Grid cells in the medial entorhinal cortex (MEC) respond when an animal occupies a periodic lattice of 'grid fields' in the environment. The grids are organized in modules with spatial periods, or scales, clustered around discrete values separated on average by ratios in the range 1.4-1.7. We propose a mechanism that produces this modular structure through dynamical self-organization in the MEC. In attractor network models of grid formation, the grid scale of a single module is set by the distance of recurrent inhibition between neurons. We show that the MEC forms a hierarchy of discrete modules if a smooth increase in inhibition distance along its dorso-ventral axis is accompanied by excitatory interactions along this axis. Moreover, constant scale ratios between successive modules arise through geometric relationships between triangular grids and have values that fall within the observed range. We discuss how interactions required by our model might be tested experimentally.
We have included the source code for our main simulation as a supporting file.
- Vijay Balasubramanian
- Vijay Balasubramanian
- Louis Kang
- Louis Kang
The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.
- Upinder Singh Bhalla, Tata Institute of Fundamental Research, India
© 2019, Kang & Balasubramanian
This article is distributed under the terms of the Creative Commons Attribution License permitting unrestricted use and redistribution provided that the original author and source are credited.
The amyloid beta (Aβ) plaques found in Alzheimer’s disease (AD) patients’ brains contain collagens and are embedded extracellularly. Several collagens have been proposed to influence Aβ aggregate formation, yet their role in clearance is unknown. To investigate the potential role of collagens in forming and clearance of extracellular aggregates in vivo, we created a transgenic Caenorhabditis elegans strain that expresses and secretes human Aβ1-42. This secreted Aβ forms aggregates in two distinct places within the extracellular matrix. In a screen for extracellular human Aβ aggregation regulators, we identified different collagens to ameliorate or potentiate Aβ aggregation. We show that a disintegrin and metalloprotease a disintegrin and metalloprotease 2 (ADM-2), an ortholog of ADAM9, reduces the load of extracellular Aβ aggregates. ADM-2 is required and sufficient to remove the extracellular Aβ aggregates. Thus, we provide in vivo evidence of collagens essential for aggregate formation and metalloprotease participating in extracellular Aβ aggregate removal.
The cerebellar granule cell layer has inspired numerous theoretical models of neural representations that support learned behaviors, beginning with the work of Marr and Albus. In these models, granule cells form a sparse, combinatorial encoding of diverse sensorimotor inputs. Such sparse representations are optimal for learning to discriminate random stimuli. However, recent observations of dense, low-dimensional activity across granule cells have called into question the role of sparse coding in these neurons. Here, we generalize theories of cerebellar learning to determine the optimal granule cell representation for tasks beyond random stimulus discrimination, including continuous input-output transformations as required for smooth motor control. We show that for such tasks, the optimal granule cell representation is substantially denser than predicted by classical theories. Our results provide a general theory of learning in cerebellum-like systems and suggest that optimal cerebellar representations are task-dependent.