Modulation of intercolumnar synchronization by endogenous electric fields in cerebral cortex.

Neurons synaptically interacting in a conductive medium generate extracellular endogenous electric fields (EFs) that reciprocally affect membrane potential. Exogenous EFs modulate neuronal activity, and their clinical applications are being profusely explored. However, whether endogenous EFs contribute to network synchronization remains unclear. We analyzed spontaneously generated slow-wave activity in the cerebral cortex network in vitro, which allowed us to distinguish synaptic from nonsynaptic mechanisms of activity propagation and synchronization. Slow oscillations generated EFs that propagated independently of synaptic transmission. We demonstrate that cortical oscillations modulate spontaneous rhythmic activity of neighboring synaptically disconnected cortical columns if layers are aligned. We provide experimental evidence that these EF-mediated effects are compatible with electric dipoles. With a model of interacting dipoles, we reproduce the experimental measurements and predict that endogenous EF-mediated synchronizing effects should be relevant in the brain. Thus, experiments and models suggest that electric-dipole interactions contribute to synchronization of neighboring cortical columns.

A kernel-based method to calculate local field potentials from networks of spiking neurons.

BACKGROUND: The local field potential (LFP) is usually calculated from current sources arising from transmembrane currents, in particular in asymmetric cellular morphologies such as pyramidal neurons. NEW METHOD: Here, we adopt a different point of view and relate the spiking of neurons to the LFP through efferent synaptic connections and provide a method to calculate LFPs. RESULTS: We show that the so-called unitary LFPs (uLFP) provide the key to such a calculation. We show experimental measurements and simulations of uLFPs in neocortex and hippocampus, for both excitatory and inhibitory neurons. We fit a "kernel" function to measurements of uLFPs, and we estimate its spatial and temporal spread by using simulations of morphologically detailed reconstructions of hippocampal pyramidal neurons. Assuming that LFPs are the sum of uLFPs generated by every neuron in the network, the LFP generated by excitatory and inhibitory neurons can be calculated by convolving the trains of action potentials with the kernels estimated from uLFPs. This provides a method to calculate the LFP from networks of spiking neurons, even for point neurons for which the LFP is not easily defined. We show examples of LFPs calculated from networks of point neurons and compare to the LFP calculated from synaptic currents. CONCLUSIONS: The kernel-based method provides a practical way to calculate LFPs from networks of point neurons.

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.

Cholinergic Switch between Two Types of Slow Waves in Cerebral Cortex.

Sleep slow waves are known to participate in memory consolidation, yet slow waves occurring under anesthesia present no positive effects on memory. Here, we shed light onto this paradox, based on a combination of extracellular recordings in vivo, in vitro, and computational models. We find two types of slow waves, based on analyzing the temporal patterns of successive slow-wave events. The first type is consistently observed in natural slow-wave sleep, while the second is shown to be ubiquitous under anesthesia. Network models of spiking neurons predict that the two slow wave types emerge due to a different gain on inhibitory versus excitatory cells and that different levels of spike-frequency adaptation in excitatory cells can account for dynamical distinctions between the two types. This prediction was tested in vitro by varying adaptation strength using an agonist of acetylcholine receptors, which demonstrated a neuromodulatory switch between the two types of slow waves. Finally, we show that the first type of slow-wave dynamics is more sensitive to external stimuli, which can explain how slow waves in sleep and anesthesia differentially affect memory consolidation, as well as provide a link between slow-wave dynamics and memory diseases.

Dendritic sodium spikes endow neurons with inverse firing rate response to correlated synaptic activity.

Many neurons possess dendrites enriched with sodium channels and are capable of generating action potentials. However, the role of dendritic sodium spikes remain unclear. Here, we study computational models of neurons to investigate the functional effects of dendritic spikes. In agreement with previous studies, we found that point neurons or neurons with passive dendrites increase their somatic firing rate in response to the correlation of synaptic bombardment for a wide range of input conditions, i.e. input firing rates, synaptic conductances, or refractory periods. However, neurons with active dendrites show the opposite behavior: for a wide range of conditions the firing rate decreases as a function of correlation. We found this property in three types of models of dendritic excitability: a Hodgkin-Huxley model of dendritic spikes, a model with integrate and fire dendrites, and a discrete-state dendritic model. We conclude that fast dendritic spikes confer much broader computational properties to neurons, sometimes opposite to that of point neurons.

Maximum-entropy models reveal the excitatory and inhibitory correlation structures in cortical neuronal activity.

Maximum entropy models can be inferred from large datasets to uncover how collective dynamics emerge from local interactions. Here, such models are employed to investigate neurons recorded by multi-electrode arrays in the human and monkey cortex. Taking advantage of the separation of excitatory and inhibitory neuron types, we construct a model including this distinction. This approach allows us to shed light on differences between excitatory and inhibitory activity across different brain states such as wakefulness and deep sleep, in agreement with previous findings. Additionally, maximum entropy models can also unveil novel features of neuronal interactions, which are found to be dominated by pairwise interactions during wakefulness, but are population-wide during deep sleep. Overall, we demonstrate that maximum entropy models can be useful to analyze datasets with classified neuron types and to reveal the respective roles of excitatory and inhibitory neurons in organizing coherent dynamics in the cerebral cortex.

Contribution of the Axon Initial Segment to Action Potentials Recorded Extracellularly.

Action potentials (APs) are electric phenomena that are recorded both intracellularly and extracellularly. APs are usually initiated in the short segment of the axon called the axon initial segment (AIS). It was recently proposed that at the onset of an AP the soma and the AIS form a dipole. We study the extracellular signature [the extracellular AP (EAP)] generated by such a dipole. First, we demonstrate the formation of the dipole and its extracellular signature in detailed morphological models of a reconstructed pyramidal neuron. Then, we study the EAP waveform and its spatial dependence in models with axonal AP initiation and contrast it with the EAP obtained in models with somatic AP initiation. We show that in the models with axonal AP initiation the dipole forms between somatodendritic compartments and the AIS, and not between soma and dendrites as in the classical models. The soma-dendrites dipole is present only in models with somatic AP initiation. Our study has consequences for interpreting extracellular recordings of single-neuron activity and determining electrophysiological neuron types, but also for better understanding the origins of the high-frequency macroscopic extracellular potentials recorded in the brain.

Refractoriness Accounts for Variable Spike Burst Responses in Somatosensory Cortex.

Neurons in the primary somatosensory cortex (S1) respond to peripheral stimulation with synchronized bursts of spikes, which lock to the macroscopic 600-Hz EEG waves. The mechanism of burst generation and synchronization in S1 is not yet understood. Using models of single-neuron responses fitted to unit recordings from macaque monkeys, we show that these synchronized bursts are the consequence of correlated synaptic inputs combined with a refractory mechanism. In the presence of noise these models reproduce also the observed trial-to-trial response variability, where individual bursts represent one of many stereotypical temporal spike patterns. When additional slower and global excitability fluctuations are introduced the single-neuron spike patterns are correlated with the population activity, as demonstrated in experimental data. The underlying biophysical mechanism of S1 responses involves thalamic inputs arriving through depressing synapses to cortical neurons in a high-conductance state. Our findings show that a simple feedforward processing of peripheral inputs could give rise to neuronal responses with nontrivial temporal and population statistics. We conclude that neural systems could use refractoriness to encode variable cortical states into stereotypical short-term spike patterns amenable to processing at neuronal time scales (tens of milliseconds).

Local field potentials primarily reflect inhibitory neuron activity in human and monkey cortex.

The local field potential (LFP) is generated by large populations of neurons, but unitary contribution of spiking neurons to LFP is not well characterised. We investigated this contribution in multi-electrode array recordings from human and monkey neocortex by examining the spike-triggered LFP average (st-LFP). The resulting st-LFPs were dominated by broad spatio-temporal components due to ongoing activity, synaptic inputs and recurrent connectivity. To reduce the spatial reach of the st-LFP and observe the local field related to a single spike we applied a spatial filter, whose weights were adapted to the covariance of ongoing LFP. The filtered st-LFPs were limited to the perimeter of 800 µm around the neuron, and propagated at axonal speed, which is consistent with their unitary nature. In addition, we discriminated between putative inhibitory and excitatory neurons and found that the inhibitory st-LFP peaked at shorter latencies, consistently with previous findings in hippocampal slices. Thus, in human and monkey neocortex, the LFP reflects primarily inhibitory neuron activity.

Local recording of biological magnetic fields using Giant Magneto Resistance-based micro-probes.

The electrical activity of brain, heart and skeletal muscles generates magnetic fields but these are recordable only macroscopically, such as in magnetoencephalography, which is used to map neuronal activity at the brain scale. At the local scale, magnetic fields recordings are still pending because of the lack of tools that can come in contact with living tissues. Here we present bio-compatible sensors based on Giant Magneto-Resistance (GMR) spin electronics. We show on a mouse muscle in vitro, using electrophysiology and computational modeling, that this technology permits simultaneous local recordings of the magnetic fields from action potentials. The sensitivity of this type of sensor is almost size independent, allowing the miniaturization and shaping required for in vivo/vitro magnetophysiology. GMR-based technology can constitute the magnetic counterpart of microelectrodes in electrophysiology, and might represent a new fundamental tool to investigate the local sources of neuronal magnetic activity.

High-frequency oscillations in human and monkey neocortex during the wake-sleep cycle.

Beta (ß)- and gamma (γ)-oscillations are present in different cortical areas and are thought to be inhibition-driven, but it is not known if these properties also apply to γ-oscillations in humans. Here, we analyze such oscillations in high-density microelectrode array recordings in human and monkey during the wake-sleep cycle. In these recordings, units were classified as excitatory and inhibitory cells. We find that γ-oscillations in human and ß-oscillations in monkey are characterized by a strong implication of inhibitory neurons, both in terms of their firing rate and their phasic firing with the oscillation cycle. The ß- and γ-waves systematically propagate across the array, with similar velocities, during both wake and sleep. However, only in slow-wave sleep (SWS) ß- and γ-oscillations are associated with highly coherent and functional interactions across several millimeters of the neocortex. This interaction is specifically pronounced between inhibitory cells. These results suggest that inhibitory cells are dominantly involved in the genesis of ß- and γ-oscillations, as well as in the organization of their large-scale coherence in the awake and sleeping brain. The highest oscillation coherence found during SWS suggests that fast oscillations implement a highly coherent reactivation of wake patterns that may support memory consolidation during SWS.

Dynamic Balance of Excitation and Inhibition in Human and Monkey Neocortex.

Balance of excitation and inhibition is a fundamental feature of in vivo network activity and is important for its computations. However, its presence in the neocortex of higher mammals is not well established. We investigated the dynamics of excitation and inhibition using dense multielectrode recordings in humans and monkeys. We found that in all states of the wake-sleep cycle, excitatory and inhibitory ensembles are well balanced, and co-fluctuate with slight instantaneous deviations from perfect balance, mostly in slow-wave sleep. Remarkably, these correlated fluctuations are seen for many different temporal scales. The similarity of these computational features with a network model of self-generated balanced states suggests that such balanced activity is essentially generated by recurrent activity in the local network and is not due to external inputs. Finally, we find that this balance breaks down during seizures, where the temporal correlation of excitatory and inhibitory populations is disrupted. These results show that balanced activity is a feature of normal brain activity, and break down of the balance could be an important factor to define pathological states.

Correlates of a single cortical action potential in the epidural EEG.

To identify the correlates of a single cortical action potential in surface EEG, we recorded simultaneously epidural EEG and single-unit activity in the primary somatosensory cortex of awake macaque monkeys. By averaging over EEG segments coincident with more than hundred thousand single spikes, we found short-lived (≈ 0.5 ms) triphasic EEG deflections dominated by high-frequency components >800 Hz. The peak-to-peak amplitude of the grand-averaged spike correlate was 80 nV, which matched theoretical predictions, while single-neuron amplitudes ranged from 12 to 966 nV. Combining these estimates with post-stimulus-time histograms of single-unit responses to median-nerve stimulation allowed us to predict the shape of the evoked epidural EEG response and to estimate the number of contributing neurons. These findings establish spiking activity of cortical neurons as a primary building block of high-frequency epidural EEG, which thus can serve as a quantitative macroscopic marker of neuronal spikes.

Are high-frequency (600 Hz) oscillations in human somatosensory evoked potentials due to phase-resetting phenomena?

OBJECTIVE: Median nerve somatosensory evoked potentials (SEP) contain a brief oscillatory wavelet burst at about 600 Hz (σ-burst) superimposed on the initial cortical component (N20). While invasive single-cell recordings suggested that this burst is generated by increased neuronal spiking activity in area 3b, recent non-invasive scalp recordings could not reveal concomitant single-trial added-activity, suggesting that the SEP burst might instead be generated by phase-reset of ongoing high-frequency EEG. Here, a statistical model and exemplary data are presented reconciling these seemingly contradictory results. METHODS: A statistical model defined the conditions required to detect added-activity in a set of single-trial SEP. Its predictions were tested by analyzing human single-trial scalp SEP recorded with custom-made low-noise amplifiers. RESULTS: The noise level in previous studies did not allow to detect single-trial added-activity in the period concomitant with the trial-averaged σ-burst. In contrast, optimized low-noise recordings do reveal added-activity in a set of single-trials. CONCLUSIONS: The experimental noise level is the decisive factor determining the detectability of added-activity in single-trials. A low-noise experiment provided direct evidence that the SEP σ-burst is at least partly generated by added-activity matching earlier invasive single-cell recordings. SIGNIFICANCE: Quantitative criteria are provided for the feasibility of single-trial detectability of band-limited added-activity.

High-frequency EEG covaries with spike burst patterns detected in cortical neurons.

Invasive microelectrode recordings measure neuronal spikes, which are commonly considered inaccessible through standard surface electroencephalogram (EEG). Yet high-frequency EEG potentials (hf-EEG, f > 400 Hz) found in somatosensory evoked potentials of primates may reflect the mean population spike responses of coactivated cortical neurons. Since cortical responses to electrical nerve stimulation vary strongly from trial to trial, we investigated whether the hf-EEG signal can also echo single-trial variability observed at the single-unit level. We recorded extracellular single-unit activity in the primary somatosensory cortex of behaving macaque monkeys and identified variable spike burst responses following peripheral stimulation. Each of these responses was classified according to the timing of its spike constituents, conforming to one of a discrete set of spike patterns. We here show that these spike patterns are accompanied by variations in the concomitant epidural hf-EEG. These variations cannot be explained by fluctuating stimulus efficacy, suggesting that they were generated within the thalamocortical network. As high-frequency EEG signals can also be reliably recorded from the scalp of human subjects, they may provide a noninvasive window on fluctuating cortical spike activity in humans.

Role of neuronal synchrony in the generation of evoked EEG/MEG responses.

Evoked EEG/MEG responses are a primary real-time measure of perceptual and cognitive activity in the human brain, but their neuronal generator mechanisms are not yet fully understood. Arguments have been put forward in favor of either "phase-reset" of ongoing oscillations or "added-energy" models. Instead of advocating for one or the other model, here we show theoretically that the differentiation between these two generation mechanisms might not be possible if based solely on macroscopic EEG/MEG recordings. Using mathematical modeling, we show that a simultaneous phase reset of multiple oscillating neuronal (microscopic) sources contributing to EEG/MEG can produce evoked responses in agreement with both, the "added-energy" and the "phase-reset" model. We observe a smooth transition between the two models by just varying the strength of synchronization between the multiple microscopic sources. Consequently, because precise knowledge about the strength of microscopic ensemble synchronization is commonly not available in noninvasive EEG/MEG studies, they cannot, in principle, differentiate between the two mechanisms for macroscopic-evoked responses.