Signal transmission among cells enables long-range coordination in biological systems. However, the scarcity of quantitative measurements hinders the development of theories that relate signal propagation to cellular heterogeneity and spatial organization. We address this problem in a bacterial community that employs electrochemical cell-to-cell communication. We developed a model based on percolation theory, which describes how signals propagate through a heterogeneous medium. Our model predicts that signal transmission becomes possible when the community is organized near a critical phase transition between a disconnected and a fully connected conduit of signaling cells. By measuring population-level signal transmission with single-cell resolution in wild-type and genetically modified communities, we confirm that the spatial distribution of signaling cells is organized at the predicted phase transition. Our findings suggest that at this critical point, the population-level benefit of signal transmission outweighs the single-cell level cost. The bacterial community thus appears to be organized according to a theoretically predicted spatial heterogeneity that promotes efficient signal transmission.

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Abstruct-We present experimental studies of a plasma-filled X-band backward wave oscillator (BWO). Depending on the background gas pressure, microwave frequency upshifts of up to 1 GHz appeared along with an enhancement by a factor of 7 in the total microwave power emission. The bandwidth of the microwave emission increased from 5 0.5 GHz to 2 GHz when the BWO was working at the rf power enhancement pressure region. The rf power enhancement appeared over a much wider pressure range in a high beam cumnt case (10-100 mT for 3 kA) as compared to a lower beam case (80-115 mT for 1.6 kA). The plasma-filled BWO has higher power output compared to the vacuum BWO over a broader region of magnetic guide field strength. Trivelpiece-Gould modes (T-G modes) are observed with frequencies up to the background plasma frequency in a plasma-filled BWO. Mode competition between the Trivelpiece-Gould modes and the X-band TMol mode prevailed when the background plasma density was below 6 x lo1' cmS3. At a critical background plasma density of ncr E 8 x 10l1 cm-3 power enhancement appeared in both X-band and the T-G modes. Power enhancement of the S-band in this mode collaboration region reached up to 8 dB. Electric fields measured by the Stark-effect method were as high as 34 kV/cm while the BWO power level was 80 MW. These electric fields lasted throughout the high power microwave pulse.

A Stark effect diagnostic yields measurements of the electric field distribution of Langmuir waves, P(E), in beam–plasma turbulence. When the destabilizing beam abruptly cuts off, the form of P(E)∝ exp(−E2) discovered earlier persists, with amplitude decaying exponentially in a microsecond. Strong fields last much longer than other time scales in strong turbulence theory. Exponential decay disagrees with recent power law scalings deduced from cascade theory. A possible explanation envisions Langmuir energy persisting at long wavelengths, slowly coalescing around nucleation density wells left by previous, ‘‘burnt-out’’ solitons.

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