Linking dynamical and functional properties of bursting neuron

INES SAMENGO · GERMAN MATO · DANIEL H. ELIJAH · SUSANNE SCHREIBER · MARCELO A. MONTEMURRO

JOURNAL OF COMPUTATIONAL NEUROSCIENCE

SPRINGER

Lugar: Berlin; Año: 2013 vol. 10.1 p. 1 - 18

0929-5313

Several studies have shown that bursting neu-rons can encode information in the number of spikes perburst: As the stimulus varies, so does the length of indi-vidual bursts. The represented stimuli, however, vary sub-stantially among different sensory modalities and differentneurons. The goal of this paper is to determine whichkind of stimulus features can be encoded in burst length,and how those features depend on the mathematical prop-erties of the underlying dynamical system. We show thatthe initiation and termination of each burst is triggered byspecific stimulus features whose temporal characteristsicsare determined by the types of bifurcations that initiateand terminate firing in each burst. As only a few bifur-cations are possible, only a restricted number of encodedfeatures exists. Here we focus specifically on describingparabolic, square-wave and elliptic bursters. We find thatparabolic bursters, whose firing is initiated and terminatedby saddle-node bifurcations, behave as prototypical integra-tors: Firing is triggered by depolarizing stimuli, and lastsfor as long as excitation is prolonged. Elliptic bursters, con-trastingly, constitute prototypical resonators, since both theinitiating and terminating bifurcations possess well-definedoscillation time scales. Firing is therefore triggered by stim-ulus stretches of matching frequency and terminated by aphase-inversion in the oscillation. The behavior of square-wave bursters is somewhat intermediate, since they aretriggered by a fold bifurcation of cycles of well-definedfrequency but are terminated by a homoclinic bifurcationlacking an oscillating time scale. These correspondencesshow that stimulus selectivity is determined by the typeof bifurcations. By testing several neuron models, we alsodemonstrate that additional biological properties that donot modify the bifurcation structure play a minor role instimulus encoding. Moreover, we show that burst-lengthvariability (and thereby, the capacity to transmit informa-tion) depends on a trade-off between the variance of theexternal signal driving the cell and the strength of the slowinternal currents modulating bursts. Thus, our work explic-itly links the computational properties of bursting neuronsto the mathematical properties of the underlying dynamicalsystems.