  from the cytoplasm to the nucleus in HeLa cells was observed. Besides, it has shown that, the selective and quantitative detection of trypsin has been established by using Ap-Au NCs. Finally, Ap-Au NCs were readily used for quantitative detection of mercury and copper. The photoluminescence of the Ap-Au NCs was quenched with the addition of the aforementioned analytes. This study not only  discusses a multifunctional nanomaterial  for cell imaging, dynamically nuclear targeting and biosensing, but also opens crucial insights on the integration of funtional biomolecule with metal nanoclusters intended for extensively biomedical applications.