Quorum sensing (QS) bacteria regulate gene expression collectively by exchanging diffusible signal molecules known as autoinducers. Although QS is often studied in well-stirred laboratory cultures, QS bacteria colonize many physically and chemically heterogeneous environments where signal molecules are transported primarily by diffusion. This raises questions of the effective distance range of QS and the degree to which colony behavior can be synchronized over such distances. We have combined experiments and modeling to investigate the spatiotemporal patterns of gene expression that develop in response to a diffusing autoinducer signal. We embedded a QS strain in a narrow agar lane and introduced exogenous autoinducer at one terminus of the lane. We then measured the expression of a QS reporter as a function of space and time as the autoinducer diffused along the lane. The diffusing signal readily activates the reporter over distances of ∼1 cm on time scales of ∼10 h. However, the patterns of activation are qualitatively unlike the familiar spreading patterns of simple diffusion, as the kinetics of response are surprisingly insensitive to the distance the signal has traveled. We were able to reproduce these patterns with a mathematical model that combines simple diffusion of the signal with logistic growth of the bacteria and cooperative activation of the reporter. In a wild-type QS strain, we also observed the propagation of a unique spatiotemporal excitation. Our results show that a chemical signal transported only by diffusion can be remarkably effective in synchronizing gene expression over macroscopic distances.

Marine protected areas (MPAs) are promoted as a tool to protect overfished stocks and increase fishery yields. Previous models suggested that adult mobility modified effects of MPAs by reducing densities of fish inside reserves, but increasing yields (i.e., increasing densities outside of MPAs). Empirical studies contradicted this prediction: as mobility increased, the relative density of fishes inside MPAs (relative to outside) increased or stayed constant. We hypothesized that this disparity between theoretical and empirical results was the result of differential movement of fish inside versus outside the MPA. We, therefore, developed a model with unequal and discontinuous diffusion, and analyzed its steady state and stability. We determined the abundance in the fishing grounds, the yield, the total abundance and the log ratio at steady-state and examined their response to adult mobility (while keeping the relative inequity in the diffusion constant). Abundance in the fishing grounds and yield increased, while total abundance and log-ratio decreased, as mobility increased. These results were all qualitatively consistent with the previous models assuming uniform diffusivity. Thus, the mismatch between empirical and theoretical results must result from other processes or other forms of differential movement. Therefore, we modified our original model by assuming that species located on the boundary of the MPA will preferentially move towards the MPA. This localized movement bias model gives rise to steady state profiles that can differ radically from the profiles in the unbiased model, especially when the bias is large. Moreover, for sufficiently large bias values, the monotonicity of the four measures with increased mobility is reversed, when compared with our original model. Thus, the movement bias model reconciles empirical data and theoretical results.

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The early detection of disease epidemics reduces the chance of successful introductions into new locales, minimizes the number of infections, and reduces the financial impact. We develop a framework to determine the optimal sampling strategy for disease detection in zoonotic host-vector epidemiological systems when a disease goes from below detectable levels to an epidemic. We find that if the time of disease introduction is known then the optimal sampling strategy can switch abruptly between sampling only from the vector population to sampling only from the host population. We also construct time-independent optimal sampling strategies when conducting periodic sampling that can involve sampling both the host and the vector populations simultaneously. Both time-dependent and -independent solutions can be useful for sampling design, depending on whether the time of introduction of the disease is known or not. We illustrate the approach with West Nile virus, a globally-spreading zoonotic arbovirus. Though our analytical results are based on a linearization of the dynamical systems, the sampling rules appear robust over a wide range of parameter space when compared to nonlinear simulation models. Our results suggest some simple rules that can be used by practitioners when developing surveillance programs. These rules require knowledge of transition rates between epidemiological compartments, which population was initially infected, and of the cost per sample for serological tests.

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