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.

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We show that the critical behavior of a driven interface, depinned from quenched random impurities, depends on the isotropy of the medium. In anisotropic media the interface is pinned by a bounding (conducting) surface characteristic of a model of mixed diodes and resistors. Different universality classes describe depinning along a hard and a generic direction. The exponents in the latter (tilted) case are highly anisotropic, and obtained exactly by a mapping to growing surfaces. Various scaling relations are proposed in the former case which explain a number of recent numerical observations.Comment: 4 pages with 2 postscript figures appended, REVTe

We study in J +1 dimensions a new deposition and evaporation model of a J-dimensional surface which bears a Potts-spin representation. For the pure deposition case, our simulations on systems up to 11 520^ sites in d'^2 and 2x192^ sites in t/^S yield roughness exponents which violate recent conjectures. Including evaporation, we observe a nonequilibrium surface-roughening transition in d'^3, but only a smooth crossover behavior in t/ -2. A logarithmic anomalous scaling form for surface width at the transition is conjectured. PACS numbers: 61.50.Cj, 05.40.+j, 05.70.Ln, 81.10.Bk Surface roughening due to thermal fluctuations has been studied extensively over the years. ^ There now exist well-established theories''^ as well as exactly solvable models ^' which come to fair agreement with observed surface roughening in copper^ and other experimental systems. In certain class of growth processes, such as Eden growth"* and vapor deposition,^ the moving surface of a compact cluster may also become rough under a stochastic growth rule. The scaling properties of the surface height fluctuation and characteristics of possible nonequilibrium roughening transitions have been the topic of a number of recent numerical and analytical investigations.^"^^ Kardar, Parisi, and Zhang proposed a nonlinear Langevin equation dh/dt-^vS/^h-hiX/Dmy-^Tjixj),