Chaos links dendritic calcium to bursting in hippocampal pyramidal cells

Abstract

We perform a multi-parameter bifurcation analysis of the Pinsky–Rinzel neuron model. Varying input currents to the soma and dendrite allows for the emergence of multiple dynamical regimes, including resting states, periodic cycles, tori, and chaotic states. The existence of tori implies the coexistence of two distinct frequency bands, which may underlie theta–gamma coupling observed in hippocampal activity. Additionally, a comprehensive bifurcation analysis reveals a novel type of chaotic attractor spanning a wide parameter region defined by inward currents to the soma and dendrite of a pyramidal neuron. This attractor facilitates the coexistence of two distinct bursting regimes as responses to the same stimulus. These bursting patterns, both previously observed experimentally in vivo and in vitro, primarily differ in dendritic calcium levels, with one exhibiting significantly elevated calcium concentrations. In this study, we introduce a robust method for identifying the bifurcation boundary of a global attractor associated with bursting behavior. The method is based on a comparative analysis of numerical continuation and grid-based simulations and can be applied analogously to other models. This rigorous approach not only provides a mechanistic explanation for experimentally observed concurrent neuronal responses to identical stimuli but also demonstrates that the Pinsky–Rinzel model, despite simplifying the pyramidal cell into two compartments, effectively captures a wide range of dynamical regimes present in pyramidal cell signaling. Moreover, it highlights the model’s robustness in describing complex neuronal dynamics, including epileptic activity.