Impact of Correlated inputs Impact of Correlated inputs on Spiking Neural Modelson Spiking Neural Models

Baktash BabadiBaktash Babadi

School of Cognitive SciencesSchool of Cognitive Sciences

PM, Tehran, IranPM, Tehran, Iran

Background Background

The neuroscientists are mostly concerned The neuroscientists are mostly concerned with how the world is represented in the with how the world is represented in the nervous system.nervous system.

But equally important is But equally important is how the neurons how the neurons communicate with each othercommunicate with each other..

Rate Coding vs. Temporal Coding Rate Coding vs. Temporal Coding

Given that the neurons transmit spike Given that the neurons transmit spike trains between each other,trains between each other,

Is there the rate of the spike train that Is there the rate of the spike train that matters,matters,

Or the timing between the individual Or the timing between the individual spikes carries the information? spikes carries the information?

In The Single Cell LevelIn The Single Cell Level

Is a single neuron and integrator (rate Is a single neuron and integrator (rate coder)?coder)?

Or a coincidence detector (temporal Or a coincidence detector (temporal coding)? coding)? (Sofkey & Koch 1993, Abeles 1988,…)(Sofkey & Koch 1993, Abeles 1988,…)

Population Level(1)Population Level(1)

Balanced excitation/inhibition in cortical Balanced excitation/inhibition in cortical network is inconsistent with temporal network is inconsistent with temporal coding (Shadlen, Newsome 1998)coding (Shadlen, Newsome 1998)

In vivo irregular ISI in cortical neurons In vivo irregular ISI in cortical neurons cannot be due to integration of input spike cannot be due to integration of input spike trains trains Rate coding Rate coding

Population Level (2)Population Level (2)

Stable synchronous spike patterns in Stable synchronous spike patterns in cortical models (Synfire Chaines) (Abeles cortical models (Synfire Chaines) (Abeles 1991, Diesman et al 1999,…)1991, Diesman et al 1999,…)

Loss of temporal information in long feed-Loss of temporal information in long feed-forward networks (Litvak et al 2002)forward networks (Litvak et al 2002)

System LevelSystem Level

Visual system: Visual system: Object detection by rank Object detection by rank order coding in ventral visual pathway order coding in ventral visual pathway (Van Rullen, Thorpe 1998-2201)(Van Rullen, Thorpe 1998-2201)Motor System:Motor System: Precise Firing Sequences Precise Firing Sequences in the motor cortex (Prut et al 1998, in the motor cortex (Prut et al 1998, Vaadia et al 1997)Vaadia et al 1997)Auditory System:Auditory System: Stimulus locked neural Stimulus locked neural activity in auditory cortexactivity in auditory cortexInvertebrates:Invertebrates: Desynchronization of bee’s Desynchronization of bee’s chemical sensitive neurons chemical sensitive neurons

Neural ModelsNeural Models

Rate coder neural models (Somplinsky, Rate coder neural models (Somplinsky, Poggio, Treves,…)Poggio, Treves,…)

Spiking neural models (Koch, Segev, Spiking neural models (Koch, Segev, Gerstner,…)Gerstner,…)

However, it is generally However, it is generally accepted that about 90% of accepted that about 90% of

information is carried by firing information is carried by firing rates (Rieke et al 1997)rates (Rieke et al 1997)

The temporal structure in the The temporal structure in the nervous systemnervous system

Two kinds of temporal structures are Two kinds of temporal structures are ubiquitous in nervous system:ubiquitous in nervous system:

OscillationsOscillations

Synchrony (correlation)Synchrony (correlation)

Neural OscillationsNeural Oscillations

Engel et al (1991).Engel et al (1991).

Singer et al (1991-2003).Singer et al (1991-2003).

CorrelationsCorrelations

Temporal Correlations in the Visual Temporal Correlations in the Visual System (1)System (1)

Usrey & Reid (1999)Usrey & Reid (1999)

Temporal Correlations in the Visual Temporal Correlations in the Visual System (2)System (2)

Sources of synchrony in Visual system Sources of synchrony in Visual system (Usrey & Reid 1999)(Usrey & Reid 1999) Due to anatomical divergence/convergence Due to anatomical divergence/convergence

(shared input)(shared input) Stimulus locked synchronyStimulus locked synchrony Emergent synchrony (and oscillation)Emergent synchrony (and oscillation)

The Role of temporal structuresThe Role of temporal structures

Given that the temporal structures are Given that the temporal structures are evident in nervous system, what role do evident in nervous system, what role do they play in information processing?they play in information processing?

OscillationsOscillations

The phase locked oscillations in different The phase locked oscillations in different areas of the nervous system are capable areas of the nervous system are capable of solving the of solving the binding problem binding problem (Gray & (Gray & Singer 1996…)Singer 1996…)

Highly controversial!Highly controversial!

CorrelationsCorrelations

Sejnowsky, Salinas (2001):Sejnowsky, Salinas (2001): Although the firing rates carry the information Although the firing rates carry the information

content of the neural signals, the correlations content of the neural signals, the correlations modulate the flow of information.modulate the flow of information.

A modest position in the controversy!A modest position in the controversy!

The effect of correlations on firing The effect of correlations on firing rate of a single neuronrate of a single neuron

Given that the firing rate is the carrier of Given that the firing rate is the carrier of the information of the neural activity, how the information of the neural activity, how does the temporal correlation modulate does the temporal correlation modulate the firing rate? the firing rate?

Salinas & sejnowski 2000, Salinas & sejnowski 2000,

Feng 2002Feng 2002

Kuhn et al 2002,2003Kuhn et al 2002,2003

How to Generate Correlated Spike How to Generate Correlated Spike Trains?Trains?

Mother spike train:Mother spike train: Poissonian, rate=Poissonian, rate=αα

Daughter spike trains:Daughter spike trains: Copies of mother trainCopies of mother train Trimmed with the Trimmed with the

probability of probability of (1-c)(1-c)

Every two daughter spike trains are pair wisecorrelated with rate r=c*αα and correlation coefficient c.

The Neuron ModelThe Neuron Model

Conductance-based Integrate-and-fire Conductance-based Integrate-and-fire model: model: The input spikes cause the synaptic channels The input spikes cause the synaptic channels

to open which intern initiate the synaptic to open which intern initiate the synaptic currentcurrent

The synaptic current will be integrated and The synaptic current will be integrated and when the membrane potential reaches a when the membrane potential reaches a threshold, the neuron fires.threshold, the neuron fires.

What does the neuron receive?What does the neuron receive?

The correlated spike The correlated spike trains (100-200)trains (100-200)

Balance inhibitory spike Balance inhibitory spike trains (similar to trains (similar to correlated but without correlated but without correlation) correlation)

Balanced non-specific Balanced non-specific uncorrelated spike uncorrelated spike trains (typical of cortical trains (typical of cortical neuronsneurons((

??

The effect of correlations on the The effect of correlations on the firing ratefiring rate

??

What causes the non monotonous What causes the non monotonous dependence of firing rate to the dependence of firing rate to the

correlations? correlations?

The correlated spike train +The correlated spike train + The background non-specific inputsThe background non-specific inputs The balanced conditionThe balanced condition The synaptic gating mechanismThe synaptic gating mechanism The membrane leakageThe membrane leakage The threshold crossing mechanismThe threshold crossing mechanism Nothing more!Nothing more!

The Model without Background The Model without Background NoiseNoise

??

The Model without Balance The Model without Balance InhibitionInhibition

??

What causes the non monotonous What causes the non monotonous dependence of firing rate to the dependence of firing rate to the

correlations? correlations?

The correlated spike train +The correlated spike train + The background non-specific inputsThe background non-specific inputs The balanced conditionThe balanced condition The synaptic gating mechanismThe synaptic gating mechanism The membrane leakageThe membrane leakage The threshold crossing mechanismThe threshold crossing mechanism Nothing more!Nothing more!

The Current-Based Integrate-and-Fire The Current-Based Integrate-and-Fire neuron neuron

The synaptic gating mechanism is The synaptic gating mechanism is replaced by a simple current injection replaced by a simple current injection upon receipt of every spike.upon receipt of every spike.

The Current-Based Integrate-and-The Current-Based Integrate-and-Fire neuron Fire neuron

??

The Non-leaky Integrate-and-fire The Non-leaky Integrate-and-fire NeuronNeuron

No membrane leakageNo membrane leakage

Simple summation of synaptic currentsSimple summation of synaptic currents

Threshold crossing Threshold crossing

The simplest possible spiking neural The simplest possible spiking neural modelmodel

The Non-leaky Integrate-and-fire The Non-leaky Integrate-and-fire NeuronNeuron

??

What causes the non monotonous What causes the non monotonous dependence of firing rate to the dependence of firing rate to the

correlations? correlations? The correlated spike train +The correlated spike train +

The synaptic gating mechanismThe synaptic gating mechanism The membrane leakageThe membrane leakage The threshold crossing mechanismThe threshold crossing mechanism Nothing more!Nothing more!

Analytical ResultsAnalytical Results

For the non-leaky For the non-leaky Integrate-and-Fire Integrate-and-Fire neuronneuron::

Where:Where: r r = Input firing rate= Input firing rate c c = Correlation coefficient= Correlation coefficient ThTh = Threshold = Threshold

1

0

)])1.(...2

..([ )(

j ccNj

cNjThErfccrcf

Capable of producing multiple peaksCapable of producing multiple peaks

Why non-monotonicity?Why non-monotonicity?In the high correlation regime, In the high correlation regime, strong synchronous spike strong synchronous spike volleys are present, but their volleys are present, but their incidence is low, and many incidence is low, and many spikes will be wasted.spikes will be wasted.

In the moderate correlation In the moderate correlation regime, many moderately regime, many moderately synchronous spike volleys synchronous spike volleys are present, so the firing rate are present, so the firing rate is higher.is higher.

ConclusionsConclusions

The pair wise correlation in the spike trains The pair wise correlation in the spike trains has a fundamental effect on the firing rate has a fundamental effect on the firing rate of the recipient neuronof the recipient neuronThe effect is qualitatively independent of The effect is qualitatively independent of the neural modelthe neural modelThe neurons have specific preferences to The neurons have specific preferences to certain levels of correlations in input trainscertain levels of correlations in input trainsThe temporal correlation can dramatically The temporal correlation can dramatically modulate the neural responsivenessmodulate the neural responsiveness