Spike Afterpotentials Shape the In Vivo Burst Activity of Principal Cells in Medial Entorhinal Cortex.

Principal neurons in rodent medial entorhinal cortex (MEC) generate high-frequency bursts during natural behavior. While in vitro studies point to potential mechanisms that could support such burst sequences, it remains unclear whether these mechanisms are effective under in vivo conditions. In this study, we focused on the membrane-potential dynamics immediately following action potentials (APs), as measured in whole-cell recordings from male mice running in virtual corridors (Domnisoru et al., 2013). These afterpotentials consisted either of a hyperpolarization, an extended ramp-like shoulder, or a depolarization reminiscent of depolarizing afterpotentials (DAPs) recorded in vitro in MEC principal neurons. Next, we correlated the afterpotentials with the cells' propensity to fire bursts. All DAP cells with known location resided in Layer II, generated bursts, and their interspike intervals (ISIs) were typically between 5 and 15 ms. The ISI distributions of Layer-II cells without DAPs peaked sharply at around 4 ms and varied only minimally across that group. This dichotomy in burst behavior is explained by cell-group-specific DAP dynamics. The same two groups of bursting neurons also emerged when we clustered extracellular spike-train autocorrelations measured in real 2D arenas (Latuske et al., 2015). Apart from slight variations in grid spacing, no difference in the spatial coding properties of the grid cells across all three groups was discernible. Layer III neurons were only sparsely bursting (SB) and had no DAPs. As various mechanisms for modulating ion-channels underlying DAPs exist, our results suggest that temporal features of MEC activity can be altered while maintaining the cells' overall spatial tuning characteristics.SIGNIFICANCE STATEMENT Depolarizing afterpotentials (DAPs) are frequently observed in principal neurons from slice preparations of rodent medial entorhinal cortex (MEC), but their functional role in vivo is unknown. Analyzing whole-cell data from mice running on virtual tracks, we show that DAPs do occur during behavior. Cells with prominent DAPs are found in Layer II; their interspike intervals (ISIs) reflect DAP time-scales. In contrast, neither the rarely bursting cells in Layer III, nor the high-frequency bursters in Layer II, have a DAP. Extracellular recordings from mice exploring real 2D arenas demonstrate that grid cells within these three groups have similar spatial coding properties. We conclude that DAPs shape the temporal response characteristics of principal neurons in MEC with little effect on spatial properties.

Burst activity plays no role in the field-to-field variability and rate remapping of grid cells.

Grid cells in rodent medial entorhinal cortex are thought to play a key role for spatial navigation. When the animal is freely moving in an open arena the firing fields of each grid cell tend to form a highly regular, hexagonal lattice spanning the environment. However, firing rates vary from field to field and change under contextual modifications, whereas the field locations shift at most by a small amount under such "rate remapping." The observed differences in firing rate could reflect overall activity changes or changes in the detailed spike-train statistics. As these two alternatives imply distinct neural coding schemes, we investigated whether temporal firing patterns vary from field to field and whether they change under rate remapping. Focusing on short time scales, we found that the proportion of bursts compared to all discharge events is similar in all firing fields of a given grid cell and does not change under rate remapping. For each cell, mean firing rates with bursts are proportional to mean firing rates without bursts. However, this ratio varies across cells. Additionally, we looked at how rate remapping relates to entorhinal theta-frequency oscillations. Theta-phase coding was preserved despite firing-rate changes from rate remapping but we did not observe differences between the first and second half of the theta cycle, as had been reported for CA1. Our results indicate that both, the heterogeneity between firing fields and rate remapping, are not due to altered firing patterns on short time scales but reflect location-specific changes at the firing-rate level.

Anticipatory Neural Activity Improves the Decoding Accuracy for Dynamic Head-Direction Signals.

Insects and vertebrates harbor specific neurons that encode the animal's head direction (HD) and provide an internal compass for spatial navigation. Each HD cell fires most strongly in one preferred direction. As the animal turns its head, however, HD cells in rat anterodorsal thalamic nucleus (ADN) and other brain areas fire already before their preferred direction is reached, as if the neurons anticipated the future HD. This phenomenon has been explained at a mechanistic level, but a functional interpretation is still missing. To close this gap, we use a computational approach based on the movement statistics of male rats and a simple model for the neural responses within the ADN HD network. Network activity is read out using population vectors in a biologically plausible manner, so that only past spikes are taken into account. We find that anticipatory firing improves the representation of the present HD by reducing the motion-induced temporal bias inherent in causal decoding. The amount of anticipation observed in ADN enhances the precision of the HD compass read-out by up to 40%. More generally, our theoretical framework predicts that neural integration times not only reflect biophysical constraints, but also the statistics of behaviorally relevant stimuli; in particular, anticipatory tuning should be found wherever neurons encode sensory signals that change gradually in time.SIGNIFICANCE STATEMENT Across different brain regions, populations of noisy neurons encode dynamically changing stimuli. Decoding a time-varying stimulus from the population response involves a trade-off: For short read-out times, stimulus estimates are unreliable as the number of stochastic spikes is small; for long read-outs, estimates are biased because they lag behind the true stimulus. We show that optimal decoding of temporally correlated stimuli not only relies on finding the right read-out time window but requires neurons to anticipate future stimulus values. We apply this general framework to the rodent head-direction system and show that the experimentally observed anticipation of future head directions can be explained at a quantitative level from the neuronal tuning properties, network size, and the animal's head-movement statistics.

Untethered firing fields and intermittent silences: Why grid-cell discharge is so variable.

Grid cells in medial entorhinal cortex are notoriously variable in their responses, despite the striking hexagonal arrangement of their spatial firing fields. Indeed, when the animal moves through a firing field, grid cells often fire much more vigorously than predicted or do not fire at all. The source of this trial-to-trial variability is not completely understood. By analyzing grid-cell spike trains from mice running in open arenas and on linear tracks, we characterize the phenomenon of "missed" firing fields using the statistical theory of zero inflation. We find that one major cause of grid-cell variability lies in the spatial representation itself: firing fields are not as strongly anchored to spatial location as the averaged grid suggests. In addition, grid fields from different cells drift together from trial to trial, regardless of whether the environment is real or virtual, or whether the animal moves in light or darkness. Spatial realignment across trials sharpens the grid representation, yielding firing fields that are more pronounced and significantly narrower. These findings indicate that ensembles of grid cells encode relative position more reliably than absolute position.

Tuft dendrites of pyramidal neurons operate as feedback-modulated functional subunits.

Dendrites of pyramidal cells exhibit complex morphologies and contain a variety of ionic conductances, which generate non-trivial integrative properties. Basal and proximal apical dendrites have been shown to function as independent computational subunits within a two-layer feedforward processing scheme. The outputs of the subunits are linearly summed and passed through a final non-linearity. It is an open question whether this mathematical abstraction can be applied to apical tuft dendrites as well. Using a detailed compartmental model of CA1 pyramidal neurons and a novel theoretical framework based on iso-response methods, we first show that somatic sub-threshold responses to brief synaptic inputs cannot be described by a two-layer feedforward model. Then, we relax the core assumption of subunit independence and introduce non-linear feedback from the output layer to the subunit inputs. We find that additive feedback alone explains the somatic responses to synaptic inputs to most of the branches in the apical tuft. Individual dendritic branches bidirectionally modulate the thresholds of their input-output curves without significantly changing the gains. In contrast to these findings for precisely timed inputs, we show that neuronal computations based on firing rates can be accurately described by purely feedforward two-layer models. Our findings support the view that dendrites of pyramidal neurons possess non-linear analog processing capabilities that critically depend on the location of synaptic inputs. The iso-response framework proposed in this computational study is highly efficient and could be directly applied to biological neurons.

Grid-Cell Activity on Linear Tracks Indicates Purely Translational Remapping of 2D Firing Patterns at Movement Turning Points.

Grid cells in rodent medial entorhinal cortex are thought to play a critical role for spatial navigation. When the animal is freely moving in an open arena the firing fields of each grid cell tend to form a hexagonal lattice spanning the environment. For movements along a linear track the cells seem to respond differently. They show multiple firing fields that are not periodically arranged and whose shape and position change when the running direction is reversed. In addition, peak firing rates vary widely from field to field. Measured along one running direction only, firing fields are, however, compatible with a slice through a two-dimensional (2D) hexagonal pattern. It is an open question, whether this is also true if leftward and rightward runs are jointly considered. By analyzing data from 15 male Long-Evans rats, we show that a single hexagonal firing pattern explains the linear-track data if translational shifts of the pattern are allowed at the movement turning points. A rotation or scaling of the grid is not required. The agreement is further improved if the peak firing rates of the underlying 2D grid fields can vary from field to field, as suggested by recent studies. These findings have direct consequences for experiments using linear tracks in virtual reality.SIGNIFICANCE STATEMENT Various types of neurons support spatial navigation. Their response properties are often studied in reduced settings and might change when the animal can freely explore its environment. Grid cells in rodents, for example, exhibit seemingly irregular firing fields when animal movement is restricted to a linear track but highly regular patterns in two-dimensional (2D) arenas. We show that linear-track responses of a cell for both leftward and rightward running directions can be explained as cuts through a single hexagonal pattern if translational remapping is allowed at movement turning points; neither rotations nor scale transformations are needed. These results provide a basis to quantify grid-cell activity in 1D virtual reality and could help to detect and categorize grid cells without experiments in 2D environments.

Grid cells in rat entorhinal cortex encode physical space with independent firing fields and phase precession at the single-trial level.

When a rat moves, grid cells in its entorhinal cortex become active in multiple regions of the external world that form a hexagonal lattice. As the animal traverses one such "firing field," spikes tend to occur at successively earlier theta phases of the local field potential. This phenomenon is called phase precession. Here, we show that spike phases provide 80% more spatial information than spike counts and that they improve position estimates from single neurons down to a few centimeters. To understand what limits the resolution and how variable spike phases are across different field traversals, we analyze spike trains run by run. We find that the multiple firing fields of a grid cell operate as independent elements for encoding physical space. In addition, phase precession is significantly stronger than the pooled-run data suggest. Despite the inherent stochasticity of grid-cell firing, phase precession is therefore a robust phenomenon at the single-trial level, making a theta-phase code for spatial navigation feasible.

Matched pre- and post-synaptic changes underlie synaptic plasticity over long time scales.

Modifications of synaptic efficacies are considered essential for learning and memory. However, it is not known how the underlying functional components of synaptic transmission change over long time scales. To address this question, we studied cortical synapses from young Wistar rats before and after 12 h intervals of spontaneous or glutamate-induced spiking activity. We found that, under these conditions, synaptic efficacies can increase or decrease by up to 10-fold. Statistical analyses reveal that these changes reflect modifications in the number of presynaptic release sites, together with postsynaptic changes that maintain the quantal size per release site. The quantitative relation between the presynaptic and postsynaptic transmission components was not affected when synaptic plasticity was enhanced or reduced using a broad range of pharmacological agents. These findings suggest that ongoing synaptic plasticity results in matched presynaptic and postsynaptic modifications, in which elementary modules that span the synaptic cleft are added or removed as a function of experience.

Channel noise from both slow adaptation currents and fast currents is required to explain spike-response variability in a sensory neuron.

Spike-timing variability has a large effect on neural information processing. However, for many systems little is known about the noise sources causing the spike-response variability. Here we investigate potential sources of spike-response variability in auditory receptor neurons of locusts, a classic insect model system. At low-spike frequencies, our data show negative interspike-interval (ISI) correlations and ISI distributions that match the inverse Gaussian distribution. These findings can be explained by a white-noise source that interacts with an adaptation current. At higher spike frequencies, more strongly peaked distributions and positive ISI correlations appear, as expected from a canonical model of suprathreshold firing driven by temporally correlated (i.e., colored) noise. Simulations of a minimal conductance-based model of the auditory receptor neuron with stochastic ion channels exclude the delayed rectifier as a possible noise source. Our analysis suggests channel noise from an adaptation current and the receptor or sodium current as main sources for the colored and white noise, respectively. By comparing the ISI statistics with generic models, we find strong evidence for two distinct noise sources. Our approach does not involve any dendritic or somatic recordings that may harm the delicate workings of many sensory systems. It could be applied to various other types of neurons, in which channel noise dominates the fluctuations that shape the neuron's spike statistics.

Resolution of nested neuronal representations can be exponential in the number of neurons.

Collective computation is typically polynomial in the number of computational elements, such as transistors or neurons, whether one considers the storage capacity of a memory device or the number of floating-point operations per second of a CPU. However, we show here that the capacity of a computational network to resolve real-valued signals of arbitrary dimensions can be exponential in N, even if the individual elements are noisy and unreliable. Nested, modular codes that achieve such high resolutions mirror the properties of grid cells in vertebrates, which underlie spatial navigation.

Optimal population codes for space: grid cells outperform place cells.

Rodents use two distinct neuronal coordinate systems to estimate their position: place fields in the hippocampus and grid fields in the entorhinal cortex. Whereas place cells spike at only one particular spatial location, grid cells fire at multiple sites that correspond to the points of an imaginary hexagonal lattice. We study how to best construct place and grid codes, taking the probabilistic nature of neural spiking into account. Which spatial encoding properties of individual neurons confer the highest resolution when decoding the animal's position from the neuronal population response? A priori, estimating a spatial position from a grid code could be ambiguous, as regular periodic lattices possess translational symmetry. The solution to this problem requires lattices for grid cells with different spacings; the spatial resolution crucially depends on choosing the right ratios of these spacings across the population. We compute the expected error in estimating the position in both the asymptotic limit, using Fisher information, and for low spike counts, using maximum likelihood estimation. Achieving high spatial resolution and covering a large range of space in a grid code leads to a trade-off: the best grid code for spatial resolution is built of nested modules with different spatial periods, one inside the other, whereas maximizing the spatial range requires distinct spatial periods that are pairwisely incommensurate. Optimizing the spatial resolution predicts two grid cell properties that have been experimentally observed. First, short lattice spacings should outnumber long lattice spacings. Second, the grid code should be self-similar across different lattice spacings, so that the grid field always covers a fixed fraction of the lattice period. If these conditions are satisfied and the spatial "tuning curves" for each neuron span the same range of firing rates, then the resolution of the grid code easily exceeds that of the best possible place code with the same number of neurons.

A Uniform and Isotropic Cytoskeletal Tiling Fills Dendritic Spines.

Dendritic spines are submicron, subcellular compartments whose shape is defined by actin filaments and associated proteins. Accurately mapping the cytoskeleton is a challenge, given the small size of its components. It remains unclear whether the actin-associated structures analyzed in dendritic spines of neurons in vitro apply to dendritic spines of intact, mature neurons in situ. Here, we combined advanced preparative methods with multitilt serial section electron microscopy (EM) tomography and computational analysis to reveal the full three-dimensional (3D) internal architecture of spines in the intact brains of male mice at nanometer resolution. We compared hippocampal (CA1) pyramidal cells and cerebellar Purkinje cells in terms of the length distribution and connectivity of filaments, their branching-angles and absolute orientations, and the elementary loops formed by the network. Despite differences in shape and size across spines and between spine heads and necks, the internal organization was remarkably similar in both neuron types and largely homogeneous throughout the spine volume. In the tortuous mesh of highly branched and interconnected filaments, branches exhibited no preferred orientation except in the immediate vicinity of the cell membrane. We found that new filaments preferentially split off from the convex side of a bending filament, consistent with the behavior of Arp2/3-mediated branching of actin under mechanical deformation. Based on the quantitative analysis, the spine cytoskeleton is likely subject to considerable mechanical force in situ.

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.

Timescale-invariant representation of acoustic communication signals by a bursting neuron.

Acoustic communication often involves complex sound motifs in which the relative durations of individual elements, but not their absolute durations, convey meaning. Decoding such signals requires an explicit or implicit calculation of the ratios between time intervals. Using grasshopper communication as a model, we demonstrate how this seemingly difficult computation can be solved in real time by a small set of auditory neurons. One of these cells, an ascending interneuron, generates bursts of action potentials in response to the rhythmic syllable-pause structure of grasshopper calls. Our data show that these bursts are preferentially triggered at syllable onset; the number of spikes within the burst is linearly correlated with the duration of the preceding pause. Integrating the number of spikes over a fixed time window therefore leads to a total spike count that reflects the characteristic syllable-to-pause ratio of the species while being invariant to playing back the call faster or slower. Such a timescale-invariant recognition is essential under natural conditions, because grasshoppers do not thermoregulate; the call of a sender sitting in the shade will be slower than that of a grasshopper in the sun. Our results show that timescale-invariant stimulus recognition can be implemented at the single-cell level without directly calculating the ratio between pulse and interpulse durations.

Timescale-invariant pattern recognition by feedforward inhibition and parallel signal processing.

The timescale-invariant recognition of temporal stimulus sequences is vital for many species and poses a challenge for their sensory systems. Here we present a simple mechanistic model to address this computational task, based on recent observations in insects that use rhythmic acoustic communication signals for mate finding. In the model framework, feedforward inhibition leads to burst-like response patterns in one neuron of the circuit. Integrating these responses over a fixed time window by a readout neuron creates a timescale-invariant stimulus representation. Only two additional processing channels, each with a feature detector and a readout neuron, plus one final coincidence detector for all three parallel signal streams, are needed to account for the behavioral data. In contrast to previous solutions to the general time-warp problem, no time delay lines or sophisticated neural architectures are required. Our results suggest a new computational role for feedforward inhibition and underscore the power of parallel signal processing.

Testing the efficiency of sensory coding with optimal stimulus ensembles.

According to Barlow's seminal "efficient coding hypothesis," the coding strategy of sensory neurons should be matched to the statistics of stimuli that occur in an animal's natural habitat. Using an automatic search technique, we here test this hypothesis and identify stimulus ensembles that sensory neurons are optimized for. Focusing on grasshopper auditory receptor neurons, we find that their optimal stimulus ensembles differ from the natural environment, but largely overlap with a behaviorally important sub-ensemble of the natural sounds. This indicates that the receptors are optimized for peak rather than average performance. More generally, our results suggest that the coding strategies of sensory neurons are heavily influenced by differences in behavioral relevance among natural stimuli.

G-Node: an integrated tool-sharing platform to support cellular and systems neurophysiology in the age of global neuroinformatics.

The global scale of neuroinformatics offers unprecedented opportunities for scientific collaborations between and among experimental and theoretical neuroscientists. To fully harvest these possibilities, a set of coordinated activities is required that will improve three key ingredients of neuroscientific research: data access, data storage, and data analysis, together with supporting activities for teaching and training. Focusing on the development of tools aiming at neurophysiological data, the newly established German Neuroinformatics Node (G-Node) aims at addressing these aspects as part of the International Neuroinformatics Coordination Facility (INCF). Based on its technical and scientific scope, the Node could play a substantial role for cellular and systems neurophysiology as well as for the neuroscience community at large.

Corrigendum: Calcium in Kenyon Cell Somata as a Substrate for an Olfactory Sensory Memory in Drosophila.

[This corrects the article on p. 128 in vol. 12, PMID: 29867361.].

Calcium in Kenyon Cell Somata as a Substrate for an Olfactory Sensory Memory in Drosophila.

Animals can form associations between temporally separated stimuli. To do so, the nervous system has to retain a neural representation of the first stimulus until the second stimulus appears. The neural substrate of such sensory stimulus memories is unknown. Here, we search for a sensory odor memory in the insect olfactory system and characterize odorant-evoked Ca2+ activity at three consecutive layers of the olfactory system in Drosophila: in olfactory receptor neurons (ORNs) and projection neurons (PNs) in the antennal lobe, and in Kenyon cells (KCs) in the mushroom body. We show that the post-stimulus responses in ORN axons, PN dendrites, PN somata, and KC dendrites are odor-specific, but they are not predictive of the chemical identity of past olfactory stimuli. However, the post-stimulus responses in KC somata carry information about the identity of previous olfactory stimuli. These findings show that the Ca2+ dynamics in KC somata could encode a sensory memory of odorant identity and thus might serve as a basis for associations between temporally separated stimuli.

Spatial Cognition: Grid Cells Harbour Three Complementary Positional Codes.

The firing fields of mammalian grid cells, which map an animal's environment, lie on hexagonal lattices. Three new studies report significant field-to-field differences in the firing rates, a finding with far-reaching consequences for how grid fields form and encode spatial information.