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.

Single cortical neurons as deep artificial neural networks

Utilizing recent advances in machine learning, we introduce a systematic approach to characterize neurons' input/output (I/O) mapping complexity. Deep neural networks (DNNs) were trained to faithfully replicate the I/O function of various biophysical models of cortical neurons at millisecond (spiking) resolution. A temporally convolutional DNN with five to eight layers was required to capture the I/O mapping of a realistic model of a layer 5 cortical pyramidal cell (L5PC). This DNN generalized well when presented with inputs widely outside the training distribution. When NMDA receptors were removed, a much simpler network (fully connected neural network with one hidden layer) was sufficient to fit the model. Analysis of the DNNs' weight matrices revealed that synaptic integration in dendritic branches could be conceptualized as pattern matching from a set of spatiotemporal templates. This study provides a unified characterization of the computational complexity of single neurons and suggests that cortical networks therefore have a unique architecture, potentially supporting their computational power.

Local glutamate-mediated dendritic plateau potentials change the state of the cortical pyramidal neuron

Dendritic spikes in thin dendritic branches (basal and oblique dendrites) are traditionally inferred from spikelets measured in the cell body. Here, we used laser-spot voltage-sensitive dye imaging in cortical pyramidal neurons (rat brain slices) to investigate the voltage waveforms of dendritic potentials occurring in response to spatially restricted glutamatergic inputs. Local dendritic potentials lasted 200-500 ms and propagated to the cell body, where they caused sustained 10- to 20-mV depolarizations. Plateau potentials propagating from dendrite to soma and action potentials propagating from soma to dendrite created complex voltage waveforms in the middle of the thin basal dendrite, comprised of local sodium spikelets, local plateau potentials, and backpropagating action potentials, superimposed on each other. Our model replicated these voltage waveforms across a gradient of glutamatergic stimulation intensities. The model then predicted that somatic input resistance (Rin) and membrane time constant (tau) may be reduced during dendritic plateau potential. We then tested these model predictions in real neurons and found that the model correctly predicted the direction of Rin and tau change but not the magnitude. In summary, dendritic plateau potentials occurring in basal and oblique branches put pyramidal neurons into an activated neuronal state ("prepared state"), characterized by depolarized membrane potential and smaller but faster membrane responses. The prepared state provides a time window of 200-500 ms, during which cortical neurons are particularly excitable and capable of following afferent inputs. At the network level, this predicts that sets of cells with simultaneous plateaus would provide cellular substrate for the formation of functional neuronal ensembles.NEW & NOTEWORTHY In cortical pyramidal neurons, we recorded glutamate-mediated dendritic plateau potentials with voltage imaging and created a computer model that recreated experimental measures from dendrite and cell body. Our model made new predictions, which were then tested in experiments. Plateau potentials profoundly change neuronal state: a plateau potential triggered in one basal dendrite depolarizes the soma and shortens membrane time constant, making the cell more susceptible to firing triggered by other afferent inputs.

Efficient Low-Pass Dendro-Somatic Coupling in the Apical Dendrite of Layer 5 Pyramidal Neurons in the Anterior Cingulate Cortex

Signal propagation in the dendrites of many neurons, including cortical pyramidal neurons in sensory cortex, is characterized by strong attenuation toward the soma. In contrast, using dual whole-cell recordings from the apical dendrite and soma of layer 5 (L5) pyramidal neurons in the anterior cingulate cortex (ACC) of adult male mice we found good coupling, particularly of slow subthreshold potentials like NMDA spikes or trains of EPSPs from dendrite to soma. Only the fastest EPSPs in the ACC were reduced to a similar degree as in primary somatosensory cortex, revealing differential low-pass filtering capabilities. Furthermore, L5 pyramidal neurons in the ACC did not exhibit dendritic Ca2+ spikes as prominently found in the apical dendrite of S1 (somatosensory cortex) pyramidal neurons. Fitting the experimental data to a NEURON model revealed that the specific distribution of Ileak, Iir, Im , and Ih was sufficient to explain the electrotonic dendritic structure causing a leaky distal dendritic compartment with correspondingly low input resistance and a compact perisomatic region, resulting in a decoupling of distal tuft branches from each other while at the same time efficiently connecting them to the soma. Our results give a biophysically plausible explanation of how a class of prefrontal cortical pyramidal neurons achieve efficient integration of subthreshold distal synaptic inputs compared with the same cell type in sensory cortices.SIGNIFICANCE STATEMENT Understanding cortical computation requires the understanding of its fundamental computational subunits. Layer 5 pyramidal neurons are the main output neurons of the cortex, integrating synaptic inputs across different cortical layers. Their elaborate dendritic tree receives, propagates, and transforms synaptic inputs into action potential output. We found good coupling of slow subthreshold potentials like NMDA spikes or trains of EPSPs from the distal apical dendrite to the soma in pyramidal neurons in the ACC, which was significantly better compared with S1. This suggests that frontal pyramidal neurons use a different integration scheme compared with the same cell type in somatosensory cortex, which has important implications for our understanding of information processing across different parts of the neocortex.

Dendritic Spikes Expand the Range of Well Tolerated Population Noise Structures

The brain operates surprisingly well despite the noisy nature of individual neurons. The central mechanism for noise mitigation in the nervous system is thought to involve averaging over multiple noise-corrupted inputs. Subsequently, there has been considerable interest in identifying noise structures that can be integrated linearly in a way that preserves reliable signal encoding. By analyzing realistic synaptic integration in biophysically accurate neuronal models, I report a complementary denoising approach that is mediated by focal dendritic spikes. Dendritic spikes might seem to be unlikely candidates for noise reduction due to their miniscule integration compartments and poor averaging abilities. Nonetheless, the extra thresholding step introduced by dendritic spike generation increases neuronal tolerance for a broad category of noise structures, some of which cannot be resolved well with averaging. This property of active dendrites compensates for compartment size constraints and expands the repertoire of conditions that can be processed by neuronal populations.SIGNIFICANCE STATEMENT Noise, or random variability, is a prominent feature of the neuronal code and poses a fundamental challenge for information processing. To reconcile the surprisingly accurate output of the brain with the inherent noisiness of biological systems, previous work examined signal integration in idealized neurons. The notion that emerged from this body of work is that accurate signal representation relies largely on input averaging in neuronal dendrites. In contrast to the prevailing view, I show that denoising in simulated neurons with realistic morphology and biophysical properties follows a different strategy: dendritic spikes act as classifiers that assist in extracting information from a variety of noise structures that have been considered before to be particularly disruptive for reliable brain function.

High- and low-conductance NMDA receptors are present in layer 4 spiny stellate and layer 2/3 pyramidal neurons of mouse barrel cortex

N‐Methyl‐D‐aspartate (NMDA) receptors are ion channels activated by the neurotransmitter glutamate in the mammalian brain and are important in synaptic function and plasticity, but are also found in extrasynaptic locations and influence neuronal excitability. There are different NMDA receptor subtypes which differ in their single‐channel conductance. Recently, synaptic plasticity has been studied in the mouse barrel cortex, the primary sensory cortex for input from the animal's whiskers. Pharmacological data imply the presence of low‐conductance NMDA receptors in spiny stellate neurons of cortical layer 4, but of high‐conductance NMDA receptors in pyramidal neurons of layer 2/3. Here, to obtain complementary electrophysiological information on the functional NMDA receptors expressed in layer 4 and layer 2/3 neurons, single NMDA receptor currents were recorded with the patch‐clamp method. Both cell types were found to contain high‐conductance as well as low‐conductance NMDA receptors. The results are consistent with the reported pharmacological data on synaptic plasticity, and with previous claims of a prominent role of low‐conductance NMDA receptors in layer 4 spiny stellate neurons, including broad integration, amplification and distribution of excitation within the barrel in response to whisker stimulation, as well as modulation of excitability by ambient glutamate. However, layer 4 cells also expressed high‐conductance NMDA receptors. The presence of low‐conductance NMDA receptors in layer 2/3 pyramidal neurons suggests that some of these functions may be shared with layer 4 spiny stellate neurons.

A simple transfer function for nonlinear dendritic integration

Relatively recent advances in patch clamp recordings and iontophoresis have enabled unprecedented study of neuronal post-synaptic integration ("dendritic integration"). Findings support a separate layer of integration in the dendritic branches before potentials reach the cell's soma. While integration between branches obeys previous linear assumptions, proximal inputs within a branch produce threshold nonlinearity, which some authors have likened to the sigmoid function. Here we show the implausibility of a sigmoidal relation and present a more realistic transfer function in both an elegant artificial form and a biophysically derived form that further considers input locations along the dendritic arbor. As the distance between input locations determines their ability to produce nonlinear interactions, models incorporating dendritic topology are essential to understanding the computational power afforded by these early stages of integration. We use the biophysical transfer function to emulate empirical data using biophysical parameters and describe the conditions under which the artificial and biophysically derived forms are equivalent.

NMDA spike/plateau potentials in dendrites of thalamocortical neurons

Dendritic NMDA spike/plateau potentials, first discovered in cortical pyramidal neurons, provide supralinear integration of synaptic inputs on thin and distal dendrites, thereby increasing the impact of these inputs on the soma. The more specific functional role of these potentials has been difficult to clarify, partly due to the complex circuitry of cortical neurons. Thalamocortical (TC) neurons in the dorsal lateral geniculate nucleus participate in simpler circuits. They receive their primary afferent input from retina and send their output to visual cortex. Cortex, in turn, regulates this output through massive feedback to distal dendrites of the TC neurons. The TC neurons can operate in two modes related to behavioral states: burst mode prevailing during sleep, when T-type calcium bursts largely disrupt the transfer of signals from retina to cortex, and tonic mode, which provides reliable transfer of retinal signals to cortex during wakefulness. We studied dendritic potentials in TC neurons with combined two-photon calcium imaging and whole-cell recording of responses to local dendritic glutamate iontophoresis in acute brain slices from mice. We found that NMDA spike/plateaus can be elicited locally at distal dendrites of TC neurons. We suggest that these dendritic potentials have important functions in the cortical regulation of thalamocortical transmission. NMDA spike/plateaus can induce shifts in the functional mode from burst to tonic by blockade of T-type calcium conductances. Moreover, in tonic mode, they can facilitate the transfer of retinal signals to cortex by depolarization of TC neurons.

Spiny neurons of amygdala, striatum, and cortex use dendritic plateau potentials to detect network UP states

Spiny neurons of amygdala, striatum, and cerebral cortex share four interesting features: (1) they are the most abundant cell type within their respective brain area, (2) covered by thousands of thorny protrusions (dendritic spines), (3) possess high levels of dendritic NMDA conductances, and (4) experience sustained somatic depolarizations in vivo and in vitro (UP states). In all spiny neurons of the forebrain, adequate glutamatergic inputs generate dendritic plateau potentials (“dendritic UP states”) characterized by (i) fast rise, (ii) plateau phase lasting several hundred milliseconds, and (iii) abrupt decline at the end of the plateau phase. The dendritic plateau potential propagates toward the cell body decrementally to induce a long-lasting (longer than 100 ms, most often 200–800 ms) steady depolarization (∼20 mV amplitude), which resembles a neuronal UP state. Based on voltage-sensitive dye imaging, the plateau depolarization in the soma is precisely time-locked to the regenerative plateau potential taking place in the dendrite. The somatic plateau rises after the onset of the dendritic voltage transient and collapses with the breakdown of the dendritic plateau depolarization. We hypothesize that neuronal UP states in vivo reflect the occurrence of dendritic plateau potentials (dendritic UP states). We propose that the somatic voltage waveform during a neuronal UP state is determined by dendritic plateau potentials. A mammalian spiny neuron uses dendritic plateau potentials to detect and transform coherent network activity into a ubiquitous neuronal UP state. The biophysical properties of dendritic plateau potentials allow neurons to quickly attune to the ongoing network activity, as well as secure the stable amplitudes of successive UP states.

Mechanisms underlying subunit independence in pyramidal neuron dendrites

Pyramidal neuron (PN) dendrites compartmentalize voltage signals and can generate local spikes, which has led to the proposal that their dendrites act as independent computational subunits within a multilayered processing scheme. However, when a PN is strongly activated, back-propagating action potentials (bAPs) sweeping outward from the soma synchronize dendritic membrane potentials many times per second. How PN dendrites maintain the independence of their voltage-dependent computations, despite these repeated voltage resets, remains unknown. Using a detailed compartmental model of a layer 5 PN, and an improved method for quantifying subunit independence that incorporates a more accurate model of dendritic integration, we first established that the output of each dendrite can be almost perfectly predicted by the intensity and spatial configuration of its own synaptic inputs, and is nearly invariant to the rate of bAP-mediated "cross-talk" from other dendrites over a 100-fold range. Then, through an analysis of conductance, voltage, and current waveforms within the model cell, we identify three biophysical mechanisms that together help make independent dendritic computation possible in a firing neuron, suggesting that a major subtype of neocortical neuron has been optimized for layered, compartmentalized processing under in-vivo-like spiking conditions.