Refractoriness Accounts for Variable Spike Burst Responses in Somatosensory Cortex

Electrophysiological characterization of the hyperdirect pathway and its functional relevance for subthalamic deep brain stimulation

The subthalamic nucleus (STN) receives input from various cortical areas via hyperdirect pathway (HDP) which bypasses the basal-ganglia loop. Recently, the HDP has gained increasing interest, because of its relevance for STN deep brain stimulation (DBS). To understand the HDP's role cortical responses evoked by STN-DBS have been investigated. These responses have short (<2 ms), medium (2-15 ms), and long (20-70 ms) latencies. Medium-latency responses are supposed to represent antidromic cortical activations via HDP. Together with long-latency responses the medium responses can potentially be used as biomarker of DBS efficacy as well as side effects. We here propose that the activation sequence of the cortical evoked responses can be conceptualized as high frequency oscillations (HFO) for signal analysis. HFO might therefore serve as marker for antidromic activation. Using existing knowledge on HFO recordings, this approach allows data analyses and physiological modeling to advance the pathophysiological understanding of cortical DBS-evoked high-frequency activity.

Long anisotropic absolute refractory periods with rapid rise times to reliable responsiveness

Refractoriness is a fundamental property of excitable elements, such as neurons, indicating the probability for re-excitation in a given time lag, and is typically linked to the neuronal hyperpolarization following an evoked spike. Here we measured the refractory periods (RPs) in neuronal cultures and observed that an average anisotropic absolute RP could exceed 10 ms and its tail is 20 ms, independent of a large stimulation frequency range. It is an order of magnitude longer than anticipated and comparable with the decaying membrane potential time scale. It is followed by a sharp rise-time (relative RP) of merely ∼1 md to complete responsiveness. Extracellular stimulations result in longer absolute RPs than solely intracellular ones, and a pair of extracellular stimulations from two different routes exhibits distinct absolute RPs, depending on their order. Our results indicate that a neuron is an accurate excitable element, where the diverse RPs cannot be attributed solely to the soma and imply fast mutual interactions between different stimulation routes and dendrites. Further elucidation of neuronal computational capabilities and their interplay with adaptation mechanisms is warranted.

Modelling unitary fields and the single-neuron contribution to local field potentials in the hippocampus

Key points

We simulate the unitary local field potential (uLFP) generated in the hippocampus CA3, using morphologically detailed models.

The model suggests that cancelling effects between apical and basal dendritic synapses explain the low amplitude of excitatory uLFPs.

Inhibitory synapses around the soma do not cancel and could explain the high‐amplitude inhibitory uLFPs.

These results suggest that somatic inhibition constitutes a strong component of LFPs, which may explain a number of experimental observations.

Abstract

Synaptic currents represent a major contribution to the local field potential (LFP) in brain tissue, but the respective contribution of excitatory and inhibitory synapses is not known. Here, we provide estimates of this contribution by using computational models of hippocampal pyramidal neurons, constrained by in vitro recordings. We focus on the unitary LFP (uLFP) generated by single neurons in the CA3 region of the hippocampus. We first reproduce experimental results for hippocampal basket cells, and in particular how inhibitory uLFP are distributed within hippocampal layers. Next, we calculate the uLFP generated by pyramidal neurons, using morphologically reconstructed CA3 pyramidal cells. The model shows that the excitatory uLFP is of small amplitude, smaller than inhibitory uLFPs. Indeed, when the two are simulated together, inhibitory uLFPs mask excitatory uLFPs, which might create the illusion that the inhibitory field is generated by pyramidal cells. These results provide an explanation for the observation that excitatory and inhibitory uLFPs are of the same polarity, in vivo and in vitro. These results suggest that somatic inhibitory currents are large contributors to the LFP, which is important information for interpreting this signal. Finally, the results of our model might form the basis of a simple method to compute the LFP, which could be applied to point neurons for each cell type, thus providing a simple biologically grounded method for calculating LFPs from neural networks.

In conclusion, computational models constrained by in vitro recordings suggest that: (1) Excitatory uLFPs are of smaller amplitude than inhibitory uLFPs. (2) Inhibitory uLFPs form the major contribution to LFPs. (3) uLFPs can be used as a simple model to generate LFPs from spiking networks.

We simulate the unitary local field potential (uLFP) generated in the hippocampus CA3, using morphologically detailed models.

The model suggests that cancelling effects between apical and basal dendritic synapses explain the low amplitude of excitatory uLFPs.

Inhibitory synapses around the soma do not cancel and could explain the high‐amplitude inhibitory uLFPs.

These results suggest that somatic inhibition constitutes a strong component of LFPs, which may explain a number of experimental observations.

A Lead Field Two-Domain Model for Longitudinal Neural Tracts-Analytical Framework and Implications for Signal Bandwidth

Somatosensory evoked potentials are a well-established tool for assessing volley conduction in afferent neural pathways. However, from a clinical perspective, recording of spinal signals is still a demanding task due to the low amplitudes compared to relevant noise sources. Computer modeling is a powerful tool for gaining insight into signal genesis and, thus, for promoting future innovations in signal extraction. However, due to the complex structure of neural pathways, modeling is computationally demanding. We present a theoretical framework which allows computing the electric potential generated by a single axon in a body surface lead by the convolution of the neural lead field function with a propagating action potential term. The signal generated by a large cohort of axons was obtained by convoluting a single axonal signal with the statistical distribution of temporal dispersion of individual axonal signals. For establishing the framework, analysis was based on an analytical model. Our approach was further adopted for a numerical computation of body surface neuropotentials employing the lead field theory. Double convolution allowed straightforward analysis in the frequency domain. The highest frequency components occurred at the cellular membrane. A bandpass type spectral shape and a peak frequency of 1800 Hz was observed. The volume conductor transmitting the signal to the recording lead acted as an additional bandpass reducing the axonal peak frequency from 200 Hz to 500 Hz. The superposition of temporally dispersed axonal signals acted as an additional low-pass filter further reducing the compound action potential peak frequency from 90 Hz to 170 Hz. Our results suggest that the bandwidth of spinal evoked potentials might be narrower than the bandwidth requested by current clinical guidelines. The present findings will allow the optimization of noise suppression. Furthermore, our theoretical framework allows the adaptation in numerical methods and application in anatomically realistic geometries in future studies.

Spike-Based Winner-Take-All Computation: Fundamental Limits and Order-Optimal Circuits

Winner-take-all (WTA) refers to the neural operation that selects a (typically small) group of neurons from a large neuron pool. It is conjectured to underlie many of the brain's fundamental computational abilities. However, not much is known about the robustness of a spike-based WTA network to the inherent randomness of the input spike trains. In this work, we consider a spike-based k-WTA model wherein n randomly generated input spike trains compete with each other based on their underlying firing rates and k winners are supposed to be selected. We slot the time evenly with each time slot of length 1 ms and model the n input spike trains as n independent Bernoulli processes. We analytically characterize the minimum waiting time needed so that a target minimax decision accuracy (success probability) can be reached. We first derive an information-theoretic lower bound on the waiting time. We show that to guarantee a (minimax) decision error ≤δ (where δ∈(0,1)), the waiting time of any WTA circuit is at least [Formula: see text]where R⊆(0,1) is a finite set of rates and TR is a difficulty parameter of a WTA task with respect to set R for independent input spike trains. Additionally, TR is independent of δ, n, and k. We then design a simple WTA circuit whose waiting time is [Formula: see text]provided that the local memory of each output neuron is sufficiently long. It turns out that for any fixed δ, this decision time is order-optimal (i.e., it matches the above lower bound up to a multiplicative constant factor) in terms of its scaling in n, k, and TR.