Jianxin Zhong

Background: Large-scale sequencing of entire genomes has ushered in a new age in biology. One of the next grand challenges is to dissect the cellular networks consisting of many individual functional modules. Defining co-expression networks without ambiguity based on genome-wide microarray data is difficult and current methods are not robust and consistent with different data sets. This is particularly problematic for little understood organisms since not much existing biological knowledge can be exploited for determining the threshold to differentiate true correlation from random noise. Random matrix theory (RMT), which has been widely and successfully used in physics, is a powerful approach to distinguish system-specific, non-random properties embedded in complex systems from random noise. Here, we have hypothesized that the universal predictions of RMT are also applicable to biological systems and the correlation threshold can be determined by characterizing the correlation matrix of microarray profiles using random matrix theory. Results: Application of random matrix theory to microarray data of S. oneidensis, E. coli, yeast, A. thaliana, Drosophila, mouse and human indicates that there is a sharp transition of nearest neighbour spacing distribution (NNSD) of correlation matrix after gradually removing certain elements insider the matrix. Testing on an in silico modular model has demonstrated that this transition can be used to determine the correlation threshold for revealing modular co-expression networks. The co-expression network derived from yeast cell cycling microarray data is supported by gene annotation. The topological properties of the resulting co-expression network agree well with the general properties of biological networks. Computational evaluations have showed that RMT approach is sensitive and robust. Furthermore, evaluation on sampled expression data of an in silico modular gene system has showed that under-sampled expressions do not affect the recovery of gene co-expression network. Moreover, the cellular roles of 215 functionally unknown genes from yeast, E. coli and S. oneidensis are predicted by the gene co-expression networks using guilt-by-association principle, many of which are supported by existing information or our experimental verification, further demonstrating the reliability of this approach for gene function prediction. Conclusion: Our rigorous analysis of gene expression microarray profiles using RMT has showed that the transition of NNSD of correlation matrix of microarray profile provides a profound theoretical criterion to determine the correlation threshold for identifying gene co-expression networks.

A concept of order-disorder separated quantum films is proposed for the design of ultrathin quantum films of a few atomic layers thick with unconventional transport properties. The concept is demonstrated through studying an atomic bilayer comprised of an ordered layer and a disordered layer. Without the disordered layer or the ordered layer, the system is a conducting two-dimensional (2D) crystal or an insulating disordered 2D electron system. Without the order-disorder phase separation, a disordered bilayer is insulating under large disorder. In an order-disorder separated atomic bilayer, however, we show that the system behaves remarkably different from conventional ordered or disordered electron systems, exhibiting metal-insulator transitions with persistent mobility edges and superdiffusive anomalous quantum diffusion.

We show that spectral fluctuation of coexpression correlation matrices of yeast gene microarray profiles follows the description of the Gaussian orthogonal ensemble (GOE) of the random matrix theory (RMT) and removal of small values of the correlation coefficients results in a transition from the GOE statistics to the Poisson statistics of the RMT. This transition is directly related to the structural change of the gene expression network from a global network to a network of isolated modules.

We propose a novel concept, namely, shell-doping of nanowires, for control of carrier mobility in nanowires. Different from traditional doping, where dopant atoms are distributed uniformly inside nanowires, shell-doping spatially confines dopant atoms within a few atomic layers in the shell region of a nanowire. Our numerical results based on the Anderson model of electronic disorder show that electrons in a shell-doped nanowire exhibit a peculiar behavior very different from that of uniformly doped nanowires. Beyond some critical doping, electron dynamics in a shell-doped nanowire undergoes a localization/quasi-delocalization transition, namely, the electron diffusion length decreases in the regime of weak disorder but increases in the regime of strong disorder. This transition is a result of the existence of quasi-mobility-edges in the energy spectrum of the system, which can be exploited experimentally through control of electron concentration, carrier density, and degree of disorder.

We show that spectral fluctuation of interaction matrices of yeast a core protein interaction network and a metabolic network follows the description of the Gaussian orthogonal ensemble (GOE) of random matrix theory (RMT). Furthermore, we demonstrate that while the global biological networks evaluated belong to GOE, removal of interactions between constituents transitions the networks to systems of isolated modules described by the Poisson statistics of RMT. Our results indicate that although biological networks are very different from other complex systems at the molecular level, they display the same statistical properties at large scale. The transition point provides a new objective approach for the identification of functional modules.