Effects of low frequency electric fields on synaptic integration in hippocampal CA1 pyramidal neurons: implications for power line emissions

Frequency-domain analysis of membrane polarization in two-compartment model neurons with weak alternating electric fields

Transcranial alternating current stimulation (tACS) is widely used in studying brain functions and the treatment of neuropsychiatric diseases in a frequency-specific manner. However, how tACS works on neuronal activity has been poorly understood. In this paper, we use linear system analysis to investigate how weak alternating electric fields (EFs) affect the membrane polarization of neurons in the frequency domain. Two biophysically realistic conductance-based two-compartment models of cortical pyramidal neurons are developed to simulate subthreshold membrane polarization with weak alternating EFs. We linearize the original nonlinear models at the stable equilibrium points and further simplify them to the two- or three-dimensional linear systems. Thus, we calculate the transfer functions of the low-dimensional linear models to model neuronal polarization patterns. Based on the transfer functions, we compute the amplitude- and phase-frequency characteristics to describe the relationship between weak EFs and membrane polarization. We also computed the parameters (gain, zeros, and poles) and structures (the number of zeros and poles) of transfer functions to reveal how neuronal intrinsic properties affect the parameters and structure of transfer functions and thus the frequency-dependent membrane polarization with alternating EFs. We find that the amplitude and phase of membrane polarization both strongly depended on EF frequency, and these frequency responses are modulated by the intrinsic properties of neurons. The compartment geometry, internal coupling conductance, and ionic currents (except Ih) affect the frequency-dependent polarization by mainly changing the gain and pole of transfer functions. Larger gain contributes to larger amplitude-frequency characteristics. The closer the pole is to the imaginary axis, the lower phase-frequency characteristics. However, Ih changes the structure of transfer function in the dendrite by introducing a new pair of zero-pole points, which decrease the amplitude at low frequencies and thus lead to a visible resonance. These results highlight the effects of passive properties and active ion currents on subthreshold membrane polarization with alternating EFs in the frequency domain, which provide an explainable connection of how intrinsic properties of neurons modulate the neuronal input-output functions with weak EF stimulation.

Induced neural phase precession through exogenous electric fields

The gradual shifting of preferred neural spiking relative to local field potentials (LFPs), known as phase precession, plays a prominent role in neural coding. Correlations between the phase precession and behavior have been observed throughout various brain regions. As such, phase precession is suggested to be a global neural mechanism that promotes local neuroplasticity. However, causal evidence and neuroplastic mechanisms of phase precession are lacking so far. Here we show a causal link between LFP dynamics and phase precession. In three experiments, we modulated LFPs in humans, a non-human primate, and computational models using alternating current stimulation. We show that continuous stimulation of motor cortex oscillations in humans lead to a gradual phase shift of maximal corticospinal excitability by ~90°. Further, exogenous alternating current stimulation induced phase precession in a subset of entrained neurons (~30%) in the non-human primate. Multiscale modeling of realistic neural circuits suggests that alternating current stimulation-induced phase precession is driven by NMDA-mediated synaptic plasticity. Altogether, the three experiments provide mechanistic and causal evidence for phase precession as a global neocortical process. Alternating current-induced phase precession and consequently synaptic plasticity is crucial for the development of novel therapeutic neuromodulation methods.

Electric field effects on neuronal input-output relationship by regulating NMDA spikes

Evidence shows that the dendritic polarization induced by weak electrical field (EF) can affect the neuronal input-output function via modulating dendritic integration of AMPA synapses, indicating that the supralinear dendritic integration of NMDA synapses can also be influenced by dendritic polarization. However, it remains unknown how dendritic polarization affects NMDA-type dendritic integration, and then contributes to neuronal input-output relationship. Here, we used a computational model of pyramidal neuron with inhomogeneous extracellular potentials to characterize the relationship among EF, dendritic integration, and somatic output. Basing on singular perturbation we analyzed the subthreshold dynamics of membrane potentials in response to NMDA synapses, and found that the equilibrium mapping of a fast subsystem can characterize the asymptotic subthreshold input-output (sI/O) relationship for EF-regulated supralinear dendritic integration, allowing us to predict the tendency of EF-regulated dendritic integration by showing the variation of equilibrium mapping under EF stimulation. EF-induced depolarization at distal dendrites receiving synapses plays a crucial role in shifting the steep change of sI/O left by facilitating dendritic NMDA spike generation and in decreasing the plateau of sI/O via reducing driving force. And more effective EF modulation appears at sparsely activated NMDA receptors compared with clustered synaptic inputs. During the action potential (AP) generation, the respective contribution of EF-regulated dendritic integration and EF-induced somatic polarization was identified to show their synergetic or antagonistic effect on AP generation, depending on neuronal excitability. These results provided insight in understanding the modulation effect of EF on neuronal computation, which is important for optimizing noninvasive brain stimulation.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11571-022-09922-y.

Induced neural phase precession through exogeneous electric fields

The gradual shifting of preferred neural spiking relative to local field potentials (LFPs), known as phase precession, plays a prominent role in neural coding. Correlations between the phase precession and behavior have been observed throughout various brain regions. As such, phase precession is suggested to be a global neural mechanism that promotes local neuroplasticity. However, causal evidence and neuroplastic mechanisms of phase precession are lacking so far. Here we show a causal link between LFP dynamics and phase precession. In three experiments, we modulated LFPs in humans, a non-human primate, and computational models using alternating current stimulation. We show that continuous stimulation of motor cortex oscillations in humans lead to a gradual phase shift of maximal corticospinal excitability by ~90°. Further, exogenous alternating current stimulation induced phase precession in a subset of entrained neurons (~30%) in the non-human primate. Multiscale modeling of realistic neural circuits suggests that alternating current stimulation-induced phase precession is driven by NMDA-mediated synaptic plasticity. Altogether, the three experiments provide mechanistic and causal evidence for phase precession as a global neocortical process. Alternating current-induced phase precession and consequently synaptic plasticity is crucial for the development of novel therapeutic neuromodulation methods.

State-dependent modulation of low-threshold-current-regulated dendritic Ca2+ response in thalamic reticular neurons with extracellular electric fields

Deep brain stimulation (DBS) in thalamic reticular nucleus (TRN) neuron provides a novel treatment for drug-resistant epilepsy via the induced electrical field (EFs). However, the mechanisms underlying EF effects remain unclear. This paper investigated how EFs regulate low-threshold dendritic Ca2+ (dCa) response and thus contribute to the input-output relationship of TRN cell. Our results showed that EFs modulate firing modes differently in a neuronal state-dependent manner. At the depolarized state, EFs only regulate the spike timing of a somatic stimulus-evoked single action potential (AP) with less contribution in the regulation of dCa response but could induce the transition between a dendritic stimulus-evoked single AP and a tonic burst of APs via the moderate regulation of dCa response. At the hyperpolarized state, EFs have significant effects on the dCa response, which modulate the large dCa response-dependent burst discharge and even cause a transition from this type of burst discharge to a single AP with less dCa response. Moreover, EF effects on stimulation threshold of somatic spiking prominently depend on EF-regulated dCa responses and the onset time differences between the stimulus and EF give rise to the distinct effect in the EF regulation of dCa responses. Finally, the larger neuronal axial resistance tends to result in the dendritic stimulus-evoked dCa response independent of somatic state. Interestingly, in this case, the EF application could reproduce the similar somatic state-dependent dCa response to dendritic stimulus which occurs in the case of lower axial resistance. These results suggest that the influence of EF on neuronal activities depends on neuronal intrinsic properties, which provides insight into understanding how DBS in TRN neuron modulates epilepsy from the point of view of biophysics.

Comparing the effects of transcranial alternating current and temporal interference (tTIS) electric stimulation through whole-brain mapping of c-Fos immunoreactivity

The analysis of the topography of brain neuromodulation following transcranial alternating current (AC) stimulation is relevant for defining strategies directed to specific nuclei stimulation in patients. Among the different procedures of AC stimulation, temporal interference (tTIS) is a novel method for non-invasive neuromodulation of specific deep brain targets. However, little information is currently available about its tissue effects and its activation topography in in vivo animal models. After a single session (30 min, 0.12 mA) of transcranial alternate current (2,000 Hz; ES/AC group) or tTIS (2,000/2,010 Hz; Es/tTIS group) stimulation, rat brains were explored by whole-brain mapping analysis of c-Fos immunostained serial sections. For this analysis, we used two mapping methods, namely density-to-color processed channels (independent component analysis (ICA) and graphical representation (MATLAB) of morphometrical and densitometrical values obtained by density threshold segmentation. In addition, to assess tissue effects, alternate serial sections were stained for glial fibrillary acidic protein (GFAP), ionized calcium-binding adapter molecule 1 (Iba1), and Nissl. AC stimulation induced a mild superficial increase in c-Fos immunoreactivity. However, tTIS stimulation globally decreased the number of c-Fos-positive neurons and increased blood brain barrier cell immunoreactivity. tTIS also had a stronger effect around the electrode placement area and preserved neuronal activation better in restricted areas of the deep brain (directional stimulation). The enhanced activation of intramural blood vessels’ cells and perivascular astrocytes suggests that low-frequency interference (10 Hz) may also have a trophic effect.

Effects of transcranial alternating current stimulation on spiking activity in computational models of single neocortical neurons

Neural oscillations are a key mechanism for information transfer in brain circuits. Rhythmic fluctuations of local field potentials control spike timing through cyclic membrane de- and hyperpolarization. Transcranial alternating current stimulation (tACS) is a non-invasive neuromodulation method which can directly interact with brain oscillatory activity by imposing an oscillating electric field on neurons. Despite its increasing use, the basic mechanisms of tACS are still not fully understood. Here, we investigate in a computational study the effects of tACS on morphologically realistic neurons with ongoing spiking activity. We characterize the membrane polarization as a function of electric field strength and subsequent effects on spiking activity in a set of 25 neurons from different neocortical layers. We find that tACS does not affect the firing rate of investigated neurons for electric field strengths applicable to human studies. However, we find that the applied electric fields entrain the spiking activity of large pyramidal neurons and large basket neurons at < 1 mV/mm field strengths. Our model results are in line with recent experimental studies and can provide a mechanistic framework to understand the effects of oscillating electric fields on single neuron activity. They highlight the importance of neuron morphology and biophysics in responsiveness to electrical stimulation.

Transcranial direct current stimulation of cerebellum alters spiking precision in cerebellar cortex: A modeling study of cellular responses

Transcranial direct current stimulation (tDCS) of the cerebellum has rapidly raised interest but the effects of tDCS on cerebellar neurons remain unclear. Assessing the cellular response to tDCS is challenging because of the uneven, highly stratified cytoarchitecture of the cerebellum, within which cellular morphologies, physiological properties, and function vary largely across several types of neurons. In this study, we combine MRI-based segmentation of the cerebellum and a finite element model of the tDCS-induced electric field (EF) inside the cerebellum to determine the field imposed on the cerebellar neurons throughout the region. We then pair the EF with multicompartment models of the Purkinje cell (PC), deep cerebellar neuron (DCN), and granule cell (GrC) and quantify the acute response of these neurons under various orientations, physiological conditions, and sequences of presynaptic stimuli. We show that cerebellar tDCS significantly modulates the postsynaptic spiking precision of the PC, which is expressed as a change in the spike count and timing in response to presynaptic stimuli. tDCS has modest effects, instead, on the PC tonic firing at rest and on the postsynaptic activity of DCN and GrC. In Purkinje cells, anodal tDCS shortens the repolarization phase following complex spikes (-14.7 ± 6.5% of baseline value, mean ± S.D.; max: -22.7%) and promotes burstiness with longer bursts compared to resting conditions. Cathodal tDCS, instead, promotes irregular spiking by enhancing somatic excitability and significantly prolongs the repolarization after complex spikes compared to baseline (+37.0 ± 28.9%, mean ± S.D.; max: +84.3%). tDCS-induced changes to the repolarization phase and firing pattern exceed 10% of the baseline values in Purkinje cells covering up to 20% of the cerebellar cortex, with the effects being distributed along the EF direction and concentrated in the area under the electrode over the cerebellum. Altogether, the acute effects of tDCS on cerebellum mainly focus on Purkinje cells and modulate the precision of the response to synaptic stimuli, thus having the largest impact when the cerebellar cortex is active. Since the spatiotemporal precision of the PC spiking is critical to learning and coordination, our results suggest cerebellar tDCS as a viable therapeutic option for disorders involving cerebellar hyperactivity such as ataxia.

Transcranial direct current stimulation (tDCS) of the cerebellum is gaining momentum as a neuromodulation tool for the treatment of neurological diseases like movement disorders. Nonetheless, the response of cells in the cerebellum to tDCS is unclear and hardly generalizes from our understanding of tDCS of the cerebral cortex. We use computational models to investigate the response of several types of cerebellar neurons to the electric field induced by tDCS and show that, differently from the cerebral cortex, tDCS has significant acute effects on the cerebellar cortex. These effects (i) primarily alter the way Purkinje cells encode synaptic stimuli from the molecular layer and (ii) can help hyperactive cells regain postsynaptic spiking precision. Since the spatiotemporal precision of the Purkinje cell spiking is critical to learning and coordination, the study shows how tDCS can operate at the cellular level to treat movement disorders like tremor and ataxia.

Conductance-based models and the fragmentation problem: A case study based on hippocampal CA1 pyramidal cell models and epilepsy

Epilepsy has been a central topic in computational neuroscience, and in silico models have shown to be excellent tools to integrate and evaluate findings from animal and clinical settings. Among the different languages and tools for computational modeling development, NEURON stands out as one of the most used and mature neurosimulators. However, despite the vast quantity of models developed with NEURON, a fragmentation problem is evident in the great majority of models related to the same type of cell or cell properties. This fragmentation causes a lack of interoperability between the models because of differences in parameters. The problem is not related to the neurosimulator, which is prepared to reuse elements of other models, but related to decisions made during the model development, when it is not uncommon to adjust parameter values according to the necessities of the study. Here, this problem is presented by studying computational models related to temporal lobe epilepsy and the definitions of hippocampal CA1 pyramidal cells. The current assessment aims to highlight the implications of fragmentation for reliable modeling and the need to adopt a framework that allows a better interoperability between different models. This article is part of the Special Issue "NEWroscience 2018".

Modulations of dendritic Ca2+ spike with weak electric fields in layer 5 pyramidal cells

Weak electric fields (EFs) modulate input/output function of pyramidal cells. Dendritic Ca²⁺ spike is an important cellular mechanism for coupling synaptic inputs from different cortical layers, which plays a critical role in neuronal computation. This study aims to understand the effects of weak EFs on Ca²⁺ spikes initiated in the distal dendrites. We use a computational model to simulate dendritic Ca²⁺ spikes and backpropagating action potentials (APs) in layer 5 pyramidal cells. We apply uniform EFs (less than 20 mV/mm) to the model and examine how they affect the threshold for activation of Ca²⁺ spikes. We show that the effects of weak field on synaptically evoked Ca²⁺ spikes depend on the timing of synaptic inputs. When distal inputs coincide with the onset of EFs within a time window of several milliseconds, field-induced depolarization facilitates the initiation of Ca²⁺ spikes, while field-induced hyperpolarization suppresses dendritic APs. Sustained field-induced depolarization leads to the inactivation of Ca²⁺ channels and increases the threshold of Ca²⁺ spike. Sustained field-induced hyperpolarization de-inactivates Ca²⁺ channels and reduces the threshold of Ca²⁺ spike. By altering the threshold of backpropagation activated Ca²⁺ firing, field-induced depolarization increases the degree of coupling between inputs of the soma and distal dendrites, while field-induced hyperpolarization results in a decrease of coupling. The modulatory effects of weak EF are governed by the field direction with respect to the cell. Our study explains a fundamental link between field-induced polarization, dendritic Ca²⁺ spike, and somato-dendritic coupling. The findings are crucial to interpret how weak EFs achieve specific modulation of cellular activity.

Ih interacts with somato-dendritic structure to determine frequency response to weak alternating electric field stimulation

Transcranial current stimulation (tCS) modulates brain dynamics using weak electric fields. Given the pathological changes in brain network oscillations in neurological and psychiatric illnesses, using alternating electric field waveforms that engage rhythmic activity has been proposed as a targeted, network-level treatment approach. Previous studies have investigated the effects of electric fields at the neuronal level. However, the biophysical basis of the cellular response to electric fields has remained limited. Here, we characterized the frequency-dependent response of different compartments in a layer V pyramidal neuron to exogenous electric fields to dissect the relative contributions of voltage-gated ion channels and neuronal morphology. Hyperpolarization-activated cation current (I_h) in the distal dendrites was the primary ionic mechanism shaping the model's response to electric field stimulation and caused subthreshold resonance in the tuft at 20 ± 4 Hz. In contrast, subthreshold I_h-mediated resonance in response to local sinusoidal current injection was present in all model compartments at 11 ± 2 Hz. The frequencies of both resonance responses were modulated by I_h conductance density. We found that the difference in resonance frequency between the two stimulation types can be explained by the fact that exogenous electric fields simultaneously polarize the membrane potentials at the distal ends of the neuron (relative to field direction) in opposite directions. Our results highlight the role of I_h in shaping the cellular response to electric field stimulation and suggest that the common model of tCS as a weak somatic current injection fails to capture the cellular effects of electric field stimulation. NEW & NOTEWORTHY Modulation of cortical oscillation by brain stimulation serves as a tool to understand the causal role of network oscillations in behavior and is a potential treatment modality that engages impaired network oscillations in disorders of the central nervous system. To develop targeted stimulation paradigms, cellular-level effects must be understood. We demonstrate that hyperpolarization-activated cation current (I_h) and cell morphology cooperatively shape the response to applied alternating electric fields.

The possible consequences for cognitive functions of external electric fields at power line frequency on hippocampal CA1 pyramidal neurons

The possible effects on cognitive processes of external electric fields, such as those generated by power line pillars and household appliances are of increasing public concern. They are difficult to study experimentally, and the relatively scarce and contradictory evidence make it difficult to clearly assess these effects. In this study, we investigate how, why and to what extent external perturbations of the intrinsic neuronal activity, such as those that can be caused by generation, transmission and use of electrical energy can affect neuronal activity during cognitive processes. For this purpose, we used a morphologically and biophysically realistic three-dimensional model of CA1 pyramidal neurons. The simulation findings suggest that an electric field oscillating at power lines frequency, and environmentally measured strength, can significantly alter both the average firing rate and temporal spike distribution properties of a hippocampal CA1 pyramidal neuron. This effect strongly depends on the specific and instantaneous relative spatial location of the neuron with respect to the field, and on the synaptic input properties. The model makes experimentally testable predictions on the possible functional consequences for normal hippocampal functions such as object recognition and spatial navigation. The results suggest that, although EF effects on cognitive processes may be difficult to occur in everyday life, their functional consequences deserve some consideration, especially when they constitute a systematic presence in living environments.