Models of hippocampus

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Author: Dr. Michael E. Hasselmo, Center for Memory and Brain, Boston University, Boston, MA

This is article is a draft in preparation.

Models of hippocampus simulate physiological phenomena or behavioral functions of the hippocampus, using the techniques of computational neuroscience.

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Anatomical overview

The hippocampus is a three-layered cortical structure at the border of the neocortex that receives afferent input from cortical regions processing a range of sensory modalities. This input arrives via the entorhinal cortex and other parahippocampal regions. The output of the hippocampus projects back to parahippocampal cortices primarily via the subiculum and projects to subcortical structures via the fornix. Models of hippocampus commonly include representations of neuron function within different subregions of the hippocampal formation, including the entorhinal cortex, the dentate gyrus, and cornu ammonis regions CA3 and CA1. There is less focus on region CA4 (consisting of cells in the hilus of the dentate gyrus) and CA2 (consisting of neurons receiving both Schaffer collateral and mossy fiber input).

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Types of models

Models of hippocampus range across many levels of abstractions. These include:

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Behavioral functions

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Human memory function

Models of hippocampus address the role of hippocampus in encoding and retrieval of information for a range of different memory-guided behaviors in humans and other animals. Many models were motivated by the effect of damage to the hippocampus by ischemia or encephalitis (Eichenbaum and Cohen, 2003), and by the bilateral removal of the anterior hippocampus in patient HM. Damage to the hippocampus in human subjects causes severe impairments for encoding of new episodic memory. In humans, hippocampal lesions cause impairments of performance on memory tasks including free recall and cued recall of paired associates (Eichenbaum and Cohen, 2003). Lesions also appear to impair recollection-based recognition, with less effect on familiarity based recognition memory. Hippocampal lesions have little effect on priming and perceptual memory.

“’Models of hippocampus’” using rate code models of neurons have explicitly modeled performance on free recall and cued recall (Hasselmo and Wyble, 1997) as well as performance in recollection-based recognition (Norman and O’Reilly, 2000). Few models have addressed the complex features of episodic memory such as the sense of reliving a full series of events, but Recent Some models have addressed complex features of episodic memory including the episodic encoding and retrieval of sequences (Jensen and Lisman, 1996a; Lisman, 1999) or complex spatial trajectories (Hasselmo, 2008).

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Rat memory function

In rats, hippocampal lesions cause impairments in a range of different tasks. These include impairments in tasks requiring memory of spatial locations, such as the *Morris water maze, the *8-arm radial maze, as well as delayed spatial alternation and spatial reversal. These also include impairments in non-spatial tasks requiring relational memory such as the transitivity and transitive inference tasks and tasks requiring aspects of sequence memory such as the order of items in a list (Kesner et al., 2002) or the end of overlapping lists (Agster et al., 2002). Hippocampal lesions also impair trace conditioning in classical conditioning paradigms.

Models of hippocampus using firing rate models of neurons have been developed to simulate rat behavior for goal-directed behavior in the open field (Muller and Stead, 1996; Burgess et al., 1997), and simulations of memory-guided behavior in the Morris water maze (Redish and Touretzky, 1998) as well as spatial alternation (Hasselmo and Eichenbaum, 2005). Other models have addressed the role of the hippocampus in trace conditioning (Rodriguez and Levy, 2000) and other conditioning phenomena (Grossberg and Schmajuk, 1989; Schmajuk and DiCarlo, 1992; Gluck and Myers, 1993). See review in Computational models of classical conditioning. Spiking models of hippocampus have also modeled rat behavior (Gerstner and Abbott, 1997).

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Function of hippocampal subregions

Models of hippocampus have addressed the potential function of individual hippocampal subregions. These include the following:

  • Pattern separation in dentate gyrus.
  • Pattern completion in region CA3.
  • Comparison of retrieval with input in region CA1.
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Pattern separation in dentate gyrus

Starting with the seminal modeling work of David Marr (Marr, 1971), the denate gyrus has been proposed to enhance the encoding of new memories by performing pattern separation. This process has been referred to as orthogonalization because it reduces the magnitude of the dot product between any two given input vectors of neural activity. The mechanisms and role of this pattern separation was described again in later studies (McNaughton and Morris, 1987; Treves and Rolls, 1994; O’Reilly and McClelland, 1994; Hasselmo and Wyble, 1997). This orthogonalization is proposed to occur by an increase in sparseness of neural activity as patterns spread from about 250,000 neurons in entorhinal cortex to 1 million neurons in dentate gyrus (McNaughton, 1991).

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Pattern completion or sequence readout in region CA3

Another component of David Marr’s model (Marr, 1971) consisted of autoassociative encoding of input patterns based on the extensive excitatory recurrent connections of the longitudinal association pathway arising from region CA3 pyramidal cells and terminating in stratum radiatum of CA3 on the dendrites of other CA3 pyramidal cells. Hebbian synaptic modification of excitatory recurrent synapses during encoding allows pattern completion during later retrieval. During retrieval, a partial cue consisting of a subset of active neurons causes activity to spread across previously modified synapses, resulting in a pattern of activity more closely matching the originally encoded pattern. This basic mechanism of autoassociative memory function has been central to many models of region CA3. McNaughton and Morris (1987) described the role of recurrent connections for both autoassociative pattern completion as well as encoding of associations between a pattern at one time and the subsequent pattern at a later time step. The encoding and retrieval of sequences in region CA3 has been extensively modeled with simplified spiking neurons (Levy, 1996; Lisman, 1999). Multiple cycles of the spread of excitatory activity can result in explosive activity unless it is balanced by inhibitory feedback, in which case the network can converge to an attractor state matching the initial encoded memory pattern. Attractor dynamics in region CA3 have been used for retrieval of encoded memory patterns in a range of hippocampal models (Treves and Rolls, 1992, 1994; Hasselmo et al., 1995; Hasselmo and Wyble, 1997; Norman and O’Reilly, 2003). As noted below, attractor dynamics in CA3 have also been used to model place cell activity (Samsonovich and McNaughton, 2002).

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Comparison of retrieval with input in region CA1

The function of region CA1 is less clear, as it receives primarily feedforward input from region CA3 and medial entorhinal cortex layer III and has little recurrent connectivity. Some models have proposed that region CA1 functions as a comparator of the input from entorhinal cortex layer III with the output from region CA3 (Gray, 1982). This comparator function was used to set the levels of acetylcholine to modulate the dynamics of encoding and retrieval in a simulation of region CA1 (Hasselmo and Schnell, 1994) and in a network simulation of hippocampal memory function (Hasselmo and Wyble, 1997).

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Physiological phenomena

Models of hippocampus address several important physiological phenomena observed within the hippocampus. These physiological phenomena include:

  • long-term potentiation and long-term depression of synaptic strength
  • Intrinsic neuron properties including bursting and adaptation
  • Spiking activity during performance of behavioral tasks
  • Local field potential dynamics
  • Interactions of spiking and local field potentials
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Long-term potentiation and depression

The properties of synaptic modification in the hippocampus constitute an essential component of most hippocampal models. In particular, considerable research focuses on the dependence of synaptic modification on the combination of presynaptic and post-synaptic activity. Modification dependent on presynaptic and postsynaptic activity is referred to as Hebbian. Activation of the NMDA receptor depends upon presynaptic glutamate release and postsynaptic depolarization, and plays an important role in many forms of Hebbian long-term potentiation. The timing properties of the NMDA receptor appear to result in a requirement for a tight timing relationship between presynaptic spikes and post-synaptic activity (Levy and Steward, 1983; Holmes and Levy, 1990). This requirement has been shown in a number of subsequent studies (Bi and Poo, 1998) and is referred to currently as spike timing dependent plasticity (STDP). Many synaptic models address the mechanisms of long-term potentiation and depression. Specific models address the role of molecular pathways in regulating synaptic strength, including the role of bistability of autophosphorylation (Lisman, 1989), or the role of different concentrations of calcium induced by different patterns of input. Many models have addressed the potential cellular mechanisms for spike timing dependent plasticity.

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Intrinsic properties

Biophysically detailed models of cells in the hippocampal formation have explored the cellular mechanisms for spiking properties of the hippocampus, including phenomena such as Bursting and spike-frequency accommodation or adaptation. Biophysically detailed compartmental models of single cells using Hodgkin-Huxley equations have demonstrated potential cellular mechanisms for bursting activity and adaptation (Traub et al., 2000). The dynamics of these intrinsic spiking properties have also analyzed in simplified models (Izhikevich, 2003).

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Spiking activity in behaving animals

Hippocampal models have addressed physiological data showing correlations between hippocampal spiking activity and a number of different variables of behavior. For example, models have addressed the appearance of place cells in the hippocampus (O’Keefe and Nadel, 1978). These are neurons that fire in a highly localized manner within the environment. Early models showed how these could arise from competitive self-organization of inputs from sensory cues (Sharp, 1990) or from error-correcting rules guiding formation of place cells. Later models have addressed how they could arise from the properties of grid cells in the entorhinal cortex, that provides afferent input to the hippocampus (Solstad et al. 2006; McNaughton et al., 2006). A number of models have addressed the potential mechanisms for the generation of grid cell firing responses (McNaughton et al., 2006; Fuhs and Touretzky, 2006; Burgess et al., 2007; Giocomo et al., 2007). Models have also demonstrated how spiking activity can depend upon variables other than current location, including the presence of specific sensory stimuli or on prior history (Hasselmo and Eichenbaum, 2005). An important model of the effects of Hebbian synaptic plasticity (Blum and Abbott, 1996) generated the experimentally verified prediction that the firing fields of place cells should shift backward with experience (Mehta et al., 2002).

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Local field potential dynamics

Hippocampal models have also addressed properties of the oscillatory dynamics of the hippocampal formation measured by electroencephalographic recordings of the local field potential. In particular, during active movement through the environment, the hippocampus shows prominent activity in the theta frequency band, with a peak in the power spectra around 6 to 7 Hz (Buzsaki, 2002). In anesthetized rats some of the same mechanisms contribute to oscillations around 3-4 Hz that are also referred to as theta rhythm. The mechanisms of theta rhythm have been modeled as due to feedback interactions between the medial septum and hippocampus (Denham and Borisyuk, 2000). Current source density data shows a systematic change in magnitude of synaptic transmission in different layers during each cycle of the hippocampal theta rhythm. Models have addressed the phase shift that occurs in the transition from stratum lacunosum-moleculare to stratum radiatum to stratum pyramidale (Leung, 1984). The shift in phase of synaptic input could provide dynamics appropriate for encoding of associations, with a dominant influence of entorhinal input and the induction of LTP, to dynamics appropriate for retrieval of associations, with a dominant influence of CA3 input and no induction of LTP (Hasselmo et al., 2002).

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Interaction of spiking and local field potentials

The spiking activity of the hippocampus shows clear relationships to local field potential oscillations. In particular, the firing of place cells on a linear track shows a systematic change in phase of firing relative to theta rhythm oscillations (O’Keefe and Recce, 1993; Skaggs et al., 1996). When the rat first enters the field of firing of a place cell, the spiking occurs at late phases, and then it shifts to earlier theta phases as the rat moves through the place field. This phenomenon is referred to as theta phase precession. A number of models have addressed theta phase precession using different mechanisms. These can be grouped into three broad categories:

  • Phase precession from sequence readout. In these models, each location cues the retrieval of a sequence of place cell spiking activity due to Hebbian modification of associations between place cells firing to adjacent locations (Tsodyks et al., 1996; Jensen and Lisman, 1996a; Wallenstein and Hasselmo, 1997).
  • Phase precession from oscillatory interference. In these models, precession arises from interference between oscillators with different frequency. This can involve interference of intrinsic oscillations with network oscillations (O’Keefe and Recce, 1993; Lengyel et al., 2003) or between oscillations in different groups of neurons (Bose et al., 2000).
  • Phase precession from progressive change in depolarization relative to network theta. In these models, precession arises from a gradual change in depolarization that results in spiking at a different phase of theta (Kamondi et al., 1998; Mehta et al., 2002).
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Summary

“’Models of hippocampus’” have addressed experimental phenomena at a levels ranging from the detailed membrane potential dynamics of hippocampal neurons, to the spiking activity in awake, behaving animals, to the role of hippocampus in memory-guided behavior. Future models will focus on linking the data on these different levels to provide constraints for a complete model of the physiological mechanisms of hippocampal function.

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References

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  • Skaggs, W. E., McNaughton, B. L., Wilson, M. A., and Barnes, C. A. (1996). Theta phase precession in hippocampal neuronal populations and the compression of temporal sequences. Hippocampus 6, 149-172.
  • Solstad, T., Moser, E.I., Einevoll, G.T. (2006) From grid cells to place cells: a mathematical model. Hippocampus 16, 1026-1031.
  • Traub, R., Wong, R.K., Miles, R., Michelson, H. (1991) A model of a CA3 hippocampal pyramidal neuron incorporating voltage-clamp data on intrinsic conductance’s. J. Neurophysiol. 66: 635-650.
  • Treves, A., and Rolls, E. T. (1992). Computational constraints suggest the need for two distinct input systems to the hippocampal CA3 network. Hippocampus 2, 189-199.
  • Treves, A., and Rolls, E. T. (1994). Computational analysis of the role of the hippocampus in memory. Hippocampus 4, 374-391.
  • Tsodyks, M. V., Skaggs, W. E., Sejnowski, T. J., and McNaughton, B. L. (1996). Population dynamics and theta rhythm phase precession of hippocampal place cell firing: a spiking neuron model. Hippocampus 6, 271-280.
  • Wallenstein, G. V., and Hasselmo, M. E. (1997). GABAergic modulation of hippocampal population activity: sequence learning, place field development, and the phase precession effect. J Neurophysiol 78, 393-408.
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Further reading

  • * Hasselmo, M.E. (2008b) Temporally structured replay of neural activity in a model of entorhinal cortex, hippocampus and postsubiculum. Eur J Neurosci, 28, 1301-1315. PDF
  • Hasselmo, M.E. and McClelland, J.L. (1999) Neural models of memory. Curr. Opinion Neurobiol. 9: 184-188. PDF
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See also

Hodgkin-Huxley model, Integrate-and-fire neuron, Wilson-Cowan model, Connectionist models,Hippocampus,Memory

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External links

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