Bifurcation analysis of a two-compartment hippocampal pyramidal cell model

Abstract

The Pinsky-Rinzel model is a non-smooth 2-compartmental CA3 pyramidal cell model that has been used widely within the field of neuroscience. Here we propose a modified (smooth) system that captures the qualitative behaviour of the original model, while allowing the use of available, numerical continuation methods to perform full-system bifurcation and fast-slow analysis. We study the bifurcation structure of the full system as a function of the applied current and the maximal calcium conductance. We identify the bifurcations that shape the transitions between resting, bursting and spiking behaviours, and which lead to the disappearance of bursting when the calcium conductance is reduced. Insights gained from this analysis, are then used to firstly illustrate how the irregular spiking activity found between bursting and stable spiking states, can be influenced by phase differences in the calcium and dendritic voltage, which lead to corresponding changes in the calcium-sensitive potassium current. Furthermore, we use fast-slow analysis to investigate the mechanisms of bursting and show that bursting in the model is dependent on the intermediately slow variable, calcium, while the other slow variable, the activation gate of the afterhyperpolarisation current, does not contribute to setting the intraburst dynamics but participates in setting the interburst interval. Finally, we discuss how some of the described bifurcations affect spiking behaviour, during sharp-wave ripples, in a larger network of Pinsky-Rinzel cells.

Dynamics of a neuron–glia system: the occurrence of seizures and the influence of electroconvulsive stimuli

“…Here, we want to highlight that numerical bifurcation analysis is already used for the investigation of neurons, see e.g. (Izhikevich 2000;Tsaneva-Atanasova et al 2005) and (Atherton et al 2016;Krupa et al 2014;Rotstein et al 2006) to mention only a few papers. The authors consider in many cases a reduced subsystem of lower dimension, cf.…”

Digital Implementation of the Two-Compartmental Pinsky–Rinzel Pyramidal Neuron Model

“…Understanding the behavior of primary building blocks of nervous system, neurons, plays a vital role in neuromorphic fields [4]. The recurrent connectivity within the CA3 network of the hippocampus, supports a strong computational capacity which can mediate behavioral processes including pattern completion [18], [19]. At the cellular level, CA3 pyramidal neurons show various firing patterns, ranging from single action potentials to complex bursts.…”