Optimal sampling strategies for detecting zoonotic disease epidemics.

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.

Traveling waves in response to a diffusing quorum sensing signal in spatially-extended bacterial colonies.

In the behavior known as quorum sensing (QS), bacteria release diffusible signal molecules known as autoinducers, which by accumulating in the environment induce population-wide changes in gene expression. Although QS has been extensively studied in well-mixed systems, the ability of diffusing QS signals to synchronize gene expression in spatially extended colonies is not well understood. Here we investigate the one-dimensional spatial propagation of QS-circuit activation in a simple, analytically tractable reaction-diffusion model for the LuxR-LuxI circuit, which regulates bioluminescence of the marine bacterium Aliivibrio fischeri. The quorum activation loop is modeled by a Hill function with a cooperativity exponent (m=2.2). The model is parameterized from laboratory data and captures the major empirical properties of the LuxR-LuxI system and its QS regulation of A. fischeri bioluminescence. Our simulations of the model show propagating waves of activation or deactivation of the QS circuit in a spatially extended colony. We further prove analytically that the model equations possess a traveling wave solution. This mathematical proof yields the rate of autoinducer degradation that is compatible with a traveling wave of gene expression as well as the critical degradation rate at which the nature of the wave switches from activation to deactivation. Our results can be used to predict the direction and activating or deactivating nature of a wave of gene expression in experimentally controlled bacterial populations subject to a diffusing autoinducer signal.

Quorum activation at a distance: spatiotemporal patterns of gene regulation from diffusion of an autoinducer signal.

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.