The robustness of phase-locking in neurons with dendro-dendritic electrical coupling

Abstract

We examine the effects of dendritic filtering on the existence, stability, and robustness of phase-locked states to heterogeneity and noise in a pair of electrically coupled ball-and-stick neurons with passive dendrites. We use the theory of weakly coupled oscillators and analytically derived filtering properties of the dendritic coupling to systematically explore how the electrotonic length and diameter of dendrites can alter phase-locking. In the case of a fixed value of the coupling conductance (g c ) taken from the literature, we find that repeated exchanges in stability between the synchronous and anti-phase states can occur as the electrical coupling becomes more distally located on the dendrites. However, the robustness of the phase-locked states in this case decreases rapidly towards zero as the distance between the electrical coupling and the somata increases. Published estimates of g c are calculated from the experimentally measured coupling coefficient (CC) based on a single-compartment description of a neuron, and therefore may be severe underestimates of g c . With this in mind, we re-examine the stability and robustness of phase-locking using a fixed value of CC, which imposes a limit on the maximum distance the electrical coupling can be located away from the somata. In this case, although the phase-locked states remain robust over the entire range of possible coupling locations, no exchanges in stability with changing coupling position are observed except for a single exchange that occurs in the case of a high somatic firing frequency and a large dendritic radius. Thus, our analysis suggests that multiple exchanges in stability with changing coupling location are unlikely to be observed in real neural systems.

A biophysical model of striatal microcircuits suggests gamma and beta oscillations interleaved at delta/theta frequencies mediate periodicity in motor control

“…We modified a previous single-compartment striatal FSI model [47] by adding a dendritic compartment (shown to be an important determinant of gap-junction mediated synchrony [48][49][50][51]) and increasing the conductance of the D-type K current to 6 mS/cm 2 . Previous work showed that two characteristic attributes of FSI activity in vitro, stuttering and γ resonance (defined as a minimal tonic firing rate in the γ frequency range), are dependent on the D-current [30,47].…”

“…The current study focuses on the oscillatory bands frequently observed in striatal local field potential: δ (1-3 Hz), θ (4-7 Hz), β (8-30 Hz), low γ (50)(51)(52)(53)(54)(55)(56)(57)(58)(59)(60), and high γ (70)(71)(72)(73)(74)(75)(76)(77)(78)(79)(80) [10,16,28]. Power in these bands consistently correlates with responses to task parameters including motor initiation, decision making, and reward [10][11][12]20].…”

Synchrony and so much more: Diverse roles for electrical synapses in neural circuits

“…Dendritic electrical synapses are often not enough to induce temporally sharp spike synchrony, perhaps because of their weakness or locations distant from spike-generating zones (axon initial segments in many neurons) (Saraga et al, 2006;Lewis and Skinner, 2012;Schwemmer and Lewis, 2014). Active conductances in dendrites (Johnston and Narayanan, 2008) may enhance or suppress the phase-locking effects of electrical synapses.…”

“…In fact, antisynchrony among electrically coupled model neurons is particularly sensitive to the shapes of action potentials and the intrinsic membrane conductances that underlie them (Chow and Kopell, 2000;Nomura et al, 2003;Pfeuty et al, 2003). Antisynchronous states are often quite fragile, particularly as the sites of electrical synapses move more distally, away from spike-generating zones (Schwemmer and Lewis, 2014).…”

Spike width and frequency alter stability of phase-locking in electrically coupled neurons

“…A number of theoretical works dealt with understanding the essential components responsible for such synchrony or failure of synchrony among electrically coupled neurons, some of them using relaxation oscillator models [9, 15, 11], and others using integrate-and-fire model neurons [16, 17, 18, 19]. The latter approach is based on the widely successful theory of weakly coupled oscillators [20, 21, 22, 23, 24] that requires specification of the coupling mechanism including the voltage time course and the neuron’s phase response curve (PRC). A knowledge of these two elements is sufficient to completely predict when and why a set of identical neurons synchronize.…”