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How does the modular organization of entorhinal grid cells develop?

Pilly PK, Grossberg S - Front Hum Neurosci (2014)

Bottom Line: Within this SOM model, grid cells with different rates of temporal integration learn modular properties with different spatial scales.Slower rates of grid cell temporal integration support learned associations with stripe cells of larger scales.The explanatory and predictive capabilities of the three types of grid cell models are comparatively analyzed in light of recent data to illustrate how the SOM model overcomes problems that other types of models have not yet handled.

View Article: PubMed Central - PubMed

Affiliation: Information and Systems Sciences Laboratory, HRL Laboratories, LLC, Center for Neural and Emergent Systems Malibu, CA, USA.

ABSTRACT
The entorhinal-hippocampal system plays a crucial role in spatial cognition and navigation. Since the discovery of grid cells in layer II of medial entorhinal cortex (MEC), several types of models have been proposed to explain their development and operation; namely, continuous attractor network models, oscillatory interference models, and self-organizing map (SOM) models. Recent experiments revealing the in vivo intracellular signatures of grid cells (Domnisoru et al., 2013; Schmidt-Heiber and Hausser, 2013), the primarily inhibitory recurrent connectivity of grid cells (Couey et al., 2013; Pastoll et al., 2013), and the topographic organization of grid cells within anatomically overlapping modules of multiple spatial scales along the dorsoventral axis of MEC (Stensola et al., 2012) provide strong constraints and challenges to existing grid cell models. This article provides a computational explanation for how MEC cells can emerge through learning with grid cell properties in modular structures. Within this SOM model, grid cells with different rates of temporal integration learn modular properties with different spatial scales. Model grid cells learn in response to inputs from multiple scales of directionally-selective stripe cells (Krupic et al., 2012; Mhatre et al., 2012) that perform path integration of the linear velocities that are experienced during navigation. Slower rates of grid cell temporal integration support learned associations with stripe cells of larger scales. The explanatory and predictive capabilities of the three types of grid cell models are comparatively analyzed in light of recent data to illustrate how the SOM model overcomes problems that other types of models have not yet handled.

No MeSH data available.


Related in: MedlinePlus

Properties of learned grid cells in the SOM model as a function of response rate μ, responding to single-scale stripe cell inputs with a spacing s = 20 cm. Panels (A–D) show gridness score, grid spacing, inter-trial stability, and the proportion of learned grid cells (with gridness score > 0.3), respectively. Peak activity As of stripe cells was 1. Each error bar in (A–C) corresponds to standard error of mean (s.e.m.). The dashed lines parallel to the x-axis in (A), (C), and (D) signify corresponding experimentally measured values for adult dorsal grid cells (Langston et al., 2010; Wills et al., 2010). Panel (E) shows the spatial rate map and autocorrelogram of the learned grid cell with the highest gridness score in the last trial (#20) in the map corresponding to the optimal response rate μ = 0.9. Color coding from blue (min.) to red (max.) is used for the rate map, and from blue (−1) to red (1) for the autocorrelogram.
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Figure 1: Properties of learned grid cells in the SOM model as a function of response rate μ, responding to single-scale stripe cell inputs with a spacing s = 20 cm. Panels (A–D) show gridness score, grid spacing, inter-trial stability, and the proportion of learned grid cells (with gridness score > 0.3), respectively. Peak activity As of stripe cells was 1. Each error bar in (A–C) corresponds to standard error of mean (s.e.m.). The dashed lines parallel to the x-axis in (A), (C), and (D) signify corresponding experimentally measured values for adult dorsal grid cells (Langston et al., 2010; Wills et al., 2010). Panel (E) shows the spatial rate map and autocorrelogram of the learned grid cell with the highest gridness score in the last trial (#20) in the map corresponding to the optimal response rate μ = 0.9. Color coding from blue (min.) to red (max.) is used for the rate map, and from blue (−1) to red (1) for the autocorrelogram.

Mentions: Simulation results presented in Figures 1–3 reveal that the optimal temporal response rate μ for grid cell learning depends on the spatial scale, even when the input stripe cells have the same scale. In particular, the smaller the grid spacing, the larger is the optimal response rate. For example, for the input stripe spacing s = 20 cm the mean gridness score of the learned map cells peaks at μ = 0.9 (Figure 1A), whereas for the input stripe spacing s = 50 cm the corresponding peak occurs at μ = 0.4 (Figure 3A). Similarly, the mean inter-trial stability and the proportion of learned grid cells exhibit similar trends in their tuning to response rate μ. Moreover, the tuning widths also increase with the spatial scale. These results provide further support to our previously described hypothesis that the rate of temporal integration of entorhinal map cells determines the subset of input stripe scales to which they can get tuned, and thereby the development of their regular hexagonal grid fields (Grossberg and Pilly, 2012). Also, whereas the mean gridness score at the optimal response rate is relatively smaller for bigger spatial scales, the mean spatial stability is larger, consistent with experimental observations (Giocomo et al., 2011).


How does the modular organization of entorhinal grid cells develop?

Pilly PK, Grossberg S - Front Hum Neurosci (2014)

Properties of learned grid cells in the SOM model as a function of response rate μ, responding to single-scale stripe cell inputs with a spacing s = 20 cm. Panels (A–D) show gridness score, grid spacing, inter-trial stability, and the proportion of learned grid cells (with gridness score > 0.3), respectively. Peak activity As of stripe cells was 1. Each error bar in (A–C) corresponds to standard error of mean (s.e.m.). The dashed lines parallel to the x-axis in (A), (C), and (D) signify corresponding experimentally measured values for adult dorsal grid cells (Langston et al., 2010; Wills et al., 2010). Panel (E) shows the spatial rate map and autocorrelogram of the learned grid cell with the highest gridness score in the last trial (#20) in the map corresponding to the optimal response rate μ = 0.9. Color coding from blue (min.) to red (max.) is used for the rate map, and from blue (−1) to red (1) for the autocorrelogram.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4042558&req=5

Figure 1: Properties of learned grid cells in the SOM model as a function of response rate μ, responding to single-scale stripe cell inputs with a spacing s = 20 cm. Panels (A–D) show gridness score, grid spacing, inter-trial stability, and the proportion of learned grid cells (with gridness score > 0.3), respectively. Peak activity As of stripe cells was 1. Each error bar in (A–C) corresponds to standard error of mean (s.e.m.). The dashed lines parallel to the x-axis in (A), (C), and (D) signify corresponding experimentally measured values for adult dorsal grid cells (Langston et al., 2010; Wills et al., 2010). Panel (E) shows the spatial rate map and autocorrelogram of the learned grid cell with the highest gridness score in the last trial (#20) in the map corresponding to the optimal response rate μ = 0.9. Color coding from blue (min.) to red (max.) is used for the rate map, and from blue (−1) to red (1) for the autocorrelogram.
Mentions: Simulation results presented in Figures 1–3 reveal that the optimal temporal response rate μ for grid cell learning depends on the spatial scale, even when the input stripe cells have the same scale. In particular, the smaller the grid spacing, the larger is the optimal response rate. For example, for the input stripe spacing s = 20 cm the mean gridness score of the learned map cells peaks at μ = 0.9 (Figure 1A), whereas for the input stripe spacing s = 50 cm the corresponding peak occurs at μ = 0.4 (Figure 3A). Similarly, the mean inter-trial stability and the proportion of learned grid cells exhibit similar trends in their tuning to response rate μ. Moreover, the tuning widths also increase with the spatial scale. These results provide further support to our previously described hypothesis that the rate of temporal integration of entorhinal map cells determines the subset of input stripe scales to which they can get tuned, and thereby the development of their regular hexagonal grid fields (Grossberg and Pilly, 2012). Also, whereas the mean gridness score at the optimal response rate is relatively smaller for bigger spatial scales, the mean spatial stability is larger, consistent with experimental observations (Giocomo et al., 2011).

Bottom Line: Within this SOM model, grid cells with different rates of temporal integration learn modular properties with different spatial scales.Slower rates of grid cell temporal integration support learned associations with stripe cells of larger scales.The explanatory and predictive capabilities of the three types of grid cell models are comparatively analyzed in light of recent data to illustrate how the SOM model overcomes problems that other types of models have not yet handled.

View Article: PubMed Central - PubMed

Affiliation: Information and Systems Sciences Laboratory, HRL Laboratories, LLC, Center for Neural and Emergent Systems Malibu, CA, USA.

ABSTRACT
The entorhinal-hippocampal system plays a crucial role in spatial cognition and navigation. Since the discovery of grid cells in layer II of medial entorhinal cortex (MEC), several types of models have been proposed to explain their development and operation; namely, continuous attractor network models, oscillatory interference models, and self-organizing map (SOM) models. Recent experiments revealing the in vivo intracellular signatures of grid cells (Domnisoru et al., 2013; Schmidt-Heiber and Hausser, 2013), the primarily inhibitory recurrent connectivity of grid cells (Couey et al., 2013; Pastoll et al., 2013), and the topographic organization of grid cells within anatomically overlapping modules of multiple spatial scales along the dorsoventral axis of MEC (Stensola et al., 2012) provide strong constraints and challenges to existing grid cell models. This article provides a computational explanation for how MEC cells can emerge through learning with grid cell properties in modular structures. Within this SOM model, grid cells with different rates of temporal integration learn modular properties with different spatial scales. Model grid cells learn in response to inputs from multiple scales of directionally-selective stripe cells (Krupic et al., 2012; Mhatre et al., 2012) that perform path integration of the linear velocities that are experienced during navigation. Slower rates of grid cell temporal integration support learned associations with stripe cells of larger scales. The explanatory and predictive capabilities of the three types of grid cell models are comparatively analyzed in light of recent data to illustrate how the SOM model overcomes problems that other types of models have not yet handled.

No MeSH data available.


Related in: MedlinePlus