Linking dynamical and functional properties of intrinsically bursting neurons

Abstract

Several studies have shown that bursting neurons can encode information in the number of spikes per burst: As the stimulus varies, so does the length of individual bursts. There presented stimuli, however, vary substantially among different sensory modalities and different neurons.The goal of this paper is to determine which kind of stimulus features can be encoded in burst length, and how those features depend on the mathematical properties of the underlying dynamical system.We show that the initiation and termination of each burst is triggered by specific stimulus features whose temporal characteristsics are determined by the types of bifurcations that initiate and terminate firing in each burst. As only a few bifurcations are possible, only a restricted number of encoded features exists. Here we focus specifically on describing parabolic, square-wave and elliptic bursters. We find that parabolic bursters, whose firing is initiated and terminated by saddle-node bifurcations, behave as prototypical integrators: Firing is triggered by depolarizing stimuli, and lasts for as long as excitation is prolonged. Elliptic bursters, contrastingly, constitute prototypical resonators, since both the initiating and terminating bifurcations possess well-defined oscillation time scales. Firing is therefore triggered by stimulus stretches of matching frequency and terminated by a phase-inversion in the oscillation. The behavior of square-wave bursters is somewhat intermediate, since they are triggered by a fold bifurcation of cycles of well-defined frequency but are terminated by a homoclinic bifurcation lacking an oscillating time scale. These correspondences show that stimulus selectivity is determined by the type of bifurcations. By testing several neuron models, we also demonstrate that additional biological properties that do not modify the bifurcation structure play a minor role in stimulus encoding. Moreover, we show that burst-length variability (and thereby, the capacity to transmit information) depends on a trade-off between the variance of the external signal driving the cell and the strength of the slow internal currents modulating bursts. Thus, our work explicitly links the computational properties of bursting neurons to the mathematical properties of the underlying dynamical systems.

Bursting Neurons in the Hippocampal Formation Encode Features of LFP Rhythms

“…It should be noticed, however, that such future encoding is also found in the simulations, where by construction, neural activity is the consequence (and not the cause) of the driving signal. As discussed in Samengo et al (2013), encoding of future input features only takes place in signals that contain temporal correlations themselves. One can only expect a burst to encode future stimulus values if the burst is driven by input currents whose present value contains information about how they will evolve in the near future.…”

“…Recent evidence suggests that bursting pyramidal neurons can lock their firing to a preferred phase range of the dominant LFP rhythm and this phase preference can change as a function of burst spike count (Samengo and Montemurro, 2010; Constantinou et al, 2015). Using this idea, computational models have proposed bursting as a mechanism to encode instantaneous features of an oscillating current into a pattern of spikes that can be transmitted to distant areas (Kepecs and Lisman, 2003; Samengo et al, 2013). In particular, models of pyramidal neurons suggested that intra-burst spike counts have the capacity to encode the slope (Kepecs et al, 2002) and phase (Samengo and Montemurro, 2010) of time-varying input signals.…”

Analysis of the role of the low threshold currents IT and Ih in intrinsic delta oscillations of thalamocortical neurons

“…These properties could be very important in situations where bursting is not perfectly periodic. In Samengo et al ( 2013 ) it was shown that, given the adequate level of variability, bursters are able to codify input information and that the coding mechanism is essentially determined by the bifurcation structure.…”

Thalamic neuron models encode stimulus information by burst-size modulation

“…In brief, ETC analysis finds a set of axes in a k -dimensional space where the variance of n -triggering stimuli differs significantly from that of randomly selected stimuli (de Ruyter van Steveninck and Bialek, 1988 ; Brenner et al, 2000 ; Rust et al, 2005 ; Fairhall et al, 2006 ; Pillow and Simoncelli, 2006 ; Schwartz et al, 2006 ; Samengo and Gollisch, 2013 ). In order to eliminate the bias introduced by the correlations in the prior stimulus distribution, we calculate the “relative covariance matrix” through a matrix multiplication between the inverse covariance matrix of randomly selected stimuli and the n -triggered stimuli covariance matrix (Samengo and Gollisch, 2013 ; Samengo et al, 2013b ). Eigenvalues of the relative covariance matrix that significantly deviate from unity are associated with eigenvectors whose directions in the k -dimensional stimulus space indicate the features evoking n -spike triggering bursts.…”

“…In a cortical neuron model this n -spike burst code also represented different slopes and phases of driving stimuli (Kepecs et al, 2002 ; Samengo and Montemurro, 2010 ). Finally, Samengo et al ( 2013b ) found that neuron models possessing different dynamical mechanisms could encode different stimuli using n -spike bursts.…”