A. SOME THERMODYNAMIC CONSIDERATIONS
T h e reaction A H2 —> A + H2 m a y be regarded as the sum of two half-cell reactions, each operating a t its characteristic potential. If the electrode
6. MICROBIAL ELECTRON TRANSPORT MECHANISMS 347
potential of the hydrogen half-cell under defined conditions is used as a standard, then a n y other reversible oxidation-reduction system m a y be compared with it. More electronegative systems (lower oxidation-reduction potential) will reduce the hydrogen half-cell a n d cause reaction (15c) to proceed from left t o right; whereas more electropositive systems will oxidize the hydrogen half-cell a n d reaction (15c) will proceed from right to left.
T h e equilibrium constant and free energy change of reaction (15c) are therefore related t o the voltage difference between t h e two oxidation-re
duction systems. These relations are given b y the following thermodynamic formulas. (Only brief t r e a t m e n t of t h e subject can be given here. Detailed treatments are given in standard texts, such as Clark.2 4)
AF° = -nFAEo (16) I n equation (16) AF° = t h e free energy change (cal./mole) in t h e standard
state (25°C, and unit activities—1 molal activity for solutes, 1 a t m . pressure for gases); η = number of electrons transferred; AE0 = poten
tial difference in volts,F = the faraday (23,063 cal. per volt equivalent).
AF° = -flTlnKeq. (17) I n equation (17) R = the gas constant a n d Τ the absolute temperature.
A t 2 5 ° C , AF° = - 1 3 6 4 log K^.. T h e free energy change, AF°, is the max
imum a m o u n t of work t h a t can be obtained from a reaction when unit activity of reagents are converted to unit activity of products. T h e general equation describing t h e free energy change for any activity of reactants is:
AF - AF" + RT lnjg; * g>; (18)
For unit activities, therefore, AF = AF°. Under standard conditions, except for hydrogen ion concentration, which is controlled a t some fixed p H , AF°
is replaced by t h e symbol AF'. When AF° is negative (exergonic or spon
taneous reaction) the equilibrium point of a reaction favors product forma
tion; when AF° is positive, a t equilibrium there is a preponderance of starting reagents over products. If AF° is zero, t h e reaction is a t equilibrium (at unit activities). T h e magnitude of t h e free energy change indicates t h e extent t o which the reaction will proceed in either direction. A large negative AF° indicates t h a t t h e reaction will r u n toward completion, a large positive AF° t h a t the reaction will proceed only very slightly towcrd completion. If AF° is zero, t h e K^. is 1. T h e free energy change is a n important q u a n t i t y
A H2 —> A + 2H+ + 2e (15a)
2H+ + 2e — H2 (15b)
Sum: A H2- > A + H2 (15c)
348 Μ. I. DOLIN
since it indicates the potential a m o u n t of energy t h a t m a y be available t o a biological system from a given reaction.
T h e electrode potential of a half-cell is given b y t h e formula
At 25°C. and a specified p H ,
E H = B.' + °™* log (20)
η (red.)
Oxidation-reduction potentials are reported as EQ', t h e standard potential of the half-reduced system [i.e., (ox.)/(red.) = 1] on a scale in which t h e potential of the standard hydrogen half-cell a t p H 0 is taken as zero. A t p H 7, Eof a t 25°C. for the hydrogen couple is —0.414 v.
Table I V lists t h e standard potentials of a variety of biologically impor
t a n t systems. I n only a few instances have the values for t h e enzymically catalyzed reactions been checked b y potentiometric methods (succinatefumarate; several of the pyridine nucleotide dehydrogenases; D P N H -D P N ) .1 7 8 , 1 7 4 Results for t h e succinate-f u m a r a t e system and t h e D P N1 7 4 couple agree well with equilibrium data. Because of the relation between EQ , AF° and Κ e q. , the oxidation-reduction potential, or a t least the theoretical oxidation-reduction potential m a y be calculated from the equilibrium con
stant of a reaction or from t h e free energy change derived from thermal and ancillary d a t a .1 7 6 T h e particular virtue of expressing results as elec
trode potentials is t h a t it becomes possible to predict a t a glance the di
rection and extent (but not t h e rate) of the reaction t h a t results from t h e coupling of a n y two half-cells. I n t h e presence of the appropriate catalyst, electron flow will t a k e place from t h e system of lower potential (more nega
tive) to the system of higher potential (more positive). T h e greater t h e voltage difference, t h e farther the reaction will go toward completion (re
duction of the electropositive system).
After dehydrogenation of a substrate, two reducing equivalents pass through the components of the electron transfer chain. T h e latter forms a transport sequence in which there occurs a stepwise increase in potential from t h a t of the D P N H couple t o t h a t of t h e oxygen electrode (Table IV, Fig. 8). T h e fate of t h e carbon skeleton left after t h e dehydrogenation is a problem separate from t h a t of electron transport. T h e structure of t h e dehydrogenated product does determine, however, the potential a t which t h e next dehydrogenation will take place, and therefore t h e kinds of carriers t h a t m a y be involved (Fig. 8). Among t h e substrate systems, t h e carbonyl to carboxyl oxidations are t h e most potent electron donors and t h e suc
cinate fumarate system (probably paraffin to olefin in general, i.e., fatty
6. MICROBIAL ELECTRON TRANSPORT MECHANISMS 349
Leucomethylene blue «=* methylene blue + +0.011 2H+ + 2e
H2 τ± 2H+ + 2e (pH 0) 0.0
Cyt. b2 + <=± cyt. b8* + le (pH 7.4) - 0 . 0 4 Old yellow enzyme (reduced) old yellow —0.122
enzyme (oxidized) + 2 H+ + 2e
1 Except where noted, values are taken from K. Burton in appendix to reference
acyl-CoA t o α,/3-unsaturated acyl-CoA) t h e most p o t e n t electron accep
tors.
B y comparing t h e potential for dehydrogenation of various typical groups, a rationale can be given t o t h e coenzyme specificities a n d t o t h e point a t which substrates enter t h e respiratory chain. Substrates usually react with carriers having potentials in t h e vicinity of (or higher t h a n ) t h e potential for t h e substrate dehydrogenation. Succinate a n d f a t t y acid
de-350 +
1.0-+
0.8-+
0.6-+
0.4-P + 0.2-|
Μ, I . DOLIN
- Ot
6q
-
0.2 0 . 4 0.2
-- -
0.6-- 0 . 8 0.6--1
2e
- C Y T . c
2e
FP
2 H+ + 2e
D P N
| 2 H+ + 2e
AEQ' = 0.57 v.
AF' = -26,000 cal.
~ P = 1
AE0' - 0.57 v.
AF' = -26,000 cal.
~ P - 2
Paraffin -> Olefin + [2H]
AEo' - 0.33 v.
AF' - -15,000 cal.
~ P = 1
• Alcohol Carbonyl + [2H]
j Carbonyl + X — Acyl ~ X + [2H]
Carbonyl + H20 Carboxyl + [2H]
FIG. 8. Comparison of electrode potentials of coenzyme and substrate systems.
The yield of ~ P for the partial reactions was determined in experiments with mam
malian mitochondria (text). For the substrate systems, the average potential and variation in potential for each type of reaction is shown (calculated from the data of reference 22). The succinate —• fumarate reaction was used for the potential of paraffin -* olefin. Figure is drawn to scale.
6. MICROBIAL ELECTRON TRANSPORT MECHANISMS 351
hydrogenases, for instance, would be expected to use flavin coenzymes, and not pyridine nucleotides, as the immediate hydrogen acceptor. T h e paraffin to olefin dehydrogenation in general seems to be a flavin-linked reaction as evidenced by t h e fact t h a t the dehydrogenases for succinate, fatty acyl-CoA and dihydroorotic a c i d2 8 b are flavoproteins.
T h e formulation shown in Table IV is not meant to indicate t h a t the mechanism of dehydrogenation involves reversible liberation of 2H+ + 2e from the substrate. I n some cases it is known t h a t the formulation does not represent the dehydrogenation mechanism. For in
stance, oxidative decarboxylation of pyruvate, with D P N as acceptor is catalyzed by a multienzyme s y s t e m1 1 0 in which several coenzymes are involved. Electron transfer for a portion of the voltage span to D P N m a y take place ionically b y transfer of the acyl anion
Ο [CH3 C:]"
II
from one to another coenzyme. Thus, (a) the reaction occurs in several steps and (b) the electrons transferred are carried by a moiety derived from t h e substrate. T h e direct Η transfers, discussed in Section I I , B, also do not conform to t h e reversible half-cell reactions shown in Table IV. Indeed, in all potentiometric determinations of the dehydrogenation potential of substrate systems, an electroactive mediator (oxidation-reduction dye of suitable potential) must be added in order for the system to behave re-versibly at an inert electrode. Nevertheless, for the purposes of thermo
dynamic calculations, it is possible to proceed as if the formulations of Table I V were correct. If t h e potentials (or theoretical potentials) are accurate, the free energy change and equilibrium constant for the over-all reaction, calculated from two half-cell potentials, will be accurate, regard
less of the mechanism.
Certain precautions should be noted. (1) T h e values given in Table I V apply when (ox.)/(red.) is unity. W h e n the ratio increases, the potential becomes more positive, when it decreases the potential becomes more nega
tive [see equation (20)]. As far as the respiratory chain is concerned, this variable m a y not introduce as much difficulty as previously thought.
Chance and Williams have shown3 t h a t during steady state oxidation car
ried out by mitochondria, the ratio (ox.)/(red.) for D P N H , flavoprotein, and cytochromes b, c, and a is close enough to unity so t h a t little error is in
volved in using standard potentials for calculations.
(2) T h e potential of electron transfer coenzymes m a y change on binding of these compounds to protein. T h e potential of t h e old yellow enzyme, for instance, is about 0.1 v. higher t h a n t h a t of free flavins (Table IV). I t is probable t h a t both lower and higher potentials will be found for other
352 Μ. I. DOLIN
flavoprotein enzymes. T h e general phenomenon of change in potential with binding is important in t h a t it allows t h e formation of efficient oxidation-reduction catalysts for a specific reaction. A theoretical t r e a t m e n t of t h e binding phenomenon (in terms of the dissociation constants of the reduced and oxidized compounds from t h e protein) has been given b y Clark2 4 for iron-porphyrins and applied to D P N a n d D P N H binding to alcohol de
hydrogenase b y Theorell and Bonnichsen.1 7 6
(3) Free energies, calculated from the d a t a in Table IV, will apply to t h e standard state (molal activities, except for [H+]). T o convert to other con
ditions, formula (18) m a y be used. When correcting to a different p H , allowance must be made for the free energy of dissociation of the various ionic species t h a t m a y be present. I t has often been pointed out t h a t there m a y be great difficulties involved in trying t o estimate t h e concentrations (activities) of compounds in the physiological state.
(4) A reaction t h a t is thermodynamically possible m a y not t a k e place rapidly enough (even in the presence of suitable catalysts) to be physiologi
cally useful.
As an example of the predictions t h a t can be made by using free energy data, it can be stated t h a t the one-step dehydrogenation of succinate t o fumarate to yield hydrogen gas is a thermodynamically impossible reac
tion (i.e., it will not proceed to any significant extent, before equilibrium is reached). Inspection of Table I V shows t h a t t h e succinate-f u m a r a t e couple will oxidize the hydrogen couple and t h a t t h e reverse reaction will be very unfavorable, b u t it is possible to calculate exactly how unfavorable
the reaction is. T h e voltage difference between t h e two systems (subtracting the potential of the reducing system—4n this instance t h e succinate-fuma-rate couple—from t h a t of the oxidizing system) gives AE0' = —0.444 v.
Using formula (16), AF' = - 4 6 , 1 2 6 X - 0 . 4 4 4 = + 2 0 , 4 0 0 cal. T h e re
action is endergonic by a wide margin. T h e equilibrium constant, from equation (17), is
B . QUANTITATIVE ASPECTS OP ELECTRON TRANSPORT
2 H+ + 2e *± H2 EQ = - 0 . 4 1 4 v.
succinate τ± fumarate + 2H+ + 2e Ε0' - +0.03 v.
Sum: succinate —• fumarate + H2 E0 — —0.444 v.
(21) (22)
20,400 = —1364 log Κ (fum.)(H,) = K = i x m
(succ.)
,-15
T h a t is, for PH 2 = 10"4 a t m . (partial pressure of H2 in t h e atmosphere) the fumarate/succinate ratio a t equilibrium is 10"1 1. T h e reduction of fumarate
6. MICROBIAL ELECTRON TRANSPORT MECHANISMS 353 t o succinate, however is obviously a very favorable reaction. Similar calcu
lations for the reaction between the succinate-fumarate couple a n d t h e pyridine nucleotide system yield a n equilibrium constant of 6 X 1 0u for the reduction of fumarate. T h e succinate-fumarate system is known to serve as the physiological oxidant for m a n y anaerobic dehydrogenations.1 0 0 Although succinate oxidation t o fumarate does not furnish molecular hy
drogen, the dehydrogenation of pyruvic acid does. T h e dehydrogenation of pyruvic acid is a major source of H2 in bacterial fermentations.1 7 7 Table V shows t h e free energy changes in t h e oxidative decarboxylation of pyruvic acid when t h e oxidation is coupled with electron acceptors of increasingly higher potential. (The theoretical potential for dehydrogenation of p y r u v a t e is obtained from free energy data, and as discussed previously, is not to be interpreted as a reversible electrode potential. T h e processes considered m a y be termed electron transport, b u t the reaction route is not specified.) W h e n electron flow from t h e p y r u v a t e system is intercepted b y the hydrogen half-cell, over-all reaction (1) (in Table V) occurs. This reaction
T A B L E V
ELECTRON TRANSPORT FROM "PYRUVIC DEHYDROGENASE COMPLEX" TO