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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

Anatomically overlapping grid cell modules. (A) Anatomical distribution of sampled grid cells belonging to different modules in one animal (Stensola et al., 2012). Simulation results of the SOM model: (B) Distribution of learned grid spacings in a SOM comprising 50 map cells, all with response rate μ =1, that are receiving adaptive inputs from stripe cells of two spacings (s1 = 20 cm, s2 = 35 cm). Only cells with gridness score > 0.3 are considered. (C) Distribution of learned grid spacings in a SOM comprising 50 cells, half with μ =1 and the remaining with μ =0.6, that are receiving adaptive inputs from stripe cells of two spacings (s1 = 20 cm, s2 = 35 cm). (D) Distribution of learned grid spacings in a SOM comprising 90 cells, one-third with μ =1, one-third with μ = 0.6, and the remaining with μ = 0.3, that are receiving adaptive inputs from stripe cells of three spacings (s1 = 20 cm, s2 = 35 cm, s3 = 50 cm). Panels (E–G) show spatial rate maps and autocorrelograms of illustrative grid cells with different learned spacings from the simulation summarized in (D). Note response rate (μ) and gridness score at the top of each rate map, and grid spacing at the top of each autocorrelogram. Peak activities As of stripe cells were 1, 0.8, 0.6 for spacings of 20, 35, 50 cm, respectively (see Equation 4). Color coding from blue (min.) to red (max.) is used in each rate map, and from blue (−1) to red (1) in each autocorrelogram. [Data in (A) is reprinted with permission from Stensola et al. (2012), and the other panels with permission from Grossberg and Pilly (2014)].
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Figure 4: Anatomically overlapping grid cell modules. (A) Anatomical distribution of sampled grid cells belonging to different modules in one animal (Stensola et al., 2012). Simulation results of the SOM model: (B) Distribution of learned grid spacings in a SOM comprising 50 map cells, all with response rate μ =1, that are receiving adaptive inputs from stripe cells of two spacings (s1 = 20 cm, s2 = 35 cm). Only cells with gridness score > 0.3 are considered. (C) Distribution of learned grid spacings in a SOM comprising 50 cells, half with μ =1 and the remaining with μ =0.6, that are receiving adaptive inputs from stripe cells of two spacings (s1 = 20 cm, s2 = 35 cm). (D) Distribution of learned grid spacings in a SOM comprising 90 cells, one-third with μ =1, one-third with μ = 0.6, and the remaining with μ = 0.3, that are receiving adaptive inputs from stripe cells of three spacings (s1 = 20 cm, s2 = 35 cm, s3 = 50 cm). Panels (E–G) show spatial rate maps and autocorrelograms of illustrative grid cells with different learned spacings from the simulation summarized in (D). Note response rate (μ) and gridness score at the top of each rate map, and grid spacing at the top of each autocorrelogram. Peak activities As of stripe cells were 1, 0.8, 0.6 for spacings of 20, 35, 50 cm, respectively (see Equation 4). Color coding from blue (min.) to red (max.) is used in each rate map, and from blue (−1) to red (1) in each autocorrelogram. [Data in (A) is reprinted with permission from Stensola et al. (2012), and the other panels with permission from Grossberg and Pilly (2014)].

Mentions: As noted above, Stensola et al. (2012) provided a comprehensive analysis of the anatomical organization of grid cells. They reported that grid cell scales are grouped into finitely many modules such that the cells in each module share some defining characteristics. In particular, grid cells that share similar scales also share similar grid orientations, and are modulated at similar theta band frequencies in their interspike interval histograms. Moreover, grid cells belonging to the same module, rather than different modules, show similarity in their rescaling responses to environmental compression along a dimension. Finally, grid cells grouped by similar attributes are not locally clustered, but are distributed with significant anatomical overlap among the modules along the dorsoventral axis (see Figure 4A).


How does the modular organization of entorhinal grid cells develop?

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

Anatomically overlapping grid cell modules. (A) Anatomical distribution of sampled grid cells belonging to different modules in one animal (Stensola et al., 2012). Simulation results of the SOM model: (B) Distribution of learned grid spacings in a SOM comprising 50 map cells, all with response rate μ =1, that are receiving adaptive inputs from stripe cells of two spacings (s1 = 20 cm, s2 = 35 cm). Only cells with gridness score > 0.3 are considered. (C) Distribution of learned grid spacings in a SOM comprising 50 cells, half with μ =1 and the remaining with μ =0.6, that are receiving adaptive inputs from stripe cells of two spacings (s1 = 20 cm, s2 = 35 cm). (D) Distribution of learned grid spacings in a SOM comprising 90 cells, one-third with μ =1, one-third with μ = 0.6, and the remaining with μ = 0.3, that are receiving adaptive inputs from stripe cells of three spacings (s1 = 20 cm, s2 = 35 cm, s3 = 50 cm). Panels (E–G) show spatial rate maps and autocorrelograms of illustrative grid cells with different learned spacings from the simulation summarized in (D). Note response rate (μ) and gridness score at the top of each rate map, and grid spacing at the top of each autocorrelogram. Peak activities As of stripe cells were 1, 0.8, 0.6 for spacings of 20, 35, 50 cm, respectively (see Equation 4). Color coding from blue (min.) to red (max.) is used in each rate map, and from blue (−1) to red (1) in each autocorrelogram. [Data in (A) is reprinted with permission from Stensola et al. (2012), and the other panels with permission from Grossberg and Pilly (2014)].
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Related In: Results  -  Collection

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Figure 4: Anatomically overlapping grid cell modules. (A) Anatomical distribution of sampled grid cells belonging to different modules in one animal (Stensola et al., 2012). Simulation results of the SOM model: (B) Distribution of learned grid spacings in a SOM comprising 50 map cells, all with response rate μ =1, that are receiving adaptive inputs from stripe cells of two spacings (s1 = 20 cm, s2 = 35 cm). Only cells with gridness score > 0.3 are considered. (C) Distribution of learned grid spacings in a SOM comprising 50 cells, half with μ =1 and the remaining with μ =0.6, that are receiving adaptive inputs from stripe cells of two spacings (s1 = 20 cm, s2 = 35 cm). (D) Distribution of learned grid spacings in a SOM comprising 90 cells, one-third with μ =1, one-third with μ = 0.6, and the remaining with μ = 0.3, that are receiving adaptive inputs from stripe cells of three spacings (s1 = 20 cm, s2 = 35 cm, s3 = 50 cm). Panels (E–G) show spatial rate maps and autocorrelograms of illustrative grid cells with different learned spacings from the simulation summarized in (D). Note response rate (μ) and gridness score at the top of each rate map, and grid spacing at the top of each autocorrelogram. Peak activities As of stripe cells were 1, 0.8, 0.6 for spacings of 20, 35, 50 cm, respectively (see Equation 4). Color coding from blue (min.) to red (max.) is used in each rate map, and from blue (−1) to red (1) in each autocorrelogram. [Data in (A) is reprinted with permission from Stensola et al. (2012), and the other panels with permission from Grossberg and Pilly (2014)].
Mentions: As noted above, Stensola et al. (2012) provided a comprehensive analysis of the anatomical organization of grid cells. They reported that grid cell scales are grouped into finitely many modules such that the cells in each module share some defining characteristics. In particular, grid cells that share similar scales also share similar grid orientations, and are modulated at similar theta band frequencies in their interspike interval histograms. Moreover, grid cells belonging to the same module, rather than different modules, show similarity in their rescaling responses to environmental compression along a dimension. Finally, grid cells grouped by similar attributes are not locally clustered, but are distributed with significant anatomical overlap among the modules along the dorsoventral axis (see Figure 4A).

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