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Temporal Code:Dynamics in neuronal networks
Alexa RiehleInstitut de Neurosciences Cognitives de la Méditerrannée
INCM - CNRS
Marseille
It is commonly accepted that perceptual and motor functions are
based on distributed processes where neurons do not act in isolation, but
organize in functional groups. It is less clear, though, how these networks organize dynamically in space and
time to cope with momentary computational demands
Neural coding:
“rate vs temporal code”
Although our knowledge about the morphology and the physiology of the cerebral cortex drastically increased since the last 30 years, its
basic operational mode is still highly controversial debated.
rate code temporal code
What is a code ? the neuronal representation of information.
1) What ?
2) How ?
3) Which precision ?
How do all known components interact to form an efficient working system?How are complex functions such as perception and action realized within
neuronal networks?
The development of a new paradigm : the concept of "cell assemblies"
it is not a matter of an alternative, but a complementary mode
“Let us .. assume as the basis of all our subsequent reasoning this law: When two elementary brain processes have been active together or in immediate succession, one of them, on re-occurring, tends to propagate its excitement into the other.”
Cooperativity in cortical networks
William James (1890)Psychology (Briefer Course)
“The general idea is an old one, that any two cells or systems of cells that are repeatedly active at the same time will tend to become associated, so that activity in one facilitates activity in the other…
This is then the cell assembly. ”
Donald O. Hebb (1949)The Organization of Behavior
Raphael Lorente de Nó (1937)
Cooperativity in cortical networks
“Each set (of neurons) excites synchronous firing in the next set, which in turn excites synchronously the next set of neurons, etc. We shall call this arrangement … the synfire chain. .. although the neuron operates as an integrator it is especially sensitive to coincident firing of a few presynaptic sources. ..It is evident that activity within a network of neurons would tend to organize itself in chains of synchronously firing groups..”
Moshe Abeles (1982)Local Cortical Circuits
Cooperativity in cortical networks
“.. (cell assemblies) are dynamic entities, defined … by the ever-changing level of correlation among the activities of their member neurons. … there is no need for the synaptic contacts to be particularly strong: the corresponding connections become effective through synchronous activity with other neurons”
Ad Aertsen et al. (1991)Z. Hirnforsch. 6: 735-743
Cooperativity in cortical networks
Functional and dynamic units
Defined by the synchronization or another precise temporal structure of the discharge
Flexibility : each neuron can participate, successively,
at differents functional groups
integration time long : 5 to 50 ms short : 1 to 5 msmean interval between spikes short long i.e., discharge rate high lowwho contributes to the generation of output ? all spikes only synchronous spikestemporal precision irrelevant relevant i.e. relevant information mean discharge rate temporal structure of spikeshow many spikes are necessary for producing a spike at the output ? ~300 ~30
Two modes of fonctioning of pyramidal neurons in the cerebral cortex
Temporal integration Coincidence detection
Synchronization of neuronal activity 1
There are two explanations for synchronous activity :* common input or* functional interaction by means of relatively
small neuronal networks
A common input modulates simultaneously the discharge patterns of the two neurons; there is, thus, no direct interaction between the two neurons. A functional interaction involves a mechanism by which the discharge of one neuron influences the discharge probability of the other.
We have to discriminate between * a structural connectivity (or an anatomic one) and * a functional connectivity (or an efficient one).
The first might be described as * stationary and fixed,
whereas the second as * dynamic having a time constant of modulation in the range of tens to hundreds of milliseconds.
Synchronization of neuronal activity 2
Are neurons able to produce action potentiels with a temporal precision
in the range of milliseconds ?
The temporal precision of neuronal discharge
Cat auditory cortex
the cat listens during 20 minutes to natural noise
Aertsen et al., Biol. Cybernetics 32: 175-185
(1979)
Aertsen et al., Biol. Cybernetics 32: 175-185
(1979)
The temporal precision of neuronal discharge
…. the same tape is repeated
Aertsen et al., Biol. Cybernetics 32: 175-185
(1979)
The temporal precision of neuronal discharge
…. the two records are then cross-correlated
The temporal precision of neuronal discharge
… a constant electrical stimulus is repeatedly applied, the precision
vanishes
The temporal precision of neuronal discharge
…. a noisy stimulus is applied, discharge is very
precise and repetitive
Two, three, many electrodes in the brain
20 m
Asynchronous action potentials
Neuron 1
Neuron 2
Synchronous action potentials
Neuron 1
Neuron 2
neuron 1
neuron 2
-3 -2 -1 0 1 2 3 time units
The most basic technique of data analysis
The cross-correlogram#
coin
cide
nces
Cross-correlation and shift predictor
Temporal precision : 1-2 ms
# of
spi
kes
/ bin
lead / lag (ms)
The binding problem
The understanding of how neurons co-operate in order to form perceptual or motor representations is one of the major objectives in neurobiology
How is individual neuronal activity integrated to form functionally efficient spatio-temporally patterns within networks?
Binding by synchrony
From: Engel et al, Cerebral Cortex 7: 571-582 (1997)
Freiwald, Kreiter & Singer, NeuroReport 6: 2348-2352 (1995)
Temporal coding in the visual cortex
Roy & Alloway, J Neurophysiol 81: 999-1013 (1999), Fig. 3
Temporal coding in the somatosensory cortex
Roy & Alloway, J Neurophysiol 81: 999-1013 (1999), Fig. 9
Temporal coding in the somatosensory cortex Width of the peak as a function of the stimulus
Raw Joint Peri-Stimulus-Time-Histogram (Joint PSTH)
Aertsen, Gerstein, Habib, Palm (1989) Dynamics of neuronal firing correlation modulation of "effective connectivity". J. Neurophysiol. 61: 900-917
Aertsen & Gerstein In: Krüger J (ed) Neuronal cooperativity. pp 52-67 (1991)
Aertsen & Gerstein In: Krüger J (ed) Neuronal cooperativity. pp 52-67 (1991)
Normalized Joint Peri-Stimulus-Time-Histogram
Joint Peri-Stimulus-Time-Histogram
(Joint PSTH)
Aertsen & Gerstein In: Krüger J (ed)
Neuronal cooperativity pp 52-67 (1991)
Normalized Joint PSTH
In two different behavioral conditions recorded in the frontal cortex of the monkey
Vaadia et al., Nature 373: 515-518 (1995)
Vaadia et al., Nature 373: 515-518 (1995)
Correlation in frontal eye field of the monkey
(1) Detection of precise spike coincidences :Activity of two simultaneously recorded neurons
Riehle et al., Science 278: 1950-1953 (1997)
(2) Detection of precise spike coincidences :Synchronous spikes (precision : 2 ms)
Riehle et al., Science 278: 1950-1953 (1997)
(3) Detection of precise spike coincidences :Measured (red) and expected (black) coincidence rates
Riehle et al., Science 278: 1950-1953 (1997)
(2) Detection of precise spike coincidences :Synchronous spikes (precision : 2 ms)
Riehle et al., Science 278: 1950-1953 (1997)
(4) Detection of precise spike coincidences :Statistically significant coincidences ("Unitary Events")
Riehle et al., Science 278: 1950-1953 (1997)
Multiple single-neuron recordings using
7 independently movable micro-electrodes
(Reitböck system, Thomas Recording, Germany)
Simple Reaction Time Task
One Movement Direction Uncertainty about Signal Occurrence
(“Conditional Probability”)Four possible Delay Durations presented
at random with equal probability: 600 - 900 - 1200 - 1500 ms
Riehle, Grün, Diesmann, Aertsen. Science 278: 1950-1953 (1997)
start switch PS 1.RS 2.RS 3.RS 4.RS
- 500ms 0 600 900 1200 1500 ms
time (ms)
Conditional Probability 0.25 0.33 0.5 1
Riehle, Grün, Diesmann, Aertsen. Science 278: 1950-1953 (1997)
Behavioral results
Conditional probability: 0.25 0.33 0.5 1
Spike synchronization in relation to signal
expectancy
Riehle et al., Science 278: 1950-1953 (1997)
Event expectancy with increasing probability
Riehle et al., Science 278: 1950-1953 (1997)
Synchronization and discharge rate
are used in a complementary way
by motor cortex
Internal event External event
% o
f pai
rs o
f neu
rons no rate
modulation rate modulation
After Riehle et al., Science 278: 1950-1953 (1997)
Bastian, Riehle, Erlhagen, Schöner. NeuroReport 9: 315-319 (1998)Grammont, Riehle. Exp. Brain Res. 128: 118-122 (1999)Erlhagen, Bastian, Jancke, Riehle, Schöner. J. Neurosci. Meth. 94: 53-66 (1999) Riehle, Grammont, Diesmann, Grün, J. Physiol (Paris) 94: 569-582 (2000)Bastian, Schöner, Riehle, Eur. J. Neurosci. (2003, in press)
Multi-directional Pointing Movement:Simple Reaction Time Task
No Uncertainty:Prior Information about Direction
Fixed Delay: 1000 ms
Schematic representation of the three main types of neurons recorded in the preparation paradigm
Riehle & Requin, 1987 - 1995
Assembly formation
Grammont & Riehle Exp. Brain Res. 128: 118-122 (1999)
Discharge rates of two simultaneously recorded neurons
The one is preparation-related (purple) and the other rather execution-related (green)
Assembly formation
Coincidences are detected with a temporal precision of 1 ms
Grammont & Riehle Exp. Brain Res. 128: 118-122 (1999)
Assembly formation
Raw (blue) and expected (black) coincidence rates
Grammont & Riehle Exp. Brain Res. 128: 118-122 (1999)
Assembly formation
statistical significance :Joint-surprise value
Grammont & Riehle Exp. Brain Res. 128: 118-122 (1999)
Assembly formation
Binding by synchronyor "shake-hand neurons":
Neurons form an assembly to strengthen the transition from
preparation to action
Unitary Events
Grammont & Riehle Exp. Brain Res. 128: 118-122 (1999)
Dynamics of synchronous spiking
activity:
Temporal precision
Binding by synchrony or "shake-hand neurons":
Neurons form an assembly to strengthen the transition from
preparation to action
Grammont & Riehle Exp. Brain Res. 128: 118-122 (1999)
Riehle, Grammont, Diesmann, Grün, J. Physiol (Paris) 94: 569-582 (2000)
Dynamics of synchronous spiking activity:
Modulation in time
Riehle, Grammont, Diesmann, Grün, J. Physiol (Paris) 94: 569-582 (2000)
Dynamics of synchronous spiking activity:
Modulation in time
Dynamics of synchronous spiking activity:
Modulation in time
Riehle, Grammont, Diesmann, Grün, J. Physiol (Paris) 94: 569-582 (2000)
Dynamics of of synchronous spiking activity:
Temporal Precision
Riehle, Grammont, Diesmann, Grün, J. Physiol (Paris) 94: 569-582 (2000)
Determining a binary vector from the joint-surprise values for each pair of neurons:
00000000000000000001111111100000011111000000000000000000000000000000
By averaging binary vectors from several pairs of neurons, one obtains the probabilibity of being significantly synchronized
Calculation of the probability of statistically significant synchronization in a population of neurons
Comparison of synchronicity and mean
firing rate
Tightening of precision and increase in firing rate toward the end of the
preparatory period
Riehle, Grammont, Diesmann, Grün, J. Physiol (Paris) 94: 569-582 (2000)
Grammont & Riehle, Exp. Brain Res. 128: 118-122 (1999)
Dynamics of cell assemblies
Multi-directional Pointing Task:Choice Reaction Time Task
Prior Information about Movement DirectionUncertainty about Signal Occurrence
(“Conditional Probability”)Two possible Delay Durations:
600 - 1200 ms
Riehle, Grammont, Diesmann, Grün, J. Physiol (Paris) 94: 569-582 (2000)Grammont & Riehle Biol Cybern 88: 360-373 (2003)
Reaction Times in relation to the Conditional Probability
short delay (p = 0.5) long delay (p = 1)
reac
tion
time
(ms )
Neuronal activity related to time estimation
Riehle, Bastian, Böye, Grammont (unpublished data, 2000)
PS ES RS
Cooperativity in cortical networks
Cell assemblies are dynamic entities, where neurons participate in different assemblies at different times
Riehle & Grammont, unpubl. data (1998)
Cooperativity in cortical networks Dynamics of synchrony: Modulation in time
Riehle, Grammont, Diesmann, Grün, J. Physiol (Paris) 94: 569-582 (2000)
Probability of significant
Synchronization and mean Firing Rate
1 pair of neurons 6 movement directions
Probability of significant
Synchronization and mean Firing Rate
1 pair of neurons 6 movement directions
Probability of significant
Synchronization and mean Firing Rate
1 pair of neurons 6 movement directions
Time course of synchrony in a
population of motor cortical neurons
Probability of significant synchronization
Grammont & RiehleBiol Cybern 88: 360-373 (2003)
Mean firing rate
Grammont & RiehleBiol Cybern 88: 360-373 (2003)
Time course of synchrony and
mean discharge rate in a population of
motor cortical neurons
Probability of significant synchronization
7 ms precision
Grammont & RiehleBiol Cybern 88: 360-373 (2003)
Time course of synchronicity and mean discharge rate of a population of motor cortical neurons
Grammont & Riehle Biol Cybern 88: 360-373 (2003)
Time course of synchronicity and mean discharge rate of a population in relation to movement direction
Grammont & Riehle Biol Cybern 88: 360-373 (2003)
Left Right
Time course of synchronicity and mean discharge rate of a population in relation to movement direction
Grammont & Riehle Biol Cybern 88: 360-373 (2003)
χ² -values per sliding window:
5.05 < χ² < 11.25
0.0001 < p < 0.05
Difference in firing rate never
statistically significant (t-test of Student)
Time course of mean discharge rate of a population of motor cortical neurons in relation to movement direction
Grammont & Riehle Biol Cybern 88: 360-373 (2003)
Distribution of Preferred Directions
Probability of significant
synchronization per movement
direction in a population
of motor cortical neurons
Grammont & Riehle Biol Cybern 88: 360-373
(2003)
Probability of significant synchronization
and mean discharge rate
per movement direction in a population of motor
cortical neurons
Grammont & Riehle Biol Cybern 88: 360-373
(2003)
Probability of significant synchronization
and mean discharge rate
per movement direction in a population of motor
cortical neurons
tuning and preferred direction during the preparatory period
Grammont & Riehle Biol Cybern 88: 360-373
(2003)
Probability of significant synchronization
and mean discharge rate
per movement direction in a population of motor
cortical neurons
…during movement onset
Grammont & Riehle Biol Cybern 88: 360-373
(2003)
Reaction times in relation to movement direction
Grammont & Riehle Biol Cybern 88: 360-373
(2003)
Same preferred direction (PD) for synchrony, firing rate, and reaction time
Grammont & Riehle Biol Cybern 88: 360-373
(2003)
Not only neuronal firing rate, but also synchrony is predictive for
performance speed
Firing rate and reaction time
after Riehle & Requin Behav. Brain Res. 53:
35-49 (1993)
Reaction times and synchrony in relation to delay duration, i.e. conditional probability
short delay (p = 0.5) long delay (p = 1)
reac
tion
time
(ms)
Time course of synchronicity and mean discharge
rate of a population of motor cortical
neurons
Normalized cross-correlations calculated
in sliding windows
Riehle & Grammont (unpublished results, 2001)
Cross-correlation histogram and its normalization
Roux & Riehle (unpublished results, 2001)
Strengthening of precise synchronization toward the end of the preparatory period
Normalized cross-correlation calculated in sliding windows
Roux & Riehle (unpublished results, 2001)
lead
/ la
g (m
s)
Roux & Riehle (unpublished results, 2001)
Precise synchronization as a function of reaction timeCalculated during the last 500 ms of the preparatory period
Precise synchronization as a function of reaction timeCalculated during the preparatory period
Roux & Riehle (unpublished results, 2001)
Conclusions
significant synchronous spiking activity is not maintained for more than 100 to 200ms, it modulates in time changes its temporal precision during the instructed delay, most often increases its precision towards the end. is predictive for performance speed
Synchrony seems often to preceed the increase of neuronal activity
… but there is no simple parallel shifting in time.
Synchrony may trigger the increase in firing rate in large neuronal networks, which in turn communicate with the
periphery for initiating the movement
Thanks !!
Theory: Ad Aertsen (Univ. Freiburg, Germany)
Sonja Grün (FU Berlin, Germany) Markus Diesmann (MPI Göttingen, Germany)
Experiments: Franck Grammont (Univ. Parma, Italy)
Sébastien Roux (CNRS Marseille, France)