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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 博士

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2005/10/14 Time scale Spike ~ms Brain wave ~10 ms- ~100 ms LTP ~ hours Learning ~ minutes- ~hours Memory ~ minutes- ~years Initiation Forming Maintain Transfer Retrieve They all start from a single neuron How the connection of these neurons can result in something meaningful ?

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2005/10/14 Information Spatial spikes@positions recurrent network Temporal Rate--spikes/time Temporal –-spikes@time Normal brain waves-- stable persistent phenomena (neural connections) Normal behavior Induced “brain waves” Working memory circuit in the frontal cortex Epilepsy Neural connections bring in information

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2005/10/14 Can inhibitory synapses generate synchronous activity Oscillation in an inhibitory network CdV/dt = -g C m 3 (V)h i (V i -V C )-g l (V i -V L )-g syn s ji (V i -V syn ) dh/dt = [h (V i )-h i ]/ h (V i ) s ji = s (V j ) = 1/{1+exp[-(V j - syn )/ syn ]} is instantaneous with syn = 2, g syn = 0.3 mS/cm 2, V C = 120 mv, V L = -60 mV and V syn = -80 mV -- inhibitory g L = 0.1 mS/cm 2 m (V) = 1/{1 + exp[-(V + 65)/7.8]}, h (V) = 1/{1 + exp[(V + 81)/11]}, h (V i ) = 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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2005/10/14 Two inhibitory neurons can “trigger” each other resulting in synchronization For g C = 0.3 mS/cm 2 Wang & Rinzel, 1992 Neural Computation, 4:84 Set dV/dt = 0 and dh/dt = 0 h = [g L (V-V L )+g syn (V-V syn )]/ [g C m 3 (V) (V C -V)] or h = h (V), g syn = 0, when no inhibition from the synapse No inhibitory signal is transmitted when V < -44 mV

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2005/10/14 For g C = 1.0 mS/cm 2 An activated V 1 can not inhibit V 2, if g C is high enough.

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2005/10/14 For g C = 1.5 mS/cm 2 A bistable system can be triggered into an oscillation with even larger g C.

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2005/10/14 The synchronization can be in phase or out of phase. For ds ij /dt = s (V i )(1-s ij )-k r s ij and k r is small enough.

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2005/10/14 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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2005/10/14 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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2005/10/14 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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2005/10/14 Number of synapse formed by interneurons can be counted Wang & Buzsaki, 1996, J. Neurosci.16:6402–6413

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2005/10/14 Model neuron Each interneuron is described by : C m (dV/dt) = -I Na - I K - I L - I syn + I app, where C m = 1 F/cm 2 and I app is the injected current (in A/cm 2 ). The leak current I L = g L (V - E L ) has a conductance g L = 0.1 mS/cm 2, so that the passive time constant 0 = C m /g L = 10 msec; E L = -65 mV. The spike-generating Na + and K + voltage-dependent ion currents (I Na and I K ) are of the Hodgkin–Huxley type (Hodgkin and Huxley, 1952). The transient sodium current I Na = g Na m 3 h(V - E Na ), 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) - h h) where h (V) = 0.07 exp(-(V + 58)/20) and h (V) = 1/(exp(-0.1(V -28)) + 1). g Na = 35 mS/cm 2 ; E Na = 55 mV, = 5. Wang & Buzsaki, 1996, J. Neurosci.16:6402–6413

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2005/10/14 The delayed rectifier I K = g K n 4 (V - E K ), where the activation variable n obeys the following equation: dn/dt = ( n (1 – n) - n n) with n (V) = -0.01(V + 34)/(exp(-0.1(V + 34)) - 1) and n (V) = 0.1-5exp(2(V + 44)/80); g K = 9 mS/cm 2, and E K = -90 mV. Parameters are chosen such that the repolarization is 15 mV below the threshold (~-55 mV) but above the E K and the firing frequency can reach high value. Wang & Buzsaki, 1996, J. Neurosci.16:6402–6413

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2005/10/14 Model synapse. The synaptic current I syn = g syn s(V - E syn ), where g syn is the maximal synaptic conductance and E syn is the reversal potential. Typically, we set g syn = 0.1 mS/cm 2 and E syn = -75 mV (inhibitory). The gating variable s represents the fraction of open synaptic ion channels. ds/dt = F(V pre )(1 – s) - s, where the normalized concentration of the postsynaptic transmitter receptor complex, F(V pre ), is assumed to be an instantaneous and sigmoid function of the presynaptic membrane potential, (Perkel et al.,1981; Wang and Rinzel 1993): F(V pre ) = 1/(1 + exp(-(V pre - 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 I syn, and the channel closing rate is the inverse of the decay time constant of the I syn ; typically, we set = 0.1/ msec ( syn = 10 msec). Wang & Buzsaki, 1996, J. Neurosci.16:6402–6413

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2005/10/14 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, M syn. 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 ( ) = l X(l)Y(l)/[ l X(l) l Y(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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2005/10/14 The simulated single interneuron has the typical excitable and inhibitory property An increased injection current causes higher firing frequency Wang & Buzsaki, 1996, J. Neurosci.16:6402–6413

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2005/10/14 A Network coupled by GABA A 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 ). Wang & Buzsaki, 1996, J. Neurosci.16:6402–6413

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2005/10/14 No synchronization occurs in the network if the synapse is excitatory (E synp = 0 mV), even though each neuron has more or less the same firing frequency (~43Hz here). Wang & Buzsaki, 1996, J. Neurosci.16:6402–6413

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2005/10/14 The synchronization breaks down if the I app is not homogeneous to all neurons The coherence of the network is reduced when the standard deviation of the I app is increased, assuming a Gaussian distribution, 0.03 0.1 although the mean firing frequency does not change many. I app = 1 A/cm 2 Wang & Buzsaki, 1996, J. Neurosci.16:6402–6413

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2005/10/14 The number of synapse on each neuron is critical of the network Synchronization (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 I app intensity is increased. The size of the network has little effect on critical synapse number of synchronization. Implication on epilepsy ? Wang & Buzsaki, 1996, J. Neurosci.16:6402–6413

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2005/10/14 There is an optimal synaptic time constant for the coherence of a not-all-connected and inhomogeneous network. (M syn = 60, I = 0.3) The optimal synaptic time constant is about 0.2 of the mean oscillation period. Wang & Buzsaki, 1996, J. Neurosci.16:6402–6413

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2005/10/14 There are also an optimal I app and synaptic conductance for the coherence. In combination, there is an optimal coherence frequency for this inhibitory network. Wang & Buzsaki, 1996, J. Neurosci.16:6402–6413

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2005/10/14 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.

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

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2005/10/14 Medial septal neuron model C m dV/dt = -I Na - I K - I KS - I L - I syn + I + (t) Horizontal O/A interneurons in Hippocampus (in stratum oriens-alveus) C m dV/dt = -I Na - I K - I h - I Ca - I KCa - I L - I syn + I The network is thought to be all-to-all N = 400

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2005/10/14 The presence of KS channel modulates the firing pattern in single 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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2005/10/14 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 Wang, 2002, J Neurophysiol 87: 889–900

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2005/10/14 A coupled septal and hippocampal networks can synchronously fire at both gamma and theta frequency Individual firing is out of phase cross the network Wang, 2002, J Neurophysiol 87: 889–900

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2005/10/14 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 Wang, 2002, J Neurophysiol 87: 889–900

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2005/10/14 The final theta frequency is stable regardless the different firing frequencies within the hippocampal network. Wang, 2002, J Neurophysiol 87: 889–900

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2005/10/14 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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2005/10/14 Some thoughts Do the networks in the brain work separately ? How s ij 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.

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