Cognitive Map Formation Through Sequence Encoding by Theta Phase Precession
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LETTER Communicated by A. David Redish Cognitive Map Formation Through Sequence Encoding by Theta Phase Precession Hiroaki Wagatsuma [email protected] Laboratory for Dynamics of Emergent Intelligence, RIKEN BSI, Wako-shi, Saitama 351-0198, Japan Yoko Yamaguchi [email protected] Laboratory for Dynamics of Emergent Intelligence, RIKEN BSI, Wako-shi, Saitama 351- 0198, Japan; College of Science and Engineering, Tokyo Denki University, Hatoyama, Saitama 350-0394, Japan; and CREST, Japan Science and Technology Corporation The rodent hippocampus has been thought to represent the spatial en- vironment as a cognitive map. The associative connections in the hip- pocampus imply that a neural entity represents the map as a geometrical network of hippocampal cells in terms of a chart. According to recent experimental observations, the cells fire successively relative to the theta oscillation of the local field potential, called theta phase precession, when the animal is running. This observation suggests the learning of temporal sequences with asymmetric connections in the hippocampus, but it also gives rather inconsistent implications on the formation of the chart that should consist of symmetric connections for space coding. In this study, we hypothesize that the chart is generated with theta phase coding through the integration of asymmetric connections. Our computer experiments use a hippocampal network model to demonstrate that a geometrical network is formed through running experiences in a few minutes. Asymmetric connections are found to remain and dis- tribute heterogeneously in the network. The obtained network exhibits the spatial localization of activities at each instance as the chart does and their propagation that represents behavioral motions with multidirec- tional properties. We conclude that theta phase precession and the Heb- bian rule with a time delay can provide the neural principles for learning the cognitive map. 1 Introduction The rodent hippocampus stores information concerning environmental space. According to the cognitive map theory of O’Keefe and Nadel (1978), an entire environment is represented by the population activities of hip- Neural Computation 16, 2665–2697 (2004) c 2004 Massachusetts Institute of Technology Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/0899766042321742 by guest on 26 September 2021 2666 H. Wagatsuma and Y. Yamaguchi pocampal cells. When an animal is in a specific portion of an environment, a “place cell” fires (O’Keefe & Dostrovsky, 1971). The portions of these in- dividual place cells, called place fields, are distributed over the entire en- vironment. After a brief exploration of an environment (about 10 minutes), pyramidal cells in the CA3 and CA1 regions of the hippocampus exhibit firing preferences based on the animal’s location (Wilson & McNaughton, 1993). This means that place cells for a new location are quickly established, and the geometry of the new environment soon becomes familiar. It is im- portant to understand how the hippocampus acquires the cognitive map after such a short running experience. The neural basis of hippocampal learning was theoretically proposed by Marr (1971) as a framework of an associative memory. After that, several theoretical models of hippocampal associative memory were proposed (Mc- Naughton & Morris, 1987; McNaughton, 1989; McNaughton & Nadel, 1989; Rolls, 1989). In this framework, Muller and his colleagues (Muller, Kubie, & Saypoff, 1991; Muller, Stead, & Pach, 1996) proposed that simultaneous firing of place cells forms a network where these cells have strong synap- tic connections with neighboring place fields. Accordingly, the geometric network of place cells, called a chart, represents the environment through a spatial relationship among place cells. Such a chart formation was demon- strated by K´ali and Dayan (2000). The strength of the connection between a pair of place cells represents the distance between two corresponding loca- tions in the environment. Associative connections in the CA3 region serve as the functional basis of a cognitive map during spatial navigation, providing neural activities that are spatially localized in the chart. Recently, Nakazawa et al. (2002) experimentally confirmed that recurrent connections of pyra- midal cells in the CA3 region serve as associative memory by using mutant mice with the ablated NMDA receptor gene specifically in the CA3 region. These studies on the cognitive map are in line with the traditional Hebbian learning rule. Several recent studies of synaptic plasticity and neural dynamics in the hippocampus suggest the importance of asymmetric connections in mem- ory encoding of the temporal sequence. O’Keefe and Recce (1993) discovered theta phase precession, which is an advancement of a place cell’s firing phase relative to the cycle of the theta rhythm (around 8 Hz) in the hippocampus as a rat goes through the place field. By using parallel recordings of the place cells, Skaggs, McNaughton, Wilson, and Barnes (1996) demonstrated that the phase precession is not only the phase advancement of individual cells, but also retains the robust phase difference in the firing of a population of cells. The firings with phase differences represent a behavioral sequence in a compressed form within each theta cycle. According to the results of Skaggs et al. (1996), the phase difference in place cells has a timescale similar to the asymmetric time window of synaptic plasticity in pyramidal cells. There- fore, they suggested that theta phase precession enables memory encoding of the behavioral temporal sequence in asymmetric connections. Rosen- Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/0899766042321742 by guest on 26 September 2021 Cognitive Map Formation by Theta Phase Precession 2667 zweig, Ekstrom, Redish, McNaughton, and Barnes (2000) observed theta phase precession in a novel environment, which suggested its contribution to the initial stage of the learning process. The asymmetric time window of synaptic plasticity in pyramidal cells was discovered in the tetanic stimulus condition (Levy & Steward, 1983; Larson & Lynch, 1989) and was further clarified in the relative timing of individual spikes (Bi & Poo, 1998). When the presynaptic neuron fires 50 msec before the postsynaptic neuron, the synapse is enhanced though long- term potentiation (LTP). The reverse timing depresses the synapse though long-term depression (LTD). This asymmetric property in synaptic plasticity enables memory storage through the firing order in the form of asymmetric connections. Yamaguchi (2003) proposed a hippocampal model of memory encoding that used theta phase precession, which encoded one-time experience into the recurrent network in the CA3 region (Yamaguchi & McNaughton, 1998). According to experimental evidence (Skaggs et al., 1996; Yamaguchi, Aota, McNaughton, & Lipa, 2002), theta phase precession is assumed to appear in the entrance of the hippocampus. The phase precession is inherited by the CA3 region and conducts temporal coding of the rat’s behavioral sequences into asymmetric connections among the cells. The theoretical model enables memory encoding with a variety of timescales of the temporal sequence (Sato & Yamaguchi, 2003) and a variety of spatiotemporal patterns (Wu & Yamaguchi, 2004). The question is whether sequence learning based on theta phase preces- sion in the presence of asymmetric synaptic plasticity can be extended to other hippocampal memories. The consideration of asymmetric synapses and theta phase precession in the cognitive map was developed by Redish and Touretzky (1998), and this theory consisted of two stages. One was for chart formation and the other separate for route learning. The chart for- mation follows the associative memory with symmetric connections, and theta phase precession is applied to route learning after the chart forma- tion. It results in the embedding of asymmetric connections encoding se- quence memory into the symmetric network of the chart formed before. They concluded that these two could coexist in the hippocampal network. Samsonovich and McNaughton (1997) also studied theta phase precession in the cognitive map. In their model, a chart with symmetric connections is assumed to be in accordance with previous studies. The phase precession during running is generated by an asymmetric property in the extrahip- pocampal layer encoding the direction of motion. In these studies, the chart formation is still within the framework of the associative memory with sym- metric connections and is independent of the experimental evidence for the synaptic plasticity of asymmetric connections. The purpose of this study is to elucidate roles of theta phase precession in chart formation and spatial representation. We reported that it was possible for a hippocampal network model with theta phase precession to gener- Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/0899766042321742 by guest on 26 September 2021 2668 H. Wagatsuma and Y. Yamaguchi ate the geometrical network of the CA3 region (Wagatsuma & Yamaguchi, 1999, 2000). Our computer experiments are devoted to clarifying how the asymmetric property of synaptic plasticity contributes to the formation and other computational functions of the cognitive map. 2 Hypothesis We hypothesize that theta phase precession provides memory encoding of the temporal sequence of a behavioral experience into asymmetric connec- tions of the CA3 region, and that the one-dimensional network encoding of