lecture #4
DESCRIPTION
Lecture #4. Chemical Reactions. Basic Properties of Chemical Reactions. Stoichiometry -- chemistry Relative rates – thermodynamics; K eq = f(P,T) Absolute rates -- kinetics Bi-linearity X + Y X:Y. DNA sequence dependent. Example: Hb assembly. Example:. TF binding. a + b ab - PowerPoint PPT PresentationTRANSCRIPT
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Lecture #4
Chemical Reactions
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Basic Properties of Chemical Reactions
• Stoichiometry -- chemistry• Relative rates – thermodynamics;
Keq= f(P,T)
• Absolute rates -- kinetics• Bi-linearity
X + Y <=> X:Y
DNA sequencedependent
Example: Hb assembly + +
Pomposiello, P.J. and Demple, B. Tibtech, 19: 109-114, (2001).
TF bindingExample:
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Cases Studied
• Reversible linear reaction
• Reversible bi-linear reaction
• Connected reversible linear reactions
• Connected reversible bi-linear reactions
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The Reversible Reaction: basic equations
dynamic massbalances
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The Reversible Reaction: a simulated response
k1=1
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The Reversible Reaction: a simulated response
k1=1
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The Reversible Reaction: forming aggregate variables
conservation variable
dis-equilibrium variable
the fraction of the pool p2 that is inthe form of x1
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The Reversible Reaction: basic equations in terms of pools
concentrations, x pooled variables, p
P maps x p
p(t) = Px(t)
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The Reversible Reaction: a simulated response
k1=1
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The Bi-linear Reaction: basic equations
=-v1,net
bi-linear term
;
conservation variables
x1+x2
v1=k1x1x2
v-1=k-1x3
x3
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The Bi-linear Reaction: forming aggregate variables
2) conservation variables
1) dis-equilibrium variable
C + A CA
p3
p2
schematic:
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The Bi-linear Reaction: a simulated response
x1(0)
x2(0)
x3(0)
disequilibrium variable
conservation variablesk-1=1/t
linearized disequilibriumvariable
k1=1/t/conc
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dynamic coupling
Connected Linear Reactions: basic equations
fast slow fast
simulate
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Connected Linear Reactions: a simulated response
k1=k2=k3=1
K1=K3=1
x10=1
x20=x30=x40=0
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Connected Linear Reactions: forming aggregate variables
If reactions are decoupled; k2=0
If reactions are dynamically coupled; k2≠0
•p1&p3 are the same dis-equilibrium variables
•p2 changed from a conservation variable to the coupling variable
•p4 changed from an individual reaction conservation to a total conservation variable for the system
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Connected Linear Reactions: simulated dynamic response
not coupled P
coupled P
K1=K3
k1=5k2=k3
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The Bi-linear Reaction: basic equations
simulateblock
diagonalterms
coupling variable
if x2=x4
this is the reversible form of the MM
mechanism
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Coupled Bi-linear Reactions: a simulated response
Concentrations Pools
x1 and x2 identical
x3
x4 and x5 identical
p1 p2
p3, p4, p5
@ equilibrium:
IC
IC
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Conservation Pools
Conservation of A
Conservation of B
Conservation of C
The 3 conservation quantities
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Summary• Dynamics of chemical reactions can be
represented in terms of aggregate variables
• Fast dis-equilibrium pools can be relaxed• Removing a dynamic variable reduces the
dynamic dimension of the description• Linearizing bi-linear kinetics does not
create much error
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Summary
• Each net reaction can be described by pooled variables that represent a dis-equilibrium quantity and a mass conservation quantity that is associated with the reaction.
• If a reaction is fast compared to its network environment, its dis-equilibrium variable can be relaxed and then described by the conservation quantity associated with the reaction.
• Removing a time scale from a model corresponds to reducing the dynamic dimension of the transient response by one.
• As the number of reactions grow, the number of conservation quantities may change.
• Irreversibility of reactions does not change the number of conservation quantities for a system.
• Linearizing bi-linear rate laws does not create much error.