Browsing by Author "Li, Rui"

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    Birational Quadratic Planar Maps with Generalized Complex Rational Representations
    (MDPI, 2023) Wang, Xuhui; Han, Yuhao; Ni, Qian; Li, Rui; Goldman, Ron
    Complex rational maps have been used to construct birational quadratic maps based on two special syzygies of degree one. Similar to complex rational curves, rational curves over generalized complex numbers have also been constructed by substituting the imaginary unit with a new independent quantity. We first establish the relationship between degree one, generalized, complex rational Bézier curves and quadratic rational Bézier curves. Then we provide conditions to determine when a quadratic rational planar map has a generalized complex rational representation. Thus, a rational quadratic planar map can be made birational by suitably choosing the middle Bézier control points and their corresponding weights. In contrast to the edges of complex rational maps of degree one, which are circular arcs, the edges of the planar maps can be generalized to hyperbolic and parabolic arcs by invoking the hyperbolic and parabolic numbers.
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    Monitoring iron-sulfur cluster content of human glutaredoxin 2 using fluorescence proteins
    (2008) Li, Rui; Silberg, Jonathan
    Current methods for directly determining whether an iron-sulfur cluster has been synthesized on a protein in vivo typically require that the protein of interest is purified prior to analysis for bound metallocluster. To establish an assay that can measure Fe/S-cluster synthesis in complex mixtures of biomolecules, we have fused a variety of fluorescent proteins (FP=BFP, CFP, GFP, and YFP) to human glutaredoxin 2 (Grx2) and characterized the effect of Grx2 metallocluster coordination on protein fluorescence. Gel filtration analysis revealed that FP-Grx2 fusion proteins are produced as a mixture of monomers and dimers when expressed in Escherichia coli , like native Grx2. The dimeric FP-Grx2 exhibited absorbance and circular dichroism spectra consistent with the presence of a Grx2-bound [2Fe2S] cluster, whereas the monomeric form of these fusion proteins lacked any detectable chromophores. Fluorescence analysis of the FP orthologs in these fusion proteins revealed that [2Fe2S]-cluster coordination produces a 30 to 50% reduction in FP fluorescence emission. These fluorescence indicators are expected to be useful for continuously monitoring Fe/S-cluster assembly on Grx2 in complex protein mixtures and should be useful for discovery of the proteins that mediate the assembly of metallocluster on Grx2 isoforms that are localized to both the nucleus and mitochondria.