Spatial representations in an HCN1 knockout mouse model Increased spatial scale of entorhinal grid cells following decreased H current kinetics

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Spatial representations in an HCN1

knockout mouse model

Increased spatial scale of entorhinal grid cells

following decreased H current kinetics

final version of the second research project report by

Paul Mertens

pecmertens@gmail.com

CSCA Master Brain & Cognitive Sciences University of Amsterdam

2010–2011

First Supervisor: Lisa M. Giocomo, PhD Co-Assesor: Prof. Edvard I. Moser

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List of Figures

1 MEC and parahippocampal system . . . 4

2 Grid cells . . . 6

3 Head direction cells and border cells . . . 9

4 Mexican hat connectivity . . . 13

5 Attractor network models of grid cells . . . 15

6 Oscillatory interference models of grid cells . . . 19

7 Examples of clusters in Tint . . . 33

8 Example grids . . . 34

9 Example HD cells and border cells . . . 35

10 Grid spacing and dorso–ventral location in MEC . . . 37

11 Spatial selectivity of HD and border cells along MEC . . . 38

12 Numbers of theta modulated grid cells . . . 40

13 Examples of theta phase precession . . . 41

14 Examples of theta phase precession . . . 42

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1 Introduction

The current project was an attempt to test several model predictions about spatial repre-sentations in the medial entorhinal cortex. Before introducing the experiment, I will give some brief introductions of neurocognitive research into spatial navigation. The focus will be on mechanistic explanations of spatial behavior in rodents, based on physiological and anatomical characteristics of the (para)hippocampal and entorhinal regions. The main model under scrutiny is a so–called ’oscillatory interference’ model, which aims to explain grid cell firing patterns in terms of an interaction between the oscillatory properties of a grid cell’s membrane potential and the local EEG theta rhythm. Besides considering a direct test of model predictions using a genetic knock–out mouse model, I will briefly compare the oscillatory interference model to the continuous attractor models; a popu-lar class of models where specific firing patterns arise from the specific distributions of excitatory and inhibitory connections between cells.

1.1 Neural representations of space form a cognitive map

1.1.1 Tolman’s map and the discovery of place cells

In 1948, Tolman famously observed that rats have the ability to navigate to locations in a familiar environment by spontaneously using shortcuts they had no previous experience with (Tolman, 1948). The one who Tolman credited with being the first to make a similar observation was Lashley in 1929. He, reportedly, observed how after his rats had learned to navigate an alley maze, some animals were able to escape the starting box and run over the top of the maze immediately to the reward site. Tolman thought that animals do not necessarily discover these quicker routes through trial and error and long strings of stimulus–response associations, as behaviorists of his day proposed. Instead, he suggested that animals navigate using a ’cognitive map’ in addition to using stimulus response associations. Tolman thought that the brain was capable of relating complex sets of internal and external stimuli not only directly to the animal itself, but also to

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eachother to make such a cognitive map; a representation of the environment which was constant and independent of the animal’s current position or behavioral goal, and which is based on spatial relationships between locations.

The hippocampus was the first substrate for the cognitive map A neural char-acterization of this map remained illusive until the 1970’s, when researchers started using implanted electrodes and automated recording methods to study the behavioral corre-lates of neuronal spiking. The first significant finding was the discovery of so–called ’place cells’, which are abundant in hippocampal areas CA1-3 (O’Keefe and Dostrovsky, 1971, O’Keefe, 1976, Lee et al., 2004, Moser et al., 2008). These cells, commonly believed to be pyramidal cells (Henze et al., 2000), only fire when an animal is in a specific location in an environment, irrespective of the direction of movement into that location. Upon introduction to an environment, place fields are formed within minutes (Wilson and Mc-Naughton, 1993) and remain stable during repeated exposures to the same environment for periods of up to several months (Thompson and Best, 1990). The apparent ability of hippocampal place cells to allocentrically locate an animal in it’s environment led to the proposition by O’Keefe and Nadel (1978) that the hippocampus contains the cognitive map originally imagined by Tolman.

Following the discovery of place cells, the past decades saw an upsurge of re-search into hippocampal spatial and mnemonic functions, which was aided by continuing advances in multi–unit recording methods for freely behaving animals (for reviews, see Eichenbaum et al., 1999, Leutgeb et al., 2005, Moser et al., 2008). Besides indicating es-sential hippocampal involvement in many (non)spatial memory paradigms (Maren et al., 1997, R.J. et al., 2001, Takehara et al., 2002, Eichenbaum and Lipton, 2008), experiments have highlighted several features of hippocampal place cell firing which support the idea of a cognitive map in the hippocampus. For example, activity of both individual cells and cell ensembles is completely decorrelated, or orthogonal, between different environ-ments (Quirk et al., 1992, Gothard et al., 1996), indicating that different locations all have an individual representation. Also, by accurately reconstructing the location of an animal from recorded ensemble activity of around 100 place cells, it was shown that the

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hippocampus outputs a representation of the current location (Wilson and McNaughton, 1993).

An illustration of hippocampal involvement in allocentric spatial processing comes form spatial reference memory tasks; here, animals which received lesions to the hip-pocampus following training perform far worse than controls (Mumby et al., 1999, R.J. et al., 2001, Clark et al., 2005). Finally, as is required of an allocentric representation, place cell activity is under strong influence of environmental landmarks (O’Keefe and Speakman, 1987, Gothard et al., 1996, Knierim, 2002, Lee et al., 2004). As an example, Muller and Kubie (1987) showed that when a cuecard is displaced in a familiar environ-ment, upon reintroduction to the environment the place fields will remain fixed relative to the cue card. When the cuecard is removed alltogether however, place fiels retain their locations relative to eachother, but they are rotated arbitrarily with respect to the environment. Introducing the animals to a very similar but larger environment led to expansion of a significant portion of place fields while they mostly retained their positions relative to the environmental borders. Introduction to an environment with a different shape (circular vs. rectangular) led to global remapping of place fields to uncorrelated locations.

Limitations of the hippocampal representation Besides representing the current location, a navigation system needs a way to meaningfully relate different parts of an environment to eachother. However, spatial representations in the place field populations are uncorrelated, with no apparent way of relating unit or ensemble activity in differ-ent spaces. This makes it unlikely for place cells to provide the rest of the brain with information on distances and angular relations between locations. Additionally, with representations orthogonolized between different environments, it is difficult to imagine how a local computation could be used to update the spatial representation as the animal moves around; even if information of the speed and direction of movement is available to place cells, they possess no general rule for subsequent translation of the representation. However, early recordings from areas upstream of the hippocampus yielded no cells with spatial firing correlates (Barnes et al., 1990, Quirk et al., 1992, Frank et al., 2000,

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Bur-well et al., 1998, BurBur-well and Hafeman, 2003). Because of that, it was long believed that the computation of location was somehow performed in the hippocampus itself (Barnes et al., 1990, Quirk et al., 1992). However, indicating that this might not be the case, CA1 place fields were found to persist following the severing of intrahippocampal projections from either the dentage gyrus (DG) to CA1 (McNaughton et al., 1989) or the schaffer collaterals from CA3 to CA1 (Brun et al., 2002). These apparent contradictions persisted until the discovery of so–called ’grid cells’ in the medial entorhinal cortex (Fyhn et al., 2004).

1.1.2 Spatial representations in the medial entorhinal cortex

Figure 1: (a) Shows the position of the MEC and other parahippocampal and as-sociated cortical structures in a schematic view of a rat brain. (b) shows the same structures in a histological preparation acquired from the indicated location. DG = dentate gyrus, CA1–CA3 = coronu amonis field 1–3, S = subiculum, PRS = Presubiculum, PAS = Parasubiculum, MEC = medial entorhinal cortex, LEC = lateral entorhinal cortex, POR = postrhinal cortex.

The main cortical inputs to the hippocampus arise in the entorhinal cortex (EC) (figure 1) (Somogyi, 2010, Moser et al., 2010). Lying only one synapse upstream of the hippocampus, the EC was considered as one of the areas which could support the mechanisms for spatial computation which the hippocampus seemed to be lacking. After earlier experiments failed to find any clear, spatial firing correlates in the EC (Barnes et al., 1990, Quirk et al., 1992, Frank et al., 2000), three spatially responsive cell types were found in the dorsolateral band of the medial entorhinal cortex (MEC). Most striking was the discovery of cells with discrete firing fields repeating at regular spatial intervals in a triangular/hexagonal pattern, termed grid cells (figure 2) (Fyhn et al., 2004, Hafting

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et al., 2005). Additionally, cells have been found in the MEC which respond to allocentric head direction (head direction (HD) cells, figure 3) (Sargolini et al., 2006) or borders of a specific orientation (boundary vector cells, or border cells, figure 3) (Solstad et al., 2008, Savelli et al., 2008). To a certain extent, the firing rates of all these cells are modulated by the velocity of the animal’s movement (Sargolini et al., 2006). Given the distribution of these cell types over the layers of the MEC, they are in all likelihood principal cells projecting to the dentate gyrus and CA fields through perforanth path (Sargolini et al., 2006, Witter, 2007b). By signalling to the hippocampus information on distance traveled (GCs), direction (HDCs), distance to borders (BCs) and ultimately velocity, these cells present a possibility for consolidating earlier differences on hippocampal computation.

The following paragraphs will discuss these cell types in a bit more detail. The focus will be on grid cells, since mainly their origin is the topic of the model under consideration in this project.

Grid cells as a neural co–ordinate system It appears that around 50% of the principal cells in MEC layer II are grid cells (Sargolini et al., 2006), which project to all subfields of the hippocampus proper through the perforant path (Witter, 2007a). When the firing locations of a grid cell are overlayed on the environment, a repeating pattern appears; the firing fields lie on the vertices of an imaginary, hexagonal grid. Between these vertices, grid cells are virtually silent (Hafting et al., 2005). With regards to their spatial firing traits, grid cells can be principally described in terms of i) the spacing between their grid fields, ii) the orientation of the grid relative to an external reference point and iii) the phase offset of their grids relative to eachother (Hafting et al., 2005, Fyhn et al., 2007).

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Strikingly, cells recorded on one tetrode show very similar orientation and spac-ing, while showing random phase differences. It is not known how clusters of cells with different orientations are anatomically organized, but grid spacing increases considerably along the dorso–ventral axis of the MEC; in rats, the most dorsal cells show grid spacings of around 30 cm, while the most ventrally recorded cells have fields several meters apart (Moser et al., 2010).

Figure 2: Two examples of grid cells recorded in the current project. The left panel shows all spike locations as red dots and the trajectory of the animal as a black line. The middle panel shows the smoothed rate map and the right panel shows the spatial autocorrelogram. Cells were recorded from the same animal on different days. Position along the dorso–ventral axis of MEC is indicated, as well as peak firing frequency (f ) and gridness score (g).

Although grid fields are not known to associate with specific environmental fea-tures or landmarks like hippocampal place fields, a cell’s grid fields do appear in the same location upon repeated introduction to a familiar environment. Also, the population of grid cells outputs an accurate representation of the environment; activity from as few as 10 grid cells is sufficient to reconstruct the location of an animal (Fyhn et al., 2004). In addition to illustrating this last point, several computational accounts of hippocampal place cell firing succesfully model place fields through linear summation of MEC grid cell activity (McNaughton et al., 2006, Rolls et al., 2006, Solstad et al., 2006). Supposing that this is a valid mechanism for place cell formation could also explain the dorsal to ventral increase in place field size (Jung et al., 1994, Maurer et al., 2005) as a result of

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the dorsoventral increase in grid field size and spacing seen in the MEC (Hafting et al., 2005).

An important feature of the entorhinal representation indicates that it could serve as a co–ordinate system, or metric, for a map–like representation of the environment (Moser and Moser, 2008). As we saw earlier, hippocampal representations are completely decorrelated between different environments, but this is not the case in the grid cell population; upon introduction to a different (novel) environment the place cell population globally remaps, whereas grids only display a random phase shift while retaining their firing orientation and spacing relative to eachother (Hafting et al., 2005, Fyhn et al., 2007). This means that, as the animal moves through it’s environment, the activity in the grid cell population changes according to a rule which is common accross environments. Features of an environment represented in the hippocampus might thus be spatially related by an entorhinal representation that is active simultaneously and which contains information on the distance of movements and their direction, in the form of grid spacings and orientations respectively (Fyhn et al., 2007, Moser et al., 2008, Moser and Moser, 2008).

Before continuing on models on the origin of grid cells, I want to introduce several other spatial signals which are present in the MEC and which feature prominently in these models. Besides two other, spatially responsive cell types, these are the local EEG theta– rhythm and the way in which an animal’s velocity could be represented in the MEC.

Head direction cells Head direction cells (HD cells) respond to allocentric head di-rection by firing at an increased rate while the animal faces in a particular, allocentric direction. HD cells of the MEC were first discovered and described by Sargolini et al. (2006). At that time however, they were already known to exist in a number of corti-cal and subcorticorti-cal structures, including the presubiculum, the antero–dorsal thalamic nucleus, the lateral mammilary nuclei and the retrosplenial cortex (reviewed by Taube, 2007). These cells appear to have similar characteristics across structures; Taube (2007) reports that angular selectivity of HD cells lies between 60 and 150 degrees and averages around 90 degrees. The increase in firing rate they display while the animal faces their

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preferred direction lies between 5 – >120 Hz, while remaining below 0.5 Hz for other directions. In MEC, Sargolini et al. (2006) reports similar findings for angular selectivity and firing rates. Angular selectivity is maintained irrespective of the current behavior of the animal, or the pitch or roll of the animal’s head. Importantly, HD cells of different structures are found to robustly maintain their relative, prefered firing directions across different environments, even following systematic desorientation and challenging cue ma-nipulations (Goodridge and Taube, 1995, Knierim et al., 1995, 1998, Yoganarasimha et al., 2006). This characteristic is important for models of path integration, where the HD cells are used for the translation of the hippocampal and entorhinal representations in the direction of movement (for instance, in the case of attractor network models) (Mc-Naughton et al., 2006, Burak and Fiete, 2009, Giocomo et al., 2011b). As we will see in more detail later, in oscillatory interference models of grid cell firing, head direction signals play an important role in establishing the spatial regularity of grids (Giocomo and Hasselmo, 2008b, Giocomo et al., 2011b).

For a large part it remains to be determined whether or not head direction cells play the roles which these models suppose. However, an intimate relationship between HD cells, place cells and grid cells is suggested by experiments. For instance, Knierim et al. (1995) show that hippocampal place cells and thalamic HD cells are strongly coupled, i.e. maintain firing correlates relative to eachother, even when their representations are not stable with respect to allothetic cues. A different illustration comes from the MEC, where grid cells and HD cells not only colocalize, but appear as part of a continuous cell class in layer III, where grid cells exist which fire selectively when the animal faces a particular direction (Sargolini et al., 2006). Finally, no instances are known where the head direction representation reorients, for instance in response to large alterations to environmental cues, whithout global remapping of place cells and realignment of grids.

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Figure 3: (a) Shows an example of a head direction cell recorded during the current project. The left panel shows the directional tuning curve, the middle panel shows the smoothed rate map and the right panel shows the spatial autocorrelogram. The mean vector length is indicated (MVL) and the peak firing rate (f ). (b) Shows an example of a border cell recorded by (Solstad et al., 2008). The three panels show smoothed rate maps of three successive trials in the same environment. Notice how the cell fires selectively along western borders, including the border of a wall inserted before and removed after the second trial. The peak firing frequency is indicated per trial (f ). Adapted without permission.

Border cells The final cell type with a clear spatial firing correlate in the MEC is the border cell. These cells fire only in proximity of environmental borders of a single or several orientations (Solstad et al., 2008, Savelli et al., 2008). For instance, a cell might fire along the entire length of the eastern wall of a square open–field box. Another cell might fire in response to the northern and western wall. A characteristic of border cells is that they fire to every border of their prefered orientation; thus, when a segment of wall is introduced anywhere in the environment parallel to the eastern wall, the border cell that fired in proximity of the eastern wall will now also fire along the western face of this wall segment (Solstad et al., 2008). In fact, any type of border could trigger a border cell to fire; a wall as well as a drop, as long as it impedes the animal’s movement.

Solstad et al. (2008) found that less than 10% of recorded cells were border cells, but they appeared in all layers of the MEC. This seems to imply that they project both within the entorhinal cortex, as well as to all downstream targets of the MEC. Therefore,

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border cells could potentially have a substantial influence of entorhinal and hippocampal representations despite their limited numbers. Like head direction cells and border cells, the border representation appears coherent and anchored to environmental features; when a cue–card is rotated in an environment, border cells rotate their activity as an ensemble. In fact, they do this together with the populations of grid cells and head direction cells, so that all cells participating in the entorhinal representation maintain a fixed, relative orientation (Solstad et al., 2008, Fyhn et al., 2007, Moser et al., 2008).

The existence of the border cell type was explicitly predicted by the so–called ’boundary vector cell model’ of place cell firing (Barry et al., 2006). This model followed from the observation by O’Keefe and Burgess (1996) that hippocampal place fields in four similar, but differently sized environments could be modeled by summation of Gaus-sian inputs which were functions of the distances of the animal to the walls. A similar observation was made for grid cells by Barry et al. (2007), who observed that the grid spacing changed after altering the dimensions of the familiar recording box. Despite the apparently strong influence of environmental borders on place and grid cell firing, no computational models except the boundary vector cell model attribute an important role to border cells when it comes to the formation of place or grid cells (McNaughton et al., 2006, Giocomo and Hasselmo, 2008b, Giocomo et al., 2011b).

As in the current project, Solstad et al. (2008) used a criterium for border cells which excludes cells that fire at a fixed distance from a border, e.g. a cell that fires maximally when the animal is 20 cm removed from any eastern border is not considered a border cell according to this criterium. Such cells have been observed however by Solstad et al. (2008), and would qualify the criteria for boundary vector cells proposed by O’Keefe and Burgess (1996) and Barry et al. (2006).

Encoding velocity in MEC We have seen the cell types in MEC which respond to distance and direction and we have discussed how the representation in the MEC, unlike that in the hippocampus, responds with striking regularities across different environ-ments. These features satisfy important requirements for a system which contains and updates a spatial code. However, in order to meaningfully update the representation of

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location, information on the velocity of movement is required in addition to information on it’s direction.

Currently, no signal has been discoverecd in the (para)hippocampal system or entorhinal cortex which exclusively encodes animal velocity. However, the firing rates of grid cells, HD cells and conjunctive HD/grid cells have all been found to be modu-lated by velocity (Sargolini et al., 2006). The same is true of hippocampal place cells mcnaughton1983,czurko1999. In addition, the frequency of the local EEG theta–rhythm in the MEC has been found to be positively correlated with the movement speed of the animal (Jeewajee et al., 2008). Models of grid cell firing typically use these modulations of firing rates and theta frequency as velocity inputs (McNaughton et al., 2006, Burgess, 2008, Giocomo and Hasselmo, 2008b, Giocomo et al., 2011b).

1.2 Models of grid cells

1.2.1 Attractor network models

Generally, an attractor is an abstract concept used to describe dynamical systems which posses one or multiple stable states (attractor states) to which the system inevitably evolves over time (Milnor, 1985, Knierim and Zhang, 2012, (review)). All possible ac-tivation patterns of a neural network can be viewed as the state space of a dynimcal system, and given the appropriate connectivity, there can be predetermined attractor states of activity to which the network will evolve following any conceivable input (Hop-field, 1982). We can think of different kinds of neural attractors, broadly seperated into point attractors with discrete, uncorrelated attractor states, and continuous attractors, whose attractor states span all points of a continuum.

Elementary basics of neural attractors The point attractor network is best known as a model for memory storage and retreival, and allows a convenient, general illustration of neural attractors (Marr, 1971, Hopfield, 1982). The behavior of the network depends on extensive recurrent connections between its cells, with the strenght of the individual connections determining the attractor states of the network. Storage of a pattern occurs by strengthening and weakening of connections using Hebbian learning rules; cells that

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are active simultaneously strengthen their recurrent connections and possibly vice versa (Hebb, 1949). A form of global inhibition is typically applied so that only cells with strong recurrent connections become active following any given input. An important fea-ture of such a network is pattern completion, which means even a deteriorated or partial presentation of the original input pattern will cause activation of the entire stored pattern through recurrent activation of the involved cells. As an example, its strong recurrent connectivity lead to hippocampal area CA3 often being modeled as a neural point attrac-tor (Treves and Rolls, 1994, Samsonovich and McNaughton, 1997, Battaglia and Treves, 1998). Ensemble activity in this area is decorrelated between different environments, which could indicate different point attractors for different spaces, while the network re-sponses to manipulations of the environment (the input to the network) seem to indicate appropriate pattern completion and pattern seperation (Lee et al., 2004, Leutgeb et al., 2004)(but see (Colgin et al., 2010) for contesting findings).

The MEC as a continuous attractor Continuous attractors are another class of neural attractors which differ from point attractors in that their attractor states are not single, discrete states which represent discrete inputs, but lie along a continuum of possible states and represent continuous input variables (Tsodyks and Sejnowski, 1995). The MEC has been modelled as a continuous attractor representing two–dimensional space. In these models, grid cells are depicted on a 2–dimensional sheet, where cells with adjacent grid fields are placed adjacent to eachother (figure 5) (Fuhs and Touretzky, 2006, McNaughton et al., 2006). Unlike in attractor models of memory, cells do not associate through Hebbian learning; instead, cells that are nearby on the neural sheet excite eachother, while cells that are further apart inhibit eachother through indirect connections. This is called ’mexican hat’ connectivity, because when we plot the connection weights for a single cell as a function of distance to that cell in the model sheet, the shape of the function resembles the silhouette of a sombrero, or mexican hat (figure 4).

In this continuous attractor, a position in the environment is represented by an activity bump in the neural sheet. Global inhibition again keeps the activity restricted to a small number of strongly connected cells.

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Figure 4: Mexican hat connectivity is illustrated. The plot shows the connection weights between a cell and it’s neighbours (y–axis) as a function of distance to the cell (x– and z–axis).

In models where the neural sheet containing the grid cells is flat however, mexican hat connectivity leads to disproportionate excitation along the edges of the environment. This boundary problem was first described for continuous attractor models of hippocam-pal place cells, where it was solved by assuming that cells with fields along an edge of the environment connected to cells with fields along the opposing edge as if they were adjacent (Samsonovich and McNaughton, 1997). By doing so, the attractor sheet is no longer flat but rather shaped like a torus. This simultaneously leads the repetitive firing fields observed in grid cells, which lead to the adoption of the torus shaped attractor in attractor models of grid cells (McNaughton et al., 2006, Guanella et al., 2007, Navratilova et al., 2011).

Moving the activity bump across the model sheet depends on a process of path integration; most attractor models suppose assymetric connections from head direction cells or conjunctive grid–head direction cells, whose activity also scales with speed (Fuhs and Touretzky, 2006, McNaughton et al., 2006, Navratilova et al., 2011, Giocomo et al., 2011b, (review)). In these cases, a conjunctive cell would receive input from grid cells selective for the same location as itself, and it would only project to those grid cells with fields which lie along its preferred direction of motion, adjacent to the original grid cells that activated it. In support of these ideas, speed modulated, conjunctive cells have been found in the MEC (Sargolini et al., 2006), although they are not silent when the rat is motionless, which is required by some, if not all models (McNaughton et al., 2006, Navratilova et al., 2011).

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Other experimental support for attractor models comes from Barry et al. (2007), who report that the dorsal to ventral increase in grid spacing occurs not with a continuous gradient, but in discrete steps. None of the current attractor models of grid cells can accomodate grid cells with different spacings in a single attractor (Navratilova et al., 2011, Giocomo et al., 2011b). This is because the necessary mexican hat connectivity is impossible for cells with grid fields repeating at different spatial intervals. Also, grid cells with different grid spacing would rely on similarly different conjunctive cells for path integration. This means that the MEC as a whole can not be one large, continuous attractor, but must be made up of several discrete attractors (Navratilova et al., 2011, Giocomo et al., 2011b).

Finally, although early attractor network models could not explain theta phase precession, Navratilova et al. (2011) propose a torus shaped attractor that utilizes theta modulated conjunctive cells and grid cells with realistic after–hyperpolarization and de-polarization conductances. When the input to grid cells collapses during a theta through, the after–spike conductances lead to rebound activity in recently active grid cells which manifests as theta phase–precession. It is yet unknown however, if the after–spike con-ductances can cause the necessary rebound activity, or whether there is a role for other, characteristic integrative properties of stellate cells (Garden et al., 2008, Giocomo et al., 2011a).

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Figure 5: An attractor network model is illustrated. The left panel shows a tutor layer which might be present in the developing cortex. Here, symmetry break-ing might occur due to hardwired mexican hat connectivity. The tutor layer then projects randomly to the population of developing grid cells in MEC. Through competitive, Hebbian learning, random groups of grid cells (in red) form strong recurrent connections, which are necessary for attractor dynamics. This way, grid phases become continuous and randomly distributed in the MEC. The middle panel shows grid cells (coloured dots) overlayed on an environment, with each cell dis-played at the location of one of it’s grid fields. Red lines indicate strong recurrent connections between cells. To prevent excessive excitation near the edges, cells con-nect to cells on the other side of the environment as well. Inhibitory concon-nections do the same, but are not indicated. The right panel shows the torus as the effective shape of the network with wrap–around connections. Adapted from Moser et al. (2008), without permission.

Constraints of the attractor network models The models described above make numerous assumptions of network connectivity which are difficult to test experimentally. Whether the extent of recurrent connectivity suggested for MEC layer II is actually present remains disputed (Dhillon and Jones, 2000, Kumar et al., 2007, Quilichini et al., 2010), and whether cells with similar spatial phases connect most strongly is not known yet. A review of the issue, more comprehensive than is possible here, was recently given by Giocomo et al. (2011b). How the proposed connectivity patterns develop also remains unclear. Rudimentary grid cells are present when rat pups leave the nest for the first time (Langston et al., 2010), indicating that their formation does not depend on spatial experience. McNaughton et al. (2006) suggest that hard–wired mexican hat connectivity in a teaching–layer could lead to the required connectivity in the fetal layer II through competitive, Hebbian plasticity. After development the teaching–layer becomes obsolete and is effectively discarded. Although a possibility, it is still unknown if such a teaching layer exists in the developing entorhinal cortex. Finally, it appears to me that torus

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shaped attractors would show similar edge effects in irregularly shaped environments. Considering that, it also seems striking that no attractor network model incorporates a function for entorhinal border cells; could they possibly circumvent edge effects by simply increasing global feedback inhibition whenever the animal approaches an environmental border?

1.2.2 Oscillatory interference models and the HCN1 knockout model

The second, prominent class of models for grid cell activity are the oscillatory interference models. These rely on single cell properties and limited network mechanisms to produce the grid firing pattern. The main advantages of these models over the attractor network models are that they readily deliver experimental predictions and that they have been able to offer a possible explanation of theta phase–precession since their earliest formu-lation (O’Keefe and Recce, 1993, O’Keefe and Burgess, 2005, Giocomo et al., 2011b). A disadvantage is that grid patterns in many, recently considered oscillatory interference models deteriorate rapidly in the face of biologically realistic noise (Zilli et al., 2009).

Place fields and theta phase precession as oscillatory interference The core mechanism of the oscillatory interference models was first suggested by O’Keefe and Recce (1993) in an attempt to explain place fields and their theta phase–precession in the hippocampus. O’Keefe and Recce (1993) suggested that a dendritic oscillator increases its frequency above the local theta frequency in response to movement in a particular direction. When this oscillator interacts with an oscillator in the soma, which is thought to be coupled to the local theta, an interference pattern emerges. For instance, imagine an animal running at a constant speed of 20 cm/s along a linear track. The local theta, and thus the somatic oscillator of a place or grid cell, might have a frequency of 9 Hz. The dendritic oscillator might have a frequency of 10 Hz. When these two oscillators interact at the soma, an interference pattern will emerge with a frequency of 9.5 Hz (sometimes called the ’carrier frequency’) with a beat frequency (or envelope) of 1 Hz, which reflects the two oscillators drifting perfectly in and out of phase once every second. The cell would fire whenever the amplitude of the interference pattern exceeds the firing

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threshold of the cell. If the animal keeps running at it’s constant speed, there will be a peak in the amplitude of the envelope, and thus the center of a firing field, once every 20 cm.

The drawback of this explanation for place cell firing was of course that hip-pocampal cells do not show regularly repeating fields, which meant that place selective firing needed to incorporate different or additional mechanisms (e.g. through summation of inputs of spatially responsive cells in the MEC (McNaughton et al., 2006, Barry et al., 2006)). However, the oscillatory interference pattern proposed by O’Keefe and Recce (1993) offered an explanation for theta phase–precession of place cells. As the frequency of the dendritic oscillator is higher than the frequency of theta, the frequency of the inter-ference pattern is also higher than theta. It follows that peaks in the interinter-ference pattern, and thus the firing of the cell, would precess with respect to theta. It is conceivable that, even when the oscillatory interference is not the main force driving the cell to threshold, interference between somatic and dendritic oscillators could influence spike timing and cause phase precession (Burgess and O’Keefe, 2011).

The grid pattern as oscillatory interference When grid cells were discovered in the MEC, the oscillatory interference models were quickly considered as an explanation for the repeating spatial firing pattern (figure 6) (O’Keefe and Burgess, 2005). Of course, in order to lead to a hexagonal pattern which is anchored to the environment and inde-pendent of movement speed and direction, the original suggestions by O’Keefe and Recce (1993) needed to be greatly elaborated upon. The first formulation of an oscillatory interference model for grid cell firing, made it clear that a minimum of three, velocity controlled oscillators (VCOs) with different directional sensitivity needed to interact with the baseline oscillator in the soma to establish the hexagonal grid pattern (Burgess et al., 2007, Hasselmo et al., 2007). These oscillators were typically located in different dendritic subunits of the stellate cell (Klink and Alonso, 1997).

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Each dendritic oscillator was suggested to increase it’s frequency above theta in proportion to movement in one prefered direction, as in the following equation suggested by Burgess et al. (2007):

wd= ws∗ βs

Where wd is the angular frequency of a dendritic oscillator, ws is the frequency

of the somatic oscillator (theta), s is the speed of movement in the preferred direction of the dendritic oscillator and β is a constant scaling factor determining the slope of the increase in wd with speed.

To lead to a regular, hexagonal grid, β needs to be the same for all dendritic oscillators in a cell, and their preferred directions need to be at angles of (multiples of) 60 degrees relative to eachother; otherwise no regular, hexagonal grid will emerge.

With the frequency of the dendritic oscillators modulated by velocity and di-rection, the phase differences between the oscillators reflect the animal’s distance from the center of a grid node (where all oscillators are in phase). When the animal is not moving, dendritic oscillators revert to the theta frequency, thus not changing their phase relationship with the baseline oscillator in the soma. This way, the cell maintains the ap-propriate response for that particular location while motionless, and since the frequency of the interference is then equal to theta, precession of spikes relative to theta should not occur when the animal is stationairy, as is observed in both the hippocampus and MEC of rats (O’Keefe and Recce, 1993, Hafting et al., 2008).

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Figure 6: An oscillatory interference model is illustrated. The left pannel shows in the bottom row a somatic oscillator (theta), above that in blue a dendritic oscillator with a slightly higher frequency which scales with the animals velocity in one preferred direction. The third row from the bottom shows the interference pattern between the dendritic and somatic oscillator. At the peak of each ’beat’ in the interference pattern, the cell fires maximally. The cell spikes preferentially at the peaks of the carrier band. The top row shows the position of these peaks relative to the phase of the somatic oscillator, illustrating theta phase precession. The middle panel shows the preferred locations of peaks in the interference envelope of three independent, dendritic oscillators of a single cell. The cell fires where the three interference patterns all have a peak in their envelope, leading to a grid pattern. The right panel shows a simulated grid pattern. Adapted from (Moser et al., 2008), without permission.

Setting the gain of velocity inputs Computational models of grid cells generally suppose that grid cells (path) integrate the current position from speed and velocity inputs (O’Keefe and Burgess, 2005, McNaughton et al., 2006, Fuhs and Touretzky, 2006, Burgess et al., 2007, Zilli and Hasselmo, 2010). As explained above, oscillatory interference models further suggest that this integration takes place in the grid cells through scaling of the frequency of (dendritic) oscillators. Speed modulated head direction cells in the MEC are the principal candidates to supply the input necessary for the scaling of these VCOs (Sargolini et al., 2006). Because the modulation of head direction firing by velocity appears similar across the MEC, the scaling factor for the increase in frequency with speed (β in the above equation) needs to be set locally in the individual grid cell in order to explain the gradient in grid spacing and grid field size along the dorsoventral axis of the MEC (Hafting et al., 2005).

The exact mechanism whereby velocity and direction inputs increase the fre-quency of the VCOs is unknown, but several electrophysiological properties of MEC

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stellate cells have been found to show gradients along the MEC, parallel to the gradient in grid spacing and field size. Giocomo et al. (2007) found that the frequency of sub-threshold oscillations in stellate cells change from fast in dorsal parts of MEC to slower in ventral parts. Similarly, the preferred resonance frequency of stellate cells changes from high to low along the dorsoventral axis. A gradient was also found for the fast time constant of sag potentials, where the membrane slightly depolarizes again following the onset of a continuous, hyperpolarizing current injection. This time constant changes from fast to slow along the dorsoventral axis of the MEC (Giocomo et al., 2007). The differ-ences in oscillatory and resonant properties fit with predictions from the first generation of oscillatory interference models that differences in dendritic oscillators are responsible for the differences in grid scale and field size (Burgess et al., 2007, Hasselmo et al., 2007). In order to test these predictions directly, the molecular basis of the oscillatory gradients needed to be identified and subsequently manipulated to observe effects on grid scaling as predicted by the oscillatory interference models. This molecular basis was found in the the hyperpolarization–activated, cyclic nucleotide–gated cation (HCN) channels, which are responsible for the inward H current (Ih). The kinetics of Ih are graded from

fast to slow along the dorsoventral axis of the MEC (Garden et al., 2008, Giocomo and Hasselmo, 2008a). The involvement of HCN channels was shown in patch studies using slices from mice which lacked the fast–acting HCN subunit, HCN1 (Giocomo and Hasselmo, 2009). In these forebrain specific knockouts (KOs), the gradients in oscillatory and resonant properties of stellate cells disappeared, as well as the differences in the time constant of the sag potential.

Finally, the HCN1 KO mice were compared to control animals using ensemble, tetrode recordings in vivo (Giocomo et al., 2011a). These animals showed a general increase in grid scale and field size along the entire dorsoventral axis of the MEC, such that the gradient in spacing and field size remained essentially intact. Additionally, grid cells in HCN1 KOs had significantly longer interspike intervals (ISIs) in the theta frequency range, in accordance with predictions of the oscillatory interference models, where the ISI in the theta range is used as an approximation of the cell’s intrinsic oscillatory frequency (Giocomo et al., 2011a, Burgess, 2008, Jeewajee et al., 2008). The observation that the

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gradient of grid scale and field size remained intact in HCN1 KOs is important because it indicates that the gradient in spacing might not come about through graded oscillatory or resonant properties. Giocomo et al. (2011a) suggest that grid spacing might be under the influence of Ih through the effect of the current’s kinetics on the synaptic input resistance;

Garden et al. (2008) found that input resistance is graded along the dorsoventral axis of the MEC and that blockade of Ih leads to a general decrease in input resistance with

preservation of it’s gradient. These last authors found that the input resistance, as well as the time window for coincidence detection of inputs, is under the influence of a gradient in leak potassium currents in addition to the kinetics of Ih. How differences in input

resistance along the dorsoventral axis of the MEC influence grid spacing exactly, or how such differences interact with the colocalized gradient of the time window for coincidence detection of inputs, is not formulated in current theories of oscillatory interference and will need to be considered in future theoretical work (Giocomo et al., 2011b).

In the current project, we were able to repeat findings from the earlier study using the HCN1 KO mice, including findings on grid spacing, the spatial selectivity of head direction cells and border cells and the stability of spatial firing correlates of grid cells and head direction cells (Giocomo et al., 2011a).

HCN1 knockout and theta phase precession Although previous research showed a correlation between larger grid spacing and longer ISIs of grid cells in HCN1 KOs (Giocomo et al., 2011a), the phase relationships of spikes relative to theta has not been studied in these animals. According to oscillatory interference models, cells will show theta phase precession as long as they are sufficiently theta modulated and have an ISI which is shorter than the theta period. Both control and HCN1 KO mice were shown to have plenty of theta modulated cells, the KOs even significantly more than the controls (Giocomo et al., 2011a). Also, the ISIs of both genotypes were shorter than the theta period. The difference between the ISI and theta period was around 20% smaller in KOs than in wildtypes however, which might decrease the amount of theta phase precession and it’s spatial information content in knockouts (O’Keefe and Burgess, 2005).

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For the current project, we attempted to compare theta phase precession between controls and KOs. We used similar circular regression methods as Hafting et al. (2008), who originally showed the existence of hippocampal independent theta phase precession in the MEC of rats. This method is described in more detail in the methods section. We were however not able to repeat the findings of Hafting et al. (2008) in mice, and believe that a different or altered method of analysis is necessary to study theta phase precession in mice.

2 Methods

2.1 Animals

In total, 8 male mice were used for the experiments; 5 wild types and 3 forebrain re-stricted HCN1 knockouts. Mice were bred at Columbia University, NY from a hybrid, 50/50% c57BL/6J:129SVEV background. The generation of the forebrain specific HCN1 knockouts was described in detail by Nolan et al. (2003). Animals arrived at the lab at the age of 3 - 6 months and were given a minimum of 2 weeks to accomodate before implantation. The mice were housed on a reversed, 12/12h day/night cycle, so they could be tested in their active phase during normal office hours. Littermates were housed together until surgery unless fighting was observed, in which case the dominant mouse was removed and housed seperately. Preceding surgery mice received food ad libitum. Following surgery, all mice were housed seperately to avoid damaging eachother’s im-plants. Experiments began after mice had recovered from surgery, typically 4–7 days post-procedure. As long as recordings were taking place, mice were food restricted and kept at 95% of ad-libitum weight to promote exploratory behavior during experiments. On days preceding recordings, usually 5 out of 7 days in a week, mice were therefor given limited access to food (1.5g – 2.5g) while being fed ad libitum on the remaining days. Water was always available ad libitum and animals were always given appropriate chewing toys and nesting material.

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2.2 Drive Implantation

Animals were implanted with a two tetrode, eight-channel microdrive over the right hemisphere (Axona, St. Albans, UK). Tetrodes consisted of four bundled platinum– iridium (90%–10%) wires (California Fine Wire, CA). Individual wires were 17 µm in diameter and insulated with a polyimide coating. Before implantion tetrodes were cut flat and platinum plated to lower resistance of each channel to around 150 kΩ.

An intraperitoneal injection of Equithesin (pentobarbital + choralhydrate, .12ml/30g) is given prior to surgery as anesthetic. After anesthesia is induced the mouse’ head is shaved using fine, electric clippers, from the first neck vertabra posteriorly until anteriorly near the eyes. Using a stereotaxic device, the head of the mouse is stabilized in a horizon-tal position by applying earbars and supporting the teeth in a mouthpiece. While in the stereotaxic device, the mouse lays on an electronic heating cushion which is kept at 37◦C to avoid hypothermia. After desinfection of the skin, an incision is made front to back across the skull and the periosteum is removed using a scalpel. Using a mounted drill, an approximately 1.5mm craniotomy is made 0.4mm posterior to lambda and 3.2mm laterally. Additionally, six holes (0.6mm) are drilled in the skull and watchmaker screws are fitted in them to later support the drive. One of the screws has an insulated copper wire attached which whill be soldered to the drive to serve as the general ground. The drive is then mounted on the stereotaxic device for implantation through the craniotomy. In order to record from as large a portion of MEC layer II as possible, the tetrodes are ideally implanted paralel to layer II. Based on experience, we chose to implant at a 5 degree angle (Hafting et al., 2005, Giocomo et al., 2011a). The drive is lowered until the tip of the tetrodes are 1100 µm below the cortical surface. The outer canula of the drive then rests on the edges of the craniotomy, which is subsequently sealed using Spongostan (Ethicon, Somerville, NJ). Dental cement is applied to the skull and bottom of the drive. Care is taken to apply dental cement around all the screws. No dental cement should be applied over the skin of the head, since this interferes with healing. Throughout the entire procedure, the level of anesthesia is regularly checked by testing the tail and toe pinch reflexes.

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After the dental cement is fully hardened, the animal is taken from the stereotaxic device and placed in a new cage to recover. This cage has high walls and has a plexiglass lid to prevent the mouse from climbing or otherwise damaging it’s implant. Until the animal awakes, the cage is placed under a heating lamp to avoid hypothermia. The first four days after surgery, mice receive their normal food pellets ad libitum as well as the same pellets soaked in water to soften them and promote eating. During the recovery from surgery, the mouse’ behavior and healing of the wound are monitored closely. Experimental training begins when the animal appears fully recoverd, but at the earliest after four days of rest.

2.3 Behavior and data aquisition

Environment and behavioral apparatus All experimental recording and pretrain-ing takes place in the same experiment room (3m by 5m). Recordpretrain-ings take place in a custom made open field (100cm by 100cm) and on a custom made linear track (150cm by 8cm). The open field is placed in the middle of the room. All recording equipment, as well as a desk for the experimenter, is situated on one of the short sides of the room. No screens or curtains obscure this part of the room, apart from the walls of the open field itself. Therefor several objects (such as some recording equipment, ceiling lights and occasionally the experimenter) remained visible to the animal. The other walls of the room were obscured behind a white curtain which hung from rails on the ceiling and which formed half a circle around the open field. During pretraining and recording, only just enough light was on in the room for the experimenter to operate the equipment.

The open field box was custom made at our lab. It consists of a square aluminum frame of 100 * 100 * 50 cm. Black plastic walls cover the entire inside of this frame. In the center of one of the walls, a 20 * 50 cm white cue-card is placed. During all sessions, the box is placed in the same, marked location on a black plastic floor-plate which is anchored to the center of the experiment room. The box is always oriented the same with respect to the experiment room.

The linear track was also custom made at the lab. It is a 180 * 8 cm aluminum beam with a smooth, black rubber top for the animal to run on. Linear track recordings

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take place in the same experiment room as the open field recordings. The linear track is placed on two 70cm high plastic supports, one on either side of the open field box. At 15cm from either end of the linear track, a barrier made from black plastic is placed. These barriers limit the traversable length of the track to 150cm and prevent the animal from climbing from the track onto the supports.

Training and recording routine Mice are known to be reluctant to explore novel environments, especially open spaces, and might not initially be stimulated by novel food rewards. We take several simple measures to greatly alleviate these problems. On the five days preceding surgery, mice are introduced to the open field box which will later be used for experimental recordings. Without being connected to the recording equipment, they freely explore for around 30 minutes, or more if they initially seem very reluctant. Although mice are not food restricted at this time, some food reward (vanilla cookie crumble) is dropped at random locations in the open field during these pretraining sessions. Additionally, to accustom them to the reward, mice receive some of the cookie in their cage after pretraining.

All recording sessions take place during daytime hours, either in the morning or the afternoon. One recording session consists of 40 minutes of food-motivated exploration in an open field box (100cm by 100cm), followed by 20 food-motivated runs, back and forth, on a linear track (150cm). Before every sessions, mice are taken from the stables to the recording room in a plexiglass cage which is covered with a fresh towel to prevent escape and exposure of the animal to strong lighting in the hallways. In the recording room, the cage with the mouse is placed on a pedestal where the mouse is connected to the head stage of the Axona recording system. Using the DaqUSB recording software (Axona Ltd., St. Albans, UK) the signal on all channels is checked and, if necessary, adjustments are made to reference channels, signal amplification and spike recording threshold. Spike recording threshold was never set below 50µV and was generally between 60µV and 120µV. If no spikes were observed with amplitudes exceeding twice the noise level, the tetrodes were turned down 25µm and recording was postponed to later that day or the next day.

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Recording of activity was started after placing the animal in the open field. The cable connecting the animal to the recording equipment is lightweight and counterbal-anced, permitting the animal to move freely. As the animal runs in the open field, occasionally small crumbles of vanilla cookie are randomly dispersed in the arena as food rewards. Too much reward interferes with exploration and can lead to disinterest in the reward. In total, the animal spends 40 minutes in the open field. Some animals have a tendency to twist the head stage cable which could permit the animal to chew through the cable. When this happens, recording is briefly interrupted, the head stage is unplugged, the cable straightened and after plugging the head stage back, recording continues. Fol-lowing recording, the animal is put back into it’s cage. Here, the head stage is unplugged, the cable is straightened and the linear track is put in place as described earlier. The head stage is then plugged in again and the animal is placed on the track, where it runs back and forth twenty times. Small food rewards are randomly placed on either side of the track every two or three laps. Again, when the animal twists the head stage cable too much, recording is briefly interrupted to straighten the cable. After the linear track session, the tetrodes are turned down 25µm. No further recordings are conducted when no cells are found on five consecutive days, which is taken to indicate that the tetrode tips have left MEC layer II.

For hygienic reasons and to prevent the possible buildup of territorial smells, the open field and linear track were cleaned after every session with 70% EtOH.

Recording equipment and data collection Data was collected using the DaqUSB recording system (Axona, St. Albans, UK) and a Dell workstation running Microsoft Windows XP. Signals from the microdrive were transfered to the recording equipment via a head stage containing AC-coupled, unity-gain operational amplifiers and passed through a lightweight cable. The signal of a channel was referenced to a channel on the other tetrode, amplified between 8000 and 25000 times and band pass filtered between 0.8 and 6.7 kHz. Spikes that crossed a pre-set threshold (typically between 60 and 120 µV, never lower than 50 µV) were stored at 48 kHz, 8 bit, and were given a 32 bit time stamp (clock rate 96 kHz). EEG was continuously recorded from a single channel referenced to

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the ground screw, amplified 3000 to 10000 times, lowpass filtered at 500 Hz and sampled at 4.8 kHz.

The animal’s movement was tracked using a ceiling mounted black-and-white camera and the DaqUSB system. The system tracked two green LEDs (sampled at 50 Hz), one larger and one smaller, which were attached five centimeters apart on the head stage and oriented perpendicular to the animals head direction.

Perfusion and histology After recordings were terminated, mice were sacrificed by injection of an overdose of Equithesin. Immediately following, animals were transcardially perfused first with 0.9% saline until full decoloration of the liver was observed, and then using 4% formaldehyde. The brain was removed and placed in 4% formaldehyde for at least 24 hours. Using a cryostat, brains were frozen and cut in 30µm sagittal sections. These were mounted and stained using cresyl violet. Determining the location of the tetrode was based on the laminar organization of the MEC and aided by an anatomical atlas (The Mouse Brain in Stereotaxic Coordinates (Paxinos and Franklin, 2003)). Measurements of the recording location were made using AxioVision LE (vers. 4.3, Carl Zeiss MicroImaging GmbH, DE).

2.4 Data processing and analysis

Spike sorting Recorded spikes were attributed to putative cells using the Tint software tool (Axona Ltd., St. Albans, UK). To attribute spikes to putative neuron, we mainly used plots of the amplitudes of all spikes on the different channels of a tetrode where spikes belonging to the same putative neuron tend to cluster together. Additionally, peak and trough voltages, the times of peak and trough occurences relative to the start of the recording and voltage plots of manually selected moments in the waveform were used to cut away noise and possibly dissociate overlapping clusters. To estimate the quality of the clusters, autocorrelograms and crosscorrelograms were inspected by eye; detection of few spikes in the refractory period (the center 2 ms of the autocorrelograms) indicated little noise in the cluster. Next, we determined whether putative cells which were recorded in the open field were also recorded in the subsequent linear track session. Clusters

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which were very similar between sessions (i.e. with spikes of very similar amplitudes and waveforms on all channels) were identified as the same putative neuron. To determine whether clusters found in sessions on multiple days belonged to the same putative neuron, the spatial firing correlates and average waveforms of cells were manually inspected. When, on multiple days, clusters showed near identical grid phase, grid spacing and grid orientation, pronounced and near identical head direction sensitivity or pronounced and near identical border sensitivity, they were identified as the same putative neuron. Clusters with less than 100 spikes were excluded from further analyses.

Position estimation and the constructiong of rate maps To track the animals position, the head stage was fitted with two, green LEDs (one larger and one smaller), which were positioned 6 cm apart and oriented perpendicular to the animals head di-rection. Using recordings from a ceiling–mounted black–and–white camera, the DaqUSB software detected the two LEDs and stored the position and head direction of the ani-mal. The velocity of the animal was computed for individual samples. For subsequent analyses, all samples with a velocity lower than 2.5 cm/s and higher than 100 cm/s were excluded. The path of the animal was then constructed by sorting the position data into 2.5 * 2.5 cm bins and smoothing the trajectory using a 400 ms boxcar window filter. Firing rate maps were computed by making individual maps for 1) spikes per bin and 2) time spent in every bin. These two maps were both smoothed using a quasi-Guassian kernel over the surrounding 5 * 5 bins (Langston et al., 2010). Firing rate per bin was determined by dividing the corresponding bins in the two maps. The peak firing rate was defined as the highest rate found in any bin of the map. The criterium that open field sessions could only be included for subsequent analyses if the mouse had covered at least 70% of the arena was met by all sessions.

Grid cells: identification and analysis To detect grid cells, ’grid scores’ or ’gridness’ were calculated.

First, a spatial autocorrelation of the rate maps of all clusters in the open field was made. The method for making autocorrelograms was based on Pearson’s product

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moment correlation and is detailed in Sargolini et al. (2006) and Langston et al. (2010). A circular sample was then taken from the autocorrelogram and correlated with rotated versions of itself. The circular sample excluded the central peak, the radius of which was defined as the distance from the center to the first local minimum in the correlation or to the first negative correlation, whichever occurred first. The outer radius of the sample was the radius which would eventually lead to the highest grid score. To calculate grid scores, the circular sample was correlated with several rotated versions of itself. A Pearson correlation of the circular sample was made for rotations of 60 and 120 degrees, as well as for 30, 90 and 150 degrees. Because firing patterns of grid cells are hexagonal, correlations should ideally be maximal for the two former rotations, while being minimal for the latter ones. The grid score of a cluster is the smallest difference in correlation between any two members of the two sets of rotations. Because of the rotational symmetry of the autocorrelograms, correlating rotations of 180 degrees or more is not useful.

Grid spacing was determined as the median distance from the center of the autocorrelogram to the six peaks nearest to the center, with a peak being any area of 100 pixels of 1,5 * 1,5 cm2 _{outside the central peak with r ≥ 0.10. If less than six total peaks}

were detected, the outermost peak was used. Grid field size was defined as the radius of the circle around the center field in the autocorrelogram (see above). Grid orientation was defined as the angle between a fixed camera-reference line and the vector to the nearest grid peak in a counterclockwise direction.

If, for a particular grid cell, the ratio between the outer radius of the circular sample of the correlogram and the grid spacing differed by more than two standard deviations from the mean ratio, the cell was excluded from the analysis.

To define grid cells, previous studies used a shuffling procedure to predict ran-domized firing patterns for all cells (Sargolini et al., 2006, Giocomo et al., 2011a). In addition to calculating grid scores for the observed firing patterns, scores were calculated for all shuffled firing patterns (these studies used 100 randomized patterns per cluster per trial). Cells with an actual firing pattern with a grid score higher than the 99th percentile of the distribution of shuffled grid scores were defined as grid cells. Because of time limitations of the current project, we were not able to complete such a shuffling

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procedure. Instead our grid cells were defined as any cell with a grid score ≥ 0.3; close to the critical values of shuffled distributions found in a previous study using the same mice lines (Giocomo et al., 2011a).

Head direction cells Head direction was calculated for every sample based on the relative positions of the two headstage–mounted LEDs which had been detected by the DacqUSB system. Using direction bins of 3 degrees, maps were made for the total number of spikes in every direction and time spent in every direction. These were individually smoothed using a 15 degrees main window filter (2 bins on either side) and a directional tuning distribution was obtained for each cluster by dividing the spike map by the time map.

Spatial selectivity was ultimately expressed as the mean vector length of the directional tuning distribution. In previous studies, the observed mean vector length was compared to a distribution of mean vector lenghts obtained from shuffled data (same procedure as for grid cells) (Sargolini et al., 2006, Langston et al., 2010). Cells with directional selectivity higher than the 99th percentile of this distribution were considered head direction modulated. Again, due to time constraints we were not able to perform a shuffling analysis and we defined head direction cells as cells whose mean vector length ≥ 0.2; close to the critical values found in the previous study (Giocomo et al., 2011a). The peak rate was defined as the highest rate found in any bin of the rate map.

Border cells To calculate border scores, the difference was taken between the maximal length of wall touching any firing field of a cell and the average distance of that firing field to the nearest wall, and then dividing this difference by the sum of those values (Solstad et al., 2008). A firing field here was any contiguous area of 200 cm2 or larger where the firing rate was at least 30% of the peak firing rate. Multiple fields could be found by deleting each detected field from the rate map and executing another search until no other fields were found. As for grid cells and head direction cells, border cells were defined as cells with border scores above the 99th percentile of a distribution of border scores constructed from shuffled data. Due to time limitations, no shuffle procedure could be

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executed and instead we defined border cells as cells with a border score ≥ 0.55, close to the critical values found earlier (Giocomo et al., 2011a).

Spatial and angular stability Within session spatial stability of grid cells was cal-culated for each cluster as the correlation between spatial firing distributions of the smoothed rate maps of the first and second halves of the trial. Angular stability of hear direction cells was computed similarly for the smoothed rate maps.

Analysis of theta phase precession Analysis of theta phase precession was per-formed using data recorded during linear track running, but only clusters identified as grid cells in the immediately preceding open field session were included in the analysis. First, to isolate the EEG theta band, signals were filtered offline using an non–causal FFT (frequency domain) filter, constructed using a Hamming window. The low and high pass– and stopbands were set at 5–6 Hz and 10–11 Hz respectively, following Hafting et al. (2008). A cell was considered theta modulated if the spectral power within 1 Hz of the autocorrelogram’s peak in the theta band was at least 3 times the mean spectral power of the autocorrelogram in the 0–125 Hz range. Spikes of a cell at time t were assigned a phase relative to theta as 360 ∗ (t − t0)/(t1 − t0), where t0 and t1 are the preceding and

succeeding theta peaks. To assess the relation between phase and location of spikes, first a one–dimensional projection was made of the animal’s path along the linear track (i.e. only the mouse’ movement in the longitudinal direction was considered). Five centime-ters on both ends of the track, where the mouse paused to turn and/or eat reward, were ignored during analysis, as well as samples where the mouse was moving at less than 10 cm/s. Grid fields on the linear track were defined as areas of minimally 4 consecutive 2.5 cm bins with a firing rate of at least 20% of the peak rate of the cell. Fields had to contain at least 50 spikes in total. The peak rate of a cell was defined as the highest rate found in any bin on the track. These criteria for field detection were chosen because they yielded optimal separation of individual fields indicated by visual inspection of rate maps. The strength and rate of phase precession were determined using a modified linear regression analysis described previously by Hafting et al. (2008). The phase by position

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matrix of each identified firing field of a cell was rotated in steps of 1 degree across 360 degrees. For each of these rotations a regression curve was fitted. The regression slope of the curve with the highest R2 _{value was taken as the indicator for the rate of phase}

precession in that field.

3 Results

In total, we recorded 466 cells from seven mice. We found 233 cells in four wild type (WT) animals and 233 cells in 3 HCN1 knockouts (KOs). We found a significantly larger amount of both grid cells and head direction (HD) cells in KO animals; 71 out of 233 cells (30.4%) were grid cells in KOs, versus 41 out of 233 (17.6%) in WTs (z=3.25, p=0.001, binomial test). Similarly, 45 cells were HD cells in KOs (19.3%), versus 23 in WTs (9.9%) (z=2.89, p=0.004, binomial test). No significant difference was found for border cells, with 17 found in KOs (7.3%), and 18 found in WTs (7.7%)(z=0.1762, p=0.865, binomial test). Conjunctive cells were counted in each category for which they reached criterium. Observed differences are likely due to the small group sizes and could reflect uneven sampling in different parts of MEC. It should be noted however, that Giocomo et al. (2011a) reported similar differences. A combined analysis of the joint dataset could be considered to establish that these differences are not systematic.

In one of the knockout animals (animal ’KO3’) we recorded 21 HD cells and 11 border cells, but no grid cells. Subsequent analyses of grid cells deal therefore only with data of 2 KOs, in addition to grid cells form the 4 WTs of course.

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3.1 Example data

The following pages show some examples of recorded cells from both wild type and knockout mice. Figure 7 shows a typical screenshot from the Tint cutting software used to identify putative cells (Axona Ltd., St. Albans, UK). Figure 8 shows examples of grid cells in the open field and on the linear track. Finally, Figure 9 shows examples of head direction cells and border cells.

Figure 7: Example clusters and waveforms viewed in the Tint cutting software. On the left, six amplitude by amplitude plots of all spikes on four channels are shown. On the right, waveforms and average waveforms for three selected clusters (putative cells) are shown.

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Figure 8: (a) Shows grid cells in the open field. From left to right, the pannels show spike location, the smoothed rate map and the autocorellogram. On the left are grid cells from a knockout mouse (KO1), on the right grid cells from a wild type animal (WT3). ’f ’ Indicates the peak firing rate, ’g’ the gridness score. Distance from the entorhinal border is indicated on the left. (b) Shows spike locations of four grid cells in both the open field (top) and on the linear track (bottom) from two KOs (KO1, KO2) and one wild type animal (WT3).

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Figure 9: (a) Shows HD cells in the open field from one knockout animal (KO2) and one wild type (WT3). From left to right, the pannels show the head direction map, the smoothed rate map and the autocorellogram. ’MVL’ indicates the mean vector length, ’f ’ the peak firing rate. Distance from the entorhinal border is indicated on the left. (b) Shows border cells in the open field. From left to right, the pannels show spike location, the smoothed rate map and the autocorrelogram. ’b’ indicates the border score.

Spatial representations in an HCN1 knockout mouse model Increased spatial scale of entorhinal grid cells following decreased H current kinetics