WINNERLESS COMPETITION PRINCIPLE IN NEUROSCIENCE

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• WINNERLESS COMPETITION PRINCIPLE IN
  NEUROSCIENCE
• Mikhail Rabinovich
• INLS University of California, San Diego

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competition stimulus Winnerless
without dependent CompetitionWINNER
clique Principle
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Hierarchy of the Models

• Network with realistic H-H model neurons random
  inhibitory excitatory connections
• Network with FitzHugh-Nagumo spiking neurons
• Lotka-Volterra type model to describe the spiking
  rate of the Principal Neurons (PNs)

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From standard rate equations to Lotka-Volterra
type model
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Stimulus dependent Rate Model
Is the firing rate of neuron i
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Canonical L-V model (Ngt3)
A heteroclinic sequence consists of finitely many
saddle equilibria and finitely many separatrices
connecting these equilibria. The heteroclinic
sequence can serve as an attracting set if every
saddle point has only one unstable direction. The
condition for this is
i1
i
Necessary condition for stability
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Canonical Lotka-Volterra model Rigorous results
(N3)
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WLC Principle SHS (rate model)

• Geometrical image of the switching activity in
  the phase space is the orbit in the vicinity of
  the heteroclinic sequence

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WLC Principle SHS (H-H neurons)

• Geometrical image of the switching activity in
  the phase space is the orbit in the vicinity of
  the heteroclinic contour

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WLC in a network of three spiking-bursting neurons
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The main questions

• How does sensory information transform into
  behavior in a robust and reproducible way?
• Do neural systems generate new information
  based on their sensory inputs?
• Can transient dynamics be reproducible?

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WLC dynamics of the piloric CPG experiment
theory
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Real timeCliones hunting behavior
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Cliones hunting behavior
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Cliones neural circuit
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WLC can generate an irregular but reproducible
sequence
Model assumptions

• All connections are inhibitory
• The SRCs are asymmetrically connected
• There is 30 connectivity among the neurons
• The hunting neuron excites allSCHs at variable
  strength

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Projection of the strange attractorfrom the 6D
phase space of the statocyst network
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Weak reciprocal excitation stabilizes WLC
dynamics Birth of the stable limit cycle in the
vicinity of the former heteroclinic sequence
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Conductance-based model for Winner take all and
Winnerless competition
Winner take all
Winnerless
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Sequential dynamics of statocyst neurons
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Motor output dynamics
Firing rates of 4 different tail motorneurons at
different burst episodes
In spite of the irregularity the sequence is
preserved
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IMAGES OF THE DYNAMICAL SEQUENCES
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Spatio-temporal coding in the Antennal Lobe
of Locust(space odor space)
Lessons from the experiments The key role of
the inhibition Nonsymmetric connections No
direct connection between PNs
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Winnerless Competition Principle New Dynamical
Object Stable Heteroclinic Sequence
WLC SHS
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Transient dynamics of the bee antennal lobe
activity during post-stimulus relaxation
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Low dimensional projection of Trajectories
Representing PN Population Response over Time
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Stable Heteroclinic Sequence
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Reproducible sequences in complex networks
Inequalities for reproducibility
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Reproducibility of the heteroclinic sequence
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Stable manifolds of the saddle points keep the
divergent directions in check in the vicinity of
a heteroclinic sequence
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WLC in complex neural ensembles

• Complex network many elements
• disordered
  connections
• Most important phenomena in complex
• systems on the edge of reproducibility are
• (i) clustering, and
• (ii) competition

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Rate model of the Random network
Q Is the step function
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TWO REGIMES
A)
B)
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What controls the dynamics?
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Phase portrait of the sequential activity
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Chaos in random network
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Reproducible transient sequence generated in
random network
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Reproducibility of the transient dynamics
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Example of sequence
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The network of songbird brain
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HVC Songbird patterns
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Self-organized WLC in a network with Hebbian
learning
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WLC in the network with local learning
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WLC networks cooperation synchronization
(i) electrical connections, (ii)
synaptic connections (iii)
ultra-subharmonic synchronization
competition
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Synchronization of the CPGs of two different
animals
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Heteroclinic synchronization Ultra-subharmonic
locking
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Heteroclinic Arnold tongues
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Chaos between stairs of synchronizaton
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Heteroclinic synchronization Maps description
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Competition between learned sequences on line
decision making
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The main messages

• The WLC principle SHS do not depend on the
  level of the neuron synapse description and can
  be realized by many different kinds of network
  architectures.
• The WLC principle is able to solve a fundamental
  contradiction between robustness sensitivity.
• The transient sequence can be reproducible.
• SHS can interact with each others compete,
• synchronized generate chaos.

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Thanks to the collaborators
Valentin Afraimovich, Rafael Levi, Allan
Selverston, Valentin Zhigulin,
Henry Abarbanel, Yuri Arshavskii
Gilles Laurent
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Spatio-temporal patterns in Cliones nerves
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WLC Dynamics of the H-H network
Neuron
time (ms)
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Reproducibility of the dynamics
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Stimulation of statocyst nerve triggers a
dynamical response in the motor neurons
Motor output electro-physiological recording
Motor output firing rates
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Statocyst receptor activity during hunting
episodes

• The constant statocyst receptor activity turns
  into bursting in physostigmine
• The activity is variable between episodes
• A single receptor is active during different
  phases of the hunting episodes