Transcript CATS

CATS International Workshop, CHANIA, CRETE, 2-3 June 2009
“Dynamics of mutually delay-coupled systems:
From Lasers to Neurons”
Claudio R. Mirasso1
1- Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC, CSIC-UIB, Palma de
Mallorca, Spain
Ingo Fischer1,2, Raúl Vicente3, Gordon Pipa3, Leonardo L. Gollo1, Miguel C. Soriano1, Flavio Ruiz1
Javier Buldú4, Jordi García Ojalvo5, Carmen Torrent5, Michael Peil6, Alessandro Villa7 & Javier Iglesias7
2- Department of Physics, Heriot Watt University, Edinburgh, Scotland
3- Max Planck Institute for Brain Research, Frankfurt, Germany
4- Complex Systems Group, Universidad Rey Juan Carlos, Madrid Spain
5- Departament de Fisica i Enginyeria Nuclear, Universitat Politecnica de Catalunya
6- Institute of Applied Physics, Darmstadt University of Technology, Germany
7- Faculty of Medicine, University of Grenoble, France
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CATS International Workshop, CHANIA, CRETE, 2-3 June 2009
Outline of the talk

Introduction and motivation

Interacting lasers with delay

Interacting neurons and neuron
populations with delay
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
Physiological plausibility

Conclusions
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Questions
Dynamics and Synchronization….
?
• What happens in semiconductor lasers (and coupled
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•
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•
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dynamical systems in general), if the information
exchange between individual elements requires a finite
(and relevant) time delay?
What kind of dynamical instabilities are being induced?
What are the consequences for synchronization?
(Under which conditions) can we achieve long-range
synchronization at zero lag?
Can we transfer the obtained results to better understand
some synchronized process in the brain?
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Dynamics and Synchronization….
What are the consequences of
delay-coupling?
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Dynamics and Synchronization….
Oscillators with Delayed Coupling
T
t ~> T
T
Delay t introduces additional dynamical degrees of freedom
Resulting dynamical phenomena:
•
•
•
•
•
Multistability of synchronized and desynchronized states
Amplitude Death in coupled limit cycle oscillators
Stochastic -, Coherence-, and Ghost resonance
Characteristic locking and oscillation phenomena
Characteristic delayed coupling-induced instabilities and
synchronization..
Delay has an ambivalent influence: destabilizing and/or stabilizing
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Dynamics and Synchronization….
Semiconductor Lasers with Delayed Coupling
Coupled semiconductor lasers with ..
similar properties (twins)
coupling
longitudinal (face-to-face)
coherent (via lasing fields)
mutual, symmetric
long (tcp > tRO) coupling delay
weak to moderate coupling
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Intensity / a.u.
Dynamical Behavior
• onset of coupling-induced
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3
2
1
0
-1
-2
-3
-4
-5
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-8
-9
0
100
200
300
400
500
600
700
800
900 1000
Time / ns
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Intensity [arb.units]
Dynamics and Synchronization….
4
2
0
530
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532
534
Time [ns]
536
538
intensity pulsations
• similar dynamics to delayed
feedback
• synchronization among the two
lasers
• synchronization of ns and sub-ns
pulsations
• however:
• one time series temporally shifted
by tcp
• spontaneous symmetry breaking
T.Heil, I.Fischer, W.Elsäßer, J.Mulet,
•- C.R.Mirasso,
leader & laggard
Phys.Rev.Lett. 86, 795 (2001)
- H.Fujino
J.Ohtsubo,
Opt. Rev. 8, 351
(2001)
(achronal
synchronized
solution)
CCmax at +/- n*t
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Dynamics and Synchronization….
tcp
leader
inverted
laggard
K.White et al., Phys. Rev. E 65, 036229 (2002)
J.Mulet et al., J. Opt. B: Quantum Semiclass. Opt.
6, 97 (2004)
isochronal solution exists, but is unstable
no zero-lag synchronization!
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Dynamics and Synchronization….
Can the isochronal (zero-lag) solution be stable /
stabilized?
LD2
LD3
LD1
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Dynamics and Synchronization….
J. Terry
et al., Phys. Rev.
59, p. 4036
(1999)
Synchronization
in aE3-Stripe
Laser
Perfect synchronization of the outer stripes
Center laser acts as mediator
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Chain of 3 Lasers
Dynamics and Synchronization….
• L1 and L3 synchronised
with zero lag
L1
L3
• center laser (L2) lags
behind the outer laser (L1)
L1
L2
• center laser (L2) lags
behind the outer laser (L3)
L2
I.Fischer et al., Phys.Rev.Lett. 97, 123902 (2006)
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L3
• excellent agreement with
modelling
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Dynamics and Synchronization….
Why does it work?
What are the detailed demands / constraints on the relay
element?
relay redistributes the incoming signals (and perturbations)
symmetrically in both directions
relay element can be mismatched to outer elements
modifies the dynamical behavior, however
the zero-lag synchrony is unperturbed
relay can even be linear and passive
with lasers:
relay element can be replaced by partially transparent mirror
• stabilization of the isochronous solution
R.Vicente, I.Fischer, C.R.Mirasso, Opt. Lett. 32, 403 (2007)
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Dynamics and Synchronization….
However......
Moving
Moving
mirror:
mirror:
f12= ff12
=p/2
f21=0
or or
p/4...
p
21=
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Moving
Moving
L2:LC
f1= 0
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Dynamics and Synchronization….
Experimental demonstration
Asymmetric case:
T1 >> T2
M. Peil, L. Larger, and I. Fischer, PHYSICAL REVIEW E 76, 045201R 2007
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Dynamics and Synchronization….
Can these results be relevante for the brain?
Zero-Lag Long-Range Synchronization in the Brain
Neurophysiological experiments: even in the presence of
substantial coupling delays different cortical areas exhibit
isochronous synchronization at zero lag
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Dynamics and Synchronization….
In the brain there is a huge anatomical and functional
specialization of the different cortical areas
How to bind the information processed at distant cortical areas?
Synchrony hypothesis: binding occurs through the formation of transiently
synchronized cell assemblies. Time domain solution.
Singer, W. Neuron 24 (1999) 49–65
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Dynamics and Synchronization….
How can two distant neural assemblies synchronize their
firings at zero-lag even in the presence of non-negligible
delays in the transfer of information between them?
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Dynamics and Synchronization….
Which is the physical and anatomical substrate for this dynamical
and precise synchrony?
- Direct cortico-cortical connections
- Inhibitory connections
Enhance synchronization
- Gap junctions
- Complex Networks
R. Traub et al., Nature 383, p. 621, 1996;
G. B. Ermentrout & N. Kopell, Proc. Natl. Acad.
Sci. USA 95, p. 1259, 1998;
 Excitatory-Inhibitory networks favor g-frequency
rhythms
 Inhibitory cells produce spike doublets
 Connections between such networks favor zerolag synchronization.
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Dynamics and Synchronization….
Can the zero-lag sync mechanism observed in lasers be
generalized to models of neuronal systems?
Neuron are excitable
systems
They couple via chemical
synapses (pulse coupling)
Model at the level of Hodgkin-Huxley:
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Dynamics and Synchronization….
Simulating conditions:
- periodic firing regime (T = 14.7 ms, f = 68.02 Hz)
- each neuron with a random initial phase
- different synaptic rise and decay times
- excitatory and inhibitory synapses
• self-organization toward the
synchronization of outer neuron
spikes
• zero-phase sync due to relay and
redistribution of EPSP / IPSP
True for E-E or I-I couplings and different a-functions
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Dynamics and Synchronization….
A crucial point to check is whether the observed synchronized state is particular to
single latency synapsis or is maintained for broad distribution of synaptic delays.
Order
parameter
Non-locking frequency area
(irregular firing)
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Large plateau where the
oscillations are isochronous
(2-9 ms )
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Dynamics and Synchronization….
Populations?
Populations of neurons with the same reciprocal connectivity subjected to independent
Poissonian input trains of spikes.
~4000 IAF neurons
80 % excitatory
internal random connectivity,
10% connectivity
V threshold : 20 mV
V reset : 10 mV
refractory time: 2 ms
time constant : 20 ms
N. Brunel, J. Comp. Neurosc. 8, 183, 2000.
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Dynamics and Synchronization….
Each neuron connects excitatory and randomly to 0.25%
of the neurons of the other population with 15 ms delay
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“Dynamical relaying can yield zero time lag neuronal synchrony despite long conduction delays”,
R. Vicente, L. L. Gollo, C. R. Mirasso, I. Fischer and G. Pipa, PNAS 105, 17157 (2008).
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Dynamics and Synchronization….
Physiological plausibility.
Thalamus is the main relay unit of sensory information to the
cortex with bidirectional connections
9-10 Hz oscillation in the thalamus.
Intact and with a cortex lesion.
Synchrony of oscillations is not
determined by intracortical connectivity
Control of Spatiotemporal Coherence of a Thalamic Oscillation by Corticothalamic Feedback,
D. Contreras, A. Destexhe, T. J. Sejnowski, M. Steriade, Science 274, 771 (1996).
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Dynamics and Synchronization….
Cortical-Pulvinar nucleus-Cortical circuits mimic direct CC pathways but with
more overlap
facilitation of transarea sync.
S. Shipp, Philos Trans R Soc Lond B Biol Sci, 358, 1605, (2003).
“The driving projections to thalamus would thus provide a significant alternative
path for inter-areal communication“.
Douglas and Martin, Annu. Rev. Neurosci.. 27:419:51, 2004
Recent studies have shown the constant latency between the thalamus and almost
any area in the rat cortex. Stronger TC connections than expected.
Change of conduction velocity by regional myelination yields constant latency
irrespective of distance between thalamus and cortex.
Salami et al., PNAS, 100, 6174, (2003).
Cortex Is Driven by Weak but Synchronously Active Thalamocortical Synapses,
Bruno and Sakmann, Science, 312, 1622, (2006).
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Dynamics and Synchronization….
Thalamo-Cortical Interaction.
(Preliminar results)
C1- Connections E, Connectivity: 1%, t= 8 ms,
strength=0.05 mV
C2- Connections E, Connectivity: 10%, t= 5 ms,
strength=0.05 mV
C3- Connections I, Connectivity: 80%, t= 2 ms,
strength=-0.0735 mV
C4- Connections E, Connectivity: 10%, t= 2 ms,
strength=0.05 mV
TC: Thalamo-Cortical Network
RT: Reticular Nuclei
PGN: Perigeniculate Nuclei
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Dynamics and Synchronization….
Each neuron is subject to an independent Poisson noise
P(t)=k ent.
We fix k and change n in TC while keeping the other n’s fixed.
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Dynamics and Synchronization….
Coincidences at zero-lag
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Modulated activity
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Dynamics and Synchronization….
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Dynamics and Synchronization….
Summary & Conclusion
 Delayed coupling induce dynamical instabilities and symmetry breaking.
 Delay-coupled lasers with relay element:
 outer elements can be synchronized at zero-lag
 synchronization mechanism is robust
 minimal requirements on relay: linear/nonlinear active/passive
 We have proposed an alternative mechanism that gives rise to zero (or
almost)-lag (phase) long-range synchronization in neuronal models.
 A relay element must mediate the dynamics between two neurons or
neuron populations.
 It might be possible that the thalamus acts as a relay element (although
cortico-cortical interaction without thalamus mediation are also
possible).
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Thanks for your
attention
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Dynamics and Synchronization….
300 pairs of neurons averaged over 100 different noise realizations
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Dynamics and Synchronization….
Also.......the proposed motif is a building block of the
mammalian cortex. But has the proposed motif a specific
role in the brain network?
Sporns & Kötter
PLoS Biology, 2,
1910, (2004).
http://www.ifisc.uib-csic.es 13
Dynamics and Synchronization….
Distributions with same shape factor k´s and different mean
times t´s: broader distributions of delays favor shorter lags
in the cross correlation
However, a distribution of delays
stabilizes the zero-phase lag.
Linear growth
(Single latency)
Lag < delay diff.
t = 8 ms
t = 11 ms
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Dynamical Relying Yields
Zero-Lag
Dynamics
and Synchronization….
The proposed motif is a building block of the mammalian cortex.
But has the proposed motif a specific role in the brain network?
Motifs in brain networks,
PLoS Biology, 2, 1910, (2004).
http://www.ifisc.uib-csic.es 13
Dynamics and Synchronization….
V
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Dynamical Relying Yields
Dynamics
Zero-Lag
and Synchronization….
Feedforward and feedback connections between cortex
and thalamus reinforce the thalamic oscillatory activity
into larger thalamocortical networks to generate sleep
spindles and spike-wave discharge of generalized
absence epilepsy (H. Huguenard & A. McCormick
Trends in Neurosc. 30, 350, 2007).
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Dynamics
Bidirectionally
and Synchronization….
coupled….
Would it be possible to observe the same effect in coupled neurons?
Neuron are excitable systems
They couple via chemical synapses (pulse coupling)
Model for Thermoreceptors in Fish and Mammals based on
Hodgkin-Huxley Model (W. Braun et al., Phys. Rev. E 62, 6352, 2000)
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Dynamics and Synchronization….
Interhemispheric Synchronization
Interhemispheric Synchronization of
Oscillatory Neuronal Responses in Cat
Vis... A. Engel, et al. Science 252, 5009
1991.
Interhemisferic synchronization is
absent when the corpus callosum is
sectioned
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Dynamics
Bidirectionally
and Synchronization….
coupled….
Period 1
Period 2
Irregular with narrow
groups of spikes
Period 3
Irregular sequence,
groups of 2/3 spikes
Period 1
0
15
W.Braun et al., Phys. Rev. E 62, 6352 (2000)
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Dynamics
Bidirectionally
and Synchronization….
coupled….
Three Bidirectionally Coupled Neurons
T=21.5 ºC
t=15 ms
Two Bidirectionally Coupled Neurons
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Dynamics
Bidirectionally
and Synchronization….
coupled….
2 neurons
3 neurons
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Dynamics
Bidirectionally
and Synchronization….
coupled….
Physiological plausibility.
Thalamus is the main relay unit of sensory information to the
cortex with bidirectional connections
Pulvinar nucleus (contains maps of V1-V5) so CPC circuits mimic direct CC
pathways but with more overlap
facilitation of transarea sync.
S. Shipp, Philos Trans R Soc Lond B Biol Sci, 358, 1605, (2003).
“The driving projections to thalamus would thus provide a significant alternative
path for inter-areal communication“.
Douglas and Martin, Annu. Rev. Neurosci.. 27:419:51, 2004
http://www.ifisc.uib-csic.es
Dynamics
Bidirectionally
and Synchronization….
coupled….
Physiological plausibility.
Recent studies have shown the constant latency between the
thalamus and almost any area in the rat cortex. Stronger TC
connections than expected.
Change of conduction velocity by regional myelination yields constant latency
irrespective of distance between thalamus and cortex.
Salami et al., PNAS, 100, 6174, (2003).
Cortex Is Driven by Weak but Synchronously Active Thalamocortical Synapses,
Bruno and Sakmann, Science, 312, 1622, (2006).
http://www.ifisc.uib-csic.es
Dynamics
Bidirectionally
and Synchronization….
coupled….
Also.......the proposed motif is a building block of the
mammalian cortex. But has the proposed motif a specific
role in the brain network?
Sporns & Kötter
PLoS Biology, 2,
1910, (2004).
http://www.ifisc.uib-csic.es 13
Dynamics
Bidirectionally
and Synchronization….
coupled….
Is this a robust phenomena?
The zero-lag synchrony is robust under the presence of
independent white noise in the external current of each cell ...
a
b
c
... and even when the relay cell is at the subthreshold regime. Not
necessarily a similar cell type.
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