the hippocampus and spatial representation · the hippocampus and spatial representation...

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The Hippocampus and spatial representation

Andrej Bicanski

NEUR3041: Neural computation

Aims

2 The hippocampus and spatial representation

• Introduce the hippocampus and place cells

• Explore an unsupervised, competitive learning model of place cells (Sharp, 1991)

• Discuss subsequent experiments emphasising importance of boundaries to place cells, and a fixed feed-forward model sufficient to explain place cell firing (Hartley et al., 2000)

• Revise the model to accommodate results suggesting place cell stability and robustness requires synaptic plasticity (Barry and Burgess 2007)

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The Hippocampal Formation

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Rat Human

The hippocampus and spatial representation

Hippocampus with its subfields (DG, CA1,2,3)Entorhinal cortex(Parahippocampal cortex)

Importance of the Hippocampus: Oliver Sacks and Jimmie G


”isolated in a single moment of being…. he is a man without a past (or future), stuck in a constantly changing, meaningless moment” (Sacks, 1985)

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In-vivo electrophysiology

Recording single neurons in behaving animals

Hafting et al., 2005

O’Keefe & Dostrovsky 1971

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Place cells allocentric location,Hippocampus

Grid cells path integration,Entorhinal cortex

In humans too!Robertson et al. 1999; Ekstrom et al. 2003; Jacobs et al. 2010; Doeller et al. 2010, Horner et al. 2016; Shine et al. 2019

Head-direction cells allocentric orientationPapez’ circuit

Ranck, 1984; Taube et al 1997

Single neuron responses in the hippocampal formation

Lever et al. 2009Hoydal et al. 2019

Boundary/Object Vector cells allocentric direction and distance of objects/boundaries

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RatMoviePC.avi

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Place fields are receptive fields (for location)

*

*

*

Compare to well known receptive fields in sensory space


Place cells

Place Cell

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Some properties of place cell firing

1. Firing is independent of the rat’s orientation in open but not narrow-armed mazes

2. Firing is robust to the removal of sensory cues


Recap: Unsupervised, competitive learning

x1 x2 x3 x4 x5

o1 o2 o3

• ‘Winner-takes-all’: For each input pattern xn , output ok

(i.e. hk>hi for all ik). Set ok=1, oi=0 for all ik

• Random initial connection weights. All-to-all connectivity

• Hebbian learning: wij→ wij + oi xjn

i.e. wkj→ wkj + xjn, other weights don’t change

where oi =0

• Normalisation: reduce total size of connection weights to

each output (so |wi| =1) by dividing each by |wi|

• Process repeats with presentation of each input pattern

The output whose weights are most similar to xn wins and its weights then

become more similar. Different outputs find their own clusters in input data

Rumelhart and Zipser 1986.

PDP book freely available on J. McClelland’s website

wij

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Sharp’s (1991) place cell firing model

A

B

C

D

E

F

GH

Cortical inputs:

Cue distances, cue directions

Competitive learning:

Competitive learning:

Entorhinal

cortex

Place cells

A B C D E F G H A B C D E F G Hnear

far

right

left


Sharp’s (1991) model continued

Simulated place cell firing is resistant to cue-removal

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Sharp’s (1991) model continued

Simulated place cells are omni-directional only after random exploration and not following directed exploration


Summary

• Sharp’s competitive learning model explains robustness and directionality of place fields

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What are the inputs to place cells?

‘simple’ place field firing is consistent

4.6 4.1

4.9 5.0

61cm 122 cm

0% 20% 40% 60% 80% peak

Y

X

N

S

W E

window

rat forages in box

O’Keefe and Burgess, 1996


What are the inputs to place cells?

O’Keefe and Burgess, 1996

5.1 3.5

6.7 6.5

14.1 2.7

8.7 4.3

Other place fields appear to respond at fixed

distances from walls, with nearer walls more

important than further ones.

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BVCs as hypothesised inputs to place cells

Hartley et al. 2000

• Each BVC tuned to respond when a barrier lies at a specific distance from the rat in a particular allocentric direction

Firing Rate

Receptive Field

Boundary Vector Cell (BVC)


BVCs as hypothesised inputs to place cells

Hartley et al. 2000

• BVC firing determined by product of two gaussians, defining distance and angle tuning to boundary:

• Sharper tuning for shorter distances, reflecting uncertainty in inputs to BVCs

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2

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2

]2/)(exp[

)(2

)](2/)(exp[),(

ang

angi

irad

iradii

d

ddrrg

−−

−−

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A fixed, feed-forward model of place cells from BVCs

S

Place field

BVC inputs

Place fields are modelled as the thresholded sum of 2 or more BVC firing fields.

Hartley et al. 2000

reminder


Modelling O’Keefe and Burgess 1996 with BVCs

Simulated Place Fields

Place Cell Data

(O’Keefe & Burgess,

1996)

2-4 BVCs orientated at

right angles to one

another and

thresholded are

sufficient to fit most

fields

Best fitting BVCs

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DataO’Keefe & Burgess (1996)



ModelHartley, et al.(2000)

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BVCs predict boundary-referenced firing of PCs across environments

Model

BVCs

Data (Lever et al)

1. Record some

place cells

4. Record same cells

in predicted environments

2. Find BVCs that best fit

those place cells

3. Use those model BVCs to predict

firing in other environments


Discovery of BVCs

Lever et al. 2009. Solstad et al. 2008

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Importance of synaptic plasticity to place field stability

• Synaptic plasticity the putative biological instantiation of weight-updating.

• ‘Vanilla’ plasticity requires NMDA receptors.

• Place field stability falls when NMDA receptors are blocked:

Saline CPP (NMDAR antagonist)

Kentros et al. 1998


Importance of synaptic plasticity to place field stability

• Robustness of place fields to cue removal also depends on NMDA receptors.

Nakazawa et al. 2002

Saline CPP (NMDAR antagonist)

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Slow, experience-dependent changes to place fields

Lever et al. 2002Likely reflect synaptic plasticity. Can’t be explained by a ‘fixed’ model.


Summary


• Subsequent results showing place cell firing is determined by geometry of environmental borders can be explained by a simple feed-forward model, given that boundary vector cells are the inputs to place cells

• But, such models cannot account for long-term dynamics of place fields in similar environments, nor the importance of synaptic plasticity in place field stability

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Extended BVC model: added learning

• Update weights using BCM ruleBVCs

Place cells

Post synaptic activity yi

sliding

threshold θ

yi = f(∑jwij xj)Δwij = xj φ(yi, θ)

θ ~ <yi2>

requires pre & post-synaptic activity (xj and yi)

reduction if post-synaptic activity low

increase if activity high

φ(yi, θ)

Barry & Burgess (2007)

xj

yi

wij


4.7 3.3 3.8 4.0 4.3

4.7 3.3 3.8 4.0 4.3

Iterations 20 40 60 80 100

Calculate place cell

firingBVC firing

Update weights

with BCM


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5.0 3.8 2.7 2.9 3.1

3.0 3.4 3.5 3.8 3.5

2.1 2.6 2.6 2.5 2.5

0 10 20 30 40

Iterations

5.7 3.7 3.9

4.9 2.8 3.6

6.5 2.8 2.8

0 5 10

Iterations



day2

day9

21.2 9.3 20.0 21.1 13.7 20.7

21.1 17.2 14.2 18.4 19.3 16.6

…

Barry (2006)

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Summary


• Subsequent results showing place cell firing is determined by geometry of environmental borders can be explained by a simple feed-forward model, given that boundary vector cells are the inputs to place cells

• But, such models cannot account for long-term dynamics of place fields in similar environments, nor the importance of synaptic plasticity in place field stability

• Combining the feed-forward BVC model and BCM learning accounts for long-term remapping

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the hippocampus and spatial representation · the hippocampus and spatial representation...

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