memo_and_correction - Kuroda Lab

Tsai et al., Science 321, 126 (2008) 数式補完
藤井雅史
東京大学大学院理学系研究科生物化学専攻黒田研
Red: 追加部分 & Blue: 削除部分
memo: 振動解を示すおおよそのパラメータ領域
1. Negative feedback and positive-plus-negative feedback cell cycle oscillators
• OK
2. Repressilator
• OK
3. Pentilator
• OK
4. Goodwin oscillator
• memo. Parameters: φ ∼ 0.1.
5. Frzilator
• correction
誤 )
(
(
)
dc
1−c
c
= kc
− dc
dt
( 0.005 + (1 − c) )
( 0.005 + c )
de
1−e
e
= kc
− de
dt
0.005 + (1 − e)
0.005 + e
→
→
正)
(
(
)
dc
1−c
c
= kc
f − dc
dt
( 0.005 + c )
( 0.005 + (1 − c) )
de
e
1−e
c − de
= kc
dt
0.005 + (1 − e)
0.005 + e
• memo. Parameters: φ ∼ 0.1.
6. Metabolator
• correction
VAcE
誤
d[OAc− ]
= VAck −k3 [HOAc]
dt
d[Aca]
= ...
dt
−
= 100([OAc ][H + ] − Keq [HOAc])
Vout = ...
→
→
→
→
• missing parameters (Fung et al., Nature (2005))
Vgly = 1
n=2
• memo. Parameters: φ ∼ 0.1.
1
正
d[OAc− ]
= VAck −VAcE − VAcs
dt
d[Acs]
= ...
dt
−
VAcE = 100([AcP ][H + ] − Keq [HOAc])
(式をまとめているので不要)
7. Meyer and Stryer of calcium oscillations
• memo. Parameters: R ∼ 0.2.
8. van der Pol oscillators
• memo. Parameters: φ ∼ 20.
9. FitzHugh-Nagumo oscillators
• memo. Parameters: φ ∼ 0.1.
10. Cyanobacteria circadian oscillators
• memo. Parameters: φ ∼ −0.3.
2

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