Intercellular Communication as a Series of Narrow Escape Problems

Molecular communication is key for multicellular organisms. In plants, the exchange of nutrients and signals between cells is facilitated by tunnels called plasmodesmata. Such transport processes in complex geometries can be simulated using particle-based approaches, these, however, are computationally expensive. Here, we evaluate the narrow escape problem as a framework for describing intercellular transport. We introduce a volumetric adjustment factor for estimating escape times from non-spherical geometries. We validate this approximation against full 3D stochastic simulations and provide results for a range of cell sizes and diffusivities. We discuss how this approach can be extended using recent results on multiple trap problems to account for different plasmodesmata distributions with varying apertures.