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Front Comput Neurosci. 2018 Feb 6;12:5. doi: 10.3389/fncom.2018.00005. eCollection 2018.

Propensity for Bistability of Bursting and Silence in the Leech Heart Interneuron.

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Neuroscience Institute, Georgia State University, Atlanta, GA, United States.
Center for Integrative Brain Research, Seattle Children's Research Institute, Seattle, WA, United States.


The coexistence of neuronal activity regimes has been reported under normal and pathological conditions. Such multistability could enhance the flexibility of the nervous system and has many implications for motor control, memory, and decision making. Multistability is commonly promoted by neuromodulation targeting specific membrane ionic currents. Here, we investigated how modulation of different ionic currents could affect the neuronal propensity for bistability. We considered a leech heart interneuron model. It exhibits bistability of bursting and silence in a narrow range of the leak current parameters, conductance (gleak ) and reversal potential (Eleak ). We assessed the propensity for bistability of the model by using bifurcation diagrams. On the diagram (gleak , Eleak ), we mapped bursting and silent regimes. For the canonical value of Eleak we determined the range of gleak which supported the bistability. We use this range as an index of propensity for bistability. We investigated how this index was affected by alterations of ionic currents. We systematically changed their conductances, one at a time, and built corresponding bifurcation diagrams in parameter planes of the maximal conductance of a given current and the leak conductance. We found that conductance of only one current substantially affected the index of propensity; the increase of the maximal conductance of the hyperpolarization-activated cationic current increased the propensity index. The second conductance with the strongest effect was the conductance of the low-threshold fast Ca2+ current; its reduction increased the propensity index although the effect was about two times smaller in magnitude. Analyzing the model with both changes applied simultaneously, we found that the diagram (gleak , Eleak ) showed a progressively expanded area of bistability of bursting and silence.


Andronov Hopf bifurcation; Homoclinic bifurcation; bifurcation diagrams; bursting activity; coexistence; multistability; neuromodulation

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