Models of hippocampus
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 cortical input arrives via the entorhinal cortex and other parahippocampal regions. The hippocampus also receives GABAergic, cholinergic and glutamatergic innervation from the medial septum and related subcortical structures as well as innervation arising from midbrain neurons containing norepinephrine, dopamine and serotonin. 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 as well as the regulatory inputs from subcortical structures. 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).
Types of models
Models of hippocampus range across many levels of abstractions. These include:
- Models of networks of biophysically detailed neurons using conductance-based models and compartmental models of membrane potential dynamics coupled with representations of voltage-gated conductances using the Hodgkin-Huxley model or other representations.
- Spike time models of the hippocampus using mechanisms such as the Integrate-and-fire neuron or other simplified spiking models.
- Firing rate models (or rate code models) of hippocampal function using simplified units with continuous values representing the firing rate per unit time. These include models using the Wilson-Cowan model or sigmoid input-output functions with winner-take-all dynamics. Firing rate models include a number of different classes of models addressing hippocampal dynamics and the role of the hippocampus in memory function and goal-directed behavior. Connectionist models of the hippocampus address memory function and goal-directed behavior with simplified learning rules based on Hebbian modification or error correction. Other functional models assume specific response patterns such as place cells and predict behavioral results such as goal-directed behavior on this basis. Some models of the hippocampus attempt to infer quantitative relations between structural and biophysical traits and parameters on the one hand and functional measures on the other, in domains not yet accessible to direct experimentation
Human memory function
Models of hippocampus address the role of hippocampus in encoding and retrieval of information for a range of different behaviors guided by memory in humans and other animals. Many models were motivated by the effect of damage to the hippocampus by the bilateral removal of the anterior hippocampus in patient HM (Scoville and Milner, 1957) or by ischemia or encephalitis (Zola-Morgan et al., 1986; Eichenbaum and Cohen, 2003). 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 (Scoville and Milner, 1957; Graf et al., 1984; 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, 2003). The definition of episodic memory includes a sense of reliving a series of events. This can be modeled as encoding and retrieval of a sequence of patterns (Jensen and Lisman, 1996a; Tsodyks et al., 1996; Wallenstein and Hasselmo, 1997; Lisman, 1999) or of a complex spatiotemporal trajectory associated with specific items or events (Hasselmo, 2009). Many early theories addressed the role of the hippocampus in tying together diverse sensory information (Teyler and DiScenna, 1986; Teyler and Rudy, 2007).
“Models of hippocampus” have also simulated temporally graded retrograde amnesia (Alvarez and Squire, 1994; McClelland et al., 1995), in which only recent episodic memories appear to be impaired by hippocampal lesions. In these models, episodic associations are initially formed in the hippocampal formation. These hippocampal associations are then reactivated during quiet waking or slow wave sleep, allowing training of long-term representations in the neocortex.
Rat memory-guided behavior
In rats, hippocampal lesions cause impairments of memory-guided behavior 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 (Eichenbaum and Cohen, 2003) 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 representations of neurons have been developed to simulate goal-directed behavior in rats. These models start with representations of place cell firing as a basis for goal-directed planning in a number of tasks, including the open field (Muller and Stead, 1996; Touretzky and Redish, 1996; Burgess et al., 1997), the Morris water maze (Redish and Touretzky, 1998; Foster et al., 2000) as well as spatial alternation (Hasselmo and Eichenbaum, 2005) and a multiple-T choice task (Johnson and Redish, 2005). Some of the models of goal-directed behavior have used replay of previously experienced spiking activity to more rapidly build the representations of the environment for goal-directed behavior (Johnson and Redish, 2005; Foster and Wilson, 2006).
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).
Function of hippocampal subregions
“Models of hippocampus” have addressed the potential function of individual hippocampal subregions. The following subregions will be addressed:
- Dentate gyrus.
- Region CA3.
- Region CA1.
- Medial septum.
- Entorhinal cortex.
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. This reduces the interference between patterns when an incomplete cue triggers retrieval of a complete stored pattern. The mechanisms and role of this pattern separation was analyzed further in later studies (McNaughton and Morris, 1987; Treves and Rolls, 1994; O’Reilly and McClelland, 1994; Hasselmo and Wyble, 1997). This orthogonalization was proposed to occur by an increase in sparseness of neural activity as patterns spread from about 250,000 neurons in rat entorhinal cortex to 1 million neurons in dentate gyrus (McNaughton, 1991). The separation of patterns can also benefit from synaptic modification of inputs to dentate gyrus generating self-organization of distinct, random representations (Treves and Rolls, 1994; O’Reilly and McClelland, 1994; Hasselmo and Wyble, 1997; Treves et al., 2008). The dentate gyrus has also been modeled as a latent attractor regulating remapping of place cell responses in different environments (Doboli et al., 2000). Neurogenesis in the dentate gyrus has been modeled as enhancing the pattern separation mechanisms (Becker, 2005), but might also play a role in providing a temporal code for memories (Aimone et al., 2009).
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 forms associations between the elements of an input pattern, allowing pattern completion during subsequent retrieval. During retrieval, a partial cue consisting of a subset of active neurons causes activity to spread across previously modified synapses to cause activity in other elements of the pattern, 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). The modeling of attractor dynamics builds on extensive earlier analysis of the memory capacity of recurrent networks (Amit et al., 1987) that was applied to models of hippocampal function (Treves and Rolls, 1992; 1994; Battaglia and Treves, 1998), including models of multiple attractors (Battaglia and Treves, 1998). The capacity limits of hippocampal circuits could constrain its role to holding intermediate term episodic memories that are eventually used to update neocortical representations.
As described in more detail below, attractor dynamics in CA3 have also been used to model place cell activity (Samsonovich and McNaughton, 1997; Redish, 1999). Similar attractor dynamics have more recently been used to model grid cell firing responses in the medial entorhinal cortex (Fuhs and Touretzky, 2006; McNaughton et al., 2006; Burak and Fiete, 2009).
In contrast to region CA3, region CA1 has little excitatory recurrent connectivity, and receives primarily feedforward input from region CA3 and medial entorhinal cortex layer III. 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; Hasselmo and Schnell, 1994; Hasselmo and Wyble, 1997). 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).
The place cell responses in region CA1 have been modeled using arrays of sensory features linked to place cell responses by self-organization of afferent synapses from entorhinal cortex (Sharp, 1996; Rolls and Treves, 1998; Arleo and Gerstner, 2000) or using error-based learning of associations with location (Shapiro and Hetherington, 1993). Based on their clear differences in anatomical connectivity, region CA3 and CA1 have been proposed to have different roles in prediction based on prior experience (Treves, 2004). Simulations show differences in this prediction property primarily when accompanied by intrinsic spike frequency adaptation of individual neurons.
The activity of GABAergic and cholinergic neurons in the medial septum paces theta rhythm oscillations in the hippocampus and provides modulatory tone regulating intrinsic properties in the hippocampus. Models have addressed the role of medial septum in regulating theta rhythm oscillations (Denham and Borisyuk, 2000) and in regulating the dynamics of encoding and retrieval within the hippocampus (Hasselmo and Schnell, 1994; Hasselmo et al., 1995). In models (Hasselmo and Wyble, 1997), the release of acetylcholine in the hippocampus enhances encoding in a number of ways: 1. Increasing the spiking response to entorhinal input through depolarization and suppression of spike frequency adaptation, 2. Enhancing synaptic modification, and 3. Reducing recurrent excitation arising from region CA3 through presynaptic inhibition of glutamate release. The reduction of recurrent excitation prevents previously encoded associations from interfering with the encoding of new associations (Hasselmo and Schnell, 1994; Hasselmo et al., 1995; Hasselmo and Wyble, 1997). Acetylcholine levels are high during theta rhythm oscillations in active waking, and decrease during quiet waking and slow wave sleep. Models show how this could allow stronger transmission from CA3 to CA1 to drive neocortical consolidation (Hasselmo, 1999). The medial septum has been proposed to regulate baseline theta rhythm oscillations for oscillatory interference models of entorhinal grid cells (Burgess et al., 2007; Burgess, 2008). This model is supported by data showing loss of entorhinal grid cell spatial periodicity during inactivation of the medial septum (Brandon et al., 2011; Koenig et al., 2011).
The entorhinal cortex provides the primary input to the hippocampal formation, with entorhinal cortex layer II projecting to dentate gyrus and region CA3, and layer III projecting to region CA1. Extensive modeling has addressed the mechanism and role of grid cells in medial entorhinal cortex of the rat. Grid cells respond in a regular array of locations in the environment falling on the vertices of tightly packed equilateral triangles. Grid cells have been modeled based on interference between oscillations with frequencies shifted by the velocity of the rat (O’Keefe and Burgess, 2005; Burgess et al., 2007; Hasselmo et al., 2007; Burgess, 2008). This model predicted (O’Keefe and Burgess, 2005; Burgess et al., 2007; Burgess, 2008) that the difference in spatial frequency of grid cells at different positions along the dorsal to ventral axis of medial entorhinal cortex could arise from differences in the intrinsic oscillation frequency of entorhinal neurons. This prediction was supported by intracellular recording data showing a gradient of intrinsic subthreshold membrane potential oscillations and resonance (Giocomo et al., 2007; Giocomo and Hasselmo, 2009) and unit recording data showing a gradient of intrinsic periodicity in autocorrelations (Burgess, 2008; Jeewajee et al., 2008). Other models have proposed that grid cells arise from attractor dynamics (Fuhs and Touretzky, 2006; McNaughton et al., 2006; Burak and Fiete, 2009; Navratilova et al., 2011) or self-organization of afferent input to the entorhinal cortex (Kropff and Treves, 2008).
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
Long-term potentiation and depression
The properties of synaptic modification in the hippocampus constitute an essential component of most hippocampal models. Neural network models of memory function demonstrated the importance of Hebbian synaptic modification (Anderson, 1972; Kohonen, 1972), in which strengthening of synapses depends a combination of presynaptic and post-synaptic activity. Models motivated the experimental studies demonstrating Hebbian synaptic modification in the hippocampus using extracellular (McNaughton et al., 1978) and intracellular recording (Kelso et al., 1986). 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 (Shouval et al., 2010).
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).
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, 1991; Arleo and Gerstner, 2000) or from error-correcting rules guiding formation of place cells (Shapiro and Hetherington, 1993. Later models simulated place cell responses based on path integration of self-motion information for self-localization (Touretzky and Redish, 1996; Samsonovich and McNaughton, 1997; Redish and Touretzky, 1998; Redish, 1999). These models also incorporated multiple different maps to account for the remapping of place cell responses based on changes in behavioral stimuli or task demands. The models of path integration for place cell responses were precursors to the models addressing the potential mechanisms for the generation of grid cell firing responses in the medial entorhinal cortex (McNaughton et al., 2006; Fuhs and Touretzky, 2006; Burgess et al., 2007; Giocomo et al., 2007; Kropff and Treves, 2008). Recent models have addressed how place cells could arise from the properties of grid cells in the entorhinal cortex (Solstad et al. 2006; McNaughton et al., 2006). However, recent data suggests that place cells may not depend upon grid cell firing. The changes in place cell responses after movement of environment boundaries led to development of a model of place cells based on boundary vector cells (O’Keefe and Burgess, 2005; Barry et al., 2006). The boundary vector cells predicted by the model were recently shown experimentally in the medial entorhinal cortex (Solstad et al., 2008) and subiculum (Lever et al., 2009). Models have also demonstrated how context-dependent 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 tend to shift backward with experience (Mehta et al., 2002).
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 8 Hz (Green and Arduini, 1954; O’Keefe and Nadel, 1978; Buzsaki et al., 1983; 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 (Brankack et al., 1993). Models have addressed the phase difference in different layers between stratum lacunosum-moleculare, stratum radiatum to stratum pyramidale (Leung, 1984). This difference in phase in different layers arises from different temporal dynamics of synaptic input to different layers. The difference in synaptic input to different layers at specific phases of theta rhythm could provide different dynamics appropriate for encoding versus retrieval of associations. The encoding of associations could take place on the phase of theta rhythm when there is a dominant influence of entorhinal input and the induction of LTP is strongest (Hasselmo et al., 2002). In contrast, the retrieval of associations could take place when there is a dominant influence of output from region CA3 and no induction of LTP (Hasselmo et al., 2002). This proposal is consistent with the region CA1 showing coherence at one phase of theta with high frequency gamma in entorhinal cortex and at a different theta phase with lower frequency gamma in region CA3 (Colgin et al., 2009).
Theta phase precession of spiking relative to 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; Hasselmo and Eichenbaum, 2005).
- 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). The same mechanism has been used to model theta phase precession in grid cells (Burgess et al., 2007; Hasselmo, 2008).
- 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).
Recent intracellular recordings from awake head-fixed mice running in a virtual world have tested predictions of these different models (Harvey et al., 2009). The intracellular membrane potential shows subthreshold oscillations that shift in phase relative to network oscillations, consistent with the oscillatory interference model rather than the sequence readout models. The data also shows a depolarization of membrane potential within the place field.
“’Models of hippocampus’” have addressed experimental phenomena at 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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