Diverse computations in the neocortex are aided byspecialized GABAergic interneurons (INs), which selectively target other INs. However, much less isknown about how these canonical disinhibitory circuit motifs contribute to network operations supporting spatial navigation and learning in the hippocampus. Using chronic two-photon calcium imaging in mice performing random foraging or goal-oriented learning tasks, we found that vasoactive intestinal polypeptide-expressing (VIP+), disinhibitory INs in hippocampal area CA1 form functional subpopulations defined by their modulation by behavioral states and task demands. Optogenetic manipulations of VIP+ INs and computational modeling further showed that VIP+ disinhibition is necessary for goal-directed learning and related reorganization of hippocampal pyramidal cell population dynamics. Our results demonstrate that disinhibitory circuits in the hippocampus play an active role in supporting spatial learning. VIDEO ABSTRACT.

The ability of a neuronal population to effectuate channel decorrelation, which is one form of response decorrelation, has been identified as an essential prelude to efficient neural encoding. To what extent are diverse forms of local and afferent heterogeneities essential in accomplishing channel decorrelation in the dentate gyrus (DG)? Here, we incrementally incorporated four distinct forms of biological heterogeneities into conductance-based network models of the DG and systematically delineate their relative contributions to channel decorrelation. First, to effectively incorporate intrinsic heterogeneities, we built physiologically validated heterogeneous populations of granule (GC) and basket cells (BC) through independent stochastic search algorithms spanning exhaustive parametric spaces. These stochastic search algorithms, which were independently constrained by experimentally determined ion channels and by neurophysiological signatures, revealed cellular-scale degeneracy in the DG. Specifically, in GC and BC populations, disparate parametric combinations yielded similar physiological signatures, with underlying parameters exhibiting significant variability and weak pair-wise correlations. Second, we introduced synaptic heterogeneities through randomization of local synaptic strengths. Third, in including adult neurogenesis, we subjected the valid model populations to randomized structural plasticity and matched neuronal excitability to electrophysiological data. We assessed networks comprising different combinations of these three local heterogeneities with identical or heterogeneous afferent inputs from the entorhinal cortex. We found that the three forms of local heterogeneities were independently and synergistically capable of mediating significant channel decorrelation when the network was driven by identical afferent inputs. However, when we incorporated afferent heterogeneities into the network to account for the divergence in DG afferent connectivity, the impact of all three forms of local heterogeneities was significantly suppressed by the dominant role of afferent heterogeneities in mediating channel decorrelation. Our results unveil a unique convergence of cellular- and network-scale degeneracy in the emergence of channel decorrelation in the DG, whereby disparate forms of local and afferent heterogeneities could synergistically drive input discriminability.

A detailed biophysical model of hippocampal region CA3 was constructed to study how GABAergic modulation influences place field development and the learning and recall of sequence information. Simulations included 1,000 multicompartmental pyramidal cells, each consisting of seven intrinsic and four synaptic currents, and 200 multicompartmental interneurons, consisting of two intrinsic and four synaptic currents. Excitatory rhythmic septal input to the apical dendrites of pyramidal cells and both excitatory and inhibitory input to interneurons at theta frequencies provided a cellular basis for the development of theta and gamma frequency oscillations in population activity. The fundamental frequency of theta oscillations was dictated by the driving rhythm from the septum. Gamma oscillation frequency, however, was determined by both the decay time of the gamma-aminobutyric acid-A (GABA(A))-receptor-mediated synaptic current and the overall level of excitability in interneurons due to alpha-amino-3-hydroxy-5-methyl-4-isoxazole proprionic acid and N-methyl-D-aspartate (NMDA)-receptor-gated channel activation. During theta population activity, total GABA(B)-receptor-mediated conductance levels were found to gradually rise and fall in rhythmic fashion with the predominant population frequency (theta rhythm). This resulted in periodic GABA(B)-receptor-mediated suppression of excitatory synaptic transmission at recurrent collaterals (intrinsic fibers) of pyramidal cells and suppression of inhibitory synaptic transmission to both pyramidal cells and interneurons. To test the ability of the model to learn and recall temporal sequence information, a completion task was employed. During learning, the network was presented a sequence of nonorthogonal spatial patterns. Each input pattern represented a spatial location of a simulated rat running a specific navigational path. Hebbian-type learning was expressed as an increase in postsynaptic NMDA-receptor-mediated conductances. Because of several factors including the sparse, asymmetric excitatory synaptic connections among pyramidal cells in the model and a sufficient degree of random background firing unrelated to the input patterns, repeated simulated runs resulted in the gradual emergence of place fields where a given cell began to respond to a contiguous segment of locations on the path. During recall, the simulated rat was placed at a random location on the previously learned path and tested to see whether the sequence of locations could be completed on the basis of this initial position. Periodic GABA(B)-receptor-mediated suppression of excitatory and inhibitory transmission at intrinsic but not afferent fibers resulted in sensory information about location being dominant during early portions of each theta cycle when GABA(B)-receptor-related effects were highest. This suppression declined with levels of GABA(B) receptor activation toward the end of a theta cycle, resulting in an increase in synaptic transmission at intrinsic fibers and the subsequent recall of a segment of the entire location sequence. This scenario typically continued across theta cycles until the full sequence was recalled. When the GABA(B)-receptor-mediated suppression of excitatory and inhibitory transmission at intrinsic fibers was not included in the model, place field development was curtailed and the network consequently exhibited poor learning and recall performance. This was, in part, due to increased competition of information from intrinsic and afferent fibers during early portions of each theta cycle. Because afferent sensory information did not dominate early in each cycle, the current location of the rat was obscured by ongoing activity from intrinsic sources. (ABSTRACT TRUNCATED)

The hippocampus constructs a map of the environment. How this cognitive map is utilized by other brain regions to guide behavior remains unexplored. To examine how neuronal firing patterns in the hippocampus are transmitted and transformed, we recorded neurons in its principal subcortical target, the lateral septum (LS). We observed that LS neurons carry reliable spatial information in the phase of action potentials, relative to hippocampal theta oscillations, while the firing rates of LS neurons remained uninformative. Furthermore, this spatial phase code had an anatomical microstructure within the LS and was bound to the hippocampal spatial code by synchronous gamma frequency cell assemblies. Using adata-driven model, we show that rate-independent spatial tuning arises through the dynamic weighting of CA1 and CA3 cell assemblies. Our findings demonstrate that transformation of the hippocampal spatial map depends on higher-order theta-dependent neuronal sequences. VIDEO ABSTRACT.

Reverse replay of hippocampal place cells occurs frequently at rewarded locations, suggesting its contribution to goal-directed path learning. Symmetric spike-timing dependent plasticity (STDP) in CA3 likely potentiates recurrent synapses for both forward (start to goal) and reverse (goal to start) replays during sequential activation of place cells. However, how reverse replay selectively strengthens forward synaptic pathway is unclear. Here, we show computationally that firing sequences bias synaptic transmissions to the opposite direction of propagation under symmetric STDP in the co-presence of short-term synaptic depression or afterdepolarization. We demonstrate that significant biases are created in biologically realistic simulation settings, and this bias enables reverse replay to enhance goal-directed spatial memory on a W-maze. Further, we show that essentially the same mechanism works in a two-dimensional open field. Our model for the first time provides the mechanistic account for the way reverse replay contributes to hippocampal sequence learning for reward-seeking spatial navigation.

Here, we show computationally that firing sequences bias synaptic transmissions to the opposite direction of propagation under symmetric STDP in the co-presence of short-term synaptic depression or afterdepolarization. Our model for the first time provides the mechanistic account for the way reverse replay contributes to hippocampal sequence learning for reward-seeking spatial navigation.

Network model with symmetric spike-timing dependent plasticity

Network model with symmetric spike-timing dependent plasticity

Grid cell circuits in the superficial layers of the medial entorhinal cortex have become a focus of considerable experimental and theoretical attention as a model for investigating neural mechanisms of cognition. Together, grid firing and associated theta-nested gamma oscillations can be considered as a minimal set of phenomena which a satisfactory model of superficial entorhinal circuits should account for. The model presented here focuses on stellate cells in layer 2 (L2SCs) and their indirect interactions through inhibitory interneurons. In the model, L2SCs and inhibitory interneurons are represented as distinct excitatory and inhibitory cell populations. To enable investigation of network activity patterns as well as network computations, the model is implemented using spiking exponential integrate and fire neurons. The model demonstrates that indirect interactions between L2SCs mediated via inhibitory neurons are sufficient for emergence of grid firing and nested game oscillations.

Abstract Cognitive flexibility likely depends on modulation of the dynamics underlying how biological neural networks process information. While dynamics can be reshaped by gradually modifying connectivity, less is known about mechanisms operating on faster timescales. A compelling entrypoint to this problem is the observation that exploratory behaviors can rapidly cause selective hippocampal sequences to replay during rest. Using a spiking network model, we asked whether simplified replay could arise from three biological components: fixed recurrent connectivity; stochastic gating inputs; and rapid gating input scaling via long-term potentiation of intrinsic excitability (LTP-IE). Indeed, these enabled both forward and reverse replay of recent sensorimotor-evoked sequences, despite unchanged recurrent weights. LTP-IE tags specific neurons with increased spiking probability under gating input, and ordering is reconstructed from recurrent connectivity. We further show how LTP-IE can implement temporary stimulus-response mappings. This elucidates a novel combination of mechanisms that might play a role in rapid cognitive flexibility.

Grid cells in the rodent medial entorhinal cortex exhibit remarkably regular spatial firing patterns that tessellate all environments visited by the animal. Two theoretical mechanisms that could generate this spatially periodic activity pattern have been proposed: oscillatory interference and continuous attractor dynamics. Although a variety of evidence has been cited in support of each, some aspects of the two mechanisms are complementary, suggesting that a combined model may best account for experimental data. The oscillatory interference model proposes that the grid pattern is formed from linear interference patterns or periodic bands in which velocity-controlled oscillators integrate self-motion to code displacement along preferred directions. However, it also allows the use of symmetric recurrent connectivity between grid cells to provide relative stability and continuous attractor dynamics. Here, we present simulations of this type of hybrid model, demonstrate that it generates intracellular membrane potential profiles that closely match those observed in vivo, addresses several criticisms aimed at pure oscillatory interference and continuous attractor models, and provides testable predictions for future empirical studies.

Cortical circuits are thought to multiplex firing rate codes with temporal codes that rely on oscillatory network activity, but the circuit mechanisms that combine these coding schemes are unclear. We establish with optogenetic activation of layer II of the medial entorhinal cortex that theta frequency drive to this circuit is sufficient to generate nested gamma frequency oscillations in synaptic activity. These nested gamma oscillations closely resemble activity during spatial exploration, are generated by local feedback inhibition without recurrent excitation, and have clock-like features suitable as reference signals for multiplexing temporal codes within rate-coded grid firing fields. In network models deduced from our data, feedback inhibition supports coexistence of theta-nested gamma oscillations with attractor states that generate grid firing fields. These results indicate that grid cells communicate primarily via inhibitory interneurons. This circuit mechanism enables multiplexing of oscillation-based temporal codes with rate-coded attractor states.

We present a model that describes the generation of the spatial (grid fields) and temporal (phase precession) properties of medial entorhinal cortical (MEC) neurons by combining network and intrinsic cellular properties. The model incorporates network architecture derived from earlier attractor map models, and is implemented in 1D for simplicity. Periodic driving of conjunctive (position head-direction) layer-III MEC cells at theta frequency with intensity proportional to the rat's speed, moves an 'activity bump' forward in network space at a corresponding speed. The addition of prolonged excitatory currents and simple after-spike dynamics resembling those observed in MEC stellate cells (for which new data are presented) accounts for both phase precession and the change in scale of grid fields along the dorso-ventral axis of MEC. Phase precession in the model depends on both synaptic connectivity and intrinsic currents, each of which drive neural spiking either during entry into, or during exit out of a grid field. Thus, the model predicts that the slope of phase precession changes between entry into and exit out of the field. The model also exhibits independent variation in grid spatial period and grid field size, which suggests possible experimental tests of the model.

O'Keefe and Recce ([1993] Hippocampus 68:317-330) have observed that the spatially selective firing of pyramidal cells in the CA1 field of the rat hippocampus tends to advance to earlier phases of the electroencephalogram theta rhythm as a rat passes through the place field of a cell. We present here a neural network model based on integrate- and-fire neurons that accounts for this effect. In this model, place selectivity in the hippocampus is a consequence of synaptic interactions between pyramidal neurons together with weakly selective external input. The phase shift of neuronal spiking arises in the model as result of asymmetric spread of activation through the network, caused by asymmetry in the synaptic interactions. Several experimentally observed properties of the phase shift effect follow naturally from the model, including 1) the observation that the first spikes a cell fires appear near the theta phase corresponding to minimal population activity, 2) the overall advance is less than 360 degrees, and 3) the location of the rat within the place field of the cell is the primary correlate of the firing phase, not the time the rat has been in the field. The model makes several predictions concerning the emergence of place fields during the earliest stages of exploration in a novel environment. It also suggests new experiments that could provide further constraints on a possible explanation of the phase precession effect.

One of the two primary classes of models of grid cell spatial firing uses interference between oscillators at dynamically modulated frequencies. Generally, these models are presented in terms of idealized oscillators (modeled as sinusoids), which differ from biological oscillators in multiple important ways. Here we show that two more realistic, noisy neural models (Izhikevich's simple model and a biophysical model of an entorhinal cortex stellate cell) can be successfully used as oscillators in a model of this type. When additive noise is included in the models such that uncoupled or sparsely coupled cells show realistic interspike interval variance, both synaptic and gap-junction coupling can synchronize networks of cells to produce comparatively less variable network-level oscillations. We show that the frequency of these oscillatory networks can be controlled sufficiently well to produce stable grid cell spatial firing on the order of at least 2-5 min, despite the high noise level. Our results suggest that the basic principles of oscillatory interference models work with more realistic models of noisy neurons. Nevertheless, a number of simplifications were still made and future work should examine increasingly realistic models.

While grid cells in the medial entorhinal cortex (MEC) of rodents have multiple, regularly arranged firing fields, place cells in the cornu ammonis (CA) regions of the hippocampus mostly have single spatial firing fields. Since there are extensive projections from MEC to the CA regions, many models have suggested that a feedforward network can transform grid cell firing into robust place cell firing. However, these models generate place fields that are consistently too small compared to those recorded in experiments. Here, we argue that it is implausible that grid cell activity alone can be transformed into place cells with robust place fields of realistic size in a feedforward network. We propose two solutions to this problem. Firstly, weakly spatially modulated cells, which are abundant throughout EC, provide input to downstream place cells along with grid cells. This simple model reproduces many place cell characteristics as well as results from lesion studies. Secondly, the recurrent connections between place cells in the CA3 network generate robust and realistic place fields. Both mechanisms could work in parallel in the hippocampal formation and this redundancy might account for the robustness of place cell responses to a range of disruptions of the hippocampal circuitry.

A minimal synaptic architecture is proposed for how the brain might perform path integration by computing the next internal representation of self-location from the current representation and from the perceived velocity of motion. In the model, a place-cell assembly called a chart contains a two-dimensional attractor set called an attractor map that can be used to represent coordinates in any arbitrary environment, once associative binding has occurred between chart locations and sensory inputs. In hippocampus, there are different spatial relations among place fields in different environments and behavioral contexts. Thus, the same units may participate in many charts, and it is shown that the number of uncorrelated charts that can be encoded in the same recurrent network is potentially quite large. According to this theory, the firing of a given place cell is primarily a cooperative effect of the activity of its neighbors on the currently active chart. Therefore, it is not particularly useful to think of place cells as encoding any particular external object or event. Because of its recurrent connections, hippocampal field CA3 is proposed as a possible location for this multichart architecture; however, other implementations in anatomy would not invalidate the main concepts. The model is implemented numerically both as a network of integrate-and-fire units and as a macroscopic (with respect to the space of states) description of the system, based on a continuous approximation defined by a system of stochastic differential equations. It provides an explanation for a number of hitherto perplexing observations on hippocampal place fields, including doubling, vanishing, reshaping in distorted environments, acquiring directionality in a two-goal shuttling task, rapid formation in a novel environment, and slow rotation after disorientation. The model makes several new predictions about the expected properties of hippocampal place cells and other cells of the proposed network.

Hippocampal activity is fundamental for episodic memory formation and consolidation. During phases of rest and sleep, it exhibits sharp-wave/ripple (SPW/R) complexes, which are short episodes of increased activity with superimposed high-frequency oscillations. Simultaneously, spike sequences reflecting previous behavior, such as traversed trajectories in space, are replayed. Whereas these phenomena are thought to be crucial for the formation and consolidation of episodic memory, their neurophysiological mechanisms are not well understood. Here we present a unified model showing how experience may be stored and thereafter replayed in association with SPW/Rs. We propose that replay and SPW/Rs are tightly interconnected as they mutually generate and support each other. The underlying mechanism is based on the nonlinear dendritic computation attributable to dendritic sodium spikes that have been prominently found in the hippocampal regions CA1 and CA3, where SPW/Rs and replay are also generated. Besides assigning SPW/Rs a crucial role for replay and thus memory processing, the proposed mechanism also explains their characteristic features, such as the oscillation frequency and the overall wave form. The results shed a new light on the dynamical aspects of hippocampal circuit learning. SIGNIFICANCE STATEMENT:During phases of rest and sleep, the hippocampus, the memory center of the brain, generates intermittent patterns of strongly increased overall activity with high-frequency oscillations, the so-called sharp-wave/ripples. We investigate their role in learning and memory processing. They occur together with replay of activity sequences reflecting previous behavior. Developing a unifying computational model, we propose that both phenomena are tightly linked, by mutually generating and supporting each other. The underlying mechanism depends on nonlinear amplification of synchronous inputs that has been prominently found in the hippocampus. Besides assigning sharp-wave/ripples a crucial role for replay generation and thus memory processing, the proposed mechanism also explains their characteristic features, such as the oscillation frequency and the overall wave form.

Behaviors ranging from delivering newspapers to waiting tables depend on remembering previous episodes to avoid incorrect repetition. Physiologically, this requires mechanisms for long-term storage and selective retrieval of episodes based on the time of occurrence, despite variable intervals and similarity of events in a familiar environment. Here, this process has been modeled based on the physiological properties of the hippocampal formation, including mechanisms for sustained activity in entorhinal cortex and theta rhythm oscillations in hippocampal subregions. The model simulates the context-sensitive firing properties of hippocampal neurons including trial-specific firing during spatial alternation and trial by trial changes in theta phase precession on a linear track. This activity is used to guide behavior, and lesions of the hippocampal network impair memory-guided behavior. The model links data at the cellular level to behavior at the systems level, describing a physiologically plausible mechanism for the brain to recall a given episode which occurred at a specific place and time.

The hippocampus is important for memory and learning, being a brain site where initial memories are formed and where sharp wave - ripples (SWR) are found, which are responsible for mapping recent memories to long-term storage during sleep-related memory replay. While this conceptual schema is well established, specific intrinsic and network-level mechanisms driving spatio-temporal patterns of hippocampal activity during sleep, and specifically controlling off-line memory reactivation are unknown. In this study, we discuss a model of hippocampal CA1-CA3 network generating spontaneous characteristic SWR activity. Our study predicts the properties of CA3 input which are necessary for successful CA1 ripple generation and the role of synaptic interactions and intrinsic excitability in spike sequence replay during SWRs. Specifically, we found that excitatory synaptic connections promote reactivation in both CA3 and CA1, but the different dynamics of sharp waves in CA3 and ripples in CA1 result in a differential role for synaptic inhibition in modulating replay: promoting spike sequence specificity in CA3 but not in CA1 areas. Finally, we describe how awake learning of spatial trajectories leads to synaptic changes sufficient to drive hippocampal cells' reactivation during sleep, as required for sleep-related memory consolidation.

A mixed-signal very large scale integration (VLSI) chip for large scale emulation of spiking neural networks is presented. The chip contains 2400 silicon neurons with fully programmable and reconfigurable synaptic connectivity. Each neuron implements a discrete-time model of a single-compartment cell. The model allows for analog membrane dynamics and an arbitrary number of synaptic connections, each with tunable conductance and reversal potential. The array of silicon neurons functions as an address-event (AE) transceiver, with incoming and outgoing spikes communicated over an asynchronous event-driven digital bus. Address encoding and conflict resolution of spiking events are implemented via a randomized arbitration scheme that ensures balanced servicing of event requests across the array. Routing of events is implemented externally using dynamically programmable random-access memory that stores a postsynaptic address, the conductance, and the reversal potential of each synaptic connection. Here, we describe the silicon neuron circuits, present experimental data characterizing the 3 mm x 3 mm chip fabricated in 0.5-microm complementary metal-oxide-semiconductor (CMOS) technology, and demonstrate its utility by configuring the hardware to emulate a model of attractor dynamics and waves of neural activity during sleep in rat hippocampus.

Complex patterns of neural activity appear during up-states in the neocortex and sharp waves in the hippocampus, including sequences that resemble those during prior behavioral experience. The mechanisms underlying this replay are not well understood. How can small synaptic footprints engraved by experience control large-scale network activity during memory retrieval and consolidation? We hypothesize that sparse and weak synaptic connectivity between Hebbian assemblies are boosted by pre-existing recurrent connectivity within them. To investigate this idea, we connect sequences of assemblies in randomly connected spiking neuronal networks with a balance of excitation and inhibition. Simulations and analytical calculations show that recurrent connections within assemblies allow for a fast amplification of signals that indeed reduces the required number of inter-assembly connections. Replay can be evoked by small sensory-like cues or emerge spontaneously by activity fluctuations. Global-potentially neuromodulatory-alterations of neuronal excitability can switch between network states that favor retrieval and consolidation.

Spike timing-dependent plasticity (STDP) is under neuromodulatory control, which is correlated with distinct behavioral states. Previously, we reported that dopamine, a reward signal, broadens the time window for synaptic potentiation and modulates the outcome of hippocampal STDP even when applied after the plasticity induction protocol (Brzosko et al., 2015). Here, we demonstrate that sequential neuromodulation of STDP by acetylcholine and dopamine offers an efficacious model of reward-based navigation. Specifically, our experimental data in mouse hippocampal slices show that acetylcholine biases STDP toward synaptic depression, whilst subsequent application of dopamine converts this depression into potentiation. Incorporating this bidirectional neuromodulation-enabled correlational synaptic learning rule into a computational model yields effective navigation toward changing reward locations, as in natural foraging behavior. Thus, temporally sequenced neuromodulation of STDP enables associations to be made between actions and outcomes and also provides a possible mechanism for aligning the time scales of cellular and behavioral learning.

Grid cells in the rat entorhinal cortex display strikingly regular firing responses to the animal's position in 2-D space and have been hypothesized to form the neural substrate for dead-reckoning. However, errors accumulate rapidly when velocity inputs are integrated in existing models of grid cell activity. To produce grid-cell-like responses, these models would require frequent resets triggered by external sensory cues. Such inadequacies, shared by various models, cast doubt on the dead-reckoning potential of the grid cell system. Here we focus on the question of accurate path integration, specifically in continuous attractor models of grid cell activity. We show, in contrast to previous models, that continuous attractor models can generate regular triangular grid responses, based on inputs that encode only the rat's velocity and heading direction. We consider the role of the network boundary in the integration performance of the network and show that both periodic and aperiodic networks are capable of accurate path integration, despite important differences in their attractor manifolds. We quantify the rate at which errors in the velocity integration accumulate as a function of network size and intrinsic noise within the network. With a plausible range of parameters and the inclusion of spike variability, our model networks can accurately integrate velocity inputs over a maximum of approximately 10-100 meters and approximately 1-10 minutes. These findings form a proof-of-concept that continuous attractor dynamics may underlie velocity integration in the dorsolateral medial entorhinal cortex. The simulations also generate pertinent upper bounds on the accuracy of integration that may be achieved by continuous attractor dynamics in the grid cell network. We suggest experiments to test the continuous attractor model and differentiate it from models in which single cells establish their responses independently of each other.

Medial entorhinal grid cells fire in periodic, hexagonally patterned locations and are proposed to support path-integration-based navigation. The recursive nature of path integration results in accumulating error and, without a corrective mechanism, a breakdown in the calculation of location. The observed long-term stability of grid patterns necessitates that the system either performs highly precise internal path integration or implements an external landmark-based error correction mechanism. To distinguish these possibilities, we examined grid cells in behaving rodents as they made long trajectories across an open arena. We found that error accumulates relative to time and distance traveled since the animal last encountered a boundary. This error reflects coherent drift in the grid pattern. Further, interactions with boundaries yield direction-dependent error correction, suggesting that border cells serve as a neural substrate for error correction. These observations, combined with simulations of an attractor network grid cell model, demonstrate that landmarks are crucial to grid stability.

Grid cells in the medial entorhinal cortex (MEC) respond when an animal occupies a periodic lattice of 'grid fields' in the environment. The grids are organized in modules with spatial periods, or scales, clustered around discrete values separated on average by ratios in the range 1.4-1.7. We propose a mechanism that produces this modular structure through dynamical self-organization in the MEC. In attractor network models of grid formation, the grid scale of a single module is set by the distance of recurrent inhibition between neurons. We show that the MEC forms a hierarchy of discrete modules if a smooth increase in inhibition distance along its dorso-ventral axis is accompanied by excitatory interactions along this axis. Moreover, constant scale ratios between successive modules arise through geometric relationships between triangular grids and have values that fall within the observed range. We discuss how interactions required by our model might be tested experimentally.

The definition of episodic memory includes the concept of mental time travel: the ability to re-experience a previously experienced trajectory through continuous dimensions of space and time, and to recall specific events or stimuli along this trajectory. Lesions of the hippocampus and entorhinal cortex impair human episodic memory function and impair rat performance in tasks that could be solved by retrieval of trajectories. Recent physiological data suggests a novel model for encoding and retrieval of trajectories, and for associating specific stimuli with specific positions along the trajectory. During encoding in the model, external input drives the activity of head direction cells. Entorhinal grid cells integrate the head direction input to update an internal representation of location, and drive hippocampal place cells. Trajectories are encoded by Hebbian modification of excitatory synaptic connections between hippocampal place cells and head direction cells driven by external action. Associations are also formed between hippocampal cells and sensory stimuli. During retrieval, a sensory input cue activates hippocampal cells that drive head direction activity via previously modified synapses. Persistent spiking of head direction cells maintains the direction and speed of the action, updating the activity of entorhinal grid cells that thereby further update place cell activity. Additional cells, termed arc length cells, provide coding of trajectory segments based on the one-dimensional arc length from the context of prior actions or states, overcoming ambiguity where the overlap of trajectory segments causes multiple head directions to be associated with one place. These mechanisms allow retrieval of complex, self-crossing trajectories as continuous curves through space and time.

Grid cells in layer II of rat entorhinal cortex fire to spatial locations in a repeating hexagonal grid, with smaller spacing between grid fields for neurons in more dorsal anatomical locations. Data from in vitro whole-cell patch recordings showed differences in frequency of subthreshold membrane potential oscillations in entorhinal neurons that correspond to different positions along the dorsal-to-ventral axis, supporting a model of physiological mechanisms for grid cell responses.

The hippocampal system contains neural populations that encode an animals position and velocity as it navigates through space. Here, we show that such populations can embed two codes within their spike trains: a firing rate code (R) conveyed by within-cell spike intervals, and a co-firing rate code (R*) conveyed by between-cell spike intervals. These two codes behave as conjugates of one another, obeying an analog of the uncertainty principle from physics: information conveyed in R comes at the expense of information in R*, and vice versa. An exception to this trade-off occurs when spike trains encode a pair of conjugate variables, such as position and velocity, which do not compete for capacity across R and R*. To illustrate this, we describe two biologically inspired methods for decoding R and R*, referred to as sigma and sigma-chi decoding, respectively. Simulations of head direction and grid cells show that if firing rates are tuned for position (but not velocity), then position is recovered by sigma decoding, whereas velocity is recovered by sigma-chi decoding. Conversely, simulations of oscillatory interference among theta-modulated speed cells show that if co-firing rates are tuned for position (but not velocity), then position is recovered by sigma-chi decoding, whereas velocity is recovered by sigma decoding. Between these two extremes, information about both variables can be distributed across both channels, and partially recovered by both decoders. These results suggest that populations with different spatial and temporal tuning properties-such as speed versus grid cells-might not encode different information, but rather, distribute similar information about position and velocity in different ways across R and R*. Such conjugate coding of position and velocity may influence how hippocampal populations are interconnected to form functional circuits, and how biological neurons integrate their inputs to decode information from firing rates and spike correlations.

In familiar environments, the firing fields of entorhinal grid cells form regular triangular lattices. However, when the geometric shape of the environment is deformed, these time-averaged grid patterns are distorted in a grid scale-dependent and local manner. We hypothesized that this distortion in part reflects dynamic anchoring of the grid code to displaced boundaries, possibly through border cell-grid cell interactions. To test this hypothesis, we first reanalyzed two existing rodent grid rescaling datasets to identify previously unrecognized boundary-tethered shifts in grid phase that contribute to the appearance of rescaling. We then demonstrated in a computational model that boundary-tethered phase shifts, as well as scale-dependent and local distortions of the time-averaged grid pattern, could emerge from border-grid interactions without altering inherent grid scale. Together, these results demonstrate that environmental deformations induce history-dependent shifts in grid phase, and implicate border-grid interactions as a potential mechanism underlying these dynamics.

Many theories of hippocampal function assume that area CA3 of hippocampus is capable of performing rapid pattern storage, as well as pattern completion when a partial version of a familiar pattern is presented, and that the dentate gyrus (DG) is a preprocessor that performs pattern separation, facilitating storage and recall in CA3. The latter assumption derives partly from the anatomical and physiological properties of DG. However, the major output of DG is from a large number of DG granule cells to a smaller number of CA3 pyramidal cells, which potentially negates the pattern separation performed in the DG. Here, we consider a simple CA3 network model, and consider how it might interact with a previously developed computational model of the DG. The resulting standard DG-CA3 model performs pattern storage and completion well, given a small set of sparse, randomly derived patterns representing entorhinal input to the DG and CA3. However, under many circumstances, the pattern separation achieved in the DG is not as robust in CA3, resulting in a low storage capacity for CA3, compared to previous mathematical estimates of the storage capacity for an autoassociative network of this size. We also examine an often-overlooked aspect of hippocampal anatomy that might increase functionality in the combined DG-CA3 model. Specifically, axon collaterals of CA3 pyramidal cells project back to the DG (backprojections), exerting inhibitory effects on granule cells that could potentially ensure that different subpopulations of granule cells are recruited to respond to similar patterns. In the model, addition of such backprojections improves both pattern separation and storage capacity. We also show that the DG-CA3 model with backprojections provides a better fit to empirical data than a model without backprojections. Therefore, we hypothesize that CA3 backprojections might play an important role in hippocampal function.

We present a model for neural circuit mechanisms underlying hippocampal memory. Central to this model are nonlinear interactions between anatomically and functionally segregated inputs onto dendrites of pyramidal cells in hippocampal areas CA3 and CA1. We study the consequences of such interactions using model neurons in which somatic burst-firing and synaptic plasticity are controlled by conjunctive processing of these separately integrated input pathways. We find that nonlinear dendritic input processing enhances the model's capacity to store and retrieve large numbers of similar memories. During memory encoding, CA3 stores heavily decorrelated engrams to prevent interference between similar memories, while CA1 pairs these engrams with information-rich memory representations that will later provide meaningful output signals during memory recall. While maintaining mathematical tractability, this model brings theoretical study of memory operations closer to the hippocampal circuit's anatomical and physiological properties, thus providing a framework for future experimental and theoretical study of hippocampal function.

A recurrent spiking neural network is proposed that implements planning as probabilistic inference for finite and infinite horizon tasks. The architecture splits this problem into two parts: The stochastic transient firing of the network embodies the dynamics of the planning task. With appropriate injected input this dynamics is shaped to generate high-reward state trajectories. A general class of reward-modulated plasticity rules for these afferent synapses is presented. The updates optimize the likelihood of getting a reward through a variant of an Expectation Maximization algorithm and learning is guaranteed to convergence to a local maximum. We find that the network dynamics are qualitatively similar to transient firing patterns during planning and foraging in the hippocampus of awake behaving rats. The model extends classical attractor models and provides a testable prediction on identifying modulating contextual information. In a real robot arm reaching and obstacle avoidance task the ability to represent multiple task solutions is investigated. The neural planning method with its local update rules provides the basis for future neuromorphic hardware implementations with promising potentials like large data processing abilities and early initiation of strategies to avoid dangerous situations in robot co-worker scenarios.

While the neurobiology of simple and habitual choices is relatively well known, our current understanding of goal-directed choices and planning in the brain is still limited. Theoretical work suggests that goal-directed computations can be productively associated to model-based (reinforcement learning) computations, yet a detailed mapping between computational processes and neuronal circuits remains to be fully established. Here we report a computational analysis that aligns Bayesian nonparametrics and model-based reinforcement learning (MB-RL) to the functioning of the hippocampus (HC) and the ventral striatum (vStr)-a neuronal circuit that increasingly recognized to be an appropriate model system to understand goal-directed (spatial) decisions and planning mechanisms in the brain. We test the MB-RL agent in a contextual conditioning task that depends on intact hippocampus and ventral striatal (shell) function and show that it solves the task while showing key behavioral and neuronal signatures of the HC-vStr circuit. Our simulations also explore the benefits of biological forms of look-ahead prediction (forward sweeps) during both learning and control. This article thus contributes to fill the gap between our current understanding of computational algorithms and biological realizations of (model-based) reinforcement learning.

The way grid cells represent space in the rodent brain has been a striking discovery, with theoretical implications still unclear. Unlike hippocampal place cells, which are known to encode multiple, environment-dependent spatial maps, grid cells have been widely believed to encode space through a single low-dimensional manifold, in which coactivity relations between different neurons are preserved when the environment is changed. Does it have to be so? Here, we compute, using two alternative mathematical models, the storage capacity of a population of grid-like units, embedded in a continuous attractor neural network, for multiple spatial maps. We show that distinct representations of multiple environments can coexist, as existing models for grid cells have the potential to express several sets of hexagonal grid patterns, challenging the view of a universal grid map. This suggests that a population of grid cells can encode multiple noncongruent metric relationships, a feature that could in principle allow a grid-like code to represent environments with a variety of different geometries and possibly conceptual and cognitive spaces, which may be expected to entail such context-dependent metric relationships.