Phasic firing and coincidence detection by subthreshold negative feedback: divisive or subtractive or, better, both

Phasic neurons typically fire only for a fast-rising input, say at the onset of a step current, but not for steady or slow inputs, a property associated with type III excitability. Phasic neurons can show extraordinary temporal precision for phase locking and coincidence detection. Exemplars are found in the auditory brain stem where precise timing is used in sound localization. Phasicness at the cellular level arises from a dynamic, voltage-gated, negative feedback that can be recruited subthreshold, preventing the neuron from reaching spike threshold if the voltage does not rise fast enough. We consider two mechanisms for phasicness: a low threshold potassium current (subtractive mechanism) and a sodium current with subthreshold inactivation (divisive mechanism). We develop and analyze three reduced models with either divisive or subtractive mechanisms or both to gain insight into the dynamical mechanisms for the potentially high temporal precision of type III-excitable neurons. We compare their firing properties and performance for a range of stimuli. The models have characteristic non-monotonic input-output relations, firing rate vs. input intensity, for either stochastic current injection or Poisson-timed excitatory synaptic conductance trains. We assess performance according to precision of phase-locking and coincidence detection by the models' responses to repetitive packets of unitary excitatory synaptic inputs with more or less temporal coherence. We find that each mechanism contributes features but best performance is attained if both are present. The subtractive mechanism confers extraordinary precision for phase locking and coincidence detection but only within a restricted parameter range when the divisive mechanism of sodium inactivation is inoperative. The divisive mechanism guarantees robustness of phasic properties, without compromising excitability, although with somewhat less precision. Finally, we demonstrate that brief transient inhibition if properly timed can enhance the reliability of firing.Postprint (published version

Increased bradykinesia in Parkinson’s disease with increased movement complexity: elbow flexion-extension movements

The present research investigates factors contributing to bradykinesia in the control of simple and complex voluntary limb movement in Parkinson’s disease (PD) patients. The functional scheme of the basal ganglia (BG)–thalamocortical circuit was described by a mathematical model based on the mean firing rates of BG nuclei. PD was simulated as a reduction in dopamine levels, and a loss of functional segregation between two competing motor modules. In order to compare model simulations with performed movements, flexion and extension at the elbow joint is taken as a test case. Results indicated that loss of segregation contributed to bradykinesia due to interference between competing modules and a reduced ability to suppress unwanted movements. Additionally, excessive neurotransmitter depletion is predicted as a possible mechanism for the increased difficulty in performing complex movements. The simulation results showed that the model is in qualitative agreement with the results from movement experiments on PD patients and healthy subjects. Furthermore, based on changes in the firing rate of BG nuclei, the model demonstrated that the effective mechanism of Deep Brain Stimulation (DBS) in STN may result from stimulation induced inhibition of STN, partial synaptic failure of efferent projections, or excitation of inhibitory afferent axons even though the underlying methods of action may be quite different for the different mechanisms

On transition to bursting via deterministic chaos

We study statistical properties of the irregular bursting arising in a class of neuronal models close to the transition from spiking to bursting. Prior to the transition to bursting, the systems in this class develop chaotic attractors, which generate irregular spiking. The chaotic spiking gives rise to irregular bursting. The duration of bursts near the transition can be very long. We describe the statistics of the number of spikes and the interspike interval distributions within one burst as functions of the distance from criticality.Comment: 8 pages, 6 figure

Soma-Axon Coupling Configurations That Enhance Neuronal Coincidence Detection

Coincidence detector neurons transmit timing information by responding preferentially to concurrent synaptic inputs. Principal cells of the medial superior olive (MSO) in the mammalian auditory brainstem are superb coincidence detectors. They encode sound source location with high temporal precision, distinguishing submillisecond timing differences among inputs. We investigate computationally how dynamic coupling between the input region (soma and dendrite) and the spike-generating output region (axon and axon initial segment) can enhance coincidence detection in MSO neurons. To do this, we formulate a two-compartment neuron model and characterize extensively coincidence detection sensitivity throughout a parameter space of coupling configurations. We focus on the interaction between coupling configuration and two currents that provide dynamic, voltage-gated, negative feedback in subthreshold voltage range: sodium current with rapid inactivation and low-threshold potassium current, IKLT. These currents reduce synaptic summation and can prevent spike generation unless inputs arrive with near simultaneity. We show that strong soma-to-axon coupling promotes the negative feedback effects of sodium inactivation and is, therefore, advantageous for coincidence detection. Furthermore, the feedforward combination of strong soma-to-axon coupling and weak axon-to-soma coupling enables spikes to be generated efficiently (few sodium channels needed) and with rapid recovery that enhances high-frequency coincidence detection. These observations detail the functional benefit of the strongly feedforward configuration that has been observed in physiological studies of MSO neurons. We find that IKLT further enhances coincidence detection sensitivity, but with effects that depend on coupling configuration. For instance, in models with weak soma-to-axon and weak axon-to-soma coupling, IKLT in the axon enhances coincidence detection more effectively than IKLT in the soma. By using a minimal model of soma-to-axon coupling, we connect structure, dynamics, and computation. Although we consider the particular case of MSO coincidence detectors, our method for creating and exploring a parameter space of two-compartment models can be applied to other neurons

Chaos at the border of criticality

The present paper points out to a novel scenario for formation of chaotic attractors in a class of models of excitable cell membranes near an Andronov-Hopf bifurcation (AHB). The mechanism underlying chaotic dynamics admits a simple and visual description in terms of the families of one-dimensional first-return maps, which are constructed using the combination of asymptotic and numerical techniques. The bifurcation structure of the continuous system (specifically, the proximity to a degenerate AHB) endows the Poincare map with distinct qualitative features such as unimodality and the presence of the boundary layer, where the map is strongly expanding. This structure of the map in turn explains the bifurcation scenarios in the continuous system including chaotic mixed-mode oscillations near the border between the regions of sub- and supercritical AHB. The proposed mechanism yields the statistical properties of the mixed-mode oscillations in this regime. The statistics predicted by the analysis of the Poincare map and those observed in the numerical experiments of the continuous system show a very good agreement.Comment: Chaos: An Interdisciplinary Journal of Nonlinear Science (tentatively, Sept 2008

Computational models of auditory perception from feature extraction to stream segregation and behavior

This is the final version. Available on open access from Elsevier via the DOI in this recordData availability: This is a review study, and as such did not generate any new data.Audition is by nature dynamic, from brainstem processing on sub-millisecond time scales, to segregating and tracking sound sources with changing features, to the pleasure of listening to music and the satisfaction of getting the beat. We review recent advances from computational models of sound localization, of auditory stream segregation and of beat perception/generation. A wealth of behavioral, electrophysiological and imaging studies shed light on these processes, typically with synthesized sounds having regular temporal structure. Computational models integrate knowledge from different experimental fields and at different levels of description. We advocate a neuromechanistic modeling approach that incorporates knowledge of the auditory system from various fields, that utilizes plausible neural mechanisms, and that bridges our understanding across disciplines.Engineering and Physical Sciences Research Council (EPSRC

Spatial coherence resonance on diffusive and small-world networks of Hodgkin-Huxley neurons

Spatial coherence resonance in a spatially extended system that is locally modeled by Hodgkin-Huxley (HH) neurons is studied in this paper. We focus on the ability of additive temporally and spatially uncorrelated Gaussian noise to extract a particular spatial frequency of excitatory waves in the medium, whereby examining also the impact of diffusive and small-world network topology determining the interactions amongst coupled HH neurons. We show that there exists an intermediate noise intensity that is able to extract a characteristic spatial frequency of the system in a resonant manner provided the latter is diffusively coupled, thus indicating the existence of spatial coherence resonance. However, as the diffusive topology of the medium is relaxed via the introduction of shortcut links introducing small-world properties amongst coupled HH neurons, the ability of additive Gaussian noise to evoke ordered excitatory waves deteriorates rather spectacularly, leading to the decoherence of the spatial dynamics and with it related absence of spatial coherence resonance. In particular, already a minute fraction of shortcut links suffices to substantially disrupt coherent pattern formation in the examined system.Comment: 8 two-column pages, 6 figures; accepted for publication in Chao