Elsevier

Neural Networks

Volume 20, Issue 2, March 2007, Pages 182-193
Neural Networks

Space, time and learning in the hippocampus: How fine spatial and temporal scales are expanded into population codes for behavioral control

https://doi.org/10.1016/j.neunet.2006.11.007Get rights and content

Abstract

The hippocampus participates in multiple functions, including spatial navigation, adaptive timing and declarative (notably, episodic) memory. How does it carry out these particular functions? The present article proposes that hippocampal spatial and temporal processing are carried out by parallel circuits within entorhinal cortex, dentate gyrus and CA3 that are variations of the same circuit design. In particular, interactions between these brain regions transform fine spatial and temporal scales into population codes that are capable of representing the much larger spatial and temporal scales that are needed to control adaptive behaviors. Previous models of adaptively timed learning propose how a spectrum of cells tuned to brief but different delays are combined and modulated by learning to create a population code for controlling goal-oriented behaviors that span hundreds of milliseconds or even seconds. Here it is proposed how projections from entorhinal grid cells can undergo a similar learning process to create hippocampal place cells that can cover a space of many meters that are needed to control navigational behaviors. The suggested homology between spatial and temporal processing may clarify how spatial and temporal information may be integrated into an episodic memory. The model proposes how a path integration process activates a spatial map of grid cells. Path integration has a limited spatial capacity, and must be reset periodically, leading to the observed grid cell periodicity. Integration-to-map transformations have been proposed to exist in other brain systems. These include cortical mechanisms for numerical representation in the parietal cortex. As in the grid-to-place cell spatial expansion, the analog representation of number is extended by additional mechanisms to represent much larger numbers. The model also suggests how visual landmarks may influence grid cell activities via feedback projections from hippocampal place cells to the entorhinal cortex.

Introduction

The multitude of seemingly independent behavioral functions carried out by the hippocampal system has attracted intense interest from researchers. Several of the most studied functions are the following: (1) The role of the hippocampal system in spatial navigation has been of special interest since O’Keefe and Dostrovsky (1971) showed the spatial correlates of pyramidal cell firing in the hippocampus. These cells tend to fire in a specific portion of the environment (place) independently of the head direction and movement speed, hence the term place cells. How place cells are formed has attracted even more interest since the recent discovery of grid cells (Hafting, Fyhn, Molden, Moser, & Moser, 2005) within entorhinal cortical circuits that project to the hippocampus. (2) The role of the hippocampus in classical conditioning is limited to certain experimental paradigms that require temporal integration over a delay period; e.g. trace conditioning and sufficiently delayed non-matching to sample, and is crucial for adaptive timing of the conditioned response (Berger and Thompson, 1978, Eichenbaum et al., 1994). (3) Another function that was first highlighted by studies of patient HM (Scoville & Milner, 1957) is the role of the hippocampal system in declarative memory, especially in episodic memory. Eichenbaum, Dudchenko, Wood, Shapiro, and Tanila (1999) suggested that each episode in memory consists of a specific spatiotemporal combination of stimuli and behavior and discussed the evidence supporting this claim.

While these functions are often studied independently and in different species, there is no reason to believe that they are, in fact, independent. Spatial information and temporal information are crucial parts of an episode, and may be used to form an episodic memory. This paper focuses on hippocampal spatial and temporal processing and proposes that these are parallel computations performed within the same system by circuits that are sufficiently homologous to be considered variations of the same design.

The adaptive timing model of Grossberg and colleagues (Grossberg and Merrill, 1992, Grossberg and Merrill, 1996, Grossberg and Schmajuk, 1989) proposed how the dentate gyrus (DG) and hippocampal field CA3 may interact to learn adaptively timed behavioral responses (e.g., Gibbon (1977), Roberts, Cheng, and Cohen (1989), Smith (1968)) and neurophysiological cell activations (Berger et al., 1986, Berger et al.and Thompson, 1980, Hoehler and Thompson, 1980) during classical and instrumental conditioning. Here we introduce a model of spatial processing that describes how the same DG–CA3 circuits may also learn place fields for spatial localization. Grossberg et al. proposed a circuit to bridge a temporal interval that can span up to several seconds, and showed how this circuit could learn to adaptively time responses within this interval. A homologous spatial circuit is described herein that can similarly expand the range of positions and distances that can be represented, up to many meters, but instead of providing the information in the form of “now is the time…”, it signals that “here is the place…”.

The spatial case is in general more complex than the temporal, but it is more easily compared with the latter by the following simplifying assumptions. First, assume that the spatial environment is one-dimensional. Second, assume that the movement always proceeds in one direction. Finally, assume that the movement speed is constant. Under these assumptions, the spatial position of the animal is linearly dependent on time from the trial onset. Experimental evidence supports the link between time and spatial properties of place cells. For example, Redish, Rosenzweig, Bohanick, McNaughton, and Barnes (2000) has shown that the elapsed time since leaving the start box on the 1D linear track is a good predictor of the place field realignment on a variable length track. Nevertheless, building the theory under all three assumptions would be overly simplistic. Thus we replace the last two assumptions by assuming that an appropriate path integration (PI) system is in place and provides the input to the model presented herein.

Behavioral studies showed the existence of a PI system in mammals (Mittelstaedt & Mittelstaedt, 1982) and PI happens at least partially outside the hippocampus (Alyan, Paul, Ellsworth, White, & McNaughton, 1997). On the other hand, the hippocampus is involved in navigation based upon integration of idiothetic information, since a fornix lesion disrupts this type of navigation (Whishaw & Gorny, 1999). A PI system by definition should accommodate for changes in an animal’s velocity and direction, and provide some measure of distance between the place where the trial started and the current location of the animal. Such a spatial output is similar to the output of a time integration system that records the time between the trial onset and the current moment.

Both spatial and temporal representational systems need to solve the following problem. The brain builds representations and guides behavior over spatial scales of many meters and temporal scales of many seconds, while many individual neurons operate on much smaller spatial and temporal scales. One approach to solving this problem is to use a population code for space and time that combines a limited number of integrators with fixed but different spatial or temporal periods. These fixed periods can span a spectrum of spatial or temporal scales, and indeed the Grossberg et al. model of adaptively timed learning is called the spectral timing model. This paper investigates how a representation of space that is much larger than any individual scale of the spectrum can be built by combining several spatial scales in a manner that strikingly resembles the circuitry that has been proposed for spectral timing; see Fig. 1.

In the spatial domain, the recent exciting discovery of grid cells in the entorhinal cortex (EC) by Hafting et al. (2005) casts a new light on the input signals that can lead to adaptive formation of the large behavioral scales that are needed for navigation. This paper shows how a proper combination of multiple scales of grid cells leads to formation of hippocampal place cells through two stages of converging inputs, as shown in Fig. 1.

In the first stage of a spectral timing model, multiple cue cell outputs from the entorhinal cortex converge on cells in the dentate gyrus. Different DG cells are tuned to respond to different temporal delays along a spatial gradient in a septo-temporal direction (Nowak & Berger, 1992). Such a gradient of temporal delays may be implemented within EC–DG projections by using a gradient of different Ca++ concentrations that influence metabotropic glutamate receptors (mGluR) across the cells in the gradient (Fiala et al., 1996, Grossberg and Merrill, 1992, Grossberg and Merrill, 1996).

An analogous gradient of spatial coordinates can be based on entorhinal grid cells. Hafting et al. (2005) reported that there exists a gradient of spatial periods, or scales, of grid cells in EC that is aligned with the dorso-ventral EC axis. Spatial scale increases from 40 cm at the most dorsal recording sites to 70 cm in the most ventral sites (Hafting et al., 2005). The dorso-ventral gradient of grid cells’ periods instantiates the spectrum of spatial scales. To further clarify the analogy between the spatial and temporal model, note that there is a topology in the projections from EC to DG such that the dorsolateral band of EC projects more to the septal end of the DG while the ventromedial band of EC projects more to the temporal end of DG (Burwell & Amaral, 1998). Thus the dorso-ventral gradient in EC corresponds to the septo-temporal gradient in DG. Within each spatial scale, grid cells have various orientations of the grid and shifted grid positions. According to these results, for a specific orientation, about five evenly shifted grid cells are sufficient to cover the space without gaps. The model presented here thus uses five cells per spatial scale. This is represented in the sketch of the first stage of the spatial model in Fig. 2. When the animal moves through the environment, different grid cells from each spatial scale are periodically active. Multiple grid cell outputs from the entorhinal cortex converge on cells in the dentate gyrus.

The spatial model outlined in Fig. 1, Fig. 2 can be called a spectral spacingmodel by comparison with its homologous spectral timing model. We show here how a spectral spacing model can, through a two stage entorhinal-dentate-CA3 network, expand the spatial scale of grid cells in a manner analogous to how the spectral timing model expands the temporal scale through its parallel entorhinal-dentate-CA3 network. Previous simulations (e.g. by Fuhs and Touretzky (2006)) showed that the combination of several spatial scales leads to a unique spatial representation over an expanded spatial interval much larger than the period of any of the individual spatial scales of entorhinal grid cells. The spectral spacing model presented herein not only replicates these results, but also provides a first theoretical explanation of why and how this expansion occurs.

In the second stage of a spectral timing model, output of DG cells with a fixed preferred delay, or temporal phase, converge on hippocampal CA3 cells (see Fig. 1) to form a full temporal spectrum that can span a behavioral time scale of hundreds of milliseconds or seconds. In the second stage of a spectral spacing model, DG cells with a fixed preferred spatial phase, as explained below, provide signals that converge on hippocampal CA3 cells to form a full spatial spectrum that can span a behavioral spatial scale of many metres.

Section snippets

Multiple spatial scales

Here we propose a mechanism for how dentate gyrus granule cells receive inputs from several nearby spatial scales in the entorhinal cortex and learn to combine these inputs to generate place cells that operate on a much larger spatial scale than individual grid cells. Fuhs and Touretzky (2006) showed to some extent that combining input from multiple spatial scales does lead to unique place fields. However, they did not analyze: (1) how the synaptic connectivity between grid cells and place

Results

The results of the first and second simulations are presented in Fig. 3a–d. They show that the periodicity of the model dentate granule cell activities follow the theoretically calculated period. Only 10 out of 25 cells show place fields for entorhinal input with periods 40 and 50 cm (Fig. 3b). All 25 cells show place fields when fed with entorhinal input with periods of 44 and 52 cm (Fig. 3d). One fifth of these place fields (fields 3, 10, 12, 19, and 21) show two peaks in different parts of

Discussion

The results of the first two simulations show that the spatial expansion was performed according to theoretical predictions. In the case of 40 and 50 cm spatial scales, only 10 cells have reliable place fields, while with scales 44 and 52 cm, all 25 cells had reliable place fields. In both cases, only about one-half of the expanded spatial interval was covered by place fields, while the other half was only marked by individual spikes that can be considered spontaneous firing. Since the size of

Acknowledgements

Stephen Grossberg was supported in part by the National Science Foundation (SBE-0354378) and the Office of Naval Research (N00014-01-1-0624). Anatoli Gorchetchnikov was supported by the National Science Foundation (SBE-0354378).

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