HIPPOCAMPUS 00:1–8 (2014)

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The Transformation From Grid Cells to Place Cells is Robust to Noise in the Grid Pattern Amir H. Azizi,1,2 Natalie Schieferstein,2,3 and Sen Cheng1,2*

ABSTRACT: Spatial navigation in rodents has been attributed to placeselective cells in the hippocampus and entorhinal cortex. However, there is currently no consensus on the neural mechanisms that generate the place-selective activity in hippocampal place cells or entorhinal grid cells. Given the massive input connections from the superficial layers of the entorhinal cortex to place cells in the hippocampal cornu ammonis (CA) regions, it was initially postulated that grid cells drive the spatial responses of place cells. However, recent experiments have found that place cell responses are stable even when grid cell responses are severely distorted, thus suggesting that place cells cannot receive their spatial information chiefly from grid cells. Here, we offer an alternative explanation. In a model with linear grid-to-place-cell transformation, the transformation can be very robust against noise in the grid patterns depending on the nature of the noise. In the two more realistic noise scenarios, the transformation was very robust, while it was not in the other two scenarios. Although current experimental data suggest that other types of placeselective cells modulate place cell responses, our results show that the simple grid-to-place-cell transformation alone can account for the origin C 2014 Wiley Periodicals, Inc. of place selectivity in the place cells. V KEY WORDS: hippocampus; medial entorhinal cortex; spatial representation; neural networks; feedforward networks

INTRODUCTION The hippocampal formation, with its place-selective cells, has long been considered the location for the cognitive map in rodents (O’Keefe and Nadel, 1979). The anatomical connections within the hippocampal formation are well studied (Witter, 1993). Specifically, it has been

This article was published online on 06 June 2014. An error was subsequently identified. This notice is included in the online and print versions to indicate that both have been corrected 13 June 2014. 1 Department of Psychology, Ruhr-University Bochum, Bochum, Germany; 2 Mercator Research Group “Structure of Memory”, RuhrUniversity Bochum, Bochum, Germany; 3 Department of Mathematics, Ruhr-University Bochum, Bochum, Germany Grant sponsor: DFG; Grant number: SFB874-Project B2; Grant sponsor: Stiftung Mercator. *Correspondence to: Sen Cheng, Mercator Research Group “Structure of Memory”, Department of Psychology, Ruhr-Universit€at Bochum, Universit€atsstr. 150, Bochum, NRW 44801, Germany. E-mail: [email protected] Accepted for publication 16 May 2014. DOI 10.1002/hipo.22306 Published online 00 Month 2014 in Wiley Online Library (wileyonlinelibrary.com). C 2014 WILEY PERIODICALS, INC. V

shown that there are massive projections from the superficial layers of medial entorhinal cortex (MEC) to the hippocampal CA regions (Zhang et al., 2013). After the discovery of grid cells in MEC layer II (Hafting et al., 2005), it was proposed that grid cells provide the spatial input signal to place cells (Fuhs and Touretzky, 2006; McNaughton et al., 2006; Rolls et al., 2006; Solstad et al., 2006; Blair et al., 2007; Franzius et al., 2007). Experimental evidence for the presence of stable place cells, while non-MEC inputs to CA1 were eliminated, indeed supports these models (Brun et al., 2002; Nakashiba et al., 2008; Van Cauter et al., 2008; Cabral et al., 2014). We showed previously that the various disparate models find similar solutions for the grid-to-place-cell transformation (Cheng and Frank, 2011). This solution is equivalent to a feedforward network, in which the connection weights from grid to place cells are monotonically decreasing with respect to the normalized spatial offset of the grid pattern. However, recent experimental results have cast doubt on the simple view that the spatial selectivity in place cells is driven mainly by grid cell inputs. Two studies reported that, when theta oscillations in the hippocampus were disrupted by reversibly inactivating the medial septum (MS; Mizumori et al., 1989), CA1 neurons continued to have normal and stable place fields even though the spatially periodic firing pattern of MEC grid cells was severely degraded (Brandon et al., 2011; Koenig et al., 2011). Two other studies found that in young rat pups place and head-direction cells develop adult-like firing patterns earlier than grid cells do (Langston et al., 2010; Wills et al., 2010). These studies conclude that spatially periodic activity patterns in grid cells is not necessary to drive stable place cell responses, thus indicating that inputs from other cells that encode spatial information primarily drive place cell responses. Recently, Bush et al. (2014) suggested that these inputs are supplied by boundary cells (Solstad et al., 2008). Here, we explore an alternative explanation and hypothesize that grid cell inputs alone could account for place cell firing, even when the periodicity of the grid cells is lost. The key is that the transformation from grid cells to place cells is very robust against biologically induced noise in the grid pattern. This is

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FIGURE 1. Definitions of the model. A) Three sinusoidal gratings, aligned at 60 , produce a hexagonal grid pattern. B) A typical example of grid cell firing pattern (upper panels) and their auto-correlograms (lower panels) in the presence of large amounts of corresponding noise. The titles in the upper panels indicate how noise was added to the grid pattern, the number in the top-

right corner of the lower panels indicate the gridness score. C) Illustration of the path integration noise. The longer the trajectory is estimated via path integration, the larger the accumulated error becomes. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

indeed what we find in neural network simulations of the gridto-place-cell transformation, where we add different types of noise to the grid pattern. While we are well aware that inputs from neurons other than grid cells strongly modulate the spatial firing of place cells, our results indicate that it is not inconceivable, given the current evidence, that grid cells provide the primary spatial input to place cells. The periodic hexagonal pattern of grid cell firing can be defined by three parameters: the spacing between peaks, the orientation, and the spatial offset of the fields with respect to a reference point. In computational models, the grid pattern can be formed by the summation of three cosine gratings, oriented at 60 apart from each other (Fig. 1A). Indeed, a two dimensional Fourier analysis of experimental data has shown that most grid cells can be characterized by three components with similar wavelength in their corresponding Fourier series (Krupic et al., 2012). We, therefore, modeled the activation of grid cells as follows.

To assess the hexagonal periodicity of the grid pattern we used the gridness score as defined in (Langston et al., 2010). Electrophysiological recordings from a large ensemble of grid cells have shown that grid spacing and orientation of grid cells are organized in discrete modules across the dorsoventral axis (Stensola et al., 2012). This topographic structure with independent modules of grid cells differs from the anatomical cortical column structure (Burgalossi et al., 2011; Ray et al., 2014). Based on theoretical (Monaco and Abbott, 2011) and experimental (Stensola et al., 2012) studies, we used four distinct modules in which all grid cells had the same spacing and orientation. The spatial offset of the grid pattern was chosen randomly for each of the cells. To model the disrupted grid patterns, we studied four different mechanisms. First, we added noise to the amplitude of each of the grid patterns, as a random number drawn from a normal distribution around 0 with different variances between 0 and 2 [na term in Eq. (1), Fig. 1B]. Second, we added noise to the phase of the grid patterns, as a positive random number drawn from a uniform distribution between 0 and 6 [np in Eq. (1)]. Our third strategy was motivated by recent observations that grid cells with more stable Fourier components tend to have more stable grid patterns. Disorientation of any of the components seems to be the reason for deviation from the regular grid pattern (Krupic et al., 2012). We modeled this process by adding noise to the direction of unit vectors [nd in Eq. (1)]. The noise was distributed uniformly between 2f and f, where 0

The transformation from grid cells to place cells is robust to noise in the grid pattern.

Spatial navigation in rodents has been attributed to place-selective cells in the hippocampus and entorhinal cortex. However, there is currently no co...
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