synchrony in neural systems: a very brief, biased, basic view
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Synchrony in Neural Systems: a very brief, biased, basic view. Tim Lewis UC Davis NIMBIOS Workshop on Synchrony April 11, 2011. neurons. synapses. connectivity. components of neuronal networks. synapses. pre-synaptic cell. network topology specific structure - PowerPoint PPT PresentationTRANSCRIPT
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Synchrony in Neural Systems:a very brief, biased, basic view
Tim LewisUC Davis
NIMBIOS Workshop on SynchronyApril 11, 2011
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neurons
cell type- intrinsic properties (densities of ionic channels, pumps, etc.)- morphology (geometry) - noisy, heterogeneous
synapsessynapses
~20nm
pre-synaptic cell
post-synaptic cell
synaptic dynamics- excitatory/inhibitory;
electrical- fast/slow- facilitating/depressing - noisy, heterogeneous- delays
connectivity
network topology- specific structure- random; small world, local- heterogeneous
components of neuronal networks
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function and
dysfunction
activity in neuronal networks,
e.g.synchron
y
intrinsic properties of
neurons
synaptic dynamics
connectivity of neural circuits
a fundamental challenge in neuroscience
function
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why could “synchrony” be important for function in neural systems?
1. coordination of overt behavior: locomotion, breathing, chewing, etc.
shrimp swimming
example: crayfish swimming
B. Mulloney et al
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why could “synchrony” be important for function in neural systems?
1. coordination of overt behavior: locomotion, breathing, chewing, etc.
2. cognition, information processing (e.g. in the cortex) …?1.5-4.5m
m
Should we expect synchrony in the cortex?
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1.5-4.5mm
Should we expect synchrony in the cortex?
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Figure 1: A geodesic net with 128 electrodes making scalp contact with a salinated sponge material is shown (Courtesy Electrical Geodesics, Inc). This is one of several kinds of EEG recording methods. Reproduced from Nunez (2002).
time (sec)
g
a
q
“raw”
EEG recordings
EEG: “brain waves”: behavioral correlates, function/dysfunction
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in vivo g-band (30-70 Hz) cortical oscillations.
large-scale cortical oscillations arise from synchronous activity in neuronal networks
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how can we gain insight into the functions and dysfunctions related to neuronal synchrony?
1. Develop appropriate/meaningful ways of measuring/quantifying synchrony.
2. Identify mechanisms underlying synchronization – both from the dynamical and biophysical standpoints.
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1. measuring correlations/levels of synchrony
Swadlow, et al.
i. limited spatio-temporal data.ii. measuring phase iii. spike-train data (embeds “discrete” spikes in continuous time) iv. appropriate assessment of chance correlations.v. higher order correlations (temporally and spatially)
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synchrony in
neuronal networks
intrinsic properties of
neurons
synaptic dynamics
connectivity of neural circuits
2. identify mechanisms underlying synchrony
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“fast” excitatory synapses
synchrony
“slow” excitatory synapse
asynchrony
[mechanism A] synchrony in networks of neuronal oscillators
movie:LIFfastEsynch.avi
movie:LIFslowEasynch.avi
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Some basic mathematical frameworks:
1. phase models (e.g. Kuramoto model)
N
kjkkjj
Njjj
Hw
NjHdtd
1
1
)(
,...,1),,...,(
qqq
[mechanism A] synchrony in networks of neuronal oscillators
)1,0[jq
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Some basic mathematical frameworks:
2. theory of weak coupling (Malkin, Neu, Kuramoto, Ermentrout-Kopell, …)
N
kjkkjj
N
k
T
kosynjkjjj
Hw
NjtdTtVITtZT
wdtd
1
1 0
)(
,...,1,~~~)~(1
q
[mechanism A] synchrony in networks of neuronal oscillators
iPRCsynaptic current
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phase response curve (PRC) Dq(q)
quantifies the phase shifts in response to small, brief (d-function) input at different phases in the oscillation.
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infinitesimal phase response curve (iPRC) Z(q)
the PRC normalized by the stimulus “amplitude” (i.e. total charge delivered).
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[mechanism A] synchrony in networks of neuronal oscillators
Some mathematical frameworks:
2. spike-time response curve (STRC) maps
k phase difference between pair of coupled neurons when neuron 1 fires for the kth time.
D qq phase response curve for neuron for a given stimulus..
))1(()1(1 kkkkk qqq DDD
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k
threshold
blue cell has just been reset after crossing threshold.
pair of coupled cells: reduction to 1-D map
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k
threshold
red cell hits threshold.
pair of coupled cells: reduction to 1-D map
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12k
blueqD
threshold
blue cell is phase advanced by synaptic input from red cell; red cell is reset.
pair of coupled cells: reduction to 1-D map
)1(21 kkk q D
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12k
threshold
blue cell hits threshold.
pair of coupled cells: reduction to 1-D map
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blueqD
12k
redqD
threshold
red cell is phase advanced by synaptic input from blue cell; blue cell is reset.
pair of coupled cells: reduction to 1-D map
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redqD
1k
blueqD
threshold
k
pair of coupled cells: reduction to 1-D map
)(21
211 D kkk q
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(similar to Strogatz and Mirillo, 1990)pair of coupled cells: reduction to 1-D map
* shape of Z determines phase-locking dynamics
)1(21 kkk q D
)(21
211 D kkk q
))1(()1(1 kkkkk qqq DDD
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[mechanism B] correlated/common input into oscillating or excitable cells (i.e., the neural Moran effect)
input
output
… possible network coupling too
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[mechanism C] self-organized activity in networks of excitable neurons: feed-forward networks
e.g. AD Reyes, Nature Neurosci 2003
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l=0.0001, 75x50 network, rc=50, c=0.37
[mechanism C] self-organized activity in networks of excitable neurons: random networks
(i) Topological target patterns units: excitable dynamics with low level of random spontaneous activation (Poisson process); network connectivity: sparse (Erdos-Renyi) random network; strong bidirectional coupling.
e.g. Lewis & Rinzel, Network: Comput. Neural Syst. 2000
movie:topotargetoscill.avi
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(i) topological target patterns waves
(ii) reentrant waves
[mechanism C] self-organized rhythms in networks of excitable neurons
e.g. Lewis & Rinzel, Neuroomput. 2001
spontaneous random activation stops
spontaneous random activation stops
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Conclusions / Discussions / Open questions