Mass action
description
Transcript of Mass action
Mass action
1
Law of mass action Cooperativity
Hill functions Bistability
fB
X
π πππ‘ |
?
X
2
Law of mass action: A little lie . . .
π πΏπΈπΉπ=πππ
ππππ=ππ π
π π πΌπΊπ»π=πππ
π π΅πππππ=ππ΅π΅
Law of mass action: A little lie . . .
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Law of mass action: A little lie . . .
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π πΏπΈπΉπ=πππ
ππππ=ππ π
π π πΌπΊπ»π=πππ
π π΅πππππ=ππ΅π΅
Law of mass action: A little lie . . .
5
ππ ππ‘
=ππ·ππ3 ππ΅ππ 3π΅
Law of mass action: A little lie . . .
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β π‘Between times and
π‘ 0
ππ ππ‘
=ππ·ππ3 ππ΅ππ 3π΅
Law of mass action: A little lie . . .
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ππ ππ‘
=ππππΈπ π΄πΏπΏπππ₯ππ π¦ πππ§β―
X
Y
ZZ
Z
Y
Y
X
X
XX
XYZ
3π +1π+1π΅ππ·ππ3 ππ΅
β
π
ππ₯ π+ππ¦π +ππ§π+β―ππππΈπ π΄πΏπΏ
β
π
Mass action
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Law of mass action Cooperativity
Hill functions Bistability
fBπ πππ‘ |
?
X X
ππΈπ΅
ππ‘ |π΅πΌππ·
=ππΈπ΅
ππ π΅
ππ π΅
ππ‘
ππΈπ΅
ππ‘ |πππ΅πΌππ·
=ππΈπ΅
ππ π
π π π
ππ‘
0=π πΈπ΅
ππ‘=ππΈπ΅
ππ‘ |π΅πΌππ·
+ππΈπ΅
ππ‘ |πππ΅πΌππ·
=ππ΅πΌππ· π4πΈπΉβππππ΅πΌππ· πΈπ΅
π π΅=π 4
π 4+ππππ΅πΌππ·
ππ΅πΌππ·
XX
XX
9
XX
XX
XX
XX
XX
XX
ππ΅πΌππ·π4πΈπΉ ππππ΅πΌππ· πΈπ΅+1 -1
ππππ΅πΌππ· πΈπ΅=ππ΅πΌππ· π4πΈπΉ
πΈπ΅
(πΈπππβπΈπ΅ )
(ππ΅πΌππ· π4+ππππ΅πΌππ· ) πΈπππππ΅πΌππ·π
4ΒΏ
EF EB XX
XX
Cooperativity and Hill functions: Another lie . . .
π 1/24
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X
X
X
X
XX
XX
π π΅=π 4
π 4+π 1 /24
Cooperativity and Hill functions: Another lie . . .
π π΅=ππ
ππ+π 1/2π X
X
X
X
X
X
. . .
. . .
n dimples n bound dimples
π π΅=ππ
ππ+π 1/2π X
X
XXX
X
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Cooperativity and Hill functions: Another lie . . .
fB
X
XX
X1/2
1
0
π π΅=ππ
ππ+π 1/2π X
X
XXX
X
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Cooperativity and Hill functions: Another lie . . .
fB
X
XX
XX
XX
π π΅=ππ
ππ+π 1/2π X
X
XXX
X
13
Cooperativity and Hill functions: Another lie . . .
fB
X
π π΅=ππ
ππ+π 1/2π X
X
XXX
X
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Cooperativity and Hill functions: Another lie . . .
fB
X
n = 1
n = 3n = 2
n = 4
n = 8n = 16
X1/2
Mass action
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Law of mass action Cooperativity
Hill functions Bistability
fBπ πππ‘ |
?
X X
π πππ‘ |
π·πΈπΊπ
= π ππ π π·
ππ π·
ππ‘π πππ‘ |
πΆπ΄π
= π πππ πΆ
ππ πΆ
ππ‘
Bistability
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X
X
X
X
XX
XX W
X X
f
π π΅=ππ
ππ+π 1/2π
π½π πΈπππ π π΅+1ππ
ππ+π1 /2π
~π½ -1 πΌ π
π πππ‘
= π πππ‘ |
πΆπ΄π
+ π πππ‘ |
π·πΈπΊπ
=~π½ ππ
ππ+π 1 /2π βπΌ π
π πππ‘ |
?
X
~π½
0
Bistability
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X
X
X
X
XX
XX W
X X
f
π πππ‘
=~π½ ππ
ππ+π 1 /2π βπΌπ
X
π πππ‘
π‘
π (π‘ )
0
0