脳の自発揺らぎの数理科学 - その起源と神経情報処理における役割 - 寺前順之介 大阪大学大学院情報科学研究科 u.ac.jp

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1 脳の自発揺らぎの数理科学 - その起源と神経情報処理における役割 - 寺前順之介 大阪大学大学院情報科学研究科 u.ac.jp

2 自己紹介 出身は群馬 大学から京都, 物理 非線形物理学 自然の秩序形成, 自己組織化 理化学研究所 理論神経科学 脳の情報処理メカニズム 大阪大学情報科学研究科 キーワードは ゆらぎと確率

3 脳 大脳皮質 膨大な数の神経細胞 からなるネットワーク 大脳皮質だけで数百億個 それぞれ数千の入出力を持つ Brainbow pyramidal neuron

4 スパイク発火による情報伝達 - 70mV 時間 時間 つながりの強さ : 興奮性シナプス後電位 (EPSP)

5 大脳皮質の自発活動 大脳皮質では入力がなくても活動が持続 自発的持続発火活動 (spontaneous ongoing acdvity) 神経細胞 時間 非同期 不規則 低頻度 (1-2Hz) 6 sec Takekawa et al. 膜電位 時間 膜電位も乱雑に大きく変動 Destexhe et al Nat. Rev. Neurosci.

6 自発発火活動の特徴 1 Synaptic noise vivo experiments 膜電位が持ち上がり 大きく揺らぐ ms GABAA GABAA Vm 50(mV) Vm (mv) Fre 静止膜電位 発火しきい値 distribution etailed biophysical models bdestexhe Detailed biophysical et al models Nat. Rev. Neurosci. AMPA AMPA al density mvms stribution mv 20 mv ctral density mv 0.1 Power spectral density Amplitude distribution Amplitude distribution a In vivo experiments Power spectral density Box 1 Synaptic noise 1

7 自発活動と神経応答 神経応答 = 刺激入力 + 自発活動 (1996 Science)

8 自発活動と神経応答 神経応答の空間構造 自発活動の空間構造 (1999 Science)

9 QuesDon 揺らぎの起源は何か? その機能は何か?

10 神経ネットワークの数理的な記述 単一の神経細胞の記述 C dv dt = g L ( v E ) L g Na m 3 h( v E ) Na g K n 4 ( v E ) K + I ext Hodgikn Huxley equadon

11 ところが, 神経ネットワークのモデルは 自発揺らぎを説明できなかった No noise source in the brain. Single neurons are silent. 活動が持続しないか爆発してしまう 神経ダイナミクスの大問題

12 なぜか? ニューロンは多数の弱入力を積算する多数決素子 EPSP ~ 1mV V thr = - 50 mv v 20 mv Dme V rest = - 70 mv 強い同期発火 or 高発火率 仮説 : 多数の弱い結合と少数の極めて強い 結合の共存が鍵ではないか

13 多数の弱い結合と 少数の極めて強い結合の共存 S. Song, P. J. Sjoestroem, M.Reigl, S. Nelson, D. B. Chklovskii PLoS Biology, 2005, 3(3) 対数正規分布 Lognormal distribudon

14 極めて不均一なネットワーク結合強度 Lognormal 興奮性細胞 個 Random net, P = 0.1 for exc. 0.5 for inh. 抑制性細胞 2000 個 G max ~ 10 mv ( ) P x 1 = exp 2πσx ( log x µ ) 2 2 2σ

15 神経細胞モデルは単純に Leaky integrate- and- fire neuron with conductance synapses dv 1 = E dt τ m dg g = + G j δ( t sj τ j) dt τ s j sj ( v V ) g ( v V ) g ( v V ) rest E I I V thr = - 50 mv v 20 mv Dme V rest = - 70 mv 外部ノイズや 背景ノイズは用いなくて良い

16 2, ,500 2,600 自発発火活動が再現される ノイズ源は要らない 20 神経細胞 1 0 2, ,400 時間 2,500 Time (ms) 2,500 2, ,000 時間 0 0 2,600 非同期 不規則 低頻度 1-2Hz 膜電位 0 40 Inhibitory pool (Hz) 0 膜電位も乱雑に大きく変動 3,000

17 膜電位の強い揺らぎ 抑制性神経細胞 興奮性神経細胞 静止膜電位 発火閾値 膜電位の UP 状態

18 10-50 l (mv) 3.0 b 少数の強結合 d Cross correlation 0.4 ゆらぎの機能は何か? C.C. 多数の弱結合への入力 0.2背景ゆらぎ Mean membrane potential (mv) c activity (Methods). Spike threshold is V thr 5250 [mv] an to V0.3 r 5260 mv after spiking. The refractory period is 1 The values 理論 of G i for excitatory-to-excitatory connectio tributed such 数値計算 that the amplitude of EPSPs x measured resting 0.2potential obey a lognormal distribution exp { log x{m px ðþ~ ð Þ2 2s 2 pffiffiffiffiffi 2p 0.1 sx Cross correlation 揺らぎがスパイク伝達効率 e を最適化! on each neuron (Fig. 1a), where the values s51.0 and m-s 2 well replicate the experimentally observed long-tailed di of EPSP 0.0 amplitudes 33,34. We declined any unrealistic valu gives an -70 amplitude larger than 20 [mv] by drawing -50 a from the Mean distribution. membrane The resultant potential amplitude (mv) of stron was about [mv] on 1.0 each neuron. 2.0 For 3.0 simplicity, to-inhibitory, inhibitory-to-excitatory Firing rate (Hz) and inhibitory-to synapses have uniform values of G i , a respectively. 0.5 Excitatory-to-excitatory synaptic transmiss an EPSP amplitude-dependent rate 膜電位の of p E 5 a/(a1ep a50.1 [mv] 34. We first demonstrate numericallyup that the state long-tailed d of EPSP amplitudes achieves aperiodic stochastic resonan sequence on a single neuron receiving random synap

19 In vitro dynamic- clamp experiment for real cordcal neurons by Yasuhiro Tsubo

20 神経細胞は確率的ゲート素子ではないか 伝統的な見方 v 多数決素子 Signal... internal environment of the local circuit (inference from many other paths)

21 自己組織的確率共鳴 G max = 10 mv v V thr = - 50 mv 20 mv V rest = - 70 mv c 0.3 neuron as a stochasdc gadng unit signal... Cross correlation Mean membrane potential (mv) Firing rate (Hz) e Noise 0.5is self- organized by network itself!

22 Context- dependent noise control AssociaDve memory with the lognormal weight distribudon Prob ξ µ i = 1 = a P G Prob ξ µ ij = ξ µ µ i ξ j i = 0 = 1 a µ=1 G ij sort G ij and map them to the lognormal distribudon G ij Hiratani, Teramae and Fukai 2013

23 Numerical simuladon sparseness a = 0.1 memory pa0ern p = 130 transient input to a memory pa0ern inhibitory neurons spontaneous ongoing firing pa0ern retrieval excitatory neurons (background) neurons of the evoked pa0ern inhibitory exc. neurons of the evoked pa0ern other excitatory neurons

24 membrane potendals spontaneous state Typical amplitude of strongest EPSPs memory retrieval condidonal prob. of output for given input on the strongest synapse Retrieval pa0ern spontaneous Background mean membrane potengal Sequence selecdon by background noise moduladon

25 大脳皮質自発揺らぎの起源と機能 稀な強結合 正確な情報の伝播 ゆらぎ不規則性 多数の弱結合 ネットワークの非常に強い不均一性 ( 多数の弱結合と少数の非常に強い結合の共存 ) が脳の自発揺らぎを生む 自発揺らぎがスパイク情報伝達を最適化自己組織的確率共鳴 文脈依存でノイズ強度をコントロールできる 内的なノイズ制御による情報処理

26 Collaborators Tomoki Fukai (RIKEN) Yasuhiro Tsubo (Ritsumeikan Univ.) Naoki Hiratani (Univ. Tokyo)

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