How adaptation makes low firing rates robust (Sherman & Ha 2017)

"Low frequency firing is modeled by Type 1 neurons with a SNIC (saddle node on an invariant circle), but, because of the vertical slope of the square-root-like f–I curve, low f only occurs over a narrow range of I. When an adaptive current is added, however, the f–I curve is linearized, and low f occurs robustly over a large I range. Ermentrout (Neural Comput. 10(7):1721-1729, 1998) showed that this feature of adaptation paradoxically arises from the SNIC that is responsible for the vertical slope. We show, using a simplified Hindmarsh–Rose neuron with negative feedback acting directly on the adaptation current, that whereas a SNIC contributes to linearization, in practice linearization over a large interval may require strong adaptation strength. We also find that a type 2 neuron with threshold generated by a Hopf bifurcation can also show linearization if adaptation strength is strong. Thus, a SNIC is not necessary. More fundamental than a SNIC is stretching the steep region near threshold, which stems from sufficiently strong adaptation, though a SNIC contributes if present. In a more realistic conductance-based model, Morris–Lecar, with negative feedback acting on the adaptation conductance, an additional assumption that the driving force of the adaptation current is independent of I is needed. If this holds, strong adaptive conductance is both necessary and sufficient for linearization of f–I curves of type 2 f–I curves."

Model Type: Neuron or other electrically excitable cell

Cell Type(s): Abstract Morris-Lecar neuron; Abstract Hindmarsh-Rose neuron

Currents: I Calcium; I K

Model Concept(s): Bifurcation

Simulation Environment: XPPAUT

Implementer(s): Sherman, Arthur [arthurs at]


Sherman AS, Ha J. (2017). How Adaptation Makes Low Firing Rates Robust. Journal of mathematical neuroscience. 7 [PubMed]

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