Spatial Navigation

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Spatial Navigation

• Zaneta Navratilova and Mei Yin
• Theoretical Neuroscience Journal Club

Yoram B., Brookings T. and Fiete I. Triangular
lattice neurons may implement an advanced numeral
system to precisely encode rat position over
large ranges.
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Temporal Lobe Spatial Memory and Navigation System

• Sensory information is first processed in primary
  and secondary sensory cortical areas.

• Cortical areas representing all of the senses is
  input to the temporal lobe association areas,
  including the perirhinal, postrhinal, and
  entorhinal cortex.
• The entorhinal cortex is the major input to the
  hippocampus.

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Listening to a single hippocampal neuron.
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Firing Rate Map

• Hippocampal neurons are called place cells
• Their place fields are represented by
  representing their firing rate on a map of the
  environment.

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Grid Cells in the Medial Entorhinal Cortex

• Grid cells are active in locations that form a
  hexagonal/ triangular/ rhomboidal grid on the
  environment.

Hafting et. al., 2005
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Modules of grid cells along the length of the
MEC

• Grid cells recorded at different places along the
  dorso-ventral axis of the MEC have different
  spacing between vertices of the grid.
• Neurons recorded at the same location form grids
  with the same orientation and spacing.

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Applying CRT to grid cells

• According to Burak et al.
• Each module of grid cells represents division
  by one modulus (?i).
• There is N? number of modules
• Each grid cell is active when the division of
  space coordinates by its modulus results in a
  particular residue (ai) or phase.
• Note that this means that each residue is
  represented not by a number, but by the identity
  of the active neuron.
• Thus according to the theory, the identity of the
  active neurons in all of the modules gives enough
  information to localize the animal in a space
  given by the least common multiple of the moduli
  of all of the modules.
• The location of the animal is additionally coded
  by place cells in the hippocampus, which are each
  active at a given location (xi).

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Use of information provided by a CRT-scheme of
place coding

• Burak et al. propose that rats can use the
  information provided by this coding scheme in two
  possible ways
• Decoding it to allow for path integration over
  large (2x2km) distances.
• Thus, rats should be able to perform homing
  behaviors in the absence of landmarks over these
  large distances.
• Using it to apply unique labels to places which
  can be attached to landmarks in the environment.
• Thus, grid cells should accurately recall the
  phases of firing upon reaching a familiar
  landmark in a large environment from a different
  path.

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Role of the hippocampus?

• Both of these functions have
• previously been assigned to the
• hippocampus.
• Is the MEC the path integrator instead?
• According to this model, the MEC with a CRT-like
  coding scheme has a larger capacity than the 106
  cells of the hippocampus with a sparse coding
  scheme.
• A lesion of the dorsolateral band of the EC
  impairs rats performance in the water maze
  (Steffanach HI, Witter M, Moser MB, Moser EI,
  2005).
• Computation of distances to a goal may be more
  efficient via a parallel compartmentalized
  computation.

• Why do animals need both grid cells and place
  cells?
• Sparse coding is better for forming random
  associations between places or memories than
  distributed coding.

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Unresolved questions from the perspective of a
biologist

• Does the fact that they are rhomboidal grids fit
  into this model?
• Does the brain actually use CRT-like computations
  to derive the coding and decoding of the MEC?
• In my opinion unlikely (Remember that grid cells
  would code phase by identity of the neuron, not a
  number, so actual arithmetic with the phases is
  hard to imagine. Neural computation is easiest to
  model as coincidence detection, and hardest as
  multiplication and subtraction.)
• But please feel free to prove me wrong!