Transcript Ca 2+

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