2005/10/14 from single to ensemble – neural synchronization 清華大學腦科學中心張修明...

2005/10/14

From Single to Ensemble –neural synchronization

清華大學腦科學中心張修明博士

2005/10/14

Time scaleSpike ~ms

Brain wave ~10 ms- ~100 ms

LTP ~ hours

Learning ~ minutes- ~hours

Memory ~ minutes- ~yearsInitiationFormingMaintainTransferRetrieve

They all start from a single neuron

How the connection of these neurons can result in something meaningful ?

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InformationSpatial

spikes@positionsrecurrent network

TemporalRate--spikes/timeTemporal –-spikes@time

Normal brain waves-- stable persistent phenomena (neural connections)

Normal behavior

Induced “brain waves”Working memory circuit in the frontal cortexEpilepsy

Neural connections bring in information

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Can inhibitory synapses generate synchronous activity

Oscillation in an inhibitory networkCdV/dt = -gCm3

(V)hi(Vi-VC)-gl(Vi-VL)-gsynsji(Vi-Vsyn)dh/dt =[h (Vi)-hi]/h(Vi)sji = s (Vj) = 1/{1+exp[-(Vj-syn)/syn]} is instantaneous

with syn = 2, gsyn = 0.3 mS/cm2, VC = 120 mv, VL = -60 mV and Vsyn = -80 mV -- inhibitorygL = 0.1 mS/cm2

m (V) = 1/{1 + exp[-(V + 65)/7.8]}, h (V) = 1/{1 + exp[(V + 81)/11]},h(Vi) = h (V)exp[(V+162.3/17.8)], and = 3

A simple though nonrealistic system shows it can.Only one type of ion channel with inactivation process is needed

Wang & Rinzel, 1992 Neural Computation, 4:84

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Two inhibitory neurons can “trigger” each other resulting in synchronization

For gC

= 0.3 mS/cm2

Wang & Rinzel, 1992 Neural Computation, 4:84

Set dV/dt = 0 and dh/dt = 0

h = [gL(V-VL)+gsyn(V-Vsyn)]/ [gCm3

(V) (VC-V)]

or h = h (V),

gsyn = 0, when no inhibition from the synapse

No inhibitory signal is transmitted whenV < -44 mV

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For gC = 1.0 mS/cm2

An activated V1 can not inhibit V2, if gC is high enough.

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For gC = 1.5 mS/cm2

A bistable system can be triggered into an oscillation with even larger gC.

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The synchronization can be in phase or out of phase.

For dsij/dt = s (Vi)(1-sij)-krsij and kr is small enough.

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Gamma wave (~40–100 Hz)

The wave is easily observed in EEG on awake animals, has been suggested to be related to various daily work, speaking, attention and learing (Miltner et al, 1999, Nature 397:434).

An interneuronal network can generate a coherent oscillatory output to the pyramidal neurons, thereby providing a substrate for the synaptic organization of coherent gamma population oscillations.

When metabotropic glutamate receptors were activated, transient oscillatory IPSPs in the 40 Hz frequency range were observed in pyramidal cells, without AMPA and NMDA activity. (Whittington et al., 1995, Naute, 373:612)

The interneuron with GABAergic synapses in the hippocampus has been shown to fire with gamma frequency (Sik et al, 1995, J. Neuroscience: 15:6651).

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Voltage-versus-depth profile of hippocampal field activity in the mouse.

G. Buzsaki et al. / Neuroscience 116 (2003) 201–211

(cx: neocortex; or: stratum oriens; pyr: pyramidal layer; rad: stratum radiatum; hf: hippocampal fissure: hil, hilus)

1mv

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bouton

interneurons

Basket cell

Sik et al, 1995, J. Neuroscience: 15:6651

o, stratum oriens; p, CA1 pyramidal layer; r, stratum radiatum.

Parvalbumin immunoreactive basket cell and interneurons in rat hippocampus

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Number of synapse formed by interneurons can be counted

Wang & Buzsaki, 1996, J. Neurosci.16:6402–6413

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Model neuron Each interneuron is described by :Cm (dV/dt) = -INa - IK - IL - Isyn + Iapp , where Cm = 1 F/cm2 and Iapp is the injected current (in A/cm2). The leak current IL = gL(V - EL) has a conductance gL = 0.1 mS/cm2, so thatthe passive time constant 0 = Cm/gL = 10 msec; EL = -65 mV.

The spike-generating Na+ and K+ voltage-dependent ion currents (INa

and IK) are of the Hodgkin–Huxley type (Hodgkin and Huxley, 1952).The transient sodium current INa = gNam3

h(V - ENa), where the activation variable m is assumed fast and substituted by its steady-state function m = m/(m + m); m(V) = -0.1(V + 35)/(exp(-0.1(V +35)) - 1), m(V) = 4exp(-(V + 60)/18). The inactivation variable h obeys a first-order kinetics:dh/dt = (h(1 – h) - hh) where h(V) = 0.07 exp(-(V + 58)/20) and h(V) = 1/(exp(-0.1(V -28)) + 1). gNa = 35 mS/cm2; ENa = 55 mV, = 5.


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The delayed rectifier IK = gKn4 (V - EK), where the activation variable n obeys the following equation:dn/dt = ( n(1 – n) - nn) with n(V) = -0.01(V + 34)/(exp(-0.1(V + 34)) - 1) and n(V) = 0.1-5exp(2(V + 44)/80); gK = 9 mS/cm2, and EK = -90 mV.Parameters are chosen such that the repolarization is 15 mV below the threshold (~-55 mV) but above the EK and the firing frequency can reach high value.


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Model synapse. The synaptic current Isyn = gsyns(V - Esyn), where gsyn

is the maximal synaptic conductance and Esyn is the reversal potential.

Typically, we set gsyn = 0.1 mS/cm2 and Esyn = -75 mV (inhibitory).

The gating variable s represents the fraction of open synaptic ion

channels.

ds/dt = F(Vpre)(1 – s) - s, where the normalized concentration of the postsynaptic transmitter receptor complex, F(Vpre), is assumed to be an instantaneous and sigmoid function of the presynaptic membrane potential, (Perkel et al.,1981; Wang and Rinzel 1993):

F(Vpre) = 1/(1 + exp(-(Vpre - syn)/2)), where

syn (set to 0 mV) is high enough so that the transmitter release occurs only when the presynaptic cell emits a spike.

The channel opening rate = 12 /msec assures a fast rise of the Isyn, and

the channel closing rate is the inverse of the decay time constant of the Isyn; typically, we set = 0.1/ msec ( syn = 10 msec).


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Random network connectivity. The network model consists of N cells. The coupling between neurons is randomly assigned, with a fixed average number of synaptic inputs per neuron, Msyn.

The coherence between two neurons i and j is measured by their cross-correlation of spike trains at zero time lag within a time bin of t = . More specifically, suppose that a long time interval T is divided into small bins of and that two spike trains are given by X(l) = 0 or 1, Y(l) = 0 or 1, l=1, 2, . . . , K (T/K = ).Define a coherence measure for the pair as:ij() = lX(l)Y(l)/[lX(l)lY(l)]1/2

The population coherence measure () is defined by the average of ij(t) over many pairs of neurons in the network. () is between 0 and 1 for all . For very small , () is close to 1 (0) in the case of maximal synchrony (asynchrony).

Initially, the membrane potential is uniformly distributed between -70 and -50 mV and the other channel-gating variables are set at their corresponding steady-state values. Coherence was calculated after 1000 msec transients. N = 100 neurons.

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The simulated single interneuron has the typical excitable and inhibitory property

An increased injection current causes higher firing frequency


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A Network coupled by GABAA synapses can synchronize

Neurons are identical and coupled in an all-to-all fashion.

The network results in a two- state synchronization if the kinetics of the Na, K current further slows down.

The network takes longer time to synchronize when kinetics of the Na, K current slows down (smaller ).


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No synchronization occurs in the network if the synapse is excitatory (Esynp = 0 mV), even though each neuron has more or less the same firing frequency (~43Hz here).


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The synchronization breaks down if the Iapp is not homogeneous to all neurons

The coherence of the network is reduced when the standard deviation of the Iapp is increased, assuming a Gaussian distribution,

0.03

0.1

although the mean firing frequency does not change many.

Iapp = 1 A/cm2


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The number of synapse on each neuron is critical of the networkSynchronization (simulation method ???)

Only ~5 is necessary of synchronization if every neuron has the same number of synapse, minimum ~40 if randomly connected in a network of 100 neurons.

The critical synapse number is not sensitive to the strength of the synapse.

The critical number is increased if the Iapp

intensity is increased.

The size of the network has little effect on critical synapse number of synchronization.

Implication on epilepsy ?


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There is an optimal synaptic time constant for the coherence of a not-all-connected and inhomogeneous network. (Msyn = 60, I = 0.3)

The optimal synaptic time constant is about 0.2 of the mean oscillation period.


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There are also an optimal Iapp and synaptic conductance for the coherence.

In combination, there is an optimal coherence frequency for this inhibitory network.


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Theta oscillations (6–10 Hz), although no consensus has yet emerged, duringREM sleep (Jouvet, 1969) and during various activities described by the subjective terms “voluntary,” “preparatory,” “orienting,” or “exploratory” (Vanderwolf, 1969). also thought to occur during navigation (Kahana et al, 1999, Nature 399:781)

Theta oscillation is observed in the str. lacunosum-moleculare of hippocampal CA1 or CA3 region and many other part in the brain such as entorhinal cortex, amigdala etc.. (Buzsaki, 2002, Neuron 33:325)

Simulation of network synchronization is done for both an isolated population of medial septal (MS) GABAergic cells and for a reciprocally inhibitory loop between the MS and the hippocampus.

2005/10/14 Hendelman 2000, Atlas of Functional Neuroanatomy, p189

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Medial septal neuron modelCmdV/dt = -INa - IK - IKS - IL - Isyn + I + (t)

Horizontal O/A interneurons in Hippocampus (in stratum oriens-alveus)

CmdV/dt = -INa - IK - Ih - ICa - IKCa - IL - Isyn + I

The network is thought to be all-to-allN = 400

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The presence of KS channelmodulates the firing pattern insingle septal GABAergic neurons

KS activation parameter KS affects only the low frequency interburst firing not the intraburst activity.

Wang, 2002, J Neurophysiol 87: 889–900

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Synchronization at the theta wave range is produced in neither the septal network nor the hippocampal network.

Synchronization at the gamma frequency range is possible in septal region

No synchronization at the gamma frequency range is possible in hippocampus


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A coupled septal and hippocampal networks can synchronouslyfire at both gamma and theta frequency

Individual firing is out of phase cross the network


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Only change the synaptic coupling within the septal network significantly affect the theta frequency.

The pace- maker is located within the septal region, probably according to the KS channel


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The final theta frequency is stable regardless the differentfiring frequencies within the hippocampal network.


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Summary

A stable synchronized firing can occur among inhibitory neurons.

Individual channel kinetics (decay time etc) may be a major factor regulating the collective properties of a neural network.

Dynamic mutual interactions generate new properties beyond the scale of individual elements

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Some thoughts

Do the networks in the brain work separately ?

How sij will become when LTP is considered ?

How a transient synchronization of a neural network form and fall ?

How far away can the “signal” be transmitted from the septal region ? A better experimental protocol become necessary to investigate the properties of neurons from individual cells to the whole network simultaneously.

2005/10/14 from single to ensemble – neural synchronization 清華大學腦科學中心 張修明...

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2005/10/14 from single to ensemble – neural synchronization 清華大學腦科學中心張修明...