The following articles summarize an emerging neural theory of how grid and place cells develop neurophysiological properties that support navigational behaviors, including properties of modular organization, spiking dynamics, effects of cholinergic inactivation, oscillations, and attention. ******************************************************************************************************************************************************************************** Grossberg, S., and Pilly, P. K. (2014). Coordinated learning of grid cell and place cell spatial and temporal properties: multiple scales, attention, and oscillations. Philosophical Transactions of the Royal Society B., 369, 20120524, http://rstb.royalsocietypublishing.org/content/369/1635/20120524.full.pdf+ht... Abstract. A neural model proposes how entorhinal grid cells and hippocampal place cells may develop as spatial categories in a hierarchy of self-organizing maps. The model responds to realistic rat navigational trajectories by learning both grid cells with hexagonal grid firing fields of multiple spatial scales, and place cells with one or more firing fields, that match neurophysiological data about their development in juvenile rats. Both grid and place cells can develop by detecting, learning, and remembering the most frequent and energetic co-occurrences of their inputs. The model’s parsimonious properties include: Similar ring attractor mechanisms process linear and angular path integration inputs that drive map learning; the same self-organizing map mechanisms can learn grid cell and place cell receptive fields; and the learning of the dorsoventral organization of multiple spatial scale modules through medial entorhinal cortex to hippocampus may use mechanisms homologous to those for temporal learning through lateral entorhinal cortex to hippocampus (“neural relativity”). The model clarifies how top-down hippocampus-to-entorhinal attentional mechanisms may stabilize map learning, simulates how hippocampal inactivation may disrupt grid cells, and explains data about theta, beta, and gamma oscillations. The article also compares the three main types of grid cell models in light of recent data. **************************************************************************************************************** Pilly, P.K., and Grossberg, S. (2013). Spiking neurons in a hierarchical self-organizing map model can learn to develop spatial and temporal properties of entorhinal grid cells and hippocampal place cells. PLOS ONE, http://dx.plos.org/10.1371/journal.pone.0060599 Abstract. Medial entorhinal grid cells and hippocampal place cells provide neural correlates of spatial representation in the brain. A place cell typically fires whenever an animal is present in one or more spatial regions, or places, of an environment. A grid cell typically fires in multiple spatial regions that form a regular hexagonal grid structure extending throughout the environment. Different grid and place cells prefer spatially offset regions, with their firing fields increasing in size along the dorsoventral axes of the medial entorhinal cortex and hippocampus. The spacing between neighboring fields for a grid cell also increases along the dorsoventral axis. This article presents a neural model whose spiking neurons operate in a hierarchy of self-organizing maps, each obeying the same laws. This spiking GridPlaceMap model simulates how grid cells and place cells may develop. It responds to realistic rat navigational trajectories by learning grid cells with hexagonal grid firing fields of multiple spatial scales and place cells with one or more firing fields that match neurophysiological data about these cells and their development in juvenile rats. The place cells represent much larger spaces than the grid cells, which enable them to support navigational behaviors. Both self-organizing maps amplify and learn to categorize the most frequent and energetic co-occurrences of their inputs. The current results build upon a previous rate-based model of grid and place cell learning, and thus illustrate a general method for converting rate-based adaptive neural models, without the loss of any of their analog properties, into models whose cells obey spiking dynamics. New properties of the spiking GridPlaceMap model include the appearance of theta band modulation. The spiking model also opens a path for implementation in brain-emulating nanochips comprised of networks of noisy spiking neurons with multiple-level adaptive weights for controlling autonomous adaptive robots capable of spatial navigation. ******************************************************************************************************************************************************************************** Pilly, P.K., and Grossberg, S. (2014) How does the modular organization of entorhinal grid cells develop? Frontiers in Human Neuroscience, doi:10.3389/fnhum.2014.0037, http://journal.frontiersin.org/Journal/10.3389/fnhum.2014.00337/full 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. ********************************************************************************************************************************************************** Pilly, P.K., and Grossberg, S. (2013). How reduction of theta rhythm by medial septum inactivation may covary with disruption of entorhinal grid cell responses due to reduced cholinergic transmission. Frontiers in Neural Circuits, doi: 10.3389/fncir.2013.00173, http://www.frontiersin.org/Journal/10.3389/fncir.2013.00173/full?utm_source=... Abstract. Oscillations in the coordinated firing of brain neurons have been proposed to play important roles in perception, cognition, attention, learning, navigation, and sensory-motor control. The network theta rhythm has been associated with properties of spatial navigation, as has the firing of entorhinal grid cells and hippocampal place cells. Two recent studies reduced the theta rhythm by inactivating the medial septum (MS) and demonstrated a correlated reduction in the characteristic hexagonal spatial firing patterns of grid cells. These results, along with properties of intrinsic membrane potential oscillations (MPOs) in slice preparations of medial entorhinal cortex (MEC), have been interpreted to support oscillatory interference models of grid cell firing. The current article shows that an alternative self-organizing map (SOM) model of grid cells can explain these data about intrinsic and network oscillations without invoking oscillatory interference. In particular, the adverse effects of MS inactivation on grid cells can be understood in terms of how the concomitant reduction in cholinergic inputs may increase the conductances of leak potassium (K+) and slow and medium after-hyperpolarization (sAHP and mAHP) channels. This alternative model can also explain data that are problematic for oscillatory interference models, including how knockout of the HCN1 gene in mice, which flattens the dorsoventral gradient in MPO frequency and resonance frequency, does not affect the development of the grid cell dorsoventral gradient of spatial scales, and how hexagonal grid firing fields in bats can occur even in the absence of theta band modulation. These results demonstrate how models of grid cell self-organization can provide new insights into the relationship between brain learning and oscillatory dynamics. ********************************************************************************************************************************************************************************* Stephen Grossberg Wang Professor of Cognitive and Neural Systems Professor of Mathematics, Psychology, and Biomedical Engineering Director, Center for Adaptive Systems http://cns.bu.edu/~steve steve@bu.edu