Navigating Through Time: A Spatial Navigation Perspective on How the Brain May Encode Time.

Interval timing, which operates on timescales of seconds to minutes, is distributed across multiple brain regions and may use distinct circuit mechanisms as compared to millisecond timing and circadian rhythms. However, its study has proven difficult, as timing on this scale is deeply entangled with other behaviors. Several circuit and cellular mechanisms could generate sequential or ramping activity patterns that carry timing information. Here we propose that a productive approach is to draw parallels between interval timing and spatial navigation, where direct analogies can be made between the variables of interest and the mathematical operations necessitated. Along with designing experiments that isolate or disambiguate timing behavior from other variables, new techniques will facilitate studies that directly address the neural mechanisms that are responsible for interval timing.

Learning the Vector Coding of Egocentric Boundary Cells from Visual Data.

The use of spatial maps to navigate through the world requires a complex ongoing transformation of egocentric views of the environment into position within the allocentric map. Recent research has discovered neurons in retrosplenial cortex and other structures that could mediate the transformation from egocentric views to allocentric views. These egocentric boundary cells respond to the egocentric direction and distance of barriers relative to an animal's point of view. This egocentric coding based on the visual features of barriers would seem to require complex dynamics of cortical interactions. However, computational models presented here show that egocentric boundary cells can be generated with a remarkably simple synaptic learning rule that forms a sparse representation of visual input as an animal explores the environment. Simulation of this simple sparse synaptic modification generates a population of egocentric boundary cells with distributions of direction and distance coding that strikingly resemble those observed within the retrosplenial cortex. Furthermore, some egocentric boundary cells learnt by the model can still function in new environments without retraining. This provides a framework for understanding the properties of neuronal populations in the retrosplenial cortex that may be essential for interfacing egocentric sensory information with allocentric spatial maps of the world formed by neurons in downstream areas, including the grid cells in entorhinal cortex and place cells in the hippocampus.SIGNIFICANCE STATEMENT The computational model presented here demonstrates that the recently discovered egocentric boundary cells in retrosplenial cortex can be generated with a remarkably simple synaptic learning rule that forms a sparse representation of visual input as an animal explores the environment. Additionally, our model generates a population of egocentric boundary cells with distributions of direction and distance coding that strikingly resemble those observed within the retrosplenial cortex. This transformation between sensory input and egocentric representation in the navigational system could have implications for the way in which egocentric and allocentric representations interface in other brain areas.

Gated transformations from egocentric to allocentric reference frames involving retrosplenial cortex, entorhinal cortex, and hippocampus.

This paper reviews the recent experimental finding that neurons in behaving rodents show egocentric coding of the environment in a number of structures associated with the hippocampus. Many animals generating behavior on the basis of sensory input must deal with the transformation of coordinates from the egocentric position of sensory input relative to the animal, into an allocentric framework concerning the position of multiple goals and objects relative to each other in the environment. Neurons in retrosplenial cortex show egocentric coding of the position of boundaries in relation to an animal. These neuronal responses are discussed in relation to existing models of the transformation from egocentric to allocentric coordinates using gain fields and a new model proposing transformations of phase coding that differ from current models. The same type of transformations could allow hierarchical representations of complex scenes. The responses in rodents are also discussed in comparison to work on coordinate transformations in humans and non-human primates.

Predictive learning by a burst-dependent learning rule.

Humans and other animals are able to quickly generalize latent dynamics of spatiotemporal sequences, often from a minimal number of previous experiences. Additionally, internal representations of external stimuli must remain stable, even in the presence of sensory noise, in order to be useful for informing behavior. In contrast, typical machine learning approaches require many thousands of samples, and generalize poorly to unexperienced examples, or fail completely to predict at long timescales. Here, we propose a novel neural network module which incorporates hierarchy and recurrent feedback terms, constituting a simplified model of neocortical microcircuits. This microcircuit predicts spatiotemporal trajectories at the input layer using a temporal error minimization algorithm. We show that this module is able to predict with higher accuracy into the future compared to traditional models. Investigating this model we find that successive predictive models learn representations which are increasingly removed from the raw sensory space, namely as successive temporal derivatives of the positional information. Next, we introduce a spiking neural network model which implements the rate-model through the use of a recently proposed biological learning rule utilizing dual-compartment neurons. We show that this network performs well on the same tasks as the mean-field models, by developing intrinsic dynamics that follow the dynamics of the external stimulus, while coordinating transmission of higher-order dynamics. Taken as a whole, these findings suggest that hierarchical temporal abstraction of sequences, rather than feed-forward reconstruction, may be responsible for the ability of neural systems to quickly adapt to novel situations.

Route-dependent spatial engram tagging in mouse dentate gyrus.

The dentate gyrus (DG) of hippocampus is hypothesized to act as a pattern separator that distinguishes between similar input patterns during memory formation and retrieval. Sparse ensembles of DG cells associated with learning and memory, i.e. engrams, have been labeled and manipulated to recall novel context memories. Functional studies of DG cell activity have demonstrated the spatial specificity and stability of DG cells during navigation. To reconcile how the DG contributes to separating global context as well as individual navigational routes, we trained mice to perform a delayed-non-match-to-position (DNMP) T-maze task and labeled DG neurons during performance of this task on a novel T-maze. The following day, mice navigated a second environment: the same T-maze, the same T-maze with one route permanently blocked but still visible, or a novel open field. We found that the degree of engram reactivation across days differed based on the traversal of maze routes, such that mice traversing only one arm had higher ensemble overlap than chance but less overlap than mice running the full two-route task. Mice experiencing the open field had similar ensemble sizes to the other groups but only chance-level ensemble reactivation. Ensemble overlap differences could not be explained by behavioral variability across groups, nor did behavioral metrics correlate to degree of ensemble reactivation. Together, these results support the hypothesis that DG contributes to spatial navigation memory and that partially non-overlapping ensembles encode different routes within the context of an environment.

Complementary representations of time in the prefrontal cortex and hippocampus.

Episodic memory binds the spatial and temporal relationships between the elements of experience. The hippocampus encodes space through place cells that fire at specific spatial locations. Similarly, time cells fire sequentially at specific time points within a temporally organized experience. Recent studies in rodents, monkeys, and humans have identified time cells with discrete firing fields and cells with monotonically changing activity in supporting the temporal organization of events across multiple timescales. Using in vivo electrophysiological tetrode recordings, we simultaneously recorded neurons from the prefrontal cortex and dorsal CA1 of the hippocampus while rats performed a delayed match to sample task. During the treadmill mnemonic delay, hippocampal time cells exhibited sparser firing fields with decreasing resolution over time, consistent with previous results. In comparison, temporally modulated cells in the prefrontal cortex showed more monotonically changing firing rates, ramping up or decaying with the passage of time, and exhibited greater temporal precision for Bayesian decoding of time at long time lags. These time cells show exquisite temporal resolution both in their firing fields and in the fine timing of spikes relative to the phase of theta oscillations. Here, we report evidence of theta phase precession in both the prefrontal cortex and hippocampus during the temporal delay, however, hippocampal cells exhibited steeper phase precession slopes and more punctate time fields. To disentangle whether time cell activity reflects elapsed time or distance traveled, we varied the treadmill running speed on each trial. While many neurons contained multiplexed representations of time and distance, both regions were more strongly influenced by time than distance. Overall, these results demonstrate the flexible integration of spatiotemporal dimensions and reveal complementary representations of time in the prefrontal cortex and hippocampus in supporting memory-guided behavior.

Hippocampal spatial memory representations in mice are heterogeneously stable.

The population of hippocampal neurons actively coding space continually changes across days as mice repeatedly perform tasks. Many hippocampal place cells become inactive while other previously silent neurons become active, challenging the idea that stable behaviors and memory representations are supported by stable patterns of neural activity. Active cell replacement may disambiguate unique episodes that contain overlapping memory cues, and could contribute to reorganization of memory representations. How active cell replacement affects the evolution of representations of different behaviors within a single task is unknown. We trained mice to perform a delayed nonmatching to place task over multiple weeks, and performed calcium imaging in area CA1 of the dorsal hippocampus using head-mounted miniature microscopes. Cells active on the central stem of the maze "split" their calcium activity according to the animal's upcoming turn direction (left or right), the current task phase (study or test), or both task dimensions, even while spatial cues remained unchanged. We found that, among reliably active cells, different splitter neuron populations were replaced at unequal rates, resulting in an increasing number of cells modulated by turn direction and a decreasing number of cells with combined modulation by both turn direction and task phase. Despite continual reorganization, the ensemble code stably segregated these task dimensions. These results show that hippocampal memories can heterogeneously reorganize even while behavior is unchanging.

Neural circuits and symbolic processing.

The ability to use symbols is a defining feature of human intelligence. However, neuroscience has yet to explain the fundamental neural circuit mechanisms for flexibly representing and manipulating abstract concepts. This article will review the research on neural models for symbolic processing. The review first focuses on the question of how symbols could possibly be represented in neural circuits. The review then addresses how neural symbolic representations could be flexibly combined to meet a wide range of reasoning demands. Finally, the review assesses the research on program synthesis and proposes that the most flexible neural representation of symbolic processing would involve the capacity to rapidly synthesize neural operations analogous to lambda calculus to solve complex cognitive tasks.

The Firing Rate Speed Code of Entorhinal Speed Cells Differs across Behaviorally Relevant Time Scales and Does Not Depend on Medial Septum Inputs.

The firing rate of speed cells, a dedicated subpopulation of neurons in the medial entorhinal cortex (MEC), is correlated with running speed. This correlation has been interpreted as a speed code used in various computational models for path integration. These models consider firing rate to be linearly tuned by running speed in real-time. However, estimation of firing rates requires integration of spiking events over time, setting constraints on the temporal accuracy of the proposed speed code. We therefore tested whether the proposed speed code by firing rate is accurate at short time scales using data obtained from open-field recordings in male rats and mice. We applied a novel filtering approach differentiating between speed codes at multiple time scales ranging from deciseconds to minutes. In addition, we determined the optimal integration time window for firing-rate estimation using a general likelihood framework and calculated the integration time window that maximizes the correlation between firing rate and running speed. Data show that these time windows are on the order of seconds, setting constraints on real-time speed coding by firing rate. We further show that optogenetic inhibition of either cholinergic, GABAergic, or glutamatergic neurons in the medial septum/diagonal band of Broca does not affect modulation of firing rates by running speed at each time scale tested. These results are relevant for models of path integration and for our understanding of how behavioral activity states may modulate firing rates and likely information processing in the MEC.SIGNIFICANCE STATEMENT Path integration is the most basic form of navigation relying on self-motion cues. Models of path integration use medial septum/diagonal band of Broca (MSDB)-dependent MEC grid-cell firing patterns as the neurophysiological substrate of path integration. These models use a linear speed code by firing rate, but do not consider temporal constraints of integration over time for firing-rate estimation. We show that firing-rate estimation for speed cells requires integration over seconds. Using optogenetics, we show that modulation of firing rates by running speed is independent of MSDB inputs. These results enhance our understanding of path integration mechanisms and the role of the MSDB for information processing in the MEC.

A Geometric Characterization of Population Coding in the Prefrontal Cortex and Hippocampus during a Paired-Associate Learning Task.

Large-scale neuronal recording techniques have enabled discoveries of population-level mechanisms for neural computation. However, it is not clear how these mechanisms form by trial-and-error learning. In this article, we present an initial effort to characterize the population activity in monkey prefrontal cortex (PFC) and hippocampus (HPC) during the learning phase of a paired-associate task. To analyze the population data, we introduce the normalized distance, a dimensionless metric that describes the encoding of cognitive variables from the geometrical relationship among neural trajectories in state space. It is found that PFC exhibits a more sustained encoding of the visual stimuli, whereas HPC only transiently encodes the identity of the associate stimuli. Surprisingly, after learning, the neural activity is not reorganized to reflect the task structure, raising the possibility that learning is accompanied by some "silent" mechanism that does not explicitly change the neural representations. We did find partial evidence on the learning-dependent changes for some of the task variables. This study shows the feasibility of using normalized distance as a metric to characterize and compare population-level encoding of task variables and suggests further directions to explore learning-dependent changes in the neural circuits.

Introduction to part two of the special issue on computational models of hippocampus and related structures.

Extensive computational modeling has focused on the hippocampal formation and related cortical structures. This introduction describes the topics addressed by individual articles in part two of this special issue of the journal Hippocampus on the topic of computational models of the hippocampus and related structures.

Overview of computational models of hippocampus and related structures: Introduction to the special issue.

Extensive computational modeling has focused on the hippocampal formation and associated cortical structures. This overview describes some of the factors that have motivated the strong focus on these structures, including major experimental findings and their impact on computational models. This overview provides a framework for describing the topics addressed by individual articles in this special issue of the journal Hippocampus.

A neural circuit model for a contextual association task inspired by recommender systems.

Behavioral data shows that humans and animals have the capacity to learn rules of associations applied to specific examples, and generalize these rules to a broad variety of contexts. This article focuses on neural circuit mechanisms to perform a context-dependent association task that requires linking sensory stimuli to behavioral responses and generalizing to multiple other symmetrical contexts. The model uses neural gating units that regulate the pattern of physiological connectivity within the circuit. These neural gating units can be used in a learning framework that performs low-rank matrix factorization analogous to recommender systems, allowing generalization with high accuracy to a wide range of additional symmetrical contexts. The neural gating units are trained with a biologically inspired framework involving traces of Hebbian modification that are updated based on the correct behavioral output of the network. This modeling demonstrates potential neural mechanisms for learning context-dependent association rules and for the change in selectivity of neurophysiological responses in the hippocampus. The proposed computational model is evaluated using simulations of the learning process and the application of the model to new stimuli. Further, human subject behavioral experiments were performed and the results validate the key observation of a low-rank synaptic matrix structure linking stimuli to responses.

Prefrontal oscillations modulate the propagation of neuronal activity required for working memory.

Cognition involves using attended information, maintained in working memory (WM), to guide action. During a cognitive task, a correct response requires flexible, selective gating so that only the appropriate information flows from WM to downstream effectors that carry out the response. In this work, we used biophysically-detailed modeling to explore the hypothesis that network oscillations in prefrontal cortex (PFC), leveraging local inhibition, can independently gate responses to items in WM. The key role of local inhibition was to control the period between spike bursts in the outputs, and to produce an oscillatory response no matter whether the WM item was maintained in an asynchronous or oscillatory state. We found that the WM item that induced an oscillatory population response in the PFC output layer with the shortest period between spike bursts was most reliably propagated. The network resonant frequency (i.e., the input frequency that produces the largest response) of the output layer can be flexibly tuned by varying the excitability of deep layer principal cells. Our model suggests that experimentally-observed modulation of PFC beta-frequency (15-30 Hz) and gamma-frequency (30-80 Hz) oscillations could leverage network resonance and local inhibition to govern the flexible routing of signals in service to cognitive processes like gating outputs from working memory and the selection of rule-based actions. Importantly, we show for the first time that nonspecific changes in deep layer excitability can tune the output gate's resonant frequency, enabling the specific selection of signals encoded by populations in asynchronous or fast oscillatory states. More generally, this represents a dynamic mechanism by which adjusting network excitability can govern the propagation of asynchronous and oscillatory signals throughout neocortex.

Bio-inspired multi-scale fusion.

We reveal how implementing the homogeneous, multi-scale mapping frameworks observed in the mammalian brain's mapping systems radically improves the performance of a range of current robotic localization techniques. Roboticists have developed a range of predominantly single- or dual-scale heterogeneous mapping approaches (typically locally metric and globally topological) that starkly contrast with neural encoding of space in mammalian brains: a multi-scale map underpinned by spatially responsive cells like the grid cells found in the rodent entorhinal cortex. Yet the full benefits of a homogeneous multi-scale mapping framework remain unknown in both robotics and biology: in robotics because of the focus on single- or two-scale systems and limits in the scalability and open-field nature of current test environments and benchmark datasets; in biology because of technical limitations when recording from rodents during movement over large areas. New global spatial databases with visual information varying over several orders of magnitude in scale enable us to investigate this question for the first time in real-world environments. In particular, we investigate and answer the following questions: why have multi-scale representations, how many scales should there be, what should the size ratio between consecutive scales be and how does the absolute scale size affect performance? We answer these questions by developing and evaluating a homogeneous, multi-scale mapping framework mimicking aspects of the rodent multi-scale map, but using current robotic place recognition techniques at each scale. Results in large-scale real-world environments demonstrate multi-faceted and significant benefits for mapping and localization performance and identify the key factors that determine performance.

Specific Basal Forebrain-Cortical Cholinergic Circuits Coordinate Cognitive Operations.

Based on recent molecular genetics, as well as functional and quantitative anatomical studies, the basal forebrain (BF) cholinergic projections, once viewed as a diffuse system, are emerging as being remarkably specific in connectivity. Acetylcholine (ACh) can rapidly and selectively modulate activity of specific circuits and ACh release can be coordinated in multiple areas that are related to particular aspects of cognitive processing. This review discusses how a combination of multiple new approaches with more established techniques are being used to finally reveal how cholinergic neurons, together with other BF neurons, provide temporal structure for behavior, contribute to local cortical state regulation, and coordinate activity between different functionally related cortical circuits. ACh selectively modulates dynamics for encoding and attention within individual cortical circuits, allows for important transitions during sleep, and shapes the fidelity of sensory processing by changing the correlation structure of neural firing. The importance of this system for integrated and fluid behavioral function is underscored by its disease-modifying role; the demise of BF cholinergic neurons has long been established in Alzheimer's disease and recent studies have revealed the involvement of the cholinergic system in modulation of anxiety-related circuits. Therefore, the BF cholinergic system plays a pivotal role in modulating the dynamics of the brain during sleep and behavior, as foretold by the intricacies of its anatomical map.

The Role of Hierarchical Dynamical Functions in Coding for Episodic Memory and Cognition.

Behavioral research in human verbal memory function led to the initial definition of episodic memory and semantic memory. A complete model of the neural mechanisms of episodic memory must include the capacity to encode and mentally reconstruct everything that humans can recall from their experience. This article proposes new model features necessary to address the complexity of episodic memory encoding and recall in the context of broader cognition and the functional properties of neurons that could contribute to this broader scope of memory. Many episodic memory models represent individual snapshots of the world with a sequence of vectors, but a full model must represent complex functions encoding and retrieving the relations between multiple stimulus features across space and time on multiple hierarchical scales. Episodic memory involves not only the space and time of an agent experiencing events within an episode but also features shown in neurophysiological data such as coding of speed, direction, boundaries, and objects. Episodic memory includes not only a spatio-temporal trajectory of a single agent but also segments of spatio-temporal trajectories for other agents and objects encountered in the environment consistent with data on encoding the position and angle of sensory features of objects and boundaries. We will discuss potential interactions of episodic memory circuits in the hippocampus and entorhinal cortex with distributed neocortical circuits that must represent all features of human cognition.

A neural microcircuit model for a scalable scale-invariant representation of time.

Scale-invariant timing has been observed in a wide range of behavioral experiments. The firing properties of recently described time cells provide a possible neural substrate for scale-invariant behavior. Earlier neural circuit models do not produce scale-invariant neural sequences. In this article, we present a biologically detailed network model based on an earlier mathematical algorithm. The simulations incorporate exponentially decaying persistent firing maintained by the calcium-activated nonspecific (CAN) cationic current and a network structure given by the inverse Laplace transform to generate time cells with scale-invariant firing rates. This model provides the first biologically detailed neural circuit for generating scale-invariant time cells. The circuit that implements the inverse Laplace transform merely consists of off-center/on-surround receptive fields. Critically, rescaling temporal sequences can be accomplished simply via cortical gain control (changing the slope of the f-I curve).

Flexible resonance in prefrontal networks with strong feedback inhibition.

Oscillations are ubiquitous features of brain dynamics that undergo task-related changes in synchrony, power, and frequency. The impact of those changes on target networks is poorly understood. In this work, we used a biophysically detailed model of prefrontal cortex (PFC) to explore the effects of varying the spike rate, synchrony, and waveform of strong oscillatory inputs on the behavior of cortical networks driven by them. Interacting populations of excitatory and inhibitory neurons with strong feedback inhibition are inhibition-based network oscillators that exhibit resonance (i.e., larger responses to preferred input frequencies). We quantified network responses in terms of mean firing rates and the population frequency of network oscillation; and characterized their behavior in terms of the natural response to asynchronous input and the resonant response to oscillatory inputs. We show that strong feedback inhibition causes the PFC to generate internal (natural) oscillations in the beta/gamma frequency range (>15 Hz) and to maximize principal cell spiking in response to external oscillations at slightly higher frequencies. Importantly, we found that the fastest oscillation frequency that can be relayed by the network maximizes local inhibition and is equal to a frequency even higher than that which maximizes the firing rate of excitatory cells; we call this phenomenon population frequency resonance. This form of resonance is shown to determine the optimal driving frequency for suppressing responses to asynchronous activity. Lastly, we demonstrate that the natural and resonant frequencies can be tuned by changes in neuronal excitability, the duration of feedback inhibition, and dynamic properties of the input. Our results predict that PFC networks are tuned for generating and selectively responding to beta- and gamma-rhythmic signals due to the natural and resonant properties of inhibition-based oscillators. They also suggest strategies for optimizing transcranial stimulation and using oscillatory networks in neuromorphic engineering.

Neural mechanisms of navigation involving interactions of cortical and subcortical structures.

Animals must perform spatial navigation for a range of different behaviors, including selection of trajectories toward goal locations and foraging for food sources. To serve this function, a number of different brain regions play a role in coding different dimensions of sensory input important for spatial behavior, including the entorhinal cortex, the retrosplenial cortex, the hippocampus, and the medial septum. This article will review data concerning the coding of the spatial aspects of animal behavior, including location of the animal within an environment, the speed of movement, the trajectory of movement, the direction of the head in the environment, and the position of barriers and objects both relative to the animal's head direction (egocentric) and relative to the layout of the environment (allocentric). The mechanisms for coding these important spatial representations are not yet fully understood but could involve mechanisms including integration of self-motion information or coding of location based on the angle of sensory features in the environment. We will review available data and theories about the mechanisms for coding of spatial representations. The computation of different aspects of spatial representation from available sensory input requires complex cortical processing mechanisms for transformation from egocentric to allocentric coordinates that will only be understood through a combination of neurophysiological studies and computational modeling.