Assessing the Impact of Ih Conductance on Cross-Frequency Coupling in Model Pyramidal Neurons.

Large cortical and hippocampal pyramidal neurons are elements of neuronal circuitry that have been implicated in cross-frequency coupling (CFC) during cognitive tasks. We investigate potential mechanisms for CFC within these neurons by examining the role that the hyperpolarization-activated mixed cation current (Ih) plays in modulating CFC characteristics in multicompartment neuronal models. We quantify CFC along the soma-apical dendrite axis and tuft of three models configured to have different spatial distributions of Ih conductance density: (1) exponential gradient along the soma-apical dendrite axis, (2) uniform distribution, and (3) no Ih conductance. We simulated two current injection scenarios: distal apical 4 Hz modulation and perisomatic 4 Hz modulation, each with perisomatic, mid-apical, and distal apical 40 Hz injections. We used two metrics to quantify CFC strength-modulation index and height ratio-and we analyzed CFC phase properties. For all models, CFC was strongest in distal apical regions when the 40 Hz injection occurred near the soma and the 4 Hz modulation occurred in distal apical dendrite. The strongest CFC values were observed in the model with uniformly distributed Ih conductance density, but when the exponential gradient in Ih conductance density was added, CFC strength decreased by almost 50%. When Ih was in the model, regions with much larger membrane potential fluctuations at 4 Hz than at 40 Hz had stronger CFC. Excluding the Ih conductance from the model resulted in CFC either reduced or comparable in strength relative to the model with the exponential gradient in Ih conductance. The Ih conductance also imposed order on the phase characteristics of CFC such that minimum (maximum) amplitude 40 Hz membrane potential oscillations occurred during Ih conductance deactivation (activation). On the other hand, when there was no Ih conductance, phase relationships between minimum and maximum 40 Hz oscillation often inverted and occurred much closer together. This analysis can help experimentalists discriminate between CFC that originates from different underlying physiological mechanisms and can help illuminate the reasons why there are differences between CFC strength observed in different regions of the brain and between different populations of neurons based on the configuration of the Ih conductance.

Enabling Large-Scale Simulations With the GENESIS Neuronal Simulator.

In this paper, we evaluate the computational performance of the GEneral NEural SImulation System (GENESIS) for large scale simulations of neural networks. While many benchmark studies have been performed for large scale simulations with leaky integrate-and-fire neurons or neuronal models with only a few compartments, this work focuses on higher fidelity neuronal models represented by 50-74 compartments per neuron. After making some modifications to the source code for GENESIS and its parallel implementation, PGENESIS, particularly to improve memory usage, we find that PGENESIS is able to efficiently scale on supercomputing resources to network sizes as large as 9 × 106 neurons with 18 × 109 synapses and 2.2 × 106 neurons with 45 × 109 synapses. The modifications to GENESIS that enabled these large scale simulations have been incorporated into the May 2019 Official Release of PGENESIS 2.4 available for download from the GENESIS web site (genesis-sim.org).

Resonance Analysis as a Tool for Characterizing Functional Division of Layer 5 Pyramidal Neurons.

Evidence suggests that layer 5 pyramidal neurons can be divided into functional zones with unique afferent connectivity and membrane characteristics that allow for post-synaptic integration of feedforward and feedback inputs. To assess the existence of these zones and their interaction, we characterized the resonance properties of a biophysically-realistic compartmental model of a neocortical layer 5 pyramidal neuron. Consistent with recently published theoretical and empirical findings, our model was configured to have a "hot zone" in distal apical dendrite and apical tuft where both high- and low-threshold Ca2+ ionic conductances had densities 1-2 orders of magnitude higher than anywhere else in the apical dendrite. We simulated injection of broad spectrum sinusoidal currents with linearly increasing frequency to calculate the input impedance of individual compartments, the transfer impedance between the soma and key compartments within the dendritic tree, and a dimensionless term we introduce called resonance quality. We show that input resonance analysis distinguished at least four distinct zones within the model based on properties of their frequency preferences: basal dendrite which displayed little resonance; soma/proximal apical dendrite which displayed resonance at 5-23 Hz, strongest at 5-10 Hz and hyperpolarized/resting membrane potentials; distal apical dendrite which displayed resonance at 8-19 Hz, strongest at 10 Hz and depolarized membrane potentials; and apical tuft which displayed a weak resonance largely between 8 and 10 Hz across a wide range of membrane potentials. Transfer resonance analysis revealed that changes in subthreshold electrical coupling were found to modulate the transfer resonant frequency of signals transmitted from distal apical dendrite and apical tuft to the soma, which would impact the frequencies that individual neurons are expected to respond to and reinforce. Furthermore, eliminating the hot zone was found to reduce amplification of resonance within the model, which contributes to reduced excitability when perisomatic and distal apical regions receive coincident stimulating current injections. These results indicate that the interactions between different functional zones should be considered in a more complete understanding of neuronal integration. Resonance analysis may therefore be a useful tool for assessing the integration of inputs across the entire neuronal membrane.

Impact of Neuronal Membrane Damage on the Local Field Potential in a Large-Scale Simulation of Cerebral Cortex.

Within multiscale brain dynamics, the structure-function relationship between cellular changes at a lower scale and coordinated oscillations at a higher scale is not well understood. This relationship may be particularly relevant for understanding functional impairments after a mild traumatic brain injury (mTBI) when current neuroimaging methods do not reveal morphological changes to the brain common in moderate to severe TBI such as diffuse axonal injury or gray matter lesions. Here, we created a physiology-based model of cerebral cortex using a publicly released modeling framework (GEneral NEural SImulation System) to explore the possibility that performance deficits characteristic of blast-induced mTBI may reflect dysfunctional, local network activity influenced by microscale neuronal damage at the cellular level. We operationalized microscale damage to neurons as the formation of pores on the neuronal membrane based on research using blast paradigms, and in our model, pores were simulated by a change in membrane conductance. We then tracked changes in simulated electrical activity. Our model contained 585 simulated neurons, comprised of 14 types of cortical and thalamic neurons each with its own compartmental morphology and electrophysiological properties. Comparing the functional activity of neurons before and after simulated damage, we found that simulated pores in the membrane reduced both action potential generation and local field potential (LFP) power in the 1-40 Hz range of the power spectrum. Furthermore, the location of damage modulated the strength of these effects: pore formation on simulated axons reduced LFP power more strongly than did pore formation on the soma and the dendrites. These results indicate that even small amounts of cellular damage can negatively impact functional activity of larger scale oscillations, and our findings suggest that multiscale modeling provides a promising avenue to elucidate these relationships.

Phase locking asymmetries at flexor-extensor transitions during fictive locomotion.

The motor output for walking is produced by a network of neurons termed the spinal central pattern generator (CPG) for locomotion. The basic building block of this CPG is a half-center oscillator composed of two mutually inhibitory sets of interneurons, each controlling one of the two dominant phases of locomotion: flexion and extension. To investigate symmetry between the two components of this oscillator, we analyzed the statistics of natural variation in timing during fictive locomotion induced by stimulation of the midbrain locomotor region in the cat. As a complement to previously published analysis of these data focused on burst and cycle durations, we present a new analysis examining the strength of phase locking at the transitions between flexion and extension. Across our sample of nerve pairs, phase locking at the transition from extension to flexion (E to F) is stronger than at the transition from flexion to extension (F to E). This pattern did not reverse when considering bouts of fictive locomotion that were flexor vs. extensor dominated, demonstrating that asymmetric locking at the transitions between phases is dissociable from which phase dominates cycle duration. We also find that the strength of phase locking is correlated with the mean latency between burst offset and burst onset. These results are interpreted in the context of a hypothesis where network inhibition and intrinsic oscillatory mechanisms make distinct contributions to flexor-extensor alternation in half-center networks.

Temporal correlations in stochastic models of double bursting during simulated locomotion.

The output of the spinal central pattern generator for locomotion falls into two broad categories: alternation between antagonistic muscles and double bursting within muscles acting on multiple joints. We first model an alternating half-center and then present two different models of double bursting. The first double-bursting model consists of a central clock with an explicit one-to-one mapping between interneuron activity and model output. The second double-bursting model consists of a half-center with an added feedback neuron. Models are built using rate-coded leaky integrator neurons with slow self-inhibition. Structure-function relationships are explored by the addition of noise. The interaction of noise with the dynamics of each network creates a unique pattern of correlation between phases of the simulated cycle. The effects of noise can be explained by perturbation of deterministic versions of the networks. Three basic results were obtained: slow self-inhibitory currents lead to correlations between parts of the step cycle that are separated in time and network relative; model outputs are most sensitive to perturbations presented just before competitive switches in network activity, and clock-like models possess substantial symmetries within the correlation structure of burst durations, whereas the correlation structure of feedback models are asymmetric. Our models suggest that variability in burst length durations can be analyzed to make inferences about the structure of the spinal networks for locomotion. In particular, correlation patterns within double-bursting outputs may yield important clues regarding the interaction between more central, clock-like networks and feedback from more peripheral interneurons.