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.

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.

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.

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.

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.

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.

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.

A model for non-monotonic intensity coding.

Peripheral neurons of most sensory systems increase their response with increasing stimulus intensity. Behavioural responses, however, can be specific to some intermediate intensity level whose particular value might be innate or associatively learned. Learning such a preference requires an adjustable trans- formation from a monotonic stimulus representation at the sensory periphery to a non-monotonic representation for the motor command. How do neural systems accomplish this task? We tackle this general question focusing on odour-intensity learning in the fruit fly, whose first- and second-order olfactory neurons show monotonic stimulus-response curves. Nevertheless, flies form associative memories specific to particular trained odour intensities. Thus, downstream of the first two olfactory processing layers, odour intensity must be re-coded to enable intensity-specific associative learning. We present a minimal, feed-forward, three-layer circuit, which implements the required transformation by combining excitation, inhibition, and, as a decisive third element, homeostatic plasticity. Key features of this circuit motif are consistent with the known architecture and physiology of the fly olfactory system, whereas alternative mechanisms are either not composed of simple, scalable building blocks or not compatible with physiological observations. The simplicity of the circuit and the robustness of its function under parameter changes make this computational motif an attractive candidate for tuneable non-monotonic intensity coding.

Local postsynaptic voltage-gated sodium channel activation in dendritic spines of olfactory bulb granule cells.

Neuronal dendritic spines have been speculated to function as independent computational units, yet evidence for active electrical computation in spines is scarce. Here we show that strictly local voltage-gated sodium channel (Nav) activation can occur during excitatory postsynaptic potentials in the spines of olfactory bulb granule cells, which we mimic and detect via combined two-photon uncaging of glutamate and calcium imaging in conjunction with whole-cell recordings. We find that local Nav activation boosts calcium entry into spines through high-voltage-activated calcium channels and accelerates postsynaptic somatic depolarization, without affecting NMDA receptor-mediated signaling. Hence, Nav-mediated boosting promotes rapid output from the reciprocal granule cell spine onto the lateral mitral cell dendrite and thus can speed up recurrent inhibition. This striking example of electrical compartmentalization both adds to the understanding of olfactory network processing and broadens the general view of spine function.

Connecting multiple spatial scales to decode the population activity of grid cells.

Mammalian grid cells fire when an animal crosses the points of an imaginary hexagonal grid tessellating the environment. We show how animals can navigate by reading out a simple population vector of grid cell activity across multiple spatial scales, even though neural activity is intrinsically stochastic. This theory of dead reckoning explains why grid cells are organized into discrete modules within which all cells have the same lattice scale and orientation. The lattice scale changes from module to module and should form a geometric progression with a scale ratio of around 3/2 to minimize the risk of making large-scale errors in spatial localization. Such errors should also occur if intermediate-scale modules are silenced, whereas knocking out the module at the smallest scale will only affect spatial precision. For goal-directed navigation, the allocentric grid cell representation can be readily transformed into the egocentric goal coordinates needed for planning movements. The goal location is set by nonlinear gain fields that act on goal vector cells. This theory predicts neural and behavioral correlates of grid cell readout that transcend the known link between grid cells of the medial entorhinal cortex and place cells of the hippocampus.

Movement dependence and layer specificity of entorhinal phase precession in two-dimensional environments.

As a rat moves, grid cells in its entorhinal cortex (EC) discharge at multiple locations of the external world, and the firing fields of each grid cell span a hexagonal lattice. For movements on linear tracks, spikes tend to occur at successively earlier phases of the theta-band filtered local field potential during the traversal of a firing field - a phenomenon termed phase precession. The complex movement patterns observed in two-dimensional (2D) open-field environments may fundamentally alter phase precession. To study this question at the behaviorally relevant single-run level, we analyzed EC spike patterns as a function of the distance traveled by the rat along each trajectory. This analysis revealed that cells across all EC layers fire spikes that phase-precess; indeed, the rate and extent of phase precession were the same, only the correlation between spike phase and path length was weaker in EC layer III. Both slope and correlation of phase precession were surprisingly similar on linear tracks and in 2D open-field environments despite strong differences in the movement statistics, including running speed. While the phase-precession slope did not correlate with the average running speed, it did depend on specific properties of the animal's path. The longer a curving path through a grid-field in a 2D environment, the shallower was the rate of phase precession, while runs that grazed a grid field tangentially led to a steeper phase-precession slope than runs through the field center. Oscillatory interference models for grid cells do not reproduce the observed phenomena.

Mongolian gerbils learn to navigate in complex virtual spaces.

Virtual reality (VR) environments are increasingly used to study spatial navigation in rodents. So far behavioral paradigms in virtual realities have been limited to linear tracks or open fields. However, little is known whether rodents can learn to navigate in more complex virtual spaces. We used a VR setup with a spherical treadmill but no head-fixation, which permits animals not only to move in a virtual environment but also to freely rotate around their vertical body axis. We trained Mongolian gerbils to perform spatial tasks in virtual mazes of different complexity. Initially the animals learned to run back and forth between the two ends of a virtual linear track for food reward. Performance, measured as path length and running time between the virtual reward locations, improved to asymptotic performance within about five training sessions. When more complex mazes were presented after this training epoch, the animals generalized and explored the new environments already at their first exposure. In a final experiment, the animals also learned to perform a two-alternative forced choice task in a virtual Y-maze. Our data thus shows that gerbils can be trained to solve spatial tasks in virtual mazes and that this behavior can be used as a readout for psychophysical measurements.

Multiscale codes in the nervous system: the problem of noise correlations and the ambiguity of periodic scales.

Encoding information about continuous variables using noisy computational units is a challenge; nonetheless, asymptotic theory shows that combining multiple periodic scales for coding can be highly precise despite the corrupting influence of noise [Mathis, Herz, and Stemmler, Phys. Rev. Lett. 109, 018103 (2012)]. Indeed, the cortex seems to use periodic, multiscale grid codes to represent position accurately. Here we show how such codes can be read out without taking the long-term limit; even on short time scales, the precision of such codes scales exponentially in the number N of neurons. Does this finding also hold for neurons that are not firing in a statistically independent fashion? To assess the extent to which biological grid codes are subject to statistical dependences, we first analyze the noise correlations between pairs of grid code neurons in behaving rodents. We find that if the grids of two neurons align and have the same length scale, the noise correlations between the neurons can reach values as high as 0.8. For increasing mismatches between the grids of the two neurons, the noise correlations fall rapidly. Incorporating such correlations into a population coding model reveals that the correlations lessen the resolution, but the exponential scaling of resolution with N is unaffected.

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.

The iso-response method: measuring neuronal stimulus integration with closed-loop experiments.

Throughout the nervous system, neurons integrate high-dimensional input streams and transform them into an output of their own. This integration of incoming signals involves filtering processes and complex non-linear operations. The shapes of these filters and non-linearities determine the computational features of single neurons and their functional roles within larger networks. A detailed characterization of signal integration is thus a central ingredient to understanding information processing in neural circuits. Conventional methods for measuring single-neuron response properties, such as reverse correlation, however, are often limited by the implicit assumption that stimulus integration occurs in a linear fashion. Here, we review a conceptual and experimental alternative that is based on exploring the space of those sensory stimuli that result in the same neural output. As demonstrated by recent results in the auditory and visual system, such iso-response stimuli can be used to identify the non-linearities relevant for stimulus integration, disentangle consecutive neural processing steps, and determine their characteristics with unprecedented precision. Automated closed-loop experiments are crucial for this advance, allowing rapid search strategies for identifying iso-response stimuli during experiments. Prime targets for the method are feed-forward neural signaling chains in sensory systems, but the method has also been successfully applied to feedback systems. Depending on the specific question, "iso-response" may refer to a predefined firing rate, single-spike probability, first-spike latency, or other output measures. Examples from different studies show that substantial progress in understanding neural dynamics and coding can be achieved once rapid online data analysis and stimulus generation, adaptive sampling, and computational modeling are tightly integrated into experiments.

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.