The constraints on metabolism

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The constraintson metabolism

• 2. Thermodynamic constraints

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Thermodynamic constraintsEntropy the driving
force of change
Second Law of Thermodynamics The total entropy of
a system and its surroundings always increases
for a spontaneous process.
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Thermodynamic constraintsEntropy a popular view
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Thermodynamic constraintsEntropy
Q Which of these systems has the highest entropy?
System A
System B
A None!
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Thermodynamic constraintsEntropy the driving
force of change
Q Does entropy increase when the two gases mix?
A Yes! (Increased number of states available)
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Thermodynamic constraintsEntropy the driving
force of change
Q Does this reaction increase or decrease the
systems entropy?
2 H2(g) O2(g) ? 2 H2O(g)
A It decreases. (Less molecules, less states)
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Thermodynamic constraintsEntropy the driving
force of change
Q Does this reaction occur spontaneously?
2 H2(g) O2(g) ? 2 H2O(g)
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Thermodynamic constraintsEntropy the driving
force of change
Second Law of Thermodynamics The total entropy of
a system and its surroundings always increases
for a spontaneous process.
Maintaining a highly designed state (i. e. one
that must have a tightly prescribed arrangement
of the parts) entails a strong entropy decrease
in the system.
Entropy of the surroundings must increase.
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Thermodynamic constraintsEntropy the driving
force of change
Some ways to decrease the systems entropyat
expense of increasing the surroundings entropy

• Dissipate heat
• Disassemble large molecules into many small
  molecules and release these
• Release gases
• Perform work on the system

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Thermodynamic constraintsEntropy the driving
force of change
2 H2(g) O2(g) ? 2 H2O(g)
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Thermodynamic constraintsEntropy the driving
force of change
How much does the entropy of the surroundings
increase due to the heat dissipated?
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Thermodynamic constraintsEntropy the driving
force of change
Gibbs free energy
For a spontaneous process, ?Glt0
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Thermodynamic constraints?G for a chemical
reaction
A B C D
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Thermodynamic constraints?G for a chemical
reaction
A B C D
Replacing above
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Thermodynamic constraintsMaking unfavorable
reactions proceed
Glucose Pi G6P H2O ?Gº13 kJ/mol
Q What is the equilibrium constant for this
reaction?
RT 310 K ? 8.31 JK-1mol-1 2.58 kJ/mol
Keq e-13/2.58 6.4?10-3
Q Considering G6P 0.04 mM, Glc 5 mM, Pi
0.7 mM, would phosphorylation or hydrolysis
proceed spontaneously?
Hydrolysis!
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Thermodynamic constraintsMaking unfavorable
reactions proceed
Q Will the whole process proceed spontaneously
if PEP 0.017 mM, Pyr 0.085 mM?
Yes!
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Thermodynamic constraintsMaking unfavorable
reactions proceed
Glucose Pi G6P H2O ?Gº13 kJ/mol
Q What is the equilibrium constant for this
reaction?
RT 310 K ? 8.31 JK-1mol-1 2.58 kJ/mol
Keq e-13/2.58 6.4?10-3
Q Considering G6P 0.04 mM, Glc 5 mM, what
minimal value should Pi have so that
phosphorylation is spontaneous?
Pigt1.25 M!
Oops!...
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Thermodynamic constraintsMaking unfavorable
reactions proceed
Spontaneous, but would proceed at the cost of a
HUGE Pi
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Thermodynamic constraintsMaking unfavorable
reactions proceed
Keq 2.8?103
Achieving favorable conditions for
phosphorylation now depends on a concentrations
ratio, rather than on absolute concentrations
Even a modest ATP/ADP ratio suffices todrive
spontaneous Glc phosphorylation
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Thermodynamic constraintsMaking unfavorable
reactions proceed
Keq 2.8?103
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Thermodynamic constraintsGood moiety-transfer
intermediates must have special thermodynamic
properties
PEP H2O Pi Pyr ?Gº-54 kJ/mol ATP
H2O Pi ADP ?Gº-33.5 kJ/mol G6P
H2O Pi Glucose ?Gº-13 kJ/mol
For both advantages to obtain, the
moiety-transfer intermediate must have an
intermediate ?Gº for hydrolysis
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Stoichiometric constraintsHubs in metabolism
Three alternative ways to transfer a moiety
(M)between a donor (DM) and an acceptor (A)
Spontaneous occurrencedepends on absolute
M, could require large M
Requires too many enzymes, complex regulation
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Thermodynamic constraintsMaking unfavorable
reactions proceed

• Key points
• Spontaneity requires ?Glt0
• Processes with ?Ggt0 can be made to function if
  coupled to spontaneous ones
• Not all such couplings of processes are
  biologically feasible or effective
• Coupling through moiety transfer cycles mediated
  by suitable moiety carriers avoid need for high
  concentrations of intermediates

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Thermodynamic constraintsReversibility

• At equilibrium
• ?G0
• ?eqBeq/AeqKeq
• vv-

If ?Gºltlt0 then Keqgtgtgt1
Only HUGE ?0 would make reaction proceed in
reverse!
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Thermodynamic constraintsReversibility
1
2
3
?G1º, ?G2º, ?G3º 0
?G1º, ?G3º 0, ?G2ºltlt0
Reaction with ?G2ºltlt0 effectively imposes
directionality
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Thermodynamic constraintsReversibility and
amphibolism
For the pathway to reverse direction,
irreversible reactionsmust be bypassed through
thermodynamically favorable ones
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Thermodynamic constraintsReversibility and
amphibolism
Glycolysis
Glc
HK
G6P
PFK
FDP
PEP
PK
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Thermodynamic constraintsReversibility and
amphibolism
Glc
Gluconeogenesis
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Thermodynamic constraintsQuasi-equilibrium
reactions
Concentrations of A and B settle to
non-equilibrium steady state.
E.g. Mass action kinetics (v k A, v- k- B,
vout kout B) Ass vin /k, Bss vin /(k- kout)
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Thermodynamic constraintsQuasi-equilibrium
reactions
E.g. Mass action kinetics (v k A, v- k- B,
vout kout B) Ass vin /k, Bss vin /(k- kout)
Fast product removal (relative to reverse
reaction) displaces mass action balance of
reversible reaction away from equilibrium.
kout/k-
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Thermodynamic constraintsQuasi-equilibrium
reactions
Enzyme-catalyzed step
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Thermodynamic constraintsQuasi-equilibrium
reactions
Enzyme-catalyzed step
Mass action ratio approaches equilibrium
constantas enzyme activity increases
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Thermodynamic constraintsQuasi-equilibrium
reactions
Capacity for regulation of fluxes and
concentrationsis greatest far from equilibrium
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Key points

• Reactions with ?Gºltlt0 are effectively
  irreversible and determine directionality of
  embedding pathways.
• In amphibolic pathways, operation in reverse is
  ensured by replacing such steps by reactions with
  favorable ?Gº.
• Steps that have moderate ?Gº approach
  equilibrium if activities of the respective
  enzymes become very large compared to the overall
  flux over the pathway
• Modulating the activities of these enzymes has
  little effect on net fluxes and concentrations