THE THERMOCHEMISTRY OF BIOLOGICAL NITROGEN FIXATION

By N. S. BAYLISS*

[Manuscript received December 21, 1955]

Summary

Using standard thermodynamic data it is shown that the oxidation of glucose by nitrogen to give carbon dioxide and ammonia is an overall reaction that involves a substantial evolution of heat and decrease in free energy. This is not in accordance with literature statements that biological nitrogen fixation is endothermic. In the concluding section a Frost diagram is used to survey the thermodynamic data of oxidation reactions related to nitrogen fixation.

I. INTRODUCTION

The literature on biological nitrogen fixation contains a number of references to the alleged energetically unfavourable nature of the fixation process, with the suggestion that it requires assistance from the energy supplied by other processes, such as respiration. Thus a recent review by Fogg (1955) states that "fixation must be an endothermic reaction," and Pethica, Roberts, and Winter (1954) use the words "it is generally conceded that the fixation process, taken as a whole, is endothermic." In an earlier review on energetic coupling, Kalckar (1941) states that the reduction of the triple bond in nitrogen is an endergonic reaction. Of these authors only Kalckar quotes a reference, which is without a page number, to Lewis (1923), a work in which the present author has been unable to find a relevant statement except one relating to the well-known great stability of the N _N bond.

On the other hand, nearly thirty years ago Burk (1927) presented thermo­dynamic evidence against the (then) current conception that energy was necessarily required for the fixation of nitrogen. However, Burk's particular examples of fixation that could occur with the liberation of energy or free energy were confined to reactions that involved the participation of oxygen gas, or hydrogen gas, or both, "or other substances, especially gases, whose standard free energies are close to zero." In· his concluding remarks he raised the question of the carbohydrate requirement of nitrogen-fixing organisms and suggested some unobserved function for carbo­hydrate, together with the possibility that fixation can make energy available for use in general metabolism.

More recently Wilson and Burris (1947), in a general review of mechanisms of nitrogen fixation, have discussed thermodynamic aspects of fixation by Azotobacter in terms of definite evidence that ammonia is the key intermediate and that glucose can be regarded as a typical nutrient medium. They considered the overall reaction in which the reduction of nitrogen to ammonia is brought about by the "metabolic hydrogen" of glucose (a reaction which chemically could equally well be described as the oxidation of glucose by nitrogen). Taking into account reasonable concentra­tions of nutrient, atmospheric nitrogen, evolved carbon dioxide, and the requirements

* Department of Chemistry, University of Western Australia.

THERMOCHEMISTRY OF BIOLOGICAL NITROGEN FIXATION

of a pH = 7, their overall equation is the following:

C6H120 6(0·05M) +4N 2(0·8 atm) +18·67H20(liq.) = 8NH4 +(1O-4M) +80H -(1O-7M)

+4·67HCOa-(0·0012M) +4·67H+(1O-7M) +1.33C02(0·01 atm) .... (1)

365

Of this reaction Wilson and Burris stated "Although the standard free energy of this reaction (LlOO)* is +5·6 kg cal per 0·5N 2' the organism actually obtains energy by carrying out the reaction under the specified conditions, LI 0 equalling -17·5 kg cal per 0·5 mole N 2 fixed" (italics are the present author's). While it is clear that Wilson and Burris envisaged the oxidation of glucose by nitrogen in terms of the overall equation (1) as a reaction which can proceed without assistance, given a suitable mechanism, their use of the words italicized by the author may suggest to others the attachment of undue importance to their positive value of the standard free energy change LlOo. Furthermore, their use of conventional standard states in connexion with (1) can be misleading unless the thermodynamic implications are clearly recognized. This point will be taken up later.

II. THE GLUCOSE-NITROGEN REACTION

We now review the thermodynamics of the overall reaction (as used by Wilson and Burris) in which glucose as a typical nutrient is oxidized by nitrogen to give carbon dioxide and ammonia as products. The relevant standard heats (LlHOf) and standard free energies (LlOOf ) of formation are given in Table 1, the data being taken from Latimer (1952) and from Burton and Krebs (1953) except where indicated otherwise. The conventions regarding standard states are those of Latimer (1952). Biological reactions occur under conditions well removed from the standard states, and, therefore, in Table 1 free energies of formation (LlO,) have been calculated for the assumed biological concentrations which are listed in column 4, and which are based on Burton and Krebs (1953). These concentrations are slightly different from those used by Wilson and Burris in equation (1); but it will be seen that the differences are not material. No attempt has been made to calculate values of LlH, for the biological concentrations; they will not differ greatly from the standard values LlHo, since heats of formation are much less sensitive to concentration changes than free energies.

For the reduction of nitrogen we use one of the formal chemical half equations

N 2+6H++6e- = 2NHa, .................. (2)

N 2+8H++6e- = 2NH4+, ................ (3)

and for the oxidation of glucose the formal half equation

CaH120s+6H20 = 6C0 2+24H++24e-. . ......... (4)

These combine to give the following alternative overall equations for the reduction of nitrogen by glucose:

CSH120 6( aq.) +4N 2(gas) +6H20(liq.) = 6C02(gas) +8NHa( aq.), .. (5)

C6H1206(aq.)+4N2(gas)+6H20(liq.)+8H+(aq.) = 6C02(gas)+8NH4+(aq.) . . . . . . . . . . . (6)

* Wilson and Burris used the symbol APo for the standard free energy change.

366 N. S. BAYLISS

Under biological conditions of pH = 7, (6) would be a better representation than (5), since at this pH aqueous ammonia would be almost entirely in the form of NH4+' From the data in Table 1 it is found that for these reactions the standard tJHo and tJGo, and the tJG for the biological concentrations, are as follows:

Reaction (5): tJHO = -11 kcal; tJGO = -59 kcal; tJG = -87 kcal,

Reaction (6): tJHo = -110 kcal; tJGo = -160 kcal; tJG = -112 kcal.

For comparison with ordinary respiration, we can also derive from Table 1 the same thermodynamic quantities for the reaction

C6H120 6(aq.)+602(gas) = 6C02(gas)+6H20(liq.), ...... (7)

with the result that for

Reaction (7): tJHo = -676 kcal; tJGo = -689 kcal; tJG = -690 kcal.

TABLE 1

FREE ENERGmS AND HEATS OF FORMATION AT 25°C

Standard Free Free Energy of

Standard Heat Energy of Assumed

Formation in

Substance of Formation

Formation Biological Biological

AHo! AGO, State

State (kcal)

(kcal) AGt

(kcal)

O.(gas) 0·0 0·0 0·2 atm -0,95 H.(gas) 0·0 0·0 H+(aq.) 0·0 0·0 pH = 7 -9·52 OH-(aq.) - -37·60 H.O(liq.) -68·32 -56·69 Liquid -56·69 CO 2(gas) -94·05 -94·26 0·05 atm -95·82 HCO.-(aq.) - -140·31 Glucose (aq.) -298* -217·02 O'OIM -219·74 Pyruvate-(aq.) -113·32 C.H.OH(aq.) -42·4 N.(gas) 0·0 0·0 0·8 atm -0·13 NH.(gas) -11·04 -3·98 NH.(aq.) -19·32 -6·36 O'OIM -9,08 NH,+(aq.) -31·74 -19·00 O'OlM -21·72 NH.OH+(aq.) -13·54 NsH.+(aq.) +21·0 NOs-(aq.) -8·25 N03-(aq.) -26·43

-

* -AHO, for glucose (aq.) calculated from data in Landolt-Bornstein (1936). Other values in this table from Latimer (1952) and Burton and Krebs (1953).

It is thus clear that the oxidation of glucose by nitrogen is a reaction which, particularly in the more probable form (6), involves a substantial evolution of heat and decrease in free energy, whether one considers standard states or biological

THERMOCHEMISTRY OF BIOLOGICAL NITROGEN FIXATION 367

concentrations. While it is true that the heat evolution and free energy decrease are considerably less than in the oxidation of glucose by oxygen, the fixation process if it occurred according to (5) or (6) would certainly require no "assistance" from any other energy-providing reaction. Although the demonstration of the thermodynamic feasibility of the reaction is no proof that biological nitrogen fixation occurs in this way, it should be remarked that nitrogen fixing organisms do consume nutrients such as glucose and do take up nitrogen, and that the simultaneous occurrence of these processes therefore makes no net demand, as far as energy is concerned, on any other metabolic process. On the contrary, the exothermic and exergonic nature of (6) lends thermodynamic support to the suggestion of Parker (1954) that nitrogen fixation might possibly be regarded as an alternative form of respiration with nitrogen serving as the oxidizing agent instead of oxygen.

Comparing reaction (6) with (1), the preceding paragraph shows that for (6) one has LlO = -14 kcal per 0·5 mole N 2' a result that is in good agreement, considering the different origin of the data and the slight differences in biological concentrations, with the value LlO = -17·5 kcal per 0·5 mole N2 found by Wilson and Burris (1947) for (1)". We are thus led to consider why the latter authors obtained a positive standard LlOO for (1) whereas this paper derives a substantially negative standard LlOo for (6).

The reason for this discrepancy is to be found in the form of (1). The occurrence together ofNH4+, OH-, HC03-, and H+ on the right side of this equation is consistent with a valid description of a chemical system as long as these substances are at or near the concentrations given in parentheses. However, the calculation of a conventional standard free energy for (1) involves the consideration of a hypothetical system in which NH4+, OH-, HC03-, and H+ exist simultaneously at unit concentration. Such a chemical system is of course quite unrealizable owing to the fact that NH40H, H 2C03 , and H 20 are weak electrolytes. The positive LlOo of reaction (1) thus actually includes concealed eontributi~ns from the chemical equilibria

CO 2+H20 = H++HC03-; LlOo = +22·27 kcal, ...... (8)

H 20 = H++OH-; LlOo = +19·09 kcal, .......... (9)

whose positive standard free energies are merely the expression of the fact that the equilibrium constants of the reactions as written are very small. In fact our equation (6) in its standard form can be derived from equation (1) by subtracting 4·67 times (8) and 8 times (9). Thus we would calculate

LlOO(6) = LlOO(1)-4'67L100(8)-8L100(9), ......... (10)

which gives LlOo (6) = -26·5 kcal per 0·5 mole N 2, a result which again is in satis­factory agreement with the calculations of this paper considering the different origins of the thermodynamic data.

The analysis of the preceding paragraph)hows that care must be taken in the definition of standard states where rapid chemical equilibria are involved. It also emphasizes the point, made by Gillespie, Maw, and Vernon (1953), that standard free energy changes have no biological significance apart from their relation to equilibrium constants.

368 N. S. BAYLISS

III. THE USE OF THE FROST DIAGRAM

So far we have been concerned exclusively with the overall glucose-nitrogen reaction. However, the biological oxidation of glucose proceeds through many inter­mediate steps, and so presumably does the reduction of nitrogen. Ammonia may not be the first stable intermediate in the fixation process, although the evidence that it is seems very strong. Glucose or one of its intermediate oxidation products may not be the reducing agent. The object of this section is to show how the thermodynamics of a number of alternative oxidation-reduction mechanisms can be visualized readily in terms of a type of diagram proposed by Frost (1951).

TABLE 2

FREE ENERGIES OF OXIDATION-REDUCTION COUPLES AT 25°C

Element and Oxidation-Reduction Couple LlGo!

Substance Oxidation State

Relative to Zero State (kcal)

H.O 0, ~2 H.O = to.+2H++2e- +56·69 H+ H, +1 tHo = H++e- 0·00 C.H5OH C, ~2 C.H.OH+H.O = (CH.0).*+4H++4e- +26·75 CO. C, +4 (CH.O)+H.O = CO.+4H++4e- ~ 1·4 Pyruvate- C, +2/3 (CH.O). = CHaCOCOO-+3H++2e- ~ 4·8 NH.+ N, ~3 NH.+ = tN.+4H++3e- +19·00 N.H5+ N, ~2 N.H5+ = N 2 +5H++4e- ~10·5

NHaOH+ N, ~1 NHaOH+ = tN.+2H++H.0+e- ~43·2

NO.- N, +3 tN.+2H.0 = NO.-+4H++3e- +105·1 NOa- N, +5 tN.+3H.0 = NOa-+6H++5e- +143·6

------------------- ---

* (CH.O) is used as an abbreviation for 1/6(C6H 1.06 ).

F

G'! at H = 7 kcal)

+

+ +

37·65 9·52

11·33 39·48 33·36 19·08 48·58 52·72 76·54 86·48

An oxidation-reduction reaction can always be split formally into two half reactions or couples, and for each half reaction one can determine a standard free energy L1Got in terms of the conventions of Latimer (1952), which include the assignment of zero for the L1Gol of H+ and of the formal electron (e-). Some couples and standard free energies of interest to the nitrogen problem are listed in Table 2 together with a few other well-known couples for purposes of comparison. The data are derived from the standard free energies of formation quoted in Table 1. The L1Go of any complete reaction can be obtained by adding algebraically the .1 GO! values of the half reactions, provided that each L1Got is multiplied if necessary by a factor to ensure that the formal electrons (e-) cancel in the addition. As pointed out previously, standard L1Go values should be corrected to actual biological conditions. For the half reactions in Table 2 the most important correction concerns H+, whose standard state is unit activity (molality), but which is at about pH = 7 under biological conditions. In the last column of Table 2 we have therefore calculated values of L1G\* for all couples for pH = 7, the other substances remaining in the standard states.

* Burton and Krebs (1953) use LlG' as a convenient notation for the LlG of a reaction in which all substances except H + are in their standard states.

THERMOCHEMISTRY OF BIOLOGICAL NITROGEN FIXATION 369

In Figure 1, the LlG't values are plotted as recommended by Frost (1951) against oxidation number, the zero oxidation state of each element (C in glucose, 0 in O2, N in N 2' H in H 2) being taken as the arbitrary reference point. In this figure there is no significance in the absolute positions or slopes of the lines representing the various couples; what is important is their relative slopes, from which one can assess rapidly the favourable or unfavourable nature of a chosen overall oxidation reaction. If, as in the inset, an oxidizing couple 0 and a reducing couple Rl have the same slope, then LlG' = 0 for the reaction and the equilibrium constant K = 1 (at pH = 7). If the slope of the reducing couple (R 2 ) is greater than that of the oxidizing couple 0, then LlG' for the reaction is positive, K<l, and the reaction could be described as "unfavourable". The reverse relation, as between R3 and 0, makes the reaction LlG' negative and K>I; the reaction could then be described as "favourable".

'00,-

I NOi 80

N02'

60

~ 40 U ~

'6 20r NH! "

/R2 /R, :...--+R3

0 /0 -20

-40 C02

-4 -3 -2 -1 o 2 3 4 5

OXIDATION NUMBER

Fig. I.-Standard free energies (with pH = 7 as the standard state for H+) of oxidation-reduction couples plotted against the oxidation num­

ber of the element concerned.

From Figure I we see that the glucose-C02 couple (as shown in Section II) is favourable with respect to the reduction ofN 2 to NH4 +, but unfavourable for reducing N 2 to hydrazine (N 2H5 +) and highly unfavourable if hydroxylamine (NH30H +) is the reduction product. Taking pyruvate (Py-) as an important inter­mediate in the oxidation of glucose, the Py--C02 couple is favourable with respect to N 2-NH4+, though somewhat less so than glucose-C0 2, The H 2-H+ couple (at pH = 7) is seen to be practically equal in reducing strength to the overall glucose­CO 2 couple, a fact that is of interest in view of suggestions that hydrogenase may be associated with the fixation process (Wilson and Burris 1947; Winfield 1955*). The glucose-C02 and glucose-ethanol couples produce the favourable fermentation reaction-rather more favourable than the oxidation of glucose by nitrogen. The 02-H20 couple is of course very favourable with respect to the oxidation of glucose, just favourable with respect to the oxidation ofN 2 to N03-, and slightly unfavourable with respect to the. oxidation of N 2 to N0 2 -. Once more it should be emphasized

* The author is indebted to Dr. Winfield for a preview of this paper in manuscript.

370 N. S. BAYLISS

that these remarks apply only to thermodynamic possibilities and leave untouched the question of mechanism. Furthermore, a positive standard JG' (as defined here) does not mean that the reaction cannot proceed at all, but only that its equilibrium constant is small «1).

IV. ACKNOWLEDGMENTS

I am grateful to Mr. C. A. Parker and Dr. M. E. Winfield for stimulating discussions.

V. REFERENCES

BURK, D. (1927).-J. Gen. PhY8iol. 10: 559. BURTON, K., and KREBS, H. A. (1953).-Biochem. J. 54: 94. FOGG, G. E. (1955).-"New Biology." No. 18. p. 60. (Penguin Books Ltd.: Middlesex.) FROST, A. A. (l95l).--J. Amer. Chem. Soc. 73: 2680. GILLESPIE, R. J., MAW, G. A., and VERNON, C. A. (1953).-Nature 171: 1147. KALCKAR, H. M. (1941).-Chem. Rev. 28: 139. LEWIS, G. N. (1923).-"Valence and the Structure of Atoms and Molecules." (Chern. Catalog.

Co.: New York.) LATIMER, W. M. (1952).-"Oxidation Potentials." (Prentice-Hall Inc.: New York.) LANDOLT-BoRNSTEIN (1936).-"Physikalisch-chemische Tabellen." 5th Ed. (Springer: Berlin.) PARKER, C. A. (1954).-Nature 173: 780. PETHICA, B. A., ROBERTS, E. R., and WINTER, E. R. S. (1954).-Biochim. BiophY8. Acta 14: 85. WILSON, P. W., and BURRIS, R. H. (1947).-Bact. Rev. 11: 4l. WINFIELD, M. E. (1955).-Rev. Pure Appl. Chem. 5: 217.