Weak electric fields promote resonance in neuronal spiking activity: Analytical results from two-compartment cell and network models.
ABSTRACT: Transcranial brain stimulation and evidence of ephaptic coupling have sparked strong interests in understanding the effects of weak electric fields on the dynamics of neuronal populations. While their influence on the subthreshold membrane voltage can be biophysically well explained using spatially extended neuron models, mechanistic analyses of neuronal spiking and network activity have remained a methodological challenge. More generally, this challenge applies to phenomena for which single-compartment (point) neuron models are oversimplified. Here we employ a pyramidal neuron model that comprises two compartments, allowing to distinguish basal-somatic from apical dendritic inputs and accounting for an extracellular field in a biophysically minimalistic way. Using an analytical approach we fit its parameters to reproduce the response properties of a canonical, spatial model neuron and dissect the stochastic spiking dynamics of single cells and large networks. We show that oscillatory weak fields effectively mimic anti-correlated inputs at the soma and dendrite and strongly modulate neuronal spiking activity in a rather narrow frequency band. This effect carries over to coupled populations of pyramidal cells and inhibitory interneurons, boosting network-induced resonance in the beta and gamma frequency bands. Our work contributes a useful theoretical framework for mechanistic analyses of population dynamics going beyond point neuron models, and provides insights on modulation effects of extracellular fields due to the morphology of pyramidal cells.
Project description:Transcranial brain stimulation and evidence of ephaptic coupling have recently sparked strong interests in understanding the effects of weak electric fields on the dynamics of brain networks and of coupled populations of neurons. The collective dynamics of large neuronal populations can be efficiently studied using single-compartment (point) model neurons of the integrate-and-fire (IF) type as their elements. These models, however, lack the dendritic morphology required to biophysically describe the effect of an extracellular electric field on the neuronal membrane voltage. Here, we extend the IF point neuron models to accurately reflect morphology dependent electric field effects extracted from a canonical spatial "ball-and-stick" (BS) neuron model. Even in the absence of an extracellular field, neuronal morphology by itself strongly affects the cellular response properties. We, therefore, derive additional components for leaky and nonlinear IF neuron models to reproduce the subthreshold voltage and spiking dynamics of the BS model exposed to both fluctuating somatic and dendritic inputs and an extracellular electric field. We show that an oscillatory electric field causes spike rate resonance, or equivalently, pronounced spike to field coherence. Its resonance frequency depends on the location of the synaptic background inputs. For somatic inputs the resonance appears in the beta and gamma frequency range, whereas for distal dendritic inputs it is shifted to even higher frequencies. Irrespective of an external electric field, the presence of a dendritic cable attenuates the subthreshold response at the soma to slowly-varying somatic inputs while implementing a low-pass filter for distal dendritic inputs. Our point neuron model extension is straightforward to implement and is computationally much more efficient compared to the original BS model. It is well suited for studying the dynamics of large populations of neurons with heterogeneous dendritic morphology with (and without) the influence of weak external electric fields.
Project description:Recent genome-wide association studies have identified a large number of genetic risk factors for schizophrenia (SCZ) featuring ion channels and calcium transporters. For some of these risk factors, independent prior investigations have examined the effects of genetic alterations on the cellular electrical excitability and calcium homeostasis. In the present proof-of-concept study, we harnessed these experimental results for modeling of computational properties on layer V cortical pyramidal cells and identified possible common alterations in behavior across SCZ-related genes.We applied a biophysically detailed multicompartmental model to study the excitability of a layer V pyramidal cell. We reviewed the literature on functional genomics for variants of genes associated with SCZ and used changes in neuron model parameters to represent the effects of these variants.We present and apply a framework for examining the effects of subtle single nucleotide polymorphisms in ion channel and calcium transporter-encoding genes on neuron excitability. Our analysis indicates that most of the considered SCZ-related genetic variants affect the spiking behavior and intracellular calcium dynamics resulting from summation of inputs across the dendritic tree.Our results suggest that alteration in the ability of a single neuron to integrate the inputs and scale its excitability may constitute a fundamental mechanistic contributor to mental disease, alongside the previously proposed deficits in synaptic communication and network behavior.
Project description:Several decades of research suggest that weak electric fields may influence neural processing, including those induced by neuronal activity and proposed as a substrate for a potential new cellular communication system, i.e., ephaptic transmission. Here we aim to model mesoscopic ephaptic activity in the human brain and explore its trajectory during aging by characterizing the electric field generated by cortical dipoles using realistic finite element modeling. Extrapolating from electrophysiological measurements, we first observe that modeled endogenous field magnitudes are comparable to those in measurements of weak but functionally relevant self-generated fields and to those produced by noninvasive transcranial brain stimulation, and therefore possibly able to modulate neuronal activity. Then, to evaluate the role of these fields in the human cortex in large MRI databases, we adapt an interaction approximation that considers the relative orientation of neuron and field to estimate the membrane potential perturbation in pyramidal cells. We use this approximation to define a simplified metric (EMOD1) that weights dipole coupling as a function of distance and relative orientation between emitter and receiver and evaluate it in a sample of 401 realistic human brain models from healthy subjects aged 16-83. Results reveal that ephaptic coupling, in the simplified mesoscopic modeling approach used here, significantly decreases with age, with higher involvement of sensorimotor regions and medial brain structures. This study suggests that by providing the means for fast and direct interaction between neurons, ephaptic modulation may contribute to the complexity of human function for cognition and behavior, and its modification across the lifespan and in response to pathology.
Project description:Neocortical network activity is generated through a dynamic balance between excitation, provided by pyramidal neurons, and inhibition, provided by interneurons. Imbalance of the excitation/inhibition ratio has been identified in several neuropsychiatric diseases, such as schizophrenia, autism and epilepsy, which also present with other cognitive deficits and symptoms associated with prefrontal cortical (PFC) dysfunction. We undertook a computational approach to study how changes in the excitation/inhibition balance in a PFC microcircuit model affect the properties of persistent activity, considered the cellular correlate of working memory function in PFC. To this end, we constructed a PFC microcircuit, consisting of pyramidal neuron models and all three different interneuron types: fast-spiking (FS), regular-spiking (RS), and irregular-spiking (IS) interneurons. Persistent activity was induced in the microcircuit model with a stimulus to the proximal apical dendrites of the pyramidal neuron models, and its properties were analyzed, such as the induction profile, the interspike intervals (ISIs) and neuronal synchronicity. Our simulations showed that (a) the induction but not the firing frequency or neuronal synchronicity is modulated by changes in the NMDA-to-AMPA ratio on FS interneuron model, (b) removing or decreasing the FS model input to the pyramidal neuron models greatly limited the biophysical modulation of persistent activity induction, decreased the ISIs and neuronal synchronicity during persistent activity, (c) the induction and firing properties could not be altered by the addition of other inhibitory inputs to the soma (from RS or IS models), and (d) the synchronicity change could be reversed by the addition of other inhibitory inputs to the soma, but beyond the levels of the control network. Thus, generic somatic inhibition acts as a pacemaker of persistent activity and FS specific inhibition modulates the output of the pacemaker.
Project description:Proper functioning of working memory involves the expression of stimulus-selective persistent activity in pyramidal neurons of the prefrontal cortex (PFC), which refers to neural activity that persists for seconds beyond the end of the stimulus. The mechanisms which PFC pyramidal neurons use to discriminate between preferred vs. neutral inputs at the cellular level are largely unknown. Moreover, the presence of pyramidal cell subtypes with different firing patterns, such as regular spiking and intrinsic bursting, raises the question as to what their distinct role might be in persistent firing in the PFC. Here, we use a compartmental modeling approach to search for discriminatory features in the properties of incoming stimuli to a PFC pyramidal neuron and/or its response that signal which of these stimuli will result in persistent activity emergence. Furthermore, we use our modeling approach to study cell-type specific differences in persistent activity properties, via implementing a regular spiking (RS) and an intrinsic bursting (IB) model neuron. We identify synaptic location within the basal dendrites as a feature of stimulus selectivity. Specifically, persistent activity-inducing stimuli consist of activated synapses that are located more distally from the soma compared to non-inducing stimuli, in both model cells. In addition, the action potential (AP) latency and the first few inter-spike-intervals of the neuronal response can be used to reliably detect inducing vs. non-inducing inputs, suggesting a potential mechanism by which downstream neurons can rapidly decode the upcoming emergence of persistent activity. While the two model neurons did not differ in the coding features of persistent activity emergence, the properties of persistent activity, such as the firing pattern and the duration of temporally-restricted persistent activity were distinct. Collectively, our results pinpoint to specific features of the neuronal response to a given stimulus that code for its ability to induce persistent activity and predict differential roles of RS and IB neurons in persistent activity expression.
Project description:Synaptic plasticity is thought to be the principal neuronal mechanism underlying learning. Models of plastic networks typically combine point neurons with spike-timing-dependent plasticity (STDP) as the learning rule. However, a point neuron does not capture the local non-linear processing of synaptic inputs allowed for by dendrites. Furthermore, experimental evidence suggests that STDP is not the only learning rule available to neurons. By implementing biophysically realistic neuron models, we study how dendrites enable multiple synaptic plasticity mechanisms to coexist in a single cell. In these models, we compare the conditions for STDP and for synaptic strengthening by local dendritic spikes. We also explore how the connectivity between two cells is affected by these plasticity rules and by different synaptic distributions. Finally, we show that how memory retention during associative learning can be prolonged in networks of neurons by including dendrites.Synaptic plasticity is the neuronal mechanism underlying learning. Here the authors construct biophysical models of pyramidal neurons that reproduce observed plasticity gradients along the dendrite and show that dendritic spike dependent LTP which is predominant in distal sections can prolong memory retention.
Project description:Capturing the response behavior of spiking neuron models with rate-based models facilitates the investigation of neuronal networks using powerful methods for rate-based network dynamics. To this end, we investigate the responses of two widely used neuron model types, the Izhikevich and augmented multi-adapative threshold (AMAT) models, to a range of spiking inputs ranging from step responses to natural spike data. We find (i) that linear-nonlinear firing rate models fitted to test data can be used to describe the firing-rate responses of AMAT and Izhikevich spiking neuron models in many cases; (ii) that firing-rate responses are generally too complex to be captured by first-order low-pass filters but require bandpass filters instead; (iii) that linear-nonlinear models capture the response of AMAT models better than of Izhikevich models; (iv) that the wide range of response types evoked by current-injection experiments collapses to few response types when neurons are driven by stationary or sinusoidally modulated Poisson input; and (v) that AMAT and Izhikevich models show different responses to spike input despite identical responses to current injections. Together, these findings suggest that rate-based models of network dynamics may capture a wider range of neuronal response properties by incorporating second-order bandpass filters fitted to responses of spiking model neurons. These models may contribute to bringing rate-based network modeling closer to the reality of biological neuronal networks.
Project description:The rise of transcranial current stimulation (tCS) techniques have sparked an increasing interest in the effects of weak extracellular electric fields on neural activity. These fields modulate ongoing neural activity through polarization of the neuronal membrane. While the somatic polarization has been investigated experimentally, the frequency-dependent polarization of the dendritic trees in the presence of alternating (AC) fields has received little attention yet. Using a biophysically detailed model with experimentally constrained active conductances, we analyze the subthreshold response of cortical pyramidal cells to weak AC fields, as induced during tCS. We observe a strong frequency resonance around 10-20 Hz in the apical dendrites sensitivity to polarize in response to electric fields but not in the basal dendrites nor the soma. To disentangle the relative roles of the cell morphology and active and passive membrane properties in this resonance, we perform a thorough analysis using simplified models, e.g. a passive pyramidal neuron model, simple passive cables and reconstructed cell model with simplified ion channels. We attribute the origin of the resonance in the apical dendrites to (i) a locally increased sensitivity due to the morphology and to (ii) the high density of h-type channels. Our systematic study provides an improved understanding of the subthreshold response of cortical cells to weak electric fields and, importantly, allows for an improved design of tCS stimuli.
Project description:Local supra-linear summation of excitatory inputs occurring in pyramidal cell dendrites, the so-called dendritic spikes, results in independent spiking dendritic sub-units, which turn pyramidal neurons into two-layer neural networks capable of computing linearly non-separable functions, such as the exclusive OR. Other neuron classes, such as interneurons, may possess only a few independent dendritic sub-units, or only passive dendrites where input summation is purely sub-linear, and where dendritic sub-units are only saturating. To determine if such neurons can also compute linearly non-separable functions, we enumerate, for a given parameter range, the Boolean functions implementable by a binary neuron model with a linear sub-unit and either a single spiking or a saturating dendritic sub-unit. We then analytically generalize these numerical results to an arbitrary number of non-linear sub-units. First, we show that a single non-linear dendritic sub-unit, in addition to the somatic non-linearity, is sufficient to compute linearly non-separable functions. Second, we analytically prove that, with a sufficient number of saturating dendritic sub-units, a neuron can compute all functions computable with purely excitatory inputs. Third, we show that these linearly non-separable functions can be implemented with at least two strategies: one where a dendritic sub-unit is sufficient to trigger a somatic spike; another where somatic spiking requires the cooperation of multiple dendritic sub-units. We formally prove that implementing the latter architecture is possible with both types of dendritic sub-units whereas the former is only possible with spiking dendrites. Finally, we show how linearly non-separable functions can be computed by a generic two-compartment biophysical model and a realistic neuron model of the cerebellar stellate cell interneuron. Taken together our results demonstrate that passive dendrites are sufficient to enable neurons to compute linearly non-separable functions.
Project description:Dendritic atrophy and impaired long-term synaptic potentiation (LTP) are hallmarks of chronic stress-induced plasticity in the hippocampus. It has been hypothesized that these disparate structural and physiological correlates of stress lead to hippocampal dysfunction by reducing postsynaptic dendritic surface, thereby adversely affecting the availability of synaptic inputs and suppressing LTP. Here we examine the validity of this framework using biophysical models of hippocampal CA3 pyramidal neurons. To statistically match with the experimentally observed region specificity of stress-induced atrophy, we use an algorithm to systematically prune three-dimensional reconstructions of CA3 pyramidal neurons. Using this algorithm, we build a biophysically realistic computational model to analyze the effects of stress on intrinsic and synaptic excitability. We find that stress-induced atrophy of CA3 dendrites leads to an increase in input resistance, which depends exponentially on the percentage of neuronal atrophy. This increase translates directly into higher spiking frequencies in response to both somatic current injections and synaptic inputs at various locations along the dendritic arbor. Remarkably, we also find that the dendritic regions that manifest atrophy-induced synaptic hyperexcitability are governed by the region specificity of the underlying dendritic atrophy. Coupled with experimentally observed modulation of N-methyl-d-aspartate receptor currents, such hyperexcitability could tilt the balance of plasticity mechanisms in favor of synaptic potentiation over depression. Thus paradoxically, our results suggest that stress may impair hippocampal learning and memory, not by directly inhibiting LTP, but because of stress-induced facilitation of intrinsic and synaptic excitability and the consequent imbalance in bidirectional synaptic plasticity.