Spatial gradient sensing and wave rectification via excitability

The social amoeba Dictyostelium discoideum perfoms chemotaxis under starvation conditions, aggregating towards emergent groups of cells that spontaneously emit cAMP. Cells sense extracellular cAMP, producing internal caches of cAMP to be released. These events lead to traveling waves of cAMP washing over the entire population of cells. While research has been performed to understand elements of the chemotaxis network in Dictyostelium, limited work has been proposed to link components of the signal relay network with the chemotaxis network to provide a holistic view of the system. We take inspiration from Dictyostelium and propose a model that links the relaying of a chemical message to the directional sensing of that signal. Utilizing excitable dynamical systems, our model provides signal amplification and perfect adaptation while also automatically matching internal time scales of adaptation to the naturally occurring periodicity of the traveling chemical waves. We show that noise plays a vital role in the system, where stochastic tunneling of transient bursts biases the system towards accurate gradient sensing. Numerical simulations were performed to study the qualitative phenomenology of the system and explore how the system responds to diverse dynamic spatiotemporal stimuli.