Tailored graph ensembles as proxies or null models for real networks I: tools for quantifying structure

We study the tailoring of structured random graph ensembles to real networks, with the objective of generating precise and practical mathematical tools for quantifying and comparing network topologies macroscopically, beyond the level of degree statistics. Our family of ensembles can produce graphs with any prescribed degree distribution and any degree-degree correlation function, its control parameters can be calculated fully analytically, and as a result we can calculate (asymptotically) formulae for entropies and complexities, and for information-theoretic distances between networks, expressed directly and explicitly in terms of their measured degree distribution and degree correlations.Comment: 25 pages, 3 figure

Gene-to-metabolite network for biosynthesis of lignans in MeJA-elicited Isatis indigotica hairy root cultures.

Root and leaf tissue of Isatis indigotica shows notable anti-viral efficacy, and are widely used as "Banlangen" and "Daqingye" in traditional Chinese medicine. The plants' pharmacological activity is attributed to phenylpropanoids, especially a group of lignan metabolites. However, the biosynthesis of lignans in I. indigotica remains opaque. This study describes the discovery and analysis of biosynthetic genes and AP2/ERF-type transcription factors involved in lignan biosynthesis in I. indigotica. MeJA treatment revealed differential expression of three genes involved in phenylpropanoid backbone biosynthesis (IiPAL, IiC4H, Ii4CL), five genes involved in lignan biosynthesis (IiCAD, IiC3H, IiCCR, IiDIR, and IiPLR), and 112 putative AP2/ERF transcription factors. In addition, four intermediates of lariciresinol biosynthesis were found to be induced. Based on these results, a canonical correlation analysis using Pearson's correlation coefficient was performed to construct gene-to-metabolite networks and identify putative key genes and rate-limiting reactions in lignan biosynthesis. Over-expression of IiC3H, identified as a key pathway gene, was used for metabolic engineering of I. indigotica hairy roots, and resulted in an increase in lariciresinol production. These findings illustrate the utility of canonical correlation analysis for the discovery and metabolic engineering of key metabolic genes in plants