Parallel fiber(PF) Climbing fiber(CF) Purkinje cell Granule cell Neural Circuit of Cerebellar Cortex

小脳長期抑圧のシミュレーション NO Glu AMPA-RVGCCmGluR Gq PLC PKC DAGIP 3 Ca 2+ Store IP 3 R PLA 2 MAPK MEK Raf AA GC Ca 2+ CRHR cGMP PKG G-substrate PP2A Lyn CF PF Positive Feedback Loop CRF

小脳と教師あり学習 登上線維 CF 平行線維 PF プルキンエ 細胞 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 ）

小脳 LTD のシグナル伝達 登上線維 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 Ca 2+ ↑ 平行線維入力を受け取る AMPA 受容体の個数 PKC

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 Ca 2+ 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. Ca 2+ 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 Ca 2+ 上昇 Wang et al., (2000) Nat Neurosci

Temporal Window of PF and CF Inputs for Ca 2+ Firing and LTD Wang et al., (2000) Nat Neurosci 3,

IP 3 受容体の性質 1. IP 3 R が開くには IP 3 と Ca 2+ の両方が必 要 2. Ca 2+ 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

Ca 2+ 上昇の分子メカニズム mGluRAMPA-RVGCC Glu PLC DAG Gq Ca 2+ Ca 2+ Store PF CF IP 3 IP 3 R

CF 入力 mGluRAMPA-R Glu PLC DAG Gq Ca 2+ Store PF CF IP 3 IP 3 R VGCC Ca 2+ VGCC

PF 入力 AMPA-R 経路 mGluR PLC DAG Gq Ca 2+ Store PF CF IP 3 IP 3 R AMPA-RVGCC Glu Ca 2+ AMPA-RVGCC Glu Ca 2+

PF 入力 mGluR 経路 AMPA-RVGCC Ca 2+ Store PF CF mGluR Glu PLC DAG Gq Ca 2+ IP 3 IP 3 R mGluR Glu PLC Gq Ca 2+ DAG IP 3 IP 3 R

PF の IP 3 産生遅延が CF を待つ Ca 2+ Ca 2+ Store PF CF IP 3 Δ IP 3 R Positive Feedback Loop AMPA-R 経路 mGluR 経路

「 PF と CF 同時」の場合 Ca 2+ Store PF CF IP 3 Δ IP 3 R Positive Feedback Loop Ca 2+ AMPA-R 経路 mGluR 経路

「 PF と CF 同時」の場合 Ca 2+ Ca 2+ Store PF CF Δ IP 3 R Positive Feedback Loop IP 3 AMPA-R 経路 mGluR 経路

「 PF 後 CF 」の場合 Ca 2+ Store PF CF IP 3 Δ IP 3 R Positive Feedback Loop Ca 2+ AMPA-R 経路 mGluR 経路

「 PF 後 CF 」の場合 Ca 2+ Store PF CF Δ Ca 2+ IP 3 IP 3 R Positive Feedback Loop IP 3 R Ca 2+ IP 3 Positive Feedback Loop AMPA-R 経路 mGluR 経路

シグナル伝達モデルの作成 mGluRAMPA-RVGCC Glu PLC DAG Gq Ca 2+ Ca 2+ pump Ca 2+ Store PF CF Ca 2+ pump Leak Na + /Ca 2+ exchanger Ca 2+ Buffer Proteins IP 3 IP 3 R IP 3 enzyme

Signal Transduction Pathways of Supralinear Ca 2+ Increase

Simulation of Supralinear Ca 2+ Increase GENESIS simulator with Kinetikit interface developed by Upi Bhalla Ordinary differential equations for molecule- molecule 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 GlumGluR Gq

化学反応速度論 生化学反応 (1) 分子間相互作用 [A]+[B] [AB] KfKf KbKb d[A]/dt = － K f [A][B] + K b [AB] [A] + [AB] = [A all] = const. 解離定数 K d =K b /K f ：平衡状態での生成物の割合 時定数 τ =1/(K f +K b ) ：平衡状態に向かう速さ

化学反応速度論 (2) 酵素反応 (Michaelis-Menten) [E]+[S][ES][E]+[P] KfKf KbKb K cat E:Enzyme, S:Substrate, P:Product 生化学反応 (1) 分子間相互作用 [A]+[B] [AB] KfKf KbKb

Supralinear Ca 2+ Increase is dependent on PF and CF Timing

Temporal Window of Ca 2+ Firing: Coincidence Detection of PF and CF Ca 2+ IP 3

Ca 2+ Dynamics explains Three Different Forms of LTD

Time Delay by IP 3 Slow Increase and Coincidence Detection by IP 3 R

線維入力から LTD まで

Na/Ca mGlu R 平行線維のみでは不十分 Positive feedback loop PKC PLC Raf cGMP Na/Ca Lyn AMPA R Gq GC mGlu R membrane NO MAP kinasePLA2 G substrate 平行線維 Glutamate AA PP2A MEK [ Ca 2+ ] DAG IP PKG 3 AMPA R Ica CRHR

登上線維のみでは不十分 登上線維 AMPA R Glutamate PLC DAG AA Lyn PLA2 IP 3 [ Ca 2+ ] Raf Gq Positive feedback loop PP2A GC PKG cGMP G substrate PKC Na/Ca mGlu R CRF membrane NO MEK MAP kinase 平行線維 CRHR Ica

NO AMPA R Glutamate [ Ca MEK Na/Ca AA MAP kinase Lyn PLA2 IP 3 Raf Gq Ica Positive feedback loop PKC CRHR GC PKG cGMP mGlu R CRF membrane 平行線維と登上線維の両方が必要 Na/Ca mGlu R AMPA R PKC Raf MAP kinasePLA2 AA MEK PLC Ica 2+ ] PP2A AA PKC Raf PLA2MAP kinase G substrate PP2A PLC [ Ca 2+ ] DAG IP PKG 3 [ Ca 2+ ] CRF NO Glutamate 登上線維 平行線維 登上線維 平行線維 MEK AMPA R cGMP Na/Ca Lyn Gq GC mGlu R CRHR Ica AMPA R

Stimulus 1Hz for 5min AMPA receptor (  M) Time (min) Phosphorylated AMPA Receptors Non-Phosphorylated AMPA Receptors 長期抑圧（ LTD ）の再現 登上線維 平行線維 EPSP (%) PP

AMPA-R 上流のシグナル解析 AMPA receptor Concentration (  M) Time (min) EPSP (%) AMPA-R PKC PP2A Time (min) PKC concentration (  M) P PP

はじめは Ca 2+ と DAG が PKC を活性化 AMPA receptor Concentration (  M) Time (min) EPSP (%) AMPA-R PKC PP2A P DAG Ca Time (min) PKC concentration (  M)

遅れて AA が PKC を活性化する AMPA receptor Concentration (  M) Time (min) EPSP (%) DAGAA Ca Time (min) PKC concentration (  M) AMPA-R PKC PP2A P

PP2A は抑制され続けている AMPA receptor Concentration (  M) Time (min) EPSP (%) Time (min) PP2A concentration (  M) DAGAA Ca Time (min) PKC concentration (  M) AMPA-R PKC PP2A P

LTD には十分量の Ca 2+ が必要 Phosphorylated AMPA receptor  M) Time (min) PF + CF PF alone CF alone Active PP2A (  M) Time (min) PF + CF PF alone CF alone Active PKC (  M) Time (min) PF + CF PF alone CF alone

経路遮断実験の再現 Simulation data Time (min) AMPA phosphorylation (  M) Deleted pathways control

PKC 阻害の再現 Simulation data Time (min) AMPA phosphorylation (  M) control PKC Block Deleted pathways

NO は LTD に必要 Simulation data Time (min) AMPA phosphorylation (  M) NO Block Deleted pathways control

Ca 2+ キレート実験の再現 Simulation data Time (min) AMPA phosphorylation (  M) Deleted pathways control Chelate Ca 2+

MAPK カスケードは LTD を保持する Simulation data Time (min) AMPA phosphorylation (  M) Block MAP kinase Deleted pathways control