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Bioenergetics

Martin Könneke

(10/2009)

Energetic Considerations

• Introduction

• Definitions

• Calculation of free energy changes

• Examples of different biologicalprocesses

• Role of ATP

• Free energy and reduction potential

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Why do microorganisms need

energy?

• Maintain the highly defined cellular

order

• Active Movement

• Detoxification

• Signaling/Communication

• Storage

• Growth / Reproduction

Chemotrophy Phototrophy

Catabolic Reactions

Anabolic Reactions

ATP

Biosynthesis

Heterotrophy Autotrophy

Metabolism

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Free Energy of Chemical Reactions

Progress of Reaction

Fre

e E

ne

rgy

A + B

C + D

A + B C + D

Progress of Reaction

A + B

C + D

!G

!G

!G < 0 (negative)

exergonic reactionYield energy

!G >0 (positive)

endergonic reaction

“Catabolic reactions are in

general exergonic reactions”

Progress of Reaction

A + B

C + D

!G

!G < 0 (negative)

exergonic reaction

ATPConserved as

Fre

e E

ne

rgy

( or other high-energy bonds)

= -32kJ/mol

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“!G provides no information

about the rate of a reaction”

Progress of Reaction

A + B

C + D

!G

!G < 0 (negative)

exergonic reaction

Fre

e E

ne

rgy

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“!G provides no information

about the pathway of the

reaction”

Progress of Reaction

A + B

C + D

!G

!G < 0 (negative)

exergonic reaction

Fre

e E

ne

rgy

Definitions

Free-energy change of a reaction aA + bB cC + dD

!G +=!G0 RT ln[C]c [D]d

[A]a [B]b

!G = Free-energy change under specific conditions (in KJ=kiloJoule)

!G0 = Standard free-energy change (25˚C, unit activities; 1atm, 1M)

R = Gas constant (8.314 J/mol/K)

T = Absolute temperature (K; K=˚C+273.15)

[ A,B ] = Molar Concentration of reactants (Activity)

[ C,D ] = Molar Concentration of products (Activity)

a,b,c,d = Stoichiometric coefficients

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!G of a reaction depends on

a) the nature of the reactants

and

b) on their concentrations

!G +=!G0 RT ln[C]c [D]d

[A]a [B]b

!G +=!G0 RT ln[C]c [D]d

[A]a [B]b

Standard free-energy changes

A) Can be calculated from standard free energies of formation

!G0 = " !Gf0 (products) - !Gf

0 (reactants)

B) Can be calculated from equilibrium constant

At equilibrium !G = 0

0 +=!G0 RT ln[C]c [D]d

[A]a [B]b!G0= - RT lnK

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Enthalpies of

formation !G°'(f) ofbiologically relevant

compounds

Standard free-energy changes

B) Can be calculated from equilibrium constant

At equilibrium !G = 0

0 +=!G0 RT ln[C]c [D]d

[A]a [B]b

!G0= - RT lnK

K = [C]c [D]d

[A]a [B]b(K = equilibrium constant)

K = e - !G0/ 2.3RT= 10- !G0/ 2.3RT

!G0 = - RT ln [C]c [D]d

[A]a [B]b

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Conditional (biochemical) standard

free-energy changes !G0 ’

!G0 ’ = Free-energy change under biochemical standard

condition at pH=7, unit activities, 25˚C = 298 K

!G0 ’ = !G0 + m !G’f (H+)

!G0 ’ = !G0 + mRT ln [H+] = !G0 + 39.95kJ m

m = net number of protons in the reaction

m < 0; when more protons are consumed than formed

m > 0; when more protons are formed than consumed

Redox potential E and

free-energy change

A+ + ne-

2H+ + 2e-

1/2 O2 + 2e-

H2 + 1/2O2

A ; E = reduction potential

H2

O2-

H2O

! E0 = Difference in potentials of half-reactions

= E0 electron-accepting - E0 electron-donating

n = Number of electrons

E0 = Standard potential for redox-half-reaction

(in V,25 ˚C, 1M)

E0’ = E0 at pH 7

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“The electron tower”

Couple E0’ (V)

CO2/glucose(-0.43) 24e-

2H+/H2 (-0.42) 2e-

NAD+/NADH (-0.32) 2e-

CO2/acetate (-0.28) 8e-

SO42-/H2S (-0.28) 8e-

NO3-/NO2

- (+0.42) 2e-

NO3-/1/2N2 (+0.74) 5e-

Fe3+/Fe2+ (+0.76) 1e-,(pH 2)1/2O2/H2O (+0.82) 2e-

-0.50

0.0

+0.50

+0.90

The standard free-energy change !G0’ is

proportional to the redox-potential

difference between e--donor and

e--acceptor ! E0’

!G0’ = - nF ! E0’

!G0 = - nF ! E0

n = Number of electrons

F = Faraday’s constant (96.48 kJ/V)

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“The electron tower”

Couple

CO2/glucose(-0.43) 24e-

2H+/H2 (-0.42) 2e-

NAD+/NADH (-0.32) 2e-

CO2/acetate (-0.28) 8e-

SO42-/H2S (-.028) 8e-

NO3-/NO2

- (+0.42) 2e-

NO3-/1/2N2 (+0.74) 5e-

Fe3+/Fe2+ (+0.76) 1e-,(pH 2)1/2O2/H2O (+0.82) 2e-

-0.50

0.0

+0.50

+0.90

!G0’= -237 kJ

!G0’ = - nF ! E0’

The substrate with lower E0’ provide the electrons (e- donor)

E0’ (V)

2H+ + 2e-

1/2 O2 + 2e-

H2 + 1/2O2

H2

O2-

H2O

Calculating free-energy changes for

hypothetical reactions

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Balancing of chemical reactions

Oxidation-reduction (redox) balance

All electrons removed from a substance on one side must betransferred to another substance on the other side

Ionic balance

Total ionic charge of all molecules must be equal on both sides

In aqueous medium, ionic balance can be achieved by adding

H+ or OH-, and H2O (for elemental balance)

Elemental balance

Total number of each element must be equal on both sides of the equation

• Oxidation state of elements in elementary substance or

combined with itself is 0 (H2, O2, N2, S(s)0)

• Except when combined with itself, H has the oxidation state +1

• Except when combined with itself, oxygen has the oxidation

state -2

• Oxidation state of an ion of an element is equal to its charge

(O2-, Na+, Fe3+)

• Sum of the oxidation states of all atoms in neutral molecule is 0

(H2O, 2 x +1, 1x -2)

• Sum of oxidation states of all atoms in an ion is equal to its

charge (OH- = -1)

• The oxidation state of individual carbon atoms in organic

compounds can vary (average ox-state can be calculated by

assuming that: N is usually -3, S is usually -2)

Determining the oxidation state

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• Aerobic respiration

• Fermentation

• Anaerobic respiration: e.g., Methanogenesis

• Syntrophic ethanol oxidation at anaerobic conditions

Calculating free-energy yields

“Biological examples”

Aerobic Respiration of Glucose:

Glucose + Oxygen Carbon dioxide

C6H12O6 + O2 CO2

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Aerobic Respiration of Glucose:

Glucose + Oxygen Carbon dioxide

C6H12O6 + O2 CO2

Elemental balancing

(6xC, 12xH, 18xO) (1xC; 2xO)

C6H12O6 + 6O2 6CO2 + 6H2O

Aerobic Respiration of Glucose:

Glucose + Oxygen Carbon dioxide

C6H12O6 + O2 CO2

Elemental balancing

(6xC, 12xH, 18xO) (1xC; 2xH; 3xO)

C6H12O6 + 6O2 6CO2 + 6H2O

Redox balancing

C (0);H 12(+I);O 6(-II); C 6(+IV) O 12(-II); H 12(+I);O 6(-II)

O 6(0)

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Aerobic Respiration of Glucose:

Glucose + Oxygen Carbon dioxide + Water

C6H12O6 + 6O2 6CO2 + 6H2O

!G0 ’ = " !Gf0 ’ (products) - !Gf

0 ’ (reactants)

= 6(-394.4)+6(-237.17) - (-917.22) = -2872.2 kJ

Aerobic Respiration of Glucose:

Glucose + Oxygen Carbon dioxide + Water

C6H12O6 + 6O2 6CO2 + 6H2O

C 6(0); H 12(+I); O 6(-II) C 6(+IV); O 18(-II); H 12(+I)

C6H12O6 6CO2+ 24 e- -0.43 V

Glucose (e- donor);

6O2 + 24e- 6 H2O +0.82V

Oxygen (e- acceptor)

!G0 ‘ = - nF ! E0’

= -24 (96.48 kJ/V)(+0.82V -(-0.43V))= -2894.4 kJ

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Fermentation of Glucose:

Glucose Ethanol + Carbon dioxide

C6H12O6 C2H6O + CO2

Elemental balancing

(6xC, 12xH, 6xO) (3xC, 6xH, 3xO)

C6H12O6 2C2H6O + 2CO2

Redox balancing

C (avg. 0) C 2(avg. -II); C 2(+II)

!G0 ‘ = (2(-394.4)+2(-181.75)) - (-917.22) = -234.28 kJ

Anaerobic Respiration (i.g.: Methanogenesis)

Hydrogen + Carbon dioxide Methane

H2 + CO2 CH4

Redox Balance

C +IV; H 0 C -IV; H 4(+I) 8 e-

4H2 + CO2 CH4

(e- donor) (e- acceptor)

Elemental Balance

8xH, 1xC, 2xO 4xH, 1xC

4H2 + CO2 CH4 + 2H2O

!G0 ’ = -50.75 + 2(-237.17) - (-394.4) = -130.7 kJ

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Ethanol fermentation

Ethanol Acetate + Hydrogen

C2H6O C2H3O2- + H2

Ionic Balance

C2H6O C2H3O2- + H2 + H+

Elemental Balance

C2H6O + H2O C2H3O2- + 2H2 + H+

Redox Balance

C 2(-II); H 6(+I); O (-II) C 2(0); H 3(+I); O 2(-II) + H (+I)

Ethanol fermentation

Ethanol Acetate + Hydrogen

C2H6O C2H3O2- + H2

Ionic Balance

C2H6O C2H3O2- + H2 + H+

Elemental Balance

C2H6O + H2O C2H3O2- + 2H2 + H+

Redox Balance

C 2(-II); H 6(+I); O (-II) C 2(0); H 3(+I); O 2(-II) + H (+I)

!G0 ’ = -369.41 + (-39.83) - [(-181.75) + (-237.17)] = 9.68 kJ

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Effect of hydrogen partial pressure

on free-energies

Ethanol fermentation:

ethanol + H2O acetate + 2H2 + H+

!G +=!G0 RT ln[C]c [D]d

[A]a [B]b

!G +=!G0 RT ln[H2]

2 [acetate] [H+ ]

[ethanol] [H2O]

!G = 9.68 + 2RT ln [10-4 ] = -36.03 kJ/mol

!G = !G0 + mRT ln [H2]

at 10-4 atm H2

Syntrophic ethanol oxidation at

anaerobic conditions

2 ethanol + 2H2O 2 acetate + 4H2 + 2H+

Ethanol fermentation

Methanogenesis

4H2 + CO2 CH4 + 2H2O

Syntrophic coupled reaction

2 ethanol + CO2 2 acetate + CH4 + 2H+

!G0’ (kJ/reaction)

+ 19.4

- 130.7

- 111.3

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Syntrophic co-culture “Methanobacillus omelianskii”

ethanol CO2

H2 H2 CH4

acetate

Strain S Strain

MoH

“Methanobacillus omelianskii”

Interspecies Hydrogen-transfer

Syntrophic co-cultures

Interspecies hydrogen transfer

Hydrogen-producer Hydrogen-consumer

Fermentation Anaerobic Respiration

fatty-acids CO2, SO4-2, NO3

-

(e.g., butyrate, propionate)

alcohols

(e.g.,ethanol)

acetate + CO2 acetate, methane, HS-, N2O,

NO, N2

Syntrophomonas Methanogens

Syntrophobacter Sulfate-reducing bacteria

Homoacetogens

Denitrifyers

H2 H2

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Adenosintriphosphate (ATP)

Free enthalpy of ATP

ATP + H2O ! ADP + Pi "G°' = -32 kJ/mol

ATP + H2O ! AMP + PPi + H+ "G°' = -45 kJ/mol

AMP + H2O ! Adenosin + Pi "G°' = -13 kJ/mol

PPi + H2O ! 2 Pi "G°' = -29 kJ/mol

ATP + AMP ! 2 ADP "G°' = 0 kJ/mol

Hydrolysis of ATP, AMP and pyrophosphate

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ATPHow much ATP is in a cell?

Energy charge, EC of the cell

EC =[ATP] + 0.5 [ADP]

[ATP] + [ADP] + [AMP]> 0.8

e.g. [ATP] # 10 mM, ADP # 1 mM, AMP # 1 mM

EC = 10.5/12 = 0.875

The cell is energetically loaded. (During starvation?)

ATPWhat is the value of ATP in the cell?

Consideration of concentrations forenergetical calculations:

"G = "G°‘ + RT ln(cProduct/cReactant)

• Textbook (standard conditions)ATP + H2O ! ADP + Pi "G°' = -32 kJ/mol

Multiply reactant concentrations, ifthere is more than 1 reactant:

"G = "G°+ RT ln(CP1 . CP2 / CR1 . CR2)

• In the cell: [ATP]#0.01 M, [H2O]='1', ADP#0.001 M, [Pi] #0.01 M Product-reactant ratio is (0.001*0.01)/(0.01 * 1) = 0.001

"Gbiol. = "G0' + RT ln 0.001

"Gbiol. = 32 kJ/mol + (8,315 J/K mol) (298 K)(ln 0.001)

"Gbiol. = "G0' + RT ln 0.001 = "G0' -17 = -49 kJ/mol

• For Regeneration of ATP spent: mostly about 75 kJ/mol ATP

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ATPWhat is the value of ATP in the cell?

• In the cell: [ATP]#0.01 M, [H2O]='1', ADP#0.001 M, [Pi] #0.01 MProduct-reactant ratio is (0.001*0.01)/(0.01 * 1) = 0.001

"Gbiol. = "G0' + RT ln 0.001 = "G0' -17 = -49 kJ/mol

"Gbiol= -50 kJ/mol

Consideration of concentrations forenergetical calculations:

"G = "G° + RT ln(cProduct/cReactant)

In the cell ATP has a higher value than under standardconditions, and requires even more energy to be regenerated.

• Textbook (standard conditions)ATP + H2O ! ADP + Pi "G°' = -32 kJ/mol

• For Regeneration of ATP spent: mostly about 75 kJ/mol ATP

Multiply reactant concentrations, ifthere is more than 1 reactant:

"G = "G°+ RT ln(CP1 . CP2 / CR1 . CR2)

Mechanisms of ATP regeneration

There are only two possibilities.

• Ion transport Phosphorylation (H+ or Na+)

(membrane bound, driven by electrical membrane potential + chemical gradient)

• Substrate level Phosphorylation

b + a (last slide) backwards, coupled to an exergonic reaction, e.g. redox reaction

Substrate level phosphorylation, dt. Substratketten-Phosphorylierung ?

There is no oxidative phosphorylation, neither electron transport-

driven phosphorylation, nor photophosphorylation

Do not get stupefied by obsolete terms!

Energy conservation

Terms:

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Gibbs free energy and reduction potential

!G0’ = - nF ! E0’

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Gibbs free energy and reduction potential of NAD

NAD+ + 2H+ + 2e- ! NADH + H+ E0‘ = -0.32 V

0.5O2 + 2H+ + 2e- ! H2O E0‘ = 0.82 V

NADH + 0.5O2 + H+ ! NAD+ + H2O

!E0‘ = E0‘O2- E0‘NADH = 0.82 V - (-0.32 V) = 1.14 V

!G0’ = - nF ! E0’

!G0‘ = -(2) (96.48kJ/V mol) (1.14V) = -220kJ/mol

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