A model of the burglar alarm hypothesis of prey alarm calls.

When approached by a predator many prey species will emit an "alarm call" as a form of anti-predator behavior. One hypothesis for the function of alarm calls is the "burglar alarm" hypothesis whereby upon attack, a prey renders itself dangerous to a predator by generating an alarm call that attracts a predator at higher trophic levels in the food chain; that is, attracts a predator to the prey's own predator. This paper concerns a model incorporating a mechanism to test the burglar alarm hypothesis. We prove in one space dimension global existence, of positive bounded classical solutions, and establish existence of non-constant equilibrium solutions and assess their stability. We provide some representative numerical simulations to emphasize the nature of pattern formation for this model and demonstrate the benefit achieved by a signal inducing prey species under the burglar alarm hypothesis.

Circumvention of Learning Increases Intoxication Efficacy of Nematicidal Engineered Bacteria.

Synthetic biology holds promise to engineer systems to treat diseases. One critical, yet underexplored, facet of designing such systems is the interplay between the system and the pathogen. Understanding this interplay may be critical to increasing efficacy and overcoming resistance against the system. Using the principles of synthetic biology, we engineer a strain of Escherichia coli to attract and intoxicate the nematode Caenorhabditis elegans. Our bacteria are engineered with a toxin module, which intoxicates the nematode upon ingestion, and an attraction module, which serves to attract and increase the feeding rate of the nematodes. When independently implemented, these modules successfully intoxicate and attract the worms, respectively. However, in combination, the efficacy of our bacteria is significantly reduced due to aversive associative learning in C. elegans. Guided by mathematical modeling, we dynamically regulate module induction to increase intoxication by circumventing learning. Our results detail the creation of a novel nematicidal bacterium that may have application against nematodes, unravel unique constraints on circuit dynamics that are governed by C. elegans physiology, and add to the growing list of design and implementation considerations associated with synthetic biology.

On the formation of persistent states in neuronal network models of feature selectivity.

We study the existence and stability of localized activity states in neuronal network models of feature selectivity with either a ring or spherical topology. We find that the neural field has mono-stable, bi-stable, and tri-stable regimes depending on the parameters of the weighting function. In the case of homogeneous inputs, these localized activity states are marginally stable with respect to rotations. The response of a stable equilibrium to an inhomogeneous input is also determined.