Neural Coding 4:information breakdown

Multi-dimensional codes can be split in different components

Information that the dimension of the code will convey when considered independently

Information due to similarities among the stimulus-conditional responses of each dimension

Information due to the correlation that the different dimensions have independently from the stimuli

Information due to the way the stimuli affect the correlation between dimensions

Linear information

1 2 2 1 1 2( ; , ) ( ; ) ( ; ) ( ; , )RED S R R I S R I S R I S R R

1 2 1 2( ; ) ( ; , ) ( ; , )linI S R I S R R I RED S R R

Signal similarity information

( ; ) lin sig sim corrI S R I I I

The signal similarity component is the part of the redundancy that does not depend on correlation. It’s given by the similarity between the stimulus modulations.

1 2( ; , ) sig sim corrRED S R R I I

Stimulus independent correlation information

corr corr ind corr depI I I

The stimulus independent correlation can increase or decrease the overall information.

Anyway, in my experience, it always decreased information

Stimulus dependent correlation information

corr corr ind corr depI I I

The stimulus dependent correlation is the only term that is ALWAYS synergistic. We can only gain information from the fact that the stimulus affects the correlations.

Neural Coding 5: oscillations

Role of fluctuations of cortical activity in sensory information coding

Cortical activity is characterized by wideband oscillations

Which frequency bands carry information about sensory variables?

Which sensory variables are encoded by each frequency band?

Prerequiste to understand function of these fluctuations – important to know what to measure and what to model

Crucial for clinical developments – Brain Machine Interfaces

Local Field Potentials

LFP

Field potentials are operationally obtained by

low pass filtering the extracellular signal

Field potentials measure (to a 1st approx) the superposition of dendrosomatic (dipole) fields generated in apical dendrites of pyramidal neurons

Being a synaptic signal, the LFP can capture subthreshold effects not captured by spikes

Integration area: approx 300 microns from electrode tip (“middle ground” signal)

Two seconds Local Field Potentials from V1During movie presentations

Two seconds Local Field Potentials from V1During movie presentations

High frequencies

Two seconds Local Field Potentials from V1During movie presentations

Low frequencies

Two seconds Local Field Potentials from V1During movie presentations

Unreliable intervals

Shannon’s Information

S = set of different “scenes” of the movies (2 seconds intervals)

R = power of different frequency bands (discretized into N levels)

s r)(

)|(log)|()();(

,2 rP

srPsrPsPRSI

sr

Computing Information about movie stimuli

• Information about which section of the dynamic stimulus elicited the considered neural response .

• This quantification of information captures information about all possible stimulus features in the movie, including what and when property

)(

)|(log)|()();(

,2 rP

srPsrPsPRSI

sr

1 sec

Panzeri, Brunel, Logothetis, Kayser (2010) Trends Neurosci

Time

Belitski, Gretton, Magri, Murayama, Montemurro, Logothetis and Panzeri (2008) J Neurosci

Information in Power of V1 LFPs with naturalistic movies

• Two informative power signals: Low frequencies and gamma frequencies• High frequencies (γ and high γ) bands and low frequencies (α,θ,δ) carry independent

information about the movie• Intermediate frequencies (β) do not carry much information

γ

β

δ,θ,α

Do different LFP bands convey similar or different information about the movie?

Signal correlation: the correlation of the trial-averaged power profiles of two frequencies across all movie scenes. Signal correlation tells if two frequencies are selective for the same scenes.

Noise correlations: correlations in the trial-by-trial fluctuations in power around the mean at fixed scene.Noise correlation tells if two frequencies share a common source of variability.

Redundancy: the difference between the information carried by the joint knowledge of the two signals and the sum of the information carried by each signal individually

Zero redundancy: the two signals carry independent information

Positive redundancy (joint information less than the sum): the two signals share at least in part the same information

Do different LFP bands convey similar or different information about the movie?

Neural Coding: models of oscillations

Excursus: how to simulate neurons

From cellular automata…..

To accurate 3D reconstructions…..

(to Blue Brain)

Integrate and fire: la simulation la plus élégante

Integration of synaptic inputs with no spike dynamics.Only threshold and reset are defined.

Synaptic dynamics given by one rising exponential step and one closing exponential step

I

PUnspecific

slowcorticalactivity

Thalamic input

Leaky integrate and fire neurons 4000 pyramidal AMPA neurons 1000 GABA interneurons. Sparse (p=0.2) random connections

Integrate and fire models of local cortical excitatory-inhibitory networks

AMPA SINK

GABA SOURCE

ELECTRODE Pyramidal neurons

Interneurons

LFP modeled as sum of absolute values of AMPA and GABA currents on pyramidal neurons

Integrate and fire models of local cortical excitatory-inhibitory networks

Interneuronsspike rate

LFP=|IAMPA|+|IGABA|

on pyramidal neurons

input:costant signal + noise

Pyramidal neuronsspike rate

Network response to constant input

I

Input

Gamma oscillations origin

I

P

Input

I

P

Input

Oscillations in the 30-150 Hz range – depending on the inhibition/excitation balance

Network response to constant input

Interneuronsspike rate

LFP=|IAMPA|+|IGABA|on pyramidal neurons

Pyramidal neuronsspike rate

Mazzoni, et al – PLoS Comp Biol (2008)

Mazzoni et al (2010) Neuroimage

The network internally generates only gamma-range (40-100 Hz) oscillations The gamma power encodes the strength of the input

Modulation of the spectrum of LFP recorded in monkey V1 (Henrie and ShapleyJ Neurophysiol 05)

LFP from simulated cortical circuit

Network response to constant input

Each constant signal is injected 20 times, every time with a different noise. In this way we can compute the information content of the spectrum. Since 8 different rates are injected the total entropy is 3 bits.

The peak of information is at ~70 Hz, slightly higher than the peak of the oscillations.

The information contained in the frequencies of the gamma band is highly redundant

information

power

Network response to constant input

Periodic signals with frequencies ranging from 4 to 16 Hz and 7 different amplitudes are used as input. Each signal is injected with 20 different noises. The total entropy is 5.6 bits.

Periodic signals entrain network LFP oscillations (the effect is stronger for lower frequencies).Information about the lowest band of the signal spectrum is then contained in the same band of the network LFP.

Network response to periodic input

LFP

Signal

Delta oscillations origin

I

P

Input

Intuitively: the slower network time constant is given by the dy-sinaptic P-I-P rhythm. Whatever is slower (<30/40 Hz) will not interfere with network rhythms and will entrain the network linearly.

Cross-frequency coupling

The peak of slowly modulated inputs to the network will cause a peak in the low frequency component of the response LFP (because of entrainment) and a particularly high gamma power (because the latter encodes the strength of the input). This will lead to the cross-frequency coupling that is often observed experimentally.

Responses of the simulated network to input stimuli matching LGN spiking activity during naturalistic movies presentations

Stimuli matching LGN spiking activity during naturalistic movies presentations display a broad range of fluctuations.According to the model, input peaks are associated to troughs in the LFP delta band and to a larger amplitude of the LFP gamma band.The model correctly reproduces the information content of recorded LFP frequency bands during presentation of naturalistic movies.

Mazzoni et al. (2008)PLoS Comp. Biol.

There are two informative bands: frequencies below 10 Hz (”low frequencies”) and 30-100 Hz (gamma band). The two bands convey independent information. Furthermore low frequencies convey independent information from each other, while gamma frequencies are redundant.

Gamma band encodes signal rateDelta band encodes slow signal components

Responses of the simulated network to input stimuli matching LGN spiking activity during naturalistic movies presentations

Changes in synaptic strength highlight the role of the different neuro-transmitters and give experimentally testable predictions

Synaptic manipulations

ConclusionsDuring naturalistic stimulation, primary visual cortex multiplexes information by generating two complementary temporal information streams: slow (<10 Hz) fluctuations of the excitability of the local network, and fast (40-100 Hz) gamma oscillations.

These complementary information channels reflect different aspects of both neural dynamics and of stimulus representations. Slow fluctuations reflect entrainment to the stimulus time course and thus provide “when” information about stimulus history

Fast oscillations (which are largely redundant to spiking activity) are internally generated by excitatory-inhibitory interactions and encode “what” information about the current stimulus strength

Toolbox

www.ibtb.org