Superconducting Networks and Quantum Phase Transitions

The I-V characteristics of 2D superconducting films and Josephson-junction arrays are extremely rich and susceptible to various finite-size and disorder effects. Although the basic mechanism for current dissipation in the classical regime has long been understood, various quantitative details relevant to a correct interpretation of simulation and experimental results are often missing in the literature. One of our recent work in this direction addresses a peculiar finite-size effect for an array under periodic boundary conditions that had previously led to an incorrect interpretation of simulation data. To construct the equilibrium phase diagram with random frustration, we have extended the multi-canonical Monte Carlo scheme developed by Berg to systems with continuous degrees of freedom, and have also improved the iterative determination of the sampling function. These improvements allow us to perform efficient sampling down to very low temperatures. Combined with analysis of the classical ground state, we have been able to provide a microscopic picture of the zero-temperature criticality in the 2D gauge-glass model, a controversial topic in the recent literature.

More recently, we have devoted our attention to theoretical and simulation studies of a JJ array in the quantum regime. By introducing a suitable form of random frustration, such a system may afford a "metallic phase" at zero temperature as characterized by short-range spatial order and gapless quasi-particle excitations. As such, it makes a good candidate for the observed low-temperature metallic behavior of thin superconducting films and, according to a recent suggestion by A. Paramekanti, L. Balents and M. P. A. Fisher, the peculiar "normal state" of cuprate superconductors. Starting from the classical limit of the model, we are currently exploring spectral properties and correlation functions so as to reach a better understanding of the state.

Conformational Transformations of Biopolymers

The folding/denaturation transformations of DNA, RNA and protein molecules have been a subject of lasting interest in structural biology. The physical interactions involved in the process are relatively well-characterized, and hence such systems are more amenable to traditional methods of statistical mechanics. For a random DNA sequence, we have been able to provide a renormalization group description of the melting transition. In collaboration with Terry Hwa at UCSD and others, we have also investigated the formation of bubbles in the DNA double helix due to either under-twisting or heating. On the RNA secondary structure formation, we have developed Monte Carlo methods to search minimum energy base pairings where pseudoknot formation is allowed. RNA's without pseudoknots have been shown to undergo a transition from specific to non-specific pairing, but the precise nature of the low temperature glass state and the mechanism of the transition have not been completely characterized. Our recent work on this problem indicates a novel log²L energy for "droplet" excitations and possibly a phase transition of infinite order. We are working on a renormalization group theory to explain these observations.

The bigger issue, however, is how to uncover the mystery hidden in protein (and to a lesser extent, RNA) sequences that allow them to fold into a unique shape and in a cooperative manner. In addition to studying simple models (such as the HP model on a lattice) for extracting generic behavior, we are also examining interactions (such as secondary structure propensities) in stabilizing real proteins.

Metabolic network

Enzyme-assisted metabolic flow is one of the best characterized molecular systems in cell biology. Its backbone is universal among nearly all living organisms while, through evolution, many add-on features have been developed to enhance the fitness of a given organism. A large percentage of cell's transcriptional regulatory circuit is devoted to the efficient channelling of resources under steady-state and change of external environments. Therefore analysis of the system-wide metabolic flow pattern under various stress conditions offers the possibility of deciphering the genetic circuit from a functional perspective. The metabolic network itself involves around a thousand reactions with a similar number of compounds and protein types, and hence is very complex. On the other hand, there exists now a large body of genome scale experimental data, including microarray gene expression and ChIP on chip TF binding data, that can be used to help reconstruct the flux pattern under different growth conditions. We have recently implemented the in silico growth models iJR904 for E. coli and iND750 for yeast (S. cerevisiae) developed by Palsson's group at UCSD, which allow for calculation of biomass production under a given nutrient condition. One of our immediate goals is to corroborate the simulated flux pattern with microarray data and to identify regulators that are responsible for activation of alternative pathways. More importantly, such simulations will bring up various design issues whose resolution will deepen our understanding of biological organization.