Irregular activity arises as a natural consequence of synaptic inhibition

TY - JOUR

T1 - Irregular activity arises as a natural consequence of synaptic inhibition

AU - Terman, D.

AU - Rubin, J. E.

AU - Diekman, C. O.

N1 - Funding Information: This work was partially supported by the National Science Foundation DMS Award Nos. 1021701, 1312508 (JR), 1022627 (DT) and 0931642 (Mathematical Biosciences Institute). We thank the Department of Mathematics at the University of Auckland for its hospitality during part of the completion of this work.

PY - 2013/10/2

Y1 - 2013/10/2

N2 - Irregular neuronal activity is observed in a variety of brain regions and states. This work illustrates a novel mechanism by which irregular activity naturally emerges in two-cell neuronal networks featuring coupling by synaptic inhibition. We introduce a one-dimensional map that captures the irregular activity occurring in our simulations of conductance-based differential equations and mathematically analyze the instability of fixed points corresponding to synchronous and antiphase spiking for this map. We find that the irregular solutions that arise exhibit expansion, contraction, and folding in phase space, as expected in chaotic dynamics. Our analysis shows that these features are produced from the interplay of synaptic inhibition with sodium, potassium, and leak currents in a conductance-based framework and provides precise conditions on parameters that ensure that irregular activity will occur. In particular, the temporal details of spiking dynamics must be present for a model to exhibit this irregularity mechanism and must be considered analytically to capture these effects.

AB - Irregular neuronal activity is observed in a variety of brain regions and states. This work illustrates a novel mechanism by which irregular activity naturally emerges in two-cell neuronal networks featuring coupling by synaptic inhibition. We introduce a one-dimensional map that captures the irregular activity occurring in our simulations of conductance-based differential equations and mathematically analyze the instability of fixed points corresponding to synchronous and antiphase spiking for this map. We find that the irregular solutions that arise exhibit expansion, contraction, and folding in phase space, as expected in chaotic dynamics. Our analysis shows that these features are produced from the interplay of synaptic inhibition with sodium, potassium, and leak currents in a conductance-based framework and provides precise conditions on parameters that ensure that irregular activity will occur. In particular, the temporal details of spiking dynamics must be present for a model to exhibit this irregularity mechanism and must be considered analytically to capture these effects.

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U2 - 10.1063/1.4831752

DO - 10.1063/1.4831752

M3 - Article

C2 - 24387589

SN - 1054-1500

VL - 23

JO - Chaos

JF - Chaos

IS - 4

M1 - 046110

ER -