How do signals propagate in neuronal compartments? Insights from the Poisson-Nernst Planck model.

The emergence of novel experimental techniques such as dendritic patch-clamp recordings or genetically-encoded Ca2+-indicators have made the activity of the dendritic tree considerably more tractable, challenging the old postulate that dendrites serve mainly to connect neurons and to convey information with no specific role in synaptic plasticity. Hence, how the dendritic tree transforms synaptic input into neuronal output and defines the relationships between active synapses is now a leading question in neuroscience. To understand the specific role of dendrites, dendritic spines and dendritic tree geometry in shaping neuronal signal, a crucial first step is to understand precisely voltage and ionic dynamics in such small neuronal compartments. For this purpose, we use the Poisson-Nernst-Planck (PNP) model, which is the recognized standard for modeling voltage dynamics and ionic electrodiffusion in electrolytes at the scale now reached by experimental techniques. This non-linear model presents significant challenges for both modeling and simulation due to its high concentration gradients and sensitivity to boundary conditions, making it difficult to simulate on complex geometries. We resolve these issues here by using a state-of-the-art finite volume method, the Discrete-Duality Finite Volume method, which we previously developed to simulate the PNP system of equations on various two-dimensional geometries representing neuronal compartments. Using this method, we investigate the propagation and attenuation of an ionic influx coming from a synapse near a dendritic branch bifurcation and at a dendritic spine, as well as signal invasion in the nearby branches and spines. By connecting these compartments to an ionic reservoir representing the dendritic shaft, we observe that the distance to the shaft strongly influences signal propagation. Notably, a spine positioned close to a large branch behaves as an isolated compartment, while a distant spine is susceptible to signal invasion. Our numerical results therefore suggest that the local geometry of the dendritic tree has a major influence on spine behavior. Consequently, this study proposes that signal integration rules would differ depending on the location of the spine on the dendritic tree. This means that modifications to neuronal structure and organization following activity are not limited to the spine morphology but depend on the entire dendritic tree architecture.