Digging through DiRT: Investigating how Trap Recharge Time Influences the Statistics of Particle Diffusion

Many diverse biological systems are described by randomly moving particles that can be captured by traps in their environment. Examples include neurotransmitters diffusing in the synaptic cleft before binding to receptors, the delivery of nanoparticles to targeted receptors, and prey roaming an environment before being captured by predators. We will investigate this stochastic process, referred to as diffusion with recharging traps (DiRT), in multiple ways: by considering the full stochastic process, via a continuous-time Markov process with discrete states approximation, and a with deterministic PDE approximation. Each framework yields interesting insights into the DiRT process, such as identifying the conditions under which trap recharge time can drastically affect key statistics (e.g., the average number of captured particles).