Replay as wavefronts and theta sequences as bump oscillations in a grid cell attractor network

A systems model of alternating theta sweeps via firing rate adaptation

Place and grid cells provide a neural system for self-location and tend to fire in sequences within each cycle of the hippocampal theta rhythm when rodents run on a linear track. These sequences correspond to the decoded location of the animal sweeping forward from its current location ("theta sweeps"). However, recent findings in open-field environments show alternating left-right theta sweeps and propose a circuit for their generation. Here, we present a computational model of this circuit, comprising theta-modulated head-direction cells, conjunctive grid × direction cells, and pure grid cells, based on continuous attractor dynamics, firing rate adaptation, and modulation by the medial-septal theta rhythm. Due to firing rate adaptation, the head-direction ring attractor exhibits left-right sweeps coding for internal direction, providing an input to the grid cell attractor network shifted along the internal direction, via an intermediate layer of conjunctive grid × direction cells, producing left-right sweeps of position by grid cells. Our model explains the empirical findings, including the alignment of internal position and direction sweeps and the dependence of sweep length on grid spacing. It makes predictions for theta-modulated head-direction cells, including relationships between theta phase precession during turning, theta skipping, anticipatory firing, and directional tuning width, several of which we verify in experimental data from anteroventral thalamus. The model also predicts relationships between position and direction sweeps, running speed, and dorsal-ventral location within the entorhinal cortex. Overall, a simple intrinsic mechanism explains the complex theta dynamics of an internal direction signal within the hippocampal formation, with testable predictions.

Firing rate adaptation affords place cell theta sweeps, phase precession, and procession

Hippocampal place cells in freely moving rodents display both theta phase precession and procession, which is thought to play important roles in cognition, but the neural mechanism for producing theta phase shift remains largely unknown. Here, we show that firing rate adaptation within a continuous attractor neural network causes the neural activity bump to oscillate around the external input, resembling theta sweeps of decoded position during locomotion. These forward and backward sweeps naturally account for theta phase precession and procession of individual neurons, respectively. By tuning the adaptation strength, our model explains the difference between 'bimodal cells' showing interleaved phase precession and procession, and 'unimodal cells' in which phase precession predominates. Our model also explains the constant cycling of theta sweeps along different arms in a T-maze environment, the speed modulation of place cells' firing frequency, and the continued phase shift after transient silencing of the hippocampus. We hope that this study will aid an understanding of the neural mechanism supporting theta phase coding in the brain.

The generative neural microdynamics of cognitive processing

The entorhinal cortex and hippocampus form a recurrent network that informs many cognitive processes, including memory, planning, navigation, and imagination. Neural recordings from these regions reveal spatially organized population codes corresponding to external environments and abstract spaces. Aligning the former cognitive functionalities with the latter neural phenomena is a central challenge in understanding the entorhinal-hippocampal circuit (EHC). Disparate experiments demonstrate a surprising level of complexity and apparent disorder in the intricate spatiotemporal dynamics of sequential non-local hippocampal reactivations, which occur particularly, though not exclusively, during immobile pauses and rest. We review these phenomena with a particular focus on their apparent lack of physical simulative realism. These observations are then integrated within a theoretical framework and proposed neural circuit mechanisms that normatively characterize this neural complexity by conceiving different regimes of hippocampal microdynamics as neuromarkers of diverse cognitive computations.

Distinguishing examples while building concepts in hippocampal and artificial networks

The hippocampal subfield CA3 is thought to function as an auto-associative network that stores experiences as memories. Information from these experiences arrives directly from the entorhinal cortex as well as indirectly through the dentate gyrus, which performs sparsification and decorrelation. The computational purpose for these dual input pathways has not been firmly established. We model CA3 as a Hopfield-like network that stores both dense, correlated encodings and sparse, decorrelated encodings. As more memories are stored, the former merge along shared features while the latter remain distinct. We verify our model's prediction in rat CA3 place cells, which exhibit more distinct tuning during theta phases with sparser activity. Finally, we find that neural networks trained in multitask learning benefit from a loss term that promotes both correlated and decorrelated representations. Thus, the complementary encodings we have found in CA3 can provide broad computational advantages for solving complex tasks.

Offline memory replay in recurrent neuronal networks emerges from constraints on online dynamics

During spatial exploration, neural circuits in the hippocampus store memories of sequences of sensory events encountered in the environment. When sensory information is absent during 'offline' resting periods, brief neuronal population bursts can 'replay' sequences of activity that resemble bouts of sensory experience. These sequences can occur in either forward or reverse order, and can even include spatial trajectories that have not been experienced, but are consistent with the topology of the environment. The neural circuit mechanisms underlying this variable and flexible sequence generation are unknown. Here we demonstrate in a recurrent spiking network model of hippocampal area CA3 that experimental constraints on network dynamics such as population sparsity, stimulus selectivity, rhythmicity and spike rate adaptation, as well as associative synaptic connectivity, enable additional emergent properties, including variable offline memory replay. In an online stimulus-driven state, we observed the emergence of neuronal sequences that swept from representations of past to future stimuli on the timescale of the theta rhythm. In an offline state driven only by noise, the network generated both forward and reverse neuronal sequences, and recapitulated the experimental observation that offline memory replay events tend to include salient locations like the site of a reward. These results demonstrate that biological constraints on the dynamics of recurrent neural circuits are sufficient to enable memories of sensory events stored in the strengths of synaptic connections to be flexibly read out during rest and sleep, which is thought to be important for memory consolidation and planning of future behaviour. KEY POINTS: A recurrent spiking network model of hippocampal area CA3 was optimized to recapitulate experimentally observed network dynamics during simulated spatial exploration. During simulated offline rest, the network exhibited the emergent property of generating flexible forward, reverse and mixed direction memory replay events. Network perturbations and analysis of model diversity and degeneracy identified associative synaptic connectivity and key features of network dynamics as important for offline sequence generation. Network simulations demonstrate that population over-representation of salient positions like the site of reward results in biased memory replay.

How our understanding of memory replay evolves

Memory reactivations and replay, widely reported in the hippocampus and cortex across species, have been implicated in memory consolidation, planning, and spatial and skill learning. Technological advances in electrophysiology, calcium imaging, and human neuroimaging techniques have enabled neuroscientists to measure large-scale neural activity with increasing spatiotemporal resolution and have provided opportunities for developing robust analytic methods to identify memory replay. In this article, we first review a large body of historically important and representative memory replay studies from the animal and human literature. We then discuss our current understanding of memory replay functions in learning, planning, and memory consolidation and further discuss the progress in computational modeling that has contributed to these improvements. Next, we review past and present analytic methods for replay analyses and discuss their limitations and challenges. Finally, looking ahead, we discuss some promising analytic methods for detecting nonstereotypical, behaviorally nondecodable structures from large-scale neural recordings. We argue that seamless integration of multisite recordings, real-time replay decoding, and closed-loop manipulation experiments will be essential for delineating the role of memory replay in a wide range of cognitive and motor functions.

Multiple bumps can enhance robustness to noise in continuous attractor networks

A central function of continuous attractor networks is encoding coordinates and accurately updating their values through path integration. To do so, these networks produce localized bumps of activity that move coherently in response to velocity inputs. In the brain, continuous attractors are believed to underlie grid cells and head direction cells, which maintain periodic representations of position and orientation, respectively. These representations can be achieved with any number of activity bumps, and the consequences of having more or fewer bumps are unclear. We address this knowledge gap by constructing 1D ring attractor networks with different bump numbers and characterizing their responses to three types of noise: fluctuating inputs, spiking noise, and deviations in connectivity away from ideal attractor configurations. Across all three types, networks with more bumps experience less noise-driven deviations in bump motion. This translates to more robust encodings of linear coordinates, like position, assuming that each neuron represents a fixed length no matter the bump number. Alternatively, we consider encoding a circular coordinate, like orientation, such that the network distance between adjacent bumps always maps onto 360 degrees. Under this mapping, bump number does not significantly affect the amount of error in the coordinate readout. Our simulation results are intuitively explained and quantitatively matched by a unified theory for path integration and noise in multi-bump networks. Thus, to suppress the effects of biologically relevant noise, continuous attractor networks can employ more bumps when encoding linear coordinates; this advantage disappears when encoding circular coordinates. Our findings provide motivation for multiple bumps in the mammalian grid network.

The grid code for ordered experience

Entorhinal cortical grid cells fire in a periodic pattern that tiles space, which is suggestive of a spatial coordinate system. However, irregularities in the grid pattern as well as responses of grid cells in contexts other than spatial navigation have presented a challenge to existing models of entorhinal function. In this Perspective, we propose that hippocampal input provides a key informative drive to the grid network in both spatial and non-spatial circumstances, particularly around salient events. We build on previous models in which neural activity propagates through the entorhinal-hippocampal network in time. This temporal contiguity in network activity points to temporal order as a necessary characteristic of representations generated by the hippocampal formation. We advocate that interactions in the entorhinal-hippocampal loop build a topological representation that is rooted in the temporal order of experience. In this way, the structure of grid cell firing supports a learned topology rather than a rigid coordinate frame that is bound to measurements of the physical world.

Spiking Neural Networks and Hippocampal Function: A Web-Accessible Survey of Simulations, Modeling Methods, and Underlying Theories

Computational modeling has contributed to hippocampal research in a wide variety of ways and through a large diversity of approaches, reflecting the many advanced cognitive roles of this brain region. The intensively studied neuron type circuitry of the hippocampus is a particularly conducive substrate for spiking neural models. Here we present an online knowledge base of spiking neural network simulations of hippocampal functions. First, we overview theories involving the hippocampal formation in subjects such as spatial representation, learning, and memory. Then we describe an original literature mining process to organize published reports in various key aspects, including: (i) subject area (e.g., navigation, pattern completion, epilepsy); (ii) level of modeling detail (Hodgkin-Huxley, integrate-and-fire, etc.); and (iii) theoretical framework (attractor dynamics, oscillatory interference, self-organizing maps, and others). Moreover, every peer-reviewed publication is also annotated to indicate the specific neuron types represented in the network simulation, establishing a direct link with the Hippocampome.org portal. The web interface of the knowledge base enables dynamic content browsing and advanced searches, and consistently presents evidence supporting every annotation. Moreover, users are given access to several types of statistical reports about the collection, a selection of which is summarized in this paper. This open access resource thus provides an interactive platform to survey spiking neural network models of hippocampal functions, compare available computational methods, and foster ideas for suitable new directions of research.

Flexible modulation of sequence generation in the entorhinal-hippocampal system

Exploration, consolidation and planning depend on the generation of sequential state representations. However, these algorithms require disparate forms of sampling dynamics for optimal performance. We theorize how the brain should adapt internally generated sequences for particular cognitive functions and propose a neural mechanism by which this may be accomplished within the entorhinal-hippocampal circuit. Specifically, we demonstrate that the systematic modulation along the medial entorhinal cortex dorsoventral axis of grid population input into the hippocampus facilitates a flexible generative process that can interpolate between qualitatively distinct regimes of sequential hippocampal reactivations. By relating the emergent hippocampal activity patterns drawn from our model to empirical data, we explain and reconcile a diversity of recently observed, but apparently unrelated, phenomena such as generative cycling, diffusive hippocampal reactivations and jumping trajectory events.