Neural Circuit of Cerebellar Cortex Parallel fiber(PF) Granule cell Purkinje cell Climbing fiber(CF) 小脳長期抑圧のシミュレーション CF NO GC PF Glu CRF CRHR AMPA-R Lyn VGCC PLC mGluR Gq DAG IP3 cGMP PKG G-substrate PP2A Raf PKC Positive MEK Feedback AA Loop MAPK PLA2 Ca2+ IP3R Ca2+ Store 小脳と教師あり学習 1. プルキンエ細胞は教師あり 学習 2. PFが文脈情報、CFが誤差 情報 3. PFが間違った出力をすると、 CFが誤差信号を送り、シナ プス荷重を減少させる（長期 抑圧、LTD） 平行線維 PF プルキンエ 細胞 登上線維 CF 小脳LTDのシグナル伝達 平行線維 スパイン 平行線維（PF）と 登上線維（CF）が ある時間幅内で入力 スパイン内Ca2+↑ PKC 平行線維入力を受け取る AMPA受容体の個数 登上線維 シグナル伝達が実現すべきこと 1. 平行線維（PF）と登上線維（CF）の両方入力の みCa2+上昇が起こる 2. PF入力よりも後のCF入力を検出する（誤差は 出力した後でないと計算できない ） 3. Ca2+上昇のあと長時間LTDを持続させる Motivations of Systems Biology Simulation • Most cerebellar learning theories (including Ito’s) require PF-CF temporal window for plasticity (STDP). • But, some experiments (photolysis, strong PF stimulation) are against this temporal window. Then, biological significance of LTD? • How altered synaptic efficacy can be maintained in medium term (several tens of minutes)? PFとCFの両方でCa2+上昇 Wang et al., (2000) Nat Neurosci Temporal Window of PF and CF Inputs for Ca2+ Firing and LTD Wang et al., (2000) Nat Neurosci 3, 1266-1273 IP3受容体の性質 1. IP3Rが開くにはIP3とCa2+の両方が必要 2. Ca2+が多すぎると閉じる Open Probability Bezprozvanny et al., Nature(1991) A New Model of IP3R based on Adkins and Taylor Four-States Model Ca2+ 上昇の分子メカニズム Glu CF VGCC AMPA-R PF mGluR Gq PLC Ca2+ DAG IP3 IP3R Ca2+Store CF入力 Glu CF VGCC AMPA-R PF mGluR Gq PLC Ca2+ DAG IP3 IP3R Ca2+Store PF入力 AMPA-R経路 Glu CF VGCC AMPA-R PF mGluR Gq PLC Ca2+ DAG IP3 IP3R Ca2+Store PF入力 mGluR経路 Glu CF VGCC AMPA-R PF mGluR Gq PLC Ca2+ DAG IP3 IP3R Ca2+Store PFのIP3産生遅延がCFを待つ CF AMPA-R経路 PF mGluR経路 Δ Ca2+ Positive Feedback Loop IP3 IP3R Ca2+Store 「PFとCF同時」の場合 CF AMPA-R経路 PF mGluR経路 Δ Ca2+ Positive Feedback Loop IP3 IP3R Ca2+Store 「PFとCF同時」の場合 CF AMPA-R経路 PF mGluR経路 Δ Ca2+ Positive Feedback Loop IP3 IP3R Ca2+Store 「PF後CF」の場合 CF AMPA-R経路 PF mGluR経路 Δ Ca2+ Positive Feedback Loop IP3 IP3R Ca2+Store 「PF後CF」の場合 CF AMPA-R経路 PF mGluR経路 Δ Ca2+ Positive Feedback Loop IP3 IP3R Ca2+Store シグナル伝達モデルの作成 Glu CF VGCC AMPA-R PF mGluR Gq Ca2+ Leak Ca2+Buffer Proteins Ca2+pump Na+/Ca2+ exchanger PLC IP3 enzyme IP3R Leak Ca2+pump Ca2+Store DAG IP3 Signal Transduction Pathways of Supralinear Ca2+ Increase Simulation of Supralinear Ca2+ Increase • GENESIS simulator with Kinetikit interface developed by Upi Bhalla • Ordinary differential equations for moleculemolecule and enzymatic reactions • 49 variables and 95 parameters • 20 initial concentrations with 3 assumed • 25 dissociation constants and Michaelis constants with 3 assumed • 9 maximum enzyme velocities with 3 assumed 例:Glu→mGluR→Gq Glu mGluR Gq 化学反応速度論 生化学反応 (1)分子間相互作用 [A]+[B] Kf Kb [AB] d[A]/dt = －Kf[A][B] + Kb[AB] [A] + [AB] = [A all] = const. 解離定数Kd=Kb/Kf ：平衡状態での生成物の割合 時定数τ =1/(Kf +Kb)：平衡状態に向かう速さ 化学反応速度論 生化学反応 (1)分子間相互作用 [A]+[B] Kf Kb [AB] (2)酵素反応(Michaelis-Menten) [E]+[S] Kf Kb [ES] Kcat [E]+[P] E:Enzyme, S:Substrate, P:Product Supralinear Ca2+ Increase is dependent on PF and CF Timing Temporal Window of Ca2+ Firing: Coincidence Detection of PF and CF Ca2+ IP3 Ca2+ Dynamics explains Three Different Forms of LTD Time Delay by IP3 Slow Increase and Coincidence Detection by IP3R 線維入力からLTDまで 登上線維 平行線維 Glutamate CRF NO CRHR membrane GC Ica AMPA R Na/Ca mGlu R Gq Lyn IP3 cGMP PLC [Ca2+] PKG Raf PKC MEK Positive feedback loop DAG G substrate PP2A MAP kinase AA PLA2 平行線維のみでは不十分 登上線維 平行線維 Glutamate CRF NO CRHR membrane GC Ica AMPA R Na/Ca mGlu R Gq Lyn IP3 cGMP PLC [Ca2+] PKG Raf PKC MEK Positive feedback loop DAG G substrate PP2A MAP kinase AA PLA2 登上線維のみでは不十分 登上線維 平行線維 Glutamate CRF CRF NO CRHR CRHR membrane GC Ica Ica AMPA R Na/Ca mGlu R Gq Lyn IP3 cGMP PLC 2+]] [Ca2+ PKG Raf PKC MEK Positive feedback loop DAG G substrate PP2A MAP kinase AA PLA2 平行線維と登上線維の両方が必要 登上線維 平行線維 Glutamate CRF NO CRHR membrane GC Ica Na/Ca AMPA R R AMPA mGlu R Gq Lyn IP3 cGMP PLC [Ca2+] PKG Raf PKC MEK Positive feedback loop DAG DAG G substrate PP2A MAP kinase AA PLA2 P P 0.5 100 0.4 80 0.3 Non-Phosphorylated 60 AMPA Receptors 0.2 40 Phosphorylated AMPA Receptors 0.1 0 Stimulus 1Hz for 5min 0 10 20 0 20 30 40 50 60 70 80 90 100 Time (min) EPSP (%) 登上線維 平行線維 AMPA receptor (mM) 長期抑圧（LTD）の再現 PKC concentration (mM) AMPA-R上流のシグナル解析 0.15 0.10 0.05 0 0 10 20 30 40 50 60 70 80 90100 AMPA-R PP2A AMPA-R P 0.5 100 0.4 80 0.3 60 0.2 40 0.1 20 0 0 0 10 20 30 40 50 60 70 80 90100 Time (min) P P EPSP (%) PKC AMPA receptor Concentration (mM) Time (min) PKC concentration (mM) はじめはCa2+とDAGがPKCを活性化 0.15 0.10 0.05 0 0 10 20 30 40 50 60 70 80 90100 Time (min) 2+ AMPA-R PP2A AMPA-R P 0.5 100 0.4 80 0.3 60 0.2 40 0.1 20 0 0 0 10 20 30 40 50 60 70 80 90100 Time (min) EPSP (%) PKC AMPA receptor Concentration (mM) Ca DAG PKC concentration (mM) 遅れてAAがPKCを活性化する 0.15 0.10 0.05 0 0 10 20 30 40 50 60 70 80 90100 Time (min) 2+ AMPA-R PP2A AMPA-R P 0.5 100 0.4 80 0.3 60 0.2 40 0.1 20 0 0 0 10 20 30 40 50 60 70 80 90100 Time (min) EPSP (%) PKC AMPA receptor Concentration (mM) Ca DAG AA PKC concentration (mM) PP2Aは抑制され続けている 0.15 0.10 0.05 0 0 10 20 30 40 50 60 70 80 90100 Time (min) 2+ PP2A concentration (mM) AMPA-R PP2A AMPA-R P 3 2 100 0.4 80 0.3 60 0.2 40 0.1 20 0 0 0 10 20 30 40 50 60 70 80 90100 Time (min) 1 0 0.5 0 10 20 30 40 50 60 70 80 90 100 Time (min) EPSP (%) PKC AMPA receptor Concentration (mM) Ca DAG AA Phosphorylated AMPA receptor (mM) 2+ LTDには十分量のCa が必要 0.3 PF + CF PF alone CF alone 0.2 0.1 0 0 20 40 60 80 100 0.1 PF + CF PF alone CF alone 0.05 0 0 20 40 60 80 100 Time (min) Active PP2A (mM) Active PKC (mM) Time (min) 3.0 PF + CF PF alone CF alone 2.0 1.0 0 0 20 40 60 80 100 Time (min) AMPA R AMPA R -RP AMPA Lyn Ca2+ Raf PKC DAG CRF MEK NO PP2A MAP kinase Positive feedback loop AA PLA2 AMPA phosphorylation (mM) 経路遮断実験の再現 Simulation data Deleted pathways 0.3 control 0.2 0.1 0 0 10 20 30 40 50 60 Time (min) 70 80 90 100 AMPA R AMPA R -RP AMPA Lyn Ca2+ Raf PKC DAG CRF MEK NO PP2A MAP kinase Positive feedback loop AA PLA2 AMPA phosphorylation (mM) PKC阻害の再現 PKC Block Simulation data 0.3 Deleted pathways control 0.2 0.1 0 0 10 20 30 40 50 60 Time (min) 70 80 90 100 AMPA R AMPA R -RP AMPA Lyn Ca2+ Raf PKC DAG CRF MEK NO PP2A MAP kinase Positive feedback loop AA PLA2 AMPA phosphorylation (mM) NOはLTDに必要 NO Block Simulation data 0.3 Deleted pathways control 0.2 0.1 0 0 10 20 30 40 50 60 Time (min) 70 80 90 100 AMPA R AMPA R -RP AMPA Lyn Ca2+ Raf PKC DAG CRF MEK NO PP2A MAP kinase Positive feedback loop AA PLA2 AMPA phosphorylation (mM) 2+ Ca キレート実験の再現 Chelate Ca2+ Simulation data 0.3 Deleted pathways control 0.2 0.1 0 0 10 20 30 40 50 60 Time (min) 70 80 90 100 AMPA R AMPA R -RP AMPA Lyn Ca2+ Raf PKC DAG CRF MEK NO PP2A MAP kinase Positive feedback loop AA PLA2 AMPA phosphorylation (mM) MAPKカスケードはLTDを保持する Simulation data Deleted pathways 0.3 control 0.2 0.1 0 0 10 Block MAP kinase 20 30 40 50 60 Time (min) 70 80 90 100
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