Fractals from genomes: exact solutions of a biology-inspired problem

This is a review of a set of recent papers with some new data added. After a brief biological introduction a visualization scheme of the string composition of long DNA sequences, in particular, of bacterial complete genomes, will be described. This scheme leads to a class of self-similar and self-overlapping fractals in the limit of infinitely long constotuent strings. The calculation of their exact dimensions and the counting of true and redundant avoided strings at different string lengths turn out to be one and the same problem. We give exact solution of the problem using two independent methods: the Goulden-Jackson cluster method in combinatorics and the method of formal language theory.Comment: 24 pages, LaTeX, 5 PostScript figures (two in color), psfi

Study of Intermediate Oxidation Products in Chemical and Enzymatic Degradation of Carbon Nanomaterials

With increasing applications of carbon nanomaterials, toxicity of the material itself and the degradation products in biological systems and environment becomes a valid concern. At present, most of the toxicity studies only focus on the bulk property of carbon nanomaterials and the relevant conclusions are ambiguous. To better understand the degradation mechanism and the potential source of toxicity, we separated the oxidation products and studied the “small molecules” and “large particles” respectively in detail. In the first oxidation method, graphene oxide was degraded by Fenton reagent (Fe2+/Fe3+/H2O2) under UV irradiation. Through techniques including mass spectrometry, nuclear magnetic resonance and liquid chromatography, we successfully proposed plausible product structures and discovered several structure patterns of the products. By using atomic force microscopy and fluorimeter, we monitored the morphology transformation of graphene oxide flakes (~ 600 nm × 1 nm) to graphene quantum dots (~ 25 nm × 5 nm), in both aqueous solution and immobilized system. Given the similarity of Fenton reagent chemical oxidation and horseradish peroxidase enzymatic degradation of carbon nanomaterials, our results will help to understand the enzymatic degradation mechanism in biosystem and in the environment and to assess the toxicity at different stages during the degradation process. In the second part, we studied the degradation of SWNTs in both MPO and NaClO systems and further optimization is required to eliminate the ion suppression resulting from the high concentration of salt in these systems