Theta phase precession emerges from a hybrid computational model of a CA3 place cell

A spatial transformation-based CAN model for information integration within grid cell modules

The hippocampal-entorhinal circuit is considered to play an important role in the spatial cognition of animals. However, the mechanism of the information flow within the circuit and its contribution to the function of the grid-cell module are still topics of discussion. Prevailing theories suggest that grid cells are primarily influenced by self-motion inputs from the Medial Entorhinal Cortex, with place cells serving a secondary role by contributing to the visual calibration of grid cells. However, recent evidence suggests that both self-motion inputs and visual cues may collaboratively contribute to the formation of grid-like patterns. In this paper, we introduce a novel Continuous Attractor Network model based on a spatial transformation mechanism. This mechanism enables the integration of self-motion inputs and visual cues within grid-cell modules, synergistically driving the formation of grid-like patterns. From the perspective of individual neurons within the network, our model successfully replicates grid firing patterns. From the view of neural population activity within the network, the network can form and drive the activated bump, which describes the characteristic feature of grid-cell modules, namely, path integration. Through further exploration and experimentation, our model can exhibit significant performance in path integration. This study provides a new insight into understanding the mechanism of how the self-motion and visual inputs contribute to the neural activity within grid-cell modules. Furthermore, it provides theoretical support for achieving accurate path integration, which holds substantial implications for various applications requiring spatial navigation and mapping.

Modeling the grid cell activity based on cognitive space transformation

The grid cells in the medial entorhinal cortex are widely recognized as a critical component of spatial cognition within the entorhinal-hippocampal neuronal circuits. To account for the hexagonal patterns, several computational models have been proposed. However, there is still considerable debate regarding the interaction between grid cells and place cells. In response, we have developed a novel grid-cell computational model based on cognitive space transformation, which established a theoretical framework of the interaction between place cells and grid cells for encoding and transforming positions between the local frame and global frame. Our model not only can generate the firing patterns of the grid cells but also reproduces the biological experiment results about the grid-cell global representation of connected environments and supports the conjecture about the underlying reason. Moreover, our model provides new insights into how grid cells and place cells integrate external and self-motion cues.

Homogeneous inhibition is optimal for the phase precession of place cells in the CA1 field

Place cells are hippocampal neurons encoding the position of an animal in space. Studies of place cells are essential to understanding the processing of information by neural networks of the brain. An important characteristic of place cell spike trains is phase precession. When an animal is running through the place field, the discharges of the place cells shift from the ascending phase of the theta rhythm through the minimum to the descending phase. The role of excitatory inputs to pyramidal neurons along the Schaffer collaterals and the perforant pathway in phase precession is described, but the role of local interneurons is poorly understood. Our goal is estimating of the contribution of field CA1 interneurons to the phase precession of place cells using mathematical methods. The CA1 field is chosen because it provides the largest set of experimental data required to build and verify the model. Our simulations discover optimal parameters of the excitatory and inhibitory inputs to the pyramidal neuron so that it generates a spike train with the effect of phase precession. The uniform inhibition of pyramidal neurons best explains the effect of phase precession. Among interneurons, axo-axonal neurons make the greatest contribution to the inhibition of pyramidal cells.

A neural network model of reliably optimized spike transmission

We studied the detailed structure of a neuronal network model in which the spontaneous spike activity is correctly optimized to match the experimental data and discuss the reliability of the optimized spike transmission. Two stochastic properties of the spontaneous activity were calculated: the spike-count rate and synchrony size. The synchrony size, expected to be an important factor for optimization of spike transmission in the network, represents a percentage of observed coactive neurons within a time bin, whose probability approximately follows a power-law. We systematically investigated how these stochastic properties could matched to those calculated from the experimental data in terms of the log-normally distributed synaptic weights between excitatory and inhibitory neurons and synaptic background activity induced by the input current noise in the network model. To ensure reliably optimized spike transmission, the synchrony size as well as spike-count rate were simultaneously optimized. This required changeably balanced log-normal distributions of synaptic weights between excitatory and inhibitory neurons and appropriately amplified synaptic background activity. Our results suggested that the inhibitory neurons with a hub-like structure driven by intensive feedback from excitatory neurons were a key factor in the simultaneous optimization of the spike-count rate and synchrony size, regardless of different spiking types between excitatory and inhibitory neurons.

State-dependencies of learning across brain scales

Learning is a complex brain function operating on different time scales, from milliseconds to years, which induces enduring changes in brain dynamics. The brain also undergoes continuous “spontaneous” shifts in states, which, amongst others, are characterized by rhythmic activity of various frequencies. Besides the most obvious distinct modes of waking and sleep, wake-associated brain states comprise modulations of vigilance and attention. Recent findings show that certain brain states, particularly during sleep, are essential for learning and memory consolidation. Oscillatory activity plays a crucial role on several spatial scales, for example in plasticity at a synaptic level or in communication across brain areas. However, the underlying mechanisms and computational rules linking brain states and rhythms to learning, though relevant for our understanding of brain function and therapeutic approaches in brain disease, have not yet been elucidated. Here we review known mechanisms of how brain states mediate and modulate learning by their characteristic rhythmic signatures. To understand the critical interplay between brain states, brain rhythms, and learning processes, a wide range of experimental and theoretical work in animal models and human subjects from the single synapse to the large-scale cortical level needs to be integrated. By discussing results from experiments and theoretical approaches, we illuminate new avenues for utilizing neuronal learning mechanisms in developing tools and therapies, e.g., for stroke patients and to devise memory enhancement strategies for the elderly.

Modeling inheritance of phase precession in the hippocampal formation

Spatial information about the environment is encoded by the activity of place and grid cells in the hippocampal formation. As an animal traverses a cell's firing field, action potentials progressively shift to earlier phases of the theta oscillation (6-10 Hz). This "phase precession" is observed also in the prefrontal cortex and the ventral striatum, but mechanisms for its generation are unknown. However, once phase precession exists in one region, it might also propagate to downstream regions. Using a computational model, we analyze such inheritance of phase precession, for example, from the entorhinal cortex to CA1 and from CA3 to CA1. We find that distinctive subthreshold and suprathreshold features of the membrane potential of CA1 pyramidal cells (Harvey et al., 2009; Mizuseki et al., 2012; Royer et al., 2012) can be explained by inheritance and that excitatory input is essential. The model explains how inhibition modulates the slope and range of phase precession and provides two main testable predictions. First, theta-modulated inhibitory input to a CA1 pyramidal cell is not necessary for phase precession. Second, theta-modulated inhibitory input on its own generates membrane potential peaks that are in phase with peaks of the extracellular field. Furthermore, we suggest that the spatial distribution of field centers of a population of phase-precessing input cells determines, not only the place selectivity, but also the characteristics of phase precession of the targeted output cell. The inheritance model thus can explain why phase precession is observed throughout the hippocampal formation and other areas of the brain.

Hippocampal phase precession from dual input components

Phase precession is a well known phenomenon in which a hippocampal place cell will fire action potentials at successively earlier phases (relative to the theta-band oscillations recorded in the local field potential) as an animal moves through the cell's receptive field (also known as a place field). We present a model in which CA1 pyramidal cell spiking is driven by dual input components arising from CA3 and EC3. The receptive fields of these two input components overlap but are offset in space from each other such that as the animal moves through the model place field, action potentials are driven first by the CA3 input component and then the EC3 input component. As CA3 synaptic input is known to arrive in CA1 at a later theta phase than EC3 input (Mizuseki et al., 2009; Montgomery et al., 2009), CA1 spiking advances in phase as the model transitions from CA3-driven spiking to EC3-driven spiking. Here spike phase is a function of animal location, placing our results in agreement with many experimental observations characterizing CA1 phase precession (O'Keefe and Recce, 1993; Huxter et al., 2003; Geisler et al., 2007). We predict that experimental manipulations that dramatically enhance or disrupt activity in either of these areas should have a significant effect on phase precession observed in CA1.

Phase precession through acceleration of local theta rhythm: a biophysical model for the interaction between place cells and local inhibitory neurons

Phase precession is one of the most well known examples within the temporal coding hypothesis. Here we present a biophysical spiking model for phase precession in hippocampal CA1 which focuses on the interaction between place cells and local inhibitory interneurons. The model's functional block is composed of a place cell (PC) connected with a local inhibitory cell (IC) which is modulated by the population theta rhythm. Both cells receive excitatory inputs from the entorhinal cortex (EC). These inputs are both theta modulated and space modulated. The dynamics of the two neuron types are described by integrate-and-fire models with conductance synapses, and the EC inputs are described using non-homogeneous Poisson processes. Phase precession in our model is caused by increased drive to specific PC/IC pairs when the animal is in their place field. The excitation increases the IC's firing rate, and this modulates the PC's firing rate such that both cells precess relative to theta. Our model implies that phase coding in place cells may not be independent from rate coding. The absence of restrictive connectivity constraints in this model predicts the generation of phase precession in any network with similar architecture and subject to a clocking rhythm, independently of the involvement in spatial tasks.

A computer model of unitary responses from associational/commissural and perforant path synapses in hippocampal CA3 pyramidal cells

Despite the central position of CA3 pyramidal cells in the hippocampal circuit, the experimental investigation of their synaptic properties has been limited. Recent slice experiments from adult rats characterized AMPA and NMDA receptor unitary synaptic responses in CA3b pyramidal cells. Here, excitatory synaptic activation is modeled to infer biophysical parameters, aid analysis interpretation, explore mechanisms, and formulate predictions by contrasting simulated somatic recordings with experimental data. Reconstructed CA3b pyramidal cells from the public repository NeuroMorpho.Org were used to allow for cell-specific morphological variation. For each cell, synaptic responses were simulated for perforant pathway and associational/commissural synapses. Means and variability for peak amplitude, time-to-peak, and half-height width in these responses were compared with equivalent statistics from experimental recordings. Synaptic responses mediated by AMPA receptors are best fit with properties typical of previously characterized glutamatergic receptors where perforant path synapses have conductances twice that of associational/commissural synapses (0.9 vs. 0.5 nS) and more rapid peak times (1.0 vs. 3.3 ms). Reanalysis of passive-cell experimental traces using the model shows no evidence of a CA1-like increase of associational/commissural AMPA receptor conductance with increasing distance from the soma. Synaptic responses mediated by NMDA receptors are best fit with rapid kinetics, suggestive of NR2A subunits as expected in mature animals. Predictions were made for passive-cell current clamp recordings, combined AMPA and NMDA receptor responses, and local dendritic depolarization in response to unitary stimulations. Models of synaptic responses in active cells suggest altered axial resistivity and the presence of synaptically activated potassium channels in spines.

A Kalman filtering approach to the representation of kinematic quantities by the hippocampal-entorhinal complex

Several regions of the brain which represent kinematic quantities are grouped under a single state-estimator framework. A theoretic effort is made to predict the activity of each cell population as a function of time using a simple state estimator (the Kalman filter). Three brain regions are considered in detail: the parietal cortex (reaching cells), the hippocampus (place cells and head-direction cells), and the entorhinal cortex (grid cells). For the reaching cell and place cell examples, we compute the perceived probability distributions of objects in the environment as a function of the observations. For the grid cell example, we show that the elastic behavior of the grids observed in experiments arises naturally from the Kalman filter. To our knowledge, the application of a tensor Kalman filter to grid cells is completely novel.

Spike-timing dependent plasticity and the cognitive map

Since the discovery of place cells – single pyramidal neurons that encode spatial location – it has been hypothesized that the hippocampus may act as a cognitive map of known environments. This putative function has been extensively modeled using auto-associative networks, which utilize rate-coded synaptic plasticity rules in order to generate strong bi-directional connections between concurrently active place cells that encode for neighboring place fields. However, empirical studies using hippocampal cultures have demonstrated that the magnitude and direction of changes in synaptic strength can also be dictated by the relative timing of pre- and post-synaptic firing according to a spike-timing dependent plasticity (STDP) rule. Furthermore, electrophysiology studies have identified persistent “theta-coded” temporal correlations in place cell activity in vivo, characterized by phase precession of firing as the corresponding place field is traversed. It is not yet clear if STDP and theta-coded neural dynamics are compatible with cognitive map theory and previous rate-coded models of spatial learning in the hippocampus. Here, we demonstrate that an STDP rule based on empirical data obtained from the hippocampus can mediate rate-coded Hebbian learning when pre- and post-synaptic activity is stochastic and has no persistent sequence bias. We subsequently demonstrate that a spiking recurrent neural network that utilizes this STDP rule, alongside theta-coded neural activity, allows the rapid development of a cognitive map during directed or random exploration of an environment of overlapping place fields. Hence, we establish that STDP and phase precession are compatible with rate-coded models of cognitive map development.

Dual coding with STDP in a spiking recurrent neural network model of the hippocampus

The firing rate of single neurons in the mammalian hippocampus has been demonstrated to encode for a range of spatial and non-spatial stimuli. It has also been demonstrated that phase of firing, with respect to the theta oscillation that dominates the hippocampal EEG during stereotype learning behaviour, correlates with an animal's spatial location. These findings have led to the hypothesis that the hippocampus operates using a dual (rate and temporal) coding system. To investigate the phenomenon of dual coding in the hippocampus, we examine a spiking recurrent network model with theta coded neural dynamics and an STDP rule that mediates rate-coded Hebbian learning when pre- and post-synaptic firing is stochastic. We demonstrate that this plasticity rule can generate both symmetric and asymmetric connections between neurons that fire at concurrent or successive theta phase, respectively, and subsequently produce both pattern completion and sequence prediction from partial cues. This unifies previously disparate auto- and hetero-associative network models of hippocampal function and provides them with a firmer basis in modern neurobiology. Furthermore, the encoding and reactivation of activity in mutually exciting Hebbian cell assemblies demonstrated here is believed to represent a fundamental mechanism of cognitive processing in the brain.

Changes in the strength of synaptic connections between neurons are believed to mediate processes of learning and memory in the brain. A computational theory of this synaptic plasticity was first provided by Donald Hebb within the context of a more general neural coding mechanism, whereby phase sequences of activity directed by ongoing external and internal dynamics propagate in mutually exciting ensembles of neurons. Empirical evidence for this cell assembly model has been obtained in the hippocampus, where neuronal ensembles encoding for spatial location repeatedly fire in sequence at different phases of the ongoing theta oscillation. To investigate the encoding and reactivation of these dual coded activity patterns, we examine a biologically inspired spiking neural network model of the hippocampus with a novel synaptic plasticity rule. We demonstrate that this allows the rapid development of both symmetric and asymmetric connections between neurons that fire at concurrent or consecutive theta phase respectively. Recall activity, corresponding to both pattern completion and sequence prediction, can subsequently be produced by partial external cues. This allows the reconciliation of two previously disparate classes of hippocampal model and provides a framework for further examination of cell assembly dynamics in spiking neural networks.

Forward shift from reverse replay

In a recent experimental paper Lee et al. (Neuron 51:639-650, 2006) showed that the firing patterns of CA1 complex-spike neurons gradually shifted forward across trials toward prospective goal locations within a recording session over multiple trials. Here we propose a simple model of this result based on the phenomenon of awake sequence reverse replay (Foster and Wilson, Nature 440(7084):615-617, 2006) which occurs when the animal pauses at the reward location. The model is based on the CA3-CA1 anatomy with modulation of CA3-CA1 synaptic plasticity by feedback from CA3 projecting CA1 interneurons. Sequence replays, which are generated in CA3 by removal of subcortical inhibition on CA1 interneurons, are recoded into the synaptic weights of individual CA1 cells. This produces spatially extended CA1 firing fields, whose response provides a value function on experienced paths toward goal locations. Simulations show that the CA1 firing fields show positive movement in center of mass toward reward locations over many trials with negative shift in first few trials, and development of positive skew.