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13th November 2013

Path integration, continuous attractors and grid cells
Path integration
It is a behaviour phenomenon that occurs in animals where their outward path (e
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from nest towards food)
is unpredictable and windy, but the return path to the starting place is direct
...
It is called ‘path integration’ because the return path is calculated mathematically by
continuously integrating the distance and direction travelled, e
...
add all of the steps of the outward path
then revert the information for the return path
...
e
...
However, it is not always
accurate, a path integration bias has been found: it’s been shown in many species that the test subject
always underestimate the angle from the goal to the starting point
...
It is always better to be short of the starting location than to be too long off,
because you might receive environmental cues as you’ve gone back over where you’ve been, i
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more likely
to re-cross a path you’ve taken
...

Experimentally it has been shown that path integration is more accurate if the person is actively moving
themselves rather than being moved passively by another force
...

Etienne et al
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While it pouched food,
the platform was rotated clockwise or
counterclockwise
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In both situations, the
subjects returned fairly directly to the arena
periphery and then searched for the nest
along the arena wall
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The greater the number of unidirectional
passive rotations or actively performed
unidirectional circles, the less they were compensated for and the greater the scatter of the homing
direction
...
”
Place cells and path-integration
Path integration appears to orient the place cell representation
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1997

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Record place cell firing in rats, then rotate
the rats and the box then the place field
stays the same
...
But
then rotate only the rat, not the box, the
place field shifts because the rat assumes
the box has also rotated
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When the rat and box was rotated together
in the light, place field stays the same
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This is
logical as path integration causes cumulative error
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So sensory cues are used to ret the path integrator
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1996

A rat runs along a track unidirectionally from a movable starting box to a fixed reward box
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There are other visual cues along the track so that rat knows that
even though it is close to the box, it is actually not at the same place as before
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This is evidence for path integration input to the place cells
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So when the rat runs an outbound journey, i
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from the movable box, the place field is
always the same distance from that box, i
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moves with the box
...
e
...
This is inferential evidence that place cells are getting distance information
inputs to determine their output place field firing
...
The peak of the field shifted
towards the wall away from which the rat was
moving
...

When this is averaged, a split firing of place field is
seen, showing the rat is trying to maintain distance
information
...
So place cells must be connected over a local network, so what are these
network interactions and how do different place cells communicate with each other? In CA3, it is a highly
densely recurrently connected network
...
g
...
A continuous attractor network is a special kind to the
attractor network
...
A continuous attractor is a set of patterns to which other patterns are attracted to,
but within which the pattern of activity can change smoothly from one to another
...
(1996) proposed that the patterns of activity shown by the place cells formed a
continuous attractor: all of them can be thought of as having the same ‘bump’ shape
...
5 m2) with a rat
running around in it
...

Each cell’s location reflects the location of its firing
field in the environment
...

As the rat runs around this environment, the place cells that have place fields next to each other will
be wired together (increase synaptic connection) due to Hebbian learning, as those two place cells
are likely to fire together when a rat is in/near that particular place field location
...
(Remembering that the place cells are projected onto the
environment as their place fields
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The
bump (z-axis plot) indicates the rat’s location and moves as the rat moves
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13th November 2013


There is noise in the network, but the peak of the active place cell is very high
...

To do path integration, then just have to move the bump (as it represents where you are) along according to
active self-movements, which gives the internal code for one’s location
...
The requisite synaptic connectivity is
often referred to as ‘Mexican hat’
...

The continuous attract network also ensures that only a
single location is represented
...
e
...

How to make the bumps move
Adding asymmetric connections in a particular direction makes the activity bump shift in that direction, with
a speed proportional to the strength of the asymmetric connections
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Shifter cells (Burgess and Barry 2014)
They are cells that are each tuned to a different direction
...


The shifter cells gives input to the synapses between the place cells
...
It does this by increasing
the synaptic strength of one place cell with another place cell
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The shifter cells can give input to the next cell along in the network
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An asymmetrical connection is added by a place cell receiving
excitatory from the neighbouring place cell and a shifter cell
...
This is biologically realistic- they have been identified in the brain including

13th November 2013
the anterior thalamus (Taube 1995, Sharp and Blair 1995), presubiculum (Markus et al
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Summary:
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

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

Path integration is the process by which an animal updates its location - relative to some starting
position – by keeping a cumulative record of internal movement information
Connecting place cells with synaptic weights that increase with the proximity of the two cell’s firing
fields can produce a particular type of activity in a neural network - a ‘bump’ in which cells with
nearby firing fields are active – and the set of all such patterns forms a continuous attractor
The pattern of activation can change, within this set, so that the activity bump moves around the
network
...
The activity bump would then
automatically follow the rat’s movement – thus performing path integration
One issue with this model is that place cells are also driven by sensory input, not just path
integration
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If this is programmed, it relies on perfect synaptic
connectivity
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Grid cells (Hafting et al
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Grid cells have been discovered in mEC
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Head direction cells are found in presubiculum and they fire only when an animal is
facing a certain direction
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Properties of grid cells:









Fire in strikingly regular array of locations as a rat explores
an environment
These arrays are stable from trial to trial
...
The network ‘wraps’
around because of orientation phase
...
Connections can be

13th November 2013
fine-tuned regardless of the specific location and environment
...

Conjunctive (grid x direction) cells (Sargolini et al
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So the grid cells firing
rate is modulated by direction
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These provide an obvious correlate of the second group of postulated ‘shifter cells’ needed to perform path
integration in a continuous attractor network
...
Shifter cells are found in the gird cell network, not the place cell network, which is more inferential
evidence for grid cells’ role in path integration
...
But they also get sensory
inputs from the place cells to reset the
error and that they are linked to
sensory cues
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So there are two interconnected networks, both with a slightly different role but
both giving inputs to the other, so that their activity can be updated when they don’t have the input they
each need
...
So grid cells should also be reshaped by
deformations of the environment? Deformation of the environment causes a complementary change in grid
scale
...
This supports the idea that place cells ‘attach’ grid cells to the
sensory environment (or vice versa) (Barry et al
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Summary:
Grid cells fire in several locations arranged on a hexagonal grid across the environment
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A small set of grid cells could perform path integration - updating their relative firing rates to track the
movement of the animal
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The grid cells could thus provide the path integration input to place cells: each place cell firing where all of
the grid cell inputting to it overlap
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