Correlations%20(part%20I)

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Correlations (part I)
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• Mechanistic/biophysical plane
• - What is the impact of correlations on the
  output rate, CV, ...
• Bernarder et al 94, Murphy Fetz 94, Shadlen
  Newsome 98, Stevens Zador 98, Burkit
  Clark 99, Feng Brown 00, Salinas Sejnowski
  00, Rudolf Destexhe 01, Moreno et al 02,
  Fellows et al 02 , Kuhn et al 03, de la Rocha
  05
• - How are correlations generated? Timescale?
• Shadlen Newsome 98, Brody 99, Svirkis
  Rinzel 00, Tiensinga et al 04, Moreno Parga,
• 2. Systems level
• - do correlations participate in the encoding of
  information?
• Shadlen Newsome 98, Singer Gray 95, Dan
  et al 98, Panzeri et al 00, DeCharms
  Merzenich 95, Meister et al, Neimberg Latham
  00
• - linked to behavior?
• Vaadia et al, 95, Fries et al 01, Steinmetz et
  al 00,

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Type of correlations
stimulus s response r1, r2, ... , rn
1.- Noise correlations
2.- Signal correlations
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Quantifying spike correlations
trial index
t1i,r t2i,r t3i,r ...
cell index
1. Stationary case

• Corrected cross-correlogram

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Quantifying spike correlations
2. Non-stationary case

• Joint Peristimulus time-histogram

• Time averaged cross-correlogram

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Quantifying spike correlations

• Correlation coefficient

• Spike count

if T gtgt
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How to generate artificial correlations? 1.
Thinning a mother train.
mother train (rate R)
deletion
rate p R
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How to generate artificial input correlations?
2. Thinning a mother train (with different
probs.)
mother train (rate R)
deletion
rate p R
rate q R
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How to generate artificial input
correlations? 3. Thinning jittering a mother
train
mother train (rate R)
deletion jitter
rate p R
random delay exp(-t/tc) / tc
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How to generate artificial input
correlations? 4. Adding a common train
common train (rate R)
summation
rate r R
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How to generate artificial input correlations?
5. Gaussian input
Diffusion approximation
1
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How to generate artificial input correlations?
5. Gaussian input
White input
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Impact of correlations
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Impact of correlations on the input current of a
single cell
Excitation Rate nE
1
2

NE
Poisson inputs Zero-lag synchrony
1
2

NI
Inhibition Rate nI
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Impact of correlations on the output rate
Balanced state
Unbalanced state
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The development of correlations a minimal model.
1. Morphological common inputs.
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The development of correlations a minimal model.
2. Afferent correlations
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The development of correlations a minimal model.
3. Connectivity
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Development of correlations common inputs
Shadlen Newsome 98
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Development of correlations common inputs
synaptic failures
R(1-x)
Rp(1-x)
p
p
Rx
Rp2xRpx(1-p)
p
R(1-x)
Rp(1-x)
p

• Independent Rp(1-x)Rpx(1-p) Rp(1-xp) Reff
  (1-xeff)
• Common Rp2x Reff xeff
• where we have defined
• Effective rate Reff R p
• Effective overlap xeff x p

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Development of correlations common inputs
synaptic failures
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Development of correlations common
inputs. Experimental data.
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Development of correlations correlated inputs.
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Development of correlations correlated inputs.
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Development of correlations correlated inputs.
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Development of correlations correlated inputs.
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Biophysical constraints of how fast neurons can
synchronize their spiking activity
Rubén Moreno Bote Nestor Parga, Jaime de la
Rocha and Hide Cateau
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Outline

• I. Introduction.
• II. Rapid responses to changes in the input
  variance.
• III. How fast correlations can be transmitted?
• Biophysical constrains.

Goals 1. To show that simple neuron models
predict responses of real neurons. 2. To
stress the fact that qualitative, non-trivial
predictions can be made using mathematical
models without solving them.
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I. Introduction. Temporal changes in correlation
Vaadia el al, 1995
deCharms and Merzenich, 1996
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I. Temporal modulations of the input.
mean
variance
Diffusion approximation
white noise process with mean zero and unit
variance
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I. Temporal modulations of the input.
common variance
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I. Problems
Problem 1 How fast a change in m and s can be
transmitted?
Leaky Integrate-and-Fire (LIF) neuron
Problem 2 How fast two neurons can synchronize
each other?
common source of noise
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II. Probability density function and the FPE
Description of the density P(V,t) with the FPE
P(V)
P(threshold)0
V
q
Firing rate
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II. Non-stationary response. Fast responses
predicted by the FPE
P(V,t)
P(threshold, t)0
V
q
Mean input current
1.
Firing rate response
time
Variance of the current
2.
Firing rate response
time
Described by the equation
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II. Rapid response to instantaneous changes of
s (validity for more general inputs)
Change in input variance
Change in the input correlations for
dif. correlation statistics
Silberberg et al, 2004
Change in the mean
Moreno et al, PRL, 2002.
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II. Stationary rate as a function of tc
?gt0
?0
?lt0
Moreno et al, PRL, 2002.
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III. Correlation between a pair of neurons
Cross-correlation function P( t1 , t2 )
time lag t1 - t2
0
Moreno-Bote and Parga, submitted
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III. Transient synchronization responses.
Exact expression for the cross-corr.
The join probability density of having spikes at
t1 and t2 for IF neurons 1 and 2 receiving
independent and common sources of white noise is
Total input variances at indicated times
for neurons 1 and 2.
Joint probability density of the potentials of
neurons 1 and 2 at indicated times
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III. Predictions

• Increasing any input variance produces an
  instantaneous increase
• of the synchronization in the firing of the
  two neurons.
• 2. If the common variance increases and the
  independent variances
• decrease in such a way that the total
  variance remains constant, the
• neurons slowly synchronize.
• 3. If the independent variances increase, there
  is a sudden increase in the
• synchronization, and then it reduces to a
  lower level.

biophysical constraints that any neuron should
obey!!
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III. Slow synchronization when the total
variances does not change.
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III. Fast synchronization to an increase
of common variance.
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III. Fast synchronization to an increase of
independent variance, and its slow reduction.