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1
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
2
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
3
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
4
“!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
5
“!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
6
!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
7
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
8
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
9
“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)
10
“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
11
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
12
• 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
13
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)
14
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
15
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
16
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
17
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
18
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
19
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
20
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
21
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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24
Gibbs free energy and reduction potential
!G0’ = - nF ! E0’
25
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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