Lei-Han Tang

Sequential Establishment of Stripe Patterns in an Expanding Cell Population

A synthetic circuit implementing density-controlled bacterial motility autonomously produces a tunable stripe pattern. Periodic stripe patterns are ubiquitous in living organisms, yet the underlying developmental processes are complex and difficult to disentangle. We describe a synthetic genetic circuit that couples cell density and motility. This system enabled programmed Escherichia coli cells to form periodic stripes of high and low cell densities sequentially and autonomously. Theoretical and experimental analyses reveal that the spatial structure arises from a recurrent aggregation process at the front of the continuously expanding cell population. The number of stripes formed could be tuned by modulating the basal expression of a single gene. The results establish motility control as a simple route to establishing recurrent structures without requiring an extrinsic pacemaker.

Phase transitions of the q-state Potts model on multiply-laced Sierpinski gaskets

We present an exact solution of the q-state Potts model on a class of generalized Sierpinski fractal lattices. The model is shown to possess an ordered phase at low temperatures and a continuous transition to the high temperature disordered phase at any q ≥ 1. Multicriticality is observed in the presence of a symmetry-breaking field. Exact renormalization group analysis yields the phase diagram of the model and a complete set of critical exponents at various transitions.

Driven interface depinning in a disordered medium

The dynamics of a driven interface in a medium with random pinning forces is analyzed. The interface undergoes a depinning transition where the order parameter is the interface velocity v, which increases as v ∼(FFc)θ for driving forces F close to its threshold value Fc. We consider a Langevin-type Eq. which is expected to be valid close to the depinning transition of an interface in a statistically isotropic medium. By a functional renormalization group scheme the critical exponents characterizing the depinning transition are obtained to the first order in ϵ = 4 — D > 0, where D is the interface dimension. The main results were published earlier [T. Nattermann et al., J. Phys. II France 2 (1992) 1483]. Here, we present details of the perturbative calculation and of the derivation of the functional flow Eq. for the random-force correlator. The fixed point function of the correlator has a cusp singularity which is related to a finite value of the threshold Fc, similar to the mean field theory. We also present extensive numerical simulations and compare them with our analytical results for the critical exponents. For ϵ = 1 the numerical and analytical results deviate from each other by only a few percent. The deviations in lower dimensions ϵ = 2, 3 are larger and suggest that the roughness exponent is somewhat larger than the value ξ = e/3 of an interface in thermal equilibrium.

Localization of denaturation bubbles in random DNA sequences

We study the thermodynamic and dynamic behaviors of twist-induced denaturation bubbles in a long, stretched random sequence of DNA. The small bubbles associated with weak twist are delocalized. Above a threshold torque, the bubbles of several tens of bases or larger become preferentially localized to AT-rich segments. In the localized regime, the bubbles exhibit “aging” and move around subdiffusively with continuously varying dynamic exponents. These properties are derived by using results of large-deviation theory together with scaling arguments and are verified by Monte Carlo simulations.

Explicit hypoxia targeting with tumor suppression by creating an “obligate” anaerobic Salmonella Typhimurium strain

Using bacteria as therapeutic agents against solid tumors is emerging as an area of great potential in the treatment of cancer. Obligate and facultative anaerobic bacteria have been shown to infiltrate the hypoxic regions of solid tumors, thereby reducing their growth rate or causing regression. However, a major challenge for bacterial therapy of cancer with facultative anaerobes is avoiding damage to normal tissues. Consequently the virulence of bacteria must be adequately attenuated for therapeutic use. By placing an essential gene under a hypoxia conditioned promoter, Salmonella Typhimurium strain SL7207 was engineered to survive only in anaerobic conditions (strain YB1) without otherwise affecting its functions. In breast tumor bearing nude mice, YB1 grew within the tumor, retarding its growth, while being rapidly eliminated from normal tissues. YB1 provides a safe bacterial vector for anti-tumor therapies without compromising the other functions or tumor fitness of the bacterium as attenuation methods normally do.

VORTEX STATISTICS IN A DISORDERED TWO-DIMENSIONAL XY MODEL

The equilibrium behavior of vortices in the classical two-dimensional (2D) XY model with uncorrelated random phase shifts is investigated. The model describes Josephson-Junction arrays with positional disorder, and has ramifications in a number of other bond-disordered 2D systems. The vortex Hamiltonian is that of a Coulomb gas in a background of quenched random dipoles, which is capable of forming either a dielectric insulator or a plasma. We confirm a recent suggestion by Nattermann, Scheidl, Korshunov, and Li [J. Phys. I (France) {\bf 5}, 565 (1995)], and by Cha and Fertig [Phys. Rev. Lett. {\bf 74}, 4867 (1995)] that, when the variance

Entrainment transition in populations of random frequency oscillators.

\sigma

Reaction-Diffusion-Branching Models of Stock Price Fluctuations

of random phase shifts is smaller than a critical value

Driven Depinning in Anisotropic Media

\sigma_c

Stripe formation in bacterial systems with density-suppressed motility

, the system is in a phase with quasi-long-range order at low temperatures, without a reentrance transition. This conclusion is reached through a nearly exact calculation of the single-vortex free energy, and a Kosterlitz-type renormalization group analysis of screening and random polarization effects from vortex-antivortex pairs. The critical strength of disorder