1. Valentino Braitenberg
The Dentate Gyrus
a spatial
random
number
Generator
Valentino Braitenberg
..but what was
the question?
SISSA

2. (1/1000 x cerebellar cousins,
neurogenesis?
so many DGCs?
(3 x CA3 pyramidal
cells, in rats)
no basal dendrites?
Zinc/ZENK?
so few DGCs?
(1/1000 x cerebellar cousins,
in humans)
mossy fibers?

3. The entire Hippocampus, or rather Medial Pallium..
Reptiles Mammals Birds
neurogenesis neurogenesis neurogenesis
Zinc Zinc Zinc
acetylcholine acetylcholine acetylcholine
recurrent nets recurrent nets recurrent nets
spatial memory spatial memory spatial memory
Turtles spatial memory
Font et al, 2001 Lindsey and Tropepe, Bingman et al, 2005
Smeets et al, Martinez-Garcia and Olucha, Montagnese et al, 1993
Reiner 1993 Krebs et al, Sherry et al, 1993
Rodriguez et al, 2002
Goldfish spatial memory

4. reptiles ≠ mammals ≠ birds
…so, is there any really new idea ?
human
cat
rat
platypus
lizard DG
reptiles ≠ mammals ≠ birds
CA1
CA3
The medial pallium
has been with us for over 300 million years…
 hippocampus
or over 200 million years…

5. watch the new
idea frozen
in evolution,
in the opossum
an idea for
engineers,
not really for
philosophers

6. Efficient storage of informative spatial representations in memory
PhD Thesis Defence
Erika Cerasti
Efficient storage of informative spatial representations in memory
I am Erika Cerasti and I work with A Treves at Sissa in Trieste. The topic of our work is to investigate the role of DG in HP.
SISSA-International School for Advanced
Studies
Cognitive Neuroscience Sector
Trieste - 29 January 2010

7. Trisynaptic circuit in the hippocampus
Introduction
The role of DG
RC contribution
Trisynaptic circuit in the hippocampus
Perforant Path
(input from EC)
CA1
Mossy fibers
(DG-CA3 connections) Sb
Schaffer collaterals
(CA3-CA1 connections)
Recurrent collaterals
(CA3-CA3 connections)
CA3 DG
CA3 mf EC pp rc DG
Let’s look to its internal organization: we can recognize three areas, DG CA1 CA3.
Input coming from EC touches all these area. Moreover there is an unidirectional flow, the input starting from dg that projects to CA3 through mossy fiber synapses,
Then from CA3 it arrives to CA1 through Schaffer collaterals
RC in CA3
In particular looking at CA3 we can see that the input comes directly from EC and also after being processed by the dg

8. What is the role of the Dentate Gyrus? Why is the Hippocampus
differentiated?
What is the role of
the Dentate Gyrus?
So what is the role of this preprocessing stage for the input arriving to CA3?
why there is such a differentiation and what are the specific functions of this subregions? And DG?

9. Autoassociative network stored in the synaptic weights of the network
Introduction
The role of DG
RC contribution
Autoassociative network
CA3
Input pattern 2
Input pattern 1
Recurrent connections
(David Marr,
Bruce McNaughton,
Edmund Rolls)
different patterns
(memories)
stored in the synaptic weights of the network
Hebbian learning
HOPFIELD Model
To try to answer this question we refer to theories which consider CA3 to work as an autoassociator to perform memory abilities.
Through the presence of a large number of RC in the areas.
when an external input comes it impose an activity to the network;
this pattern of activity is the network representation of the external input
Hebbian learning that is modification of synaptic weights
Storage capacity – the maximum number of storable patterns
depends on the connectivity of the network and on the sparseness of its representations

10. Autoassociative network
Introduction
The role of DG
RC contribution
Autoassociative network
CA3
Partial Input
pattern 1
Recurrent connections
Attractor
HOPFIELD Model
Pattern Completion
The retrieval is possible thaks to the action of recurrent activity after the weights has been modified
Retrieval occurs through the dominance of recurrent activity in the network

11. Introduction
The role of DG
RC contribution
the Hopfield model does not say how representations are established
Memory storage is difficult to implement in CA3 by itself because of the interference
due to previously stored memories
(and recurrent connection dominance)‏
Differentiation of storage and retrieval phase
External Input activity should prevail during storage
Recurrent collateral activity should prevail during retrieval
CA3
External input
CA3
mossy
fibers DG
Some studies suggest the DG could also
help CA3 to form memory representation
McNaughton’s detonator synapses
The Acetylcholine
hypothesis
(Hasselmo et al)
However the hopfield model does not say what determines the activity distribution relative to each pattern or external input
That is how the storage occurs
In particular for dg some studies suggest can help in solving this problem
DG can impose in the CA3 activity the new pattern to store
MF have strong and sparse synapses, suitable for that, as shown in the work of treves and rolls 1992
DENTATE GYRUS
a preprocessing stage can separate storage and retrieval, imposing to CA3 the new pattern to store
MF have strong and sparse synapses

12. MF inputs establish new representations
Introduction
The role of DG
RC contribution
Functional differentiation of the afferent inputs to CA3 - Information measures
the information available for retrieval should be at least equal to the amount
which is indeed retrievable by the net
Information vs CA3 sparseness (a)
Comparison of the amount of storable information carried by afferent inputs to CA3
the Perforant Path input is too weak to force learning
and that mf input to CA3 is the one crucial to establish informative representation in CA3, as shown in treves… this theoretical work involves only discrete representations
Treves & Rolls, Hippocampus 1992
Binary distribution of DG activity - Discrete patterns
Hypothesis:
MF inputs establish new representations
PP inputs relay the cue for retrieval

13. Spatial tasks in rodents
Introduction
The role of DG
RC contribution
Experimental tests of the hypothesis:
Spatial tasks in rodents
While the experimental support to this hypothesis come from studies with rodents performing spatial task, involving spatial representations.
So we want to concentrate in our study on the role of DG in the storage of spatial representations in CA3.
We can do that because now we know the firing code of DG, As leutgeb et al shows in their work the dg cells present multiple firing fields

14. Spatial tasks in rodents
Introduction
The role of DG
RC contribution
Experimental tests of the hypothesis:
Spatial tasks in rodents
While the experimental support to this hypothesis come from studies with rodents performing spatial task, involving spatial representations.
So we want to concentrate in our study on the role of DG in the storage of spatial representations in CA3.
We can do that because now we know the firing code of DG, As leutgeb et al shows in their work the dg cells present multiple firing fields

15. Spatial tasks in rodents
Introduction
The role of DG
RC contribution
Experimental tests of the hypothesis:
Spatial tasks in rodents
Acquisition Index: Errors (T1-5 D1) - (T6-10 D1)
Retrieval Index: Errors (T6-10 D1) - (T1-5 D2)
While the experimental support to this hypothesis come from studies with rodents performing spatial task, involving spatial representations.
So we want to concentrate in our study on the role of DG in the storage of spatial representations in CA3.
We can do that because now we know the firing code of DG, As leutgeb et al shows in their work the dg cells present multiple firing fields

16. Introduction Experimental tests of the hypothesis:
The role of DG
RC contribution
Experimental tests of the hypothesis:
Spatial tasks in rodents
Modified Hebb-Williams maze
Neurotoxic lesions of DG and electrolytic lesions of PP CA3 to study the functional dissociation between inputs afferent to CA3.
Lesions of PP input seem to impair retrieval, while lesions of MF input seem to impair the encoding of spatial information
Lee and Kesner, Hippocampus 2004
Support the hypothesis
Morris water maze
Reversible inactivation of MF synapses
Mice tested on navigation task in the Morris water maze
The deactivation of MF results in encoding impairment
While the experimental support to this hypothesis come from studies with rodents performing spatial task, involving spatial representations.
So we want to concentrate in our study on the role of DG in the storage of spatial representations in CA3.
We can do that because now we know the firing code of DG, As leutgeb et al shows in their work the dg cells present multiple firing fields
Lassalle et al, Neurobiology of Learning and Memory 2000

17. Discrete representations Continuous representations
Introduction
The role of DG
RC contribution
Information from DG relative to spatial locations
Discrete representations Continuous representations
(x0 y0)
Continuous 2-Dimensional Attractor
(x1 y1)
In an IDEAL continuous attractor each position in space corresponds to an attractor for the activity in the network.
The ensemble of such attractors for
all locations in space comprises the memory of the environment (chart).
The theoretical study discrete representation while the experimental work involve spatial representation in rodents
We want in our study on the role of DG we want to pass from discrete representations to continuous representation in the network and
to do that we have to refer to the concept of the 2D continuous attractor
in the storage of spatial representations in CA3
If we want to represent spatial locations in the network we need configurations of the network to be change continuously, as the spatial input does.
as the space we want to represent
(x2 y2)
Attractor state for the population vector
Memory of multiple environments may require
the storage of multiple charts.
Multi-charts model (Samsonovich and MNaughton 1997)

18. Multiple firing fields for DG cells
Introduction
The role of DG
RC contribution
Spatial Representations in DG :
Firing activity in DG:
spatial localized receptive fields, place-like.
Multiple firing fields for DG cells
Coding model:
While the experimental support to this hypothesis come from studies with rodents performing spatial task, involving spatial representations.
So we want to concentrate in our study on the role of DG in the storage of spatial representations in CA3.
We can do that because now we know the firing code of DG. As leutgeb et al shows in their work the dg cells present multiple firing fields
Sparse level of firing p ≃ 0.03
Number of firing fields given
by Poisson probability with q ≃ 1.7
Leutgeb et al, Science 2007

19. Model

20. The role of DG Storing a new map δ Introduction RC contribution DG
(x)‏
Hypothesis
Mossy fibers drive the storage of new information
External Input
Modeling assumption
only DG inputs carry the
relevant information about a new spatial map to be stored in CA3.
CA3 DG c δ
noise
AMOUNT of INFORMATION
about a new spatial map
mossy fibers
The model we build is composed by a layer of DG cells projecting to a layer of CA3 cell, the connectivity level is indicated by c that is the number of dg cells projecting to a single ca3 cell.
We remove the recurrent connections in ca3 and consider them as noise. Then we define the fields and study how the amount of info depend on the paramenters storage of a new map, representative of an environment

21. c = # DGCs projecting to a single CA3 cell
The role of DG
Introduction
RC contribution c δ
CA3 DG c δ
AMOUNT of INFORMATION
about a new spatial map
Sum of Gaussian functions
noise
c = # DGCs projecting to a single CA3 cell DG
pDG ≃ 0.03
The model we build is composed by a layer of DG cells projecting to a layer of CA3 cell, the connectivity level is indicated by c that is the number of dg cells projecting to a single ca3 cell. Then we define the fields and study how the amount of info depend on the parameters
A Gaussian for each fields on the dg unit
The firing in CA3 then results from this formula
Poisson distribution
with q = 1.7
CA3
Threshold-linear units
Qj = number of field for cell j

22. Analytical Calculation

23. The role of DG Mutual Information Introduction RC contribution
We calculate the amount of information about a new environment (x) that is established in CA3 cells (η) by DG spatial activity (β)‏
Mutual Information
ENTROPY
CONDITIONAL ENTROPY

24. The role of DG
Introduction
RC contribution ?

25. m-fields decomposition
The role of DG
Introduction
RC contribution
Mutual Information per single CA3 cell
<I> = ∑mCm < Dm>
m-fields decomposition
m-fields contribution to the information
<> Quenched variables
average
Decomposed in pieces each one considering the contribution of a fixed number of input fields x y
Dm - spatial signal produced by m DG fields
Cm - combination of Poisson coefficients

26. Simulations

27. Total strength of input
The role of DG
Introduction
RC contribution
Dependence on the connectivity c between DG and CA3:
Information vs number of CA3 cells
Total strength of input
is constant
dots = simulations
lines = fitting curves
Fitting curve:
The study of the info has been performed through simulations and analytical calculation, here you can see the results.
First of all we see hoe the inf depend on the connectivity between the DG and CA3 area.
Regarding the dependence on the connectivity... in this graph
We extract from the simulations two relevant parameters to describe the information behaviour: 1
Slope of the information curve (information per single cell) 
Total amount of information (for N to infinity)

28. Total strength of input
The role of DG
Introduction
RC contribution
Dependence on the connectivity c between DG and CA3:
Information vs number of CA3 cells
maximum in connectivity c
Total strength of input
is constant
Information per single CA3 cell vs c
The study of the info has been performed through simulations and analytical calculation, here you can see the results.
Regarding the dependence on the connectivity... in this graph
Simulations
Analytical Result

29. The role of DG Resulting CA3 Fields - Statistics
Introduction
RC contribution
Resulting CA3 Fields - Statistics
Realistic range for C ~ 30-50 a‏ b‏
percentage of active cells among all CA3 cells
percentage of cell with multiple fields among all active CA3 cells
a)‏
A sparse MF connectivity is optimal, but not too sparse
b)‏

30. The role of DG
Introduction
RC contribution
Plasticity on MF synapses
The effect of plasticity on mossy fibers is to shift the maximum of information as a function of the connectivity
Information per single CA3 cell vs c
Since plasticity effectively selects a subset of connections among the initial ones and make them stronger, it is more convenient to start with a larger pool, that is with a larger value for CMF
The study of the info has been performed through simulations and analytical calculation, here you can see the results.
Regarding the dependence on the connectivity... in this graph
Examples of CA3 fields
before learning
after learning

31. Exponential distribution Single Field per DG cell
The role of DG
Introduction
RC contribution
OTHER DISTRIBUTIONS FOR DG FIELDS
Poissonian distribution
Information measure is not affected by different distributions of the place fields among the DG cells
Exponential distribution
Information per single CA3 cell vs c
Single Field per DG cell
We study how the info change using different distributions for dg fields.
Then having seen the results of leutgeb study we thought that having multiple fields was crucial feature for the optimization
Of the information going to CA3, but it is not.we performed simulations keeping constant the nu but changing the distribution of input field among dg cell
And we can see that the info is unaffected by this change as long as the numb is kept constant
Q = number of DG fields

32. Information measure is not affected
The role of DG
Introduction
RC contribution
DIFFERENT DISTRIBUTIONS FOR THE INPUT FIELDS
Different distributions of input fields in DG cells
The mean number of input DG fields per CA3 cell is kept constant, c and q vary. DG
cells
CA3 cell
Information vs number of CA3 cells DG
cell
CA3 cell
We study how the info change using different distributions for dg fields.
Then having seen the results of leutgeb study we thought that having multiple fields was crucial feature for the optimization
Of the information going to CA3, but it is not.we performed simulations keeping constant the nu but changing the distribution of input field among dg cell
And we can see that the info is unaffected by this change as long as the numb is kept constant
μ = c pDG q CONSTANT
Information measure is not affected

33.  * ≠     The role of DG . DECODING Procedure:
Introduction
RC contribution
DECODING Procedure:
Neural representation
(firing population vector)‏ η1 η2 ηn
Real position r (x,y)
Decoded position r’ (x’,y’) . 
difference
between r and r’  
Information from decoding (simulations)‏
Information from theoretical calculation  * ≠ 

34. Errors spread near the real position
The role of DG
Introduction
RC contribution
Information calculated from the Confusion Matrix:
probability for each position to be decoded as the real one
AVERAGE
Whole Confusion Matrix EPISODIC
Reduced Confusion Matrix SPATIAL
Errors spread near the real position
Information per single CA3 cell vs c
Another interesting thing come up looking at the confusion matrices used to calculate the information:
When the rat is in a position in the given environment the conf mat give the probabilities for all the positions to be decoded as the real one, then the rat moves and there is another conf mat…
So we can calculate the info from the whole conf mat that have an episodic content or using the reduced one that is an average of the conf mat per each position experienced, a conf mat for all the environment
DARK INFO
This does not affect the dependence of information on the code parameters (c, μ)‏

35. Recurrent Collaterals
Adding
Recurrent Collaterals
Now we look at what happen when we add the RC collateral in our system,

36. RC contribution Learning RC
Introduction
The role of DG
New Maps
(x)‏
Retrieving a stored map
New Map
(x)‏
External Input c MF
Learning
AMOUNT of INFORMATION
about the stored spatial map RC
Till now we considered only the storage now and in particular the retrieval of the spatial representations established in CA3 by the DG
Now we add the activity of RC, allowing the plasticity oh them when the input is present and then
So the model is the same as before, with the add of such terms in the firing of CA3 units.
Now we have the input from the DG and the input coming from the other CA3 unit that determine the activity of a CA3 unit, with noise and a threshold as before.
Jij weights
Differently from before we allow plasticity during the presentation of the input
So we have an external input coming from dg about a new map, a learning phase in which J are allowed to change, and then a recover phase in which the input is turned off and the system have to maintain the information
We see the amount of information the RC activity contain about a previously presented map, in absence of input.
So we study the retrieval of a single spatial map when a single map is stored and when multiple maps are stored
RC + 

37. Pre-wired connectivity
RC contribution
Introduction
The role of DG
LEARNING ?
Pre-wired connectivity
Hebbian Learning
1d 2d established in several model
The learning could be represented by a pre-wired connectivity or a hebbian learning
We study the system and compare the two cases.
For the pre-wired connectivity the weights are chosen as exponential decreasing functions of the distance between place centers,
What happen is quite well established by previous studies on 1D or 2D models
While for the self organizing connectivity we allow weights to change in the learning phase according to this formula.
Where a trace term is present.

38. RETRIEVAL OF SPATIAL MAP IN ABSENCE OF INPUT
RC contribution
Introduction
The role of DG
INFORMATION VS FAST NOISE
RETRIEVAL OF SPATIAL MAP IN ABSENCE OF INPUT
Slope parameter
Recurrent Collaterals maintain spatial information in absence of input
Total information parameter
As said before, we measure the information during the retrieval of a spatial map, in absence of input. The figures show the slope parameter and the total information parameter that describe the information curves, as before, plotted as functions of the fast noise.
We see that RC maintain spatial information when the dg input is turned off.
Information decrease with the increasing of the noise.
Moreover in the regime of low noise the information consequent to hebbian learning is higher than the one occurring with the pre-wired connectivity
noise
Information retrievable for hebbian learning is similar and even higher than for exponential weights
for low level of noise
noise

39. Stronger learning helps but not much
RC contribution
Introduction
The role of DG
Does information depend much on learning?
Stronger learning helps but not much
MF input on
MF input on + RC 
= #step = 
MF input off
= #step = 10000 
= #step = 10000
no learning
noise  = 0.1
CA3 FIRING FIELDS
Here we see the same curves for one value of the noise, 0.1.
the line represents the information for different strength of the learning and we see that the learning helps but not much
Learning –no learning comparison gray line.
The correspondent firing maps in CA3 units learning non-learning and input off case
MF+RC no learning
MF+RC learning
MF inputs off

40. RC contribution Introduction The role of DG
STORAGE CAPACITY – STORING MORE THAN ONE MAP
RETRIEVAL OF THE FIRST STORED CHART
RETRIEVAL IN THE PRE-WIRED NETWORK
Till now only one map was stored so we did not have the effect of the quenched noise. Now we see what happen if we store
And whether and how the retrieval ability changes.
The figure in the left show the information relative to he first stored charts for several loading levels for the system, for a hebbian process and pre-wired connectivity.
A main difference is that for the pre-wired connectivity the order of storage of different maps do not matter.
We do not observe the decreasing of but it seems that the information loss we have with the storage of 2 charts is the same as the one we get for up to 100 charts.
What is remarkable is the presence of a residual information, we can see when we ask the system to recall a map that has not been stored.
noise  = 0.1
RESIDUAL INFORMATION
due to the disorder in the system

41. THE 2D QUASI–CONTINUOUS ATTRACTOR
RC contribution
Introduction
The role of DG
THE 2D QUASI–CONTINUOUS ATTRACTOR
Exponential
Hebbian
BUMP
Localized activity
Along with information measures, we can look at the properties of the continuous attractor established in CA3. First of all, we see that the activity is in fact localized with a bump of activity
There is a bump in both cases of learning . When the input is turned off a quasi-continuous attractor
Drift with fewer final positions for the bump than the possible one, as shown in previous study as Stringer and Rolls, Roudi and Treves
Then we can ask how smooth is the attractor
Drift of the attractor on the manifold
when input is turned off
How smooth is it?
Rolls & Stringer, Network: Comput Neural Syst, 2002
Roudi & Treves, PLoS Comput Bio, 2008

42. RC contribution Introduction The role of DG
THE 2D QUASI–CONTINUOUS ATTRACTOR
noise  = 0.002
NETWORK SIZE DEPENDANCE OF THE 2D ATTRACTOR
Hebbian learning
Exp prewired, and wider
We can quantify this by looking at these graph showing the spatial resolution plotted versus the network size
We get an high spatial resolution
Similar result for exp Hebb
Same for density
Hebbian learning
Exponential connectivity
Very high spatial resolution for both pre-wired and self organizing connectivity

43. Neurogenesis? Grid units?
RC contribution
Introduction
The role of DG
MEAN DISPLACEMENT vs NETWORK SIZE
Hebbian
Pre-wired
What is different between the two is instead the mean displacement between the initial and final location
N=1500
nn= 0.002
Gamma=0.002
Different metric
The metric is different from the real space one
Neurogenesis?
Grid units?

44. THANK YOU! Alessandro Treves Gergely Papp Eleonora Russo Bailu Si
…and THANKS to:
Alessandro Treves
Gergely Papp
Eleonora Russo
THANK YOU!
Bailu Si
Alessio Isaja
Valentina Daelli
Athena Akrami
Federico Stella
Federica Menghini

45.         
Gamble Faces
“Ital­ian Pok­er­Stars qual­i­fier Erika Cerasti is exactly the kind of player I love to meet at the PCA.
For a start, she’s a neu­ro­sci­en­tist and who doesn’t want to meet one of them?!,
writes Mad Harper
Sec­ondly, she bust in the Main Event in 42nd place and, instead of get­ting all upset because she hasn’t won a gazil­lion dol­lars, she is totally thrilled that she got to spend a week in the Bahamas and the fact that she is going home $52,000 richer!”

46. Teleportation paradigm Flickering memories in CA3
Watch out for
the paper by
Karel Jezek in
Nature later
this month
May-Britt &
Edvard Moser
In Trondheim
Teleportation paradigm
Flickering memories in CA3

47. The Braitenberg model: glocal associative memory
The statistical/
modular
perspective
The Braitenberg model: glocal associative memory
N pyramidal cells
√N compartments
√N cells each
A pical synapses
B asal synapses

48. word

49. pc  S ?!?! pc  C S 2 !! Potts units with dilute connectivity
S+1 Potts states
Sparse Potts patterns
Reduced to a Potts model
(Kropff & Treves, 2005)
Structured long-range
connectivity
“0” state included
Sparse global patterns
updated to remove the
‘memory glass’ problem
(Fulvi Mari & Treves, 1998)
Cortical modules
Local attractor states (=S)
Global activity patterns
A simple semantic network
(O’Kane & Treves, 1992)
..but all cortical modules
share the same organization…
pc  C S 2 !!
pc  S ?!?!

50. Simulations which include a model of neuronal fatigue Simulations
show that the Potts semantic network
can hop from global attractor to global attractor:
Latching dynamics

51. (ratio local / long-range)
Eleonora Russo
wanted to understand
the phase diagram
for latching dynamics
(noise)
No Latching
(finite) Latching
Infinite Latching
(ratio local / long-range)
Model for
free-wheeling
thoughts..
Time for dinner!