Bifurcation Analysis of a Two-Compartment Hippocampal Pyramidal Cell Model

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 fastslow 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.LAA is supported by the Engineering and Physical Sciences Research Council (EPSRC) and Eli Lilly & Company; LYP is supported by the Wellcome Trust; and KT-A is supported by grant EP/N014391/1 of the EPSRC

Computational bifurcation analysis to find dynamic transitions of the corticotroph model

The corticotroph model is a 7th order nonlinear differential equation system derived for representing the action potential dynamics of corticotrophs; one of the endocrine cells that are responsible for stress regulation. Here we use numerical continuation methods to perform bifurcation analysis since controlling bifurcations in the hormonal dynamics may bring some new insights in the treatment of stress-related disorders. We study the bifurcation structure of the system as a function of the BK-channel dynamic parameters and all maximal conductances. We identify the regions of bistability and bifurcations that shape the transitions between resting, bursting, and spiking behaviors, and which lead to the appearance of bursting which is directly connected to stress regulation. Furthermore, we find that there are two routes to bursting, one is the experimentally observed BK-channel dynamics and the other is Ca2+ channel conductance only. Finally, we discuss how some of the described bifurcations affect the dynamic behavior and can be tested experimentally.No sponso