T H E REVERSIBILITY O F COUPLED REACTIOSS I S BIOLOGICAL SYSTEMS AND T H E S E C O S D L-AW O F T H E R l I O D Y S A S I I C S BY DEAN BURK
The problem of the general applicability of the second law of thermodynamics to biological systems has of late years received at tention of substantial character ( I , z , 3 , 4 , s, 6, ?, 8,9,I O , 11, 1 z , 1 3 , 13a). The two following different but hardly conflicting views summarize the present position. Lewis and Randall (8, p. 1 2 0 ) state, “The second law of thermodynamics is a principle which has never failed to satisfy the severest test of experiment.” Donnan ( 1 2 ) states, as a result of probability calculations, “It seems, therefore, that there exist biological systems of such minute dimensions that the laws of classical thermodynamics are no longer applicable to them.J’ I t is the purpose of the present paper to offer some rather exact support for the first of these statements, without, however, detracting in any way from the suggestiveness of the second. Both proof and disproof of the biological applicability of the second law, according to which no isothermal biological machine may spontaneously yield more free energy than it receives, have been difficult to establish experimentally in any particular instances. There is only one general class of biological reactions where, so far as experiment has been capable of deciding, it is certain that the second law is operating. This class may be designated as “the entjre life processes of a n organism.” I t has been universal experience that the thermodynamic work done by any organism has always been considerably less than the free energy consumed by that organism, Le., in net effect heat has always been given to, and not taken from, the environment in amount greater than that minimum required by the second law. KO perfectly reversible “whole life process” of a n organism has ever been observed; the chemical free energy of t,he oxidizable organic matter supplied heterotrophic organisms or the radiant energy or oxidizable inorganic matter supplied autotrophic organisms has always been gradually, continuously, and often completely dissipated into heat. The aforementioned class of biological reactions is, however, obviously extremely limited in number compared to the total number of biological reactions, when it is considered that the life process as a whole of any one organism is made up of an almost infinite number of more or less independent specific reactions. This opens the question of whether in some one or more of these specific reactions the law does not obtain but the infraction is not usually observed owing to the relatively overwhelming irreversible effects in the remaining specific reactions. The net reversibility of a life process as a whole is rarely greater than j o 7 c and is generally only 107~ or less, hence the free energy efficiency of any particular specific reaction under investigation has always been to a certain extent considerably obscured by the free energy
REVERSIBILITY A S D THE SECOND LAW O F THERMODYXAMICS
433
losses in other simultaneous independent life processes. I t has not been easy to exclude the frictional, and other irreversible, similarly irrelevant losses consequent upon life processes from the free energy balance sheets, so that only empirical “machine” efficiencies have been measurable, rather than what may be termed “second law” efficiencies.* The best review of the data concerning such machine efficiencies has been given by Baas-Becking and Parks ( 1 1 ) for the autotrophic processes whereby CO, is reduced by living forms by means of chemical energy supplied by the oxidation of sulfur, ammonia, carbon monoxide, hydrogen, etc. Machine free energy efficiencies give serviceable information regarding the fraction of useful work (Le., COz reduction) obtained in one process intricably and necessarily bound to many other useful chemical processes (i.e., growth, maintenance, etc.) which also consume free energy reversibly or irreversibly, as the case may be. Cnfortunately they give no indication as to the degree of irreversibility of the isolated process itself, and can not, therefore, be employed as a test of the second law with respect to the isolated process (as has upon occasion been assumed) but only with respect to all life processes as a whole. The necessity for experimental, as distinguished from a priorz, proof of the validity of the law has always been clearly recognized, particularly by its early formulators *The machine free energy efficiency is defined by the writer as the work done in any specific reaction occurring in a biological system divided by the free energy consumed by the system as a whole. The second law free energy efficiency is defined as the efficiency obtained upon correcting the machine free energy efficiency for the irrelevant losses involved in simultaneous extraneous metabolism (i. e., the work done in any specific reaction is divided by the free energy dissipated by that reaction only); specifically, it measures, in per cent, the real reversibility of an isolated reaction. Where reversibility is perfect and the second law operates, the efficiency attains one hundred per cent, but values higher than this may result in event that the second law does not obtain. When on the other hand, reversibility is not perfect (i. e., stoichiometric yields are not obtained, see nitrate reduction case), but where the second law operates, the efficiency is then less than one hundred per cent. I n other words, there is one condition where the efficiency may be less than one hundred per cent, one condition where greater. The writer was for some time uncertain as to the nomenclature most suited to distinguishing the two efficiencies. Both efficiencies, as will he more evident upon consideration of specific cases, are “second law efficiencies” in the sense that they deal with relations of phenomena which take place in accordance with, or in exception to, the second law. The second law efficiency has been designed as a teat of the law in cases where there might he considerable expectation as to the failure of its operation, and has been so named accordingly. In the case of the machine efficiency, on the other hand, more than one independent free energy consuming process is concerned, but only one is evaluated with respect to the free energy consumed in all processes and hence no test of the operation of the law in the one process is possible except in the unique event that the independent process so far disobeys the law as to more than cover the amounts of free energy disappearing in the other processes. But even here the quantitative extent of the disobeyal would be masked so long as the amounts thus disappearing in the other processes were unknown. The following contrasting terms have been considered as possible alternative nomenclature: ( I ) “machine efficiencv” and“corrected machine efficiency”; ( 2 ) “overall efficiency” and “efficiency of isolated step””;or, in the case of autotrophic processes, (3) “efficiency as a machine for storing COz” and “efficiency as a machine for reducing CO1”. Each of these distinguishing designations has its objections, however. I t is believed that the two terms finally chosen are fairly accurate descriptions of what they are intended to represent, especially when, as has been the case throughout this paper, an attempt bas been made t o point out that for the more fundamental applications of thermodynamics to life processes a great deal more is to be gained by isolating each process for consideration than by lumping together a number of genera!ly chemically independent but physically inseparable processes. The proposed nomenclature therefore receives justification from its usefulness as an arbitrary convention based upon the proposed principle of isolation. This isolation may amount to either a physical reality. or, more often, to merely a mathematical convenience.
DEAN BURX
43 4
(14,IS, 16, 16a*). In view of the historical interest attached to the various and almost solely theoretical discussions of the subject during the past hundred years, it has appeared desirable to present an experimental proof of applicability accurate to a n order of about one per cent. This is now possible in a fundamental case (autotrophic hydrogen oxidation) involving a highly endothermic biochemical energy transfer process, only one important, but entirely probable, assumption obtaining.
Autotrophic Hydrogen Oxidation We shall consider the non-photochemical reduction of carbon dioxide by the autotrophic hydrogen bacterium, B a c i l l u s pycnoticus. This organism derives its energy from the oxidation of hydrogen. Its metabolism has been exhaustively investigated by Ruhland ( I ; ) . Under the most favorable conditions only six and eight-tenths volumes of hydrogen are consumed for every volume of carbon dioxide finally changed to organic carbon. Calculations show that this ratio corresponds to a maximum machine free energy efficiency of (10j140X IOO~;),’( j 4 2 3 0 X 6.8)) or z8.4C,;, where roj140 and - j 4 2 3 0 are the respective molal free energies of reduction of carbon dioxide and oxidation of hydrogen under the conditions of Iiuhland’s experiments (see below). However, such a machine free energy efficiency does not take into consideration the carbon dioxide reduced and then lost subsequently through respiration processes. Therefore, since it is not based upon the total carbon dioxide reduced, it can not be employed as a test of the second law with respect to autotrophic reduction of carbon dioxide by hydrogen. * * The second law *Clauaius (I6a) says, “ I can not but think that when it is asserted that heat never passes from a colder to a warmer body (however complicated the process) without some permanent change occurring which may he regarded as an equivalent thereof, this theorem ought not to he treated as self-tvident.” **It will perhaps clarify matters further to illustrate the difference between the two efficiencies in the case of some purely non-biological system of energy transfers. Let us imagine a single motor arranged to perform simultaneously in an isothermal system a number of types of mechanical work, such as (a), moving a house, (b), sawing wood, (c), running a watch, etc., and that the amounts of work done in each case are respectively u, v, and w, and that the total mechanical work is u v w = hl. Let the motor be driven by free energy supplied from a galvanic cell, and A be the total amount of free chemical energy last as heat and work from the galvanic cell. We note that in the whole system there are five possible sources of irreversible production of heat, viz., m, n, 0,p, and q, in respectively (a), (b), (c), in the running of the motor (d), and in the o eration of the galvanic cell (e), the sum of the five heat losses being equal, let us say, to so that A = (M N). The machine free energy efficiencies in the cases of (a), (b), (e), (d), and (e) are then respecn,+ w,+?)!A, and (u m y n w o +p)/A; tively u/A, v/A, w/A, (u m v in each case the work done in any arbitranly Isolated process is divided by the work done and heat liberated in all five processes. The whole system, involving five processes (and therefore four energy transfers), is considered as a machine in which, in any one process, both the heat and the work used in the other processes before it and adjacent to it in the transfers are considered dissipated and unavailable with respect to the one process except the actual work done in that process. The corresponding second law free energy efficiencles areu/(A - v - n - w - o - p - q ) = u/(u m), v / ( S - u - m - w - o - p - q) = v/(v n), w/(A - v - n - u - m - p - q) = W / ( N o), (u m v n W+O)/ (A - q) = (M N - p - q)/(M N - q), and (u m 4-v n w o 4 p)/ (A) = (M N - q ) / ( M N); in each case the nrork done in any arbitrarily isolated process is divided by the work done and heat liberated only in that s a m e process, i. e., here the denominators are not all the same, but are all different. Comparing, in any one process, such as (a), the machine efficiency u/A with the second law efficiency u/(u m), it can he (Footnote continued on next page)
+ +
8,
+ + + + +
+ + +
+
+
,+.
+
+
+
+
+
+ + + + + + +
+
+
REVERSIBILITY .kXD THE S E C O S D LAW O F THERMODYSAMICS
43 5
efficiency may, and probably ordinarily should, be independent of the observed ratio of hydrogen to carbon dioxide used, variations in the ratio depending upon the relative amounts of respiration to organic carbon formed, i.e., upon the amount of energy expended to produce a given dry weight of organism. Fortunately, in addition to measuring the hydrogen and carbon dioxide changes, Ruhland determined the oxygen consumption. The oxygen consumption provides a measure of the metabolic energy. Owing to this opportune circumstance, it is possible to determine the “second law” ias distinguished from the “machine”) free energy efficiency and thereby test the law with respect to CO? reduction. Ruhland gives eleven experiments with complete and unambiguous data concerning hydrogen and oxygen consumed and organic carbon produced, S o s . z 1 3 , 4) I j , 19,2 2 , 2 8 , 29, 30, 3 I , 3 2 , as shown in Table I. Cultures of the organisms were grown at constant volume in approximately half liter, mercury sealed, flasks containing fifty cc. of mineral nutrient solution free from organic niattcr. -4mmonium salts were employed as a source of fixed nitrogen. After gas evacuation the culture flasks were filled with varying amounts of oxygen, hydrogen, carbon dioxide and nitrogen, and immersed in a constant temperature bath at 3 z ° C ’ . Gas analyses were made at the beginning and a t the end of the experiments. These usually lasted about ten days. Organic carbon was determinpd by wet combustion. K h e n the organisms are supplied suitable organic compounds of carbon no hydrogen is c0nsumed.l On this account and others‘ it may be concluded that the process of carbon dioxide reduction and hydrogen oxidation can not be dissociated and that no reaction between hydrogen and ordinary’ oxygen to form water takes place directly,3 and that a high order of revereihility **Footnote (coriiiiiued f r o m page 434) seen why the former is no test of the law as applied to the process (a), since A contains a great many terms in addition to, and obscuring, (u m ) ; only so far as (a) may disobey the law in such a manner that u > A would the disoheyal be detected, and then, only qualitativelr. IT-e m a r note also the arbitrarv nature of the principle of isolation, that, just as the system as a whble (described above) can be divided into various processes, so each of these processes might be divided into sub-processes of energy transfer more or less indefinitely; thus in (c), for example, we might isolate and determine the second law free energv efficiency of the transfer of the free energy of the motor to the stem of the watch, and t h i n from the stem to the mainspring., and then from the mainspring to the minute hand, and then from the minute hand t o the air currents set in motion, and so on. I n the case of hvdrogen bacteria, it may be considered t h a t the free energy available in hydrogen oxidatcon, corresponding, let us say, t o the free energy given t o the motor above by the galvanic cell, is transferred, in effect, into ( I ) storing reduced CO? (corresponding to the u m terms) and into ( 2 ) heat by reacting directly or indirectly with oxygen (corresponding to the p term), hut t o no other process (i. e., there are no corresponding v, n, w,or o terms); we shall be interested in distinguishing chiefly between the machine efficiency u!(u m p) and the second law efficiency u’(u m). Here the number of terms is small, and all terms are experimentally measurable with but little uncertainty; in other biological cases, as will be shown, a greater number of terms (corresponding t o v, n, m, 0,etc.) are often involved and generally are difficult if not impossible to measure experimentally, and it is for this reason that it is so difficult to prove or disprove the application of the second law to the overwhelming majority of biological processes. (Footnotes 1, 2 , and 3 on next page)
+
+
+
+ +
43 6
DEAN BURK
probably obtains. All the hydrogen consumed being used to reduce carbon dioxide, all the oxygen consumed is therefore used in respiration, Le., in metabolism, and oxygen consumption is a measure of metabolic energy. Oxygen consumption measures that fraction of the HS used for reducing the COZ which is later reoxidized back to COS in the metabolic processes of the -
(Footnotes f o r page 4%) Ruhland neither gives data nor mentions a single experiment showing hydrogen consumption to take place under heterotrophic conditions otherwise favorable for hydrogen consumption. However, he describes some dozen or more experiments wherein organisms were maintained heterotrophically in the presence of H Zin .5% and 1 7glucose ~ with and without C a C 0 3 or MgC03 without showing a trace of HZconsumption although growth took place. In the cases without CaCOa.or MgC03 the pH sank from 7.4 to 6.1 in 3 days and to 4.8 in 5 days. Ruhland was inclined to believe that this change in hydrogen ion concentration accounted for the lack of hydrogen consumption (in spite of growth occurring), yet his own data show that even in short time autotrophic experiments where the pH was initially low relatively large amounts of H Z were consumed (many times the maximum experimental error of about .5 cc.), as reported in Table 11. The ex eriments of Table I1 show that a certain amount of H, oxidation might have been expectefin the heterotrophic experiments without CaC03 or MgCO, (taking place at least during the time that the pH was not inhibitory but only becoming so, which required about four days), provided that any H Z could have been consumed a t all. The experiments with CaC03 and MgC03, where presumably the pH was maintained constant a t a favorable value, about 7 . 0 , would seem to show conclusively, however, that no H Z and COZ consumption takes place under truly heterotrophic conditions. A number of other experimental facts confirm this view. ( I ) The addition of sugar to an autotrophic culture actively and rapidly consuming Hz (which was easily accomplished in Ruhland’s apparatus without disturbing the gas mixture therein except momentarily) immediately stopped HZ consumption but the oxygen consumption proceeded a t practically the same rate (as shown by the behaviour of the manometer attached to the apparatus). (2) Mannite was observed to have the same effect as glucose. (3) In the system HZ CO Oz, no CO is reduced by Hz, indicating that COz must he reduced in order for H 2 to react. (4) Formate is not used as a source of carbon in the absence of HZor other organic matter, and yet HZmay be used in its presence (COS being present also), indicating that H 2 oxidation is resorted to only when a source of suficiently available reduced carbon is not a t hand. ( 5 ) Even H2-consumption in the presence of sugar (and CO,) under certain circumstances would not necessarily mean direct reaction with oxygen. In the case of normal inhibition of HI consumption there obviously must nevertheless be a certain low concentration of sugar which is not sufficient to completely inhibit H,-consumption, and it is conceivable that the normal completely inhibiting concentration (i. e., about ,570 a t most) may not, under certain circumstances, be entirely effective. From any or all of these numerous reaaons it appears to be reasonably safe to conclude that hydrogen never reacts to a measurable extent directly with ordinary oxygen. The designation “ordinary” oxygen is used to distinguish it from oxygen which might appear in such an equation as COz H 2 0 e CHZO 0 2 9 , where 0 2 , is not in equilibrium with the ordinary oxygen supplied in the reaction chamber but is activated in the sense that hydrogen may react with it. I t actually may be a gas, or a peroxide form, etc., hydrogen actin as an oxygen acce ter. 3 8ultures of washed ieavy cell suspensions of the organisms in a medium from which carbon dioxide and carbonate were excluded yielded a ratio of hydrogen to oxygen consumed of less than 2 , about 1.8, hut this can throw no light on the possibility of the direct water reaction taking place since a respiratory uotient of carbon dioxide to oxygen of less than I under these conditions could account for ?he result. Under such conditions of carbon d i o x i d e a n d therefore carbohydrate compound-starvation, a value of leas than I is quite possible since bacterial proteins, and possibly to a very small extent fats, would be attacked, no compounds of the nature of organic acids being resent, as Ruhland showed. derived from such respiraAnother explanation of the low H 2 :O2ratio might be that the tion could then have been reduced again by the hydrogen, but not entirely, because of a partially efficient CO,-absorbing alkali cup suspended in the reaction chamber which would have tended to remove some of the C o r . With a respiration coefficient of I , the observed ratio of H z : ~of, 1.8 would be accounted for if one eighth of the respired COZwas absorbed in the alkali, whereas if the respiration coefficient were less than I , as suggested, alkaliabsorption of even more than one eighth of the respired COQcould still leave the Hz:OZ ratio of 1.8 accounted for. Using the Warburg apparatus Ruhland showed in fact that in the absence of H I , CO,, and HCO,, hut in the presence of 0 2 , large amounts of COZwere respired, the organic material being derived from the bodies of the organism themselves; in one experiment lasting only 5 hours, 6.4 mg. of bacterial dry matter gave off 2 . 1 mg. of COS
+
+
+
+
80,
REVERSIBILITY AND THE SECOND LAW OF THERMODYNAMICS
437
organism. The remaining H Z is a measure of the H2 required to reduce the C O z to organic C found in the cells at the end of the experiment (Table I, Column 3). We see from Table I, Column 7 that this latter ratio, (Hz- z 0 2 ) / zC02,is (1169.22 - ( z X455.21) ) / ( z X I ~ ~ . O or Z ).966 , i .OIZ.* The probable error has been calculated by means of the usual formula P. E = (.6745 - d / Z d / n ) / d n - I on the ratios (Hz-202)/zC02 obtained from each of the eleven individual experiments, without, however, making a slight additive correction of several per cent for the fact that only eleven experiments are involved. This ratio is to be compared with the theoretical free energy efficiency ratio calculated from thermodynamic data, and then yields a measure of the second law efficiency and reversibility of the reaction. Fortunately the thermodynamic data for the involved coupled reactions in their standard states is of the highest order of accuracy, owing, no doubt, to the general importance of the reactions. The coupled reaction in the standard state zHz(g)
+ COz(g) = 1/6 CoH120d.s) + HzO (1)
(1)
A F " = 1184
(2)
may be divided into its two components and the actual states of the reacting substances indicated. zH2(.35 atm)
AF
+ 0 ~ ( . 0 6atm)
=
zHzO (1)
(3)
=
OF" - RT l n ( . 3 ~) ~R T h(.o6) - R T A S
=
(2
X -56560)
+
1250
+ 1630 + 1780 =
-108460
(4)
where A F " = ( z X -56560); R T A N is a factor correcting for the circumstance that the reaction takes place at constant volume (Le., without external work), N being the mol volume change, in this instance -3; and the stated pressures of the gases are the averages between the initial and final pressures in each of the eleven experiments.
+ HzO (1) = 1/6 CeHlzOo(Io+M)+ 02(.06 atm) AF = A F " - R T ln(.o6) + R T ln(.o6) + RT ln(Io+)"6 = 114300 + 1630 - 1630 - 1365 = 112935
COz(.06 atm)
(5)
(6)
where A F " = 114300, and the activity of glucose is considered to be that of about I/IOOO the average cell carbon in 50 cc. of medium (and the maximum solubility of glucose jM), Le., (I/IOOO) ( I O cc. 1'2) ( 1 / 2 2 4 0 0 ) ( I O O O / 50 cc.) ( I / S M) = ca. IO+ M per (CSHI2O6). *The same value might have been obtained in a more roundabout manner by dividing the total hydrogen consumption by twice the total carbon dioxide reduced as obtained from the observed reduction (as or anic carbon) plus that amount corresponding to the loss through oxygen consumption. T i e latter amount is equal to the oxygen consum tion multiplied by the factor of about 1.03 obtained from stoichiometric considerations. &her ratio arrangements of known quantities in the three equations ( I ) , (3), and (5) also yield the same result. See also footnote p. 439.
438
D E h S BURK
However, from the experimental data, the empirical formula of the reduced Co2 as in equation ( 5 ) is not (CsH&,) but (C(6Hl&,) where x is slightly less than unity, ( 1 1 6 9 . 2 - ( 2 X 4 j j . z 1 ) - 1 3 4 . 0 2 ) , ~ 1 3 4 . 0 ~or, .931, i.e., icc. H2 actually consumed, minus cc. H? appearing as H20 as a result of combining with the 02 lost from the gas phase of the system, minus cc. H 2 appearing as HZ0 as a result of combining with one half the 0 2 in CO? as in equation ( I ) ) (cc. H, theoretically combined with C as in glucose). This gives for the true free energy of reduction of CO,, ,931 X 11z93j = 1oj140. This assumption involving the method of deriving a conversion factor for obtaining the free energy of reduction of C6H.931 , 2 0 6 from CsH120sis the most uncertain element in the second law efficiency calculation.* What is indicated literally is that equation 5 should read c'02(.06 atm.) 1.031 z
+ .931 HzO(1)
O2(.o6atm ) ;
AF
= I
6
120
CJI.g31
+
IIO-~M)
(5')
= 1oj140
i.e., that (100X ir.o00--.931j ), or 6.9";, less H20 must be decomposed t o yield the necessary H ? to reduce the ('0,. I n accordance with Equation 4 the oxidation of z mols of H, can furnish 108460 cal. of free energy. In accordance with Equation j1 the reduction of onr mol of C O Brequires a slightly smaller amount. Hence we should expect the following relation between the numbers of rnols (or cc.) involved,
(Yo. of niols H, nccded, 2
X ( S o . of mols COP reduced)
IOjI.+O
=-_
108460
-
.9io
On the other hand, as ha> been hhown, in accordance with Table I C olumn the experiments gave ( S o of mol. of H uped 1 2
X ( S o . of niols C OSreduced)
= ,966
;I
j; . O I ?
Hence there wab apparently very slightly les- hydrogen o\idized than n a s necessary to produce the dvailable energy needed for the reduction of COS, the efficiency of the process being IO0
if j;
x
.9io i
96h
000
= 100.4 j; 1 . 2 7 ~ ~
=t 0 1 2
one assign n probable error (in distinction to any other type of error) of .ooo t o the thermodynamic data
V e bee thu? that i highly revcrqihle, arid
I)
if
the reduction of carbon dioxide by hydrogen is a the figures be taken literally, perfectly re\ersible
*Ruhland showed that no more than traces of fats or anaerobic carbohydrate decomposition products such as organic acids were detectable in culture of B . p y c r ~ o l i c u sgrowing under autotrophic conditions. Burk and Lineweaver (18) have shown that the energy change from ammonia and glucose to hacterial protein involves only a small fraction of the (,ombustion energy of the glucose, one to two per cent, ordinarily.
REYERSIBILITY A S D THE SECOSD LAW O F THERblODYKAMICS
439
process,* and ( 2 ) the second law is not transgressed,** since the free energy The exact agreement can efficiency is not significantly greater than 1007~. not, of course, be taken too literally, both on account of the experimental and probable errors involved in Ruhland's work and the thermodynamic calculations,+ and the important assumption made that the free energy of reduction *By perfect reversibility is here meant the perfect reversibility of the isolated process of stored carbon dioxide reduction, and that a22 of the free energy of hydrogen oxidation concerned has been stored in the free energy of the stored reduced COz, rather than being converted irreversibly into a certain amount of heat. A certain amount of heat is of course given off in the isolated process since A F of Equation (3) is considerablysmaller than A H . I t is important to note that the ratio (H2 - zO?)/zCO, gives no indication as to the possible extent of any direct reaction of hydrogen wlth ordinary oxygen; evidence on this point must be derived from other experimental sources (see footnote p. 436). The independence of this ratio from the amounts of hydrogen which might react directly with ordinary oxygen may be shown as follows: Let us assume that the major reactions which accompany the life processes of the bacteria are 1.93 Hf COz = 1/6(CsH.oixi>Oe) H20 (a) 1,6(CsH.~axizO6) 1.93,'Z 0 2 = Cog .93 H?O (b) z H ~ 02 = ~ H z 0 (c) Let x = no. cc. HPused in (a) y = no. cc. reduced COn used in (b) z = no. cc. H P used in (c) Then the total no. of cc. of Hz used is H 2 = x z
+
+
+
+
+
+
+2 The net no. of cc. of reduced C 0 2 is C 0 2 = _if_ - y The total number of cc. 0 , used is O 2
Combining we obtain (Hz - 2 0 2 ) - x
=
'93 y
1.93
+z
- 1.95s - z -
x - 1.93 y 2c02 ZiI.93X - Zy Zi1.93X - 2)' with the complete elimination of z , the number of cc. of H? reacting directly with ordinary 02. The value of the fraction (x - 1,93y)/(z x'1.93 - z y ) is, of course, by experiment ,966, from thermodynamic data ,970. **It might be thought that perhaps the value of the ratio (H? - 2 0 2 ) IzCO2 is approximately unity merely as a necessary consequence of the major reactions that accompany the life of the bacteria. This is true, however, only so far as the second law holds. I t is just this circumstance which permits the data to become a test of the law. Let us conceive of a case of transgression. If the organisms were able to make some such reaction as Equation 5 , which requires a large amount of free energy, proceed spontaneously by means of heat energy taken from the surroundings in temperature equilibrium with themselves, they could then either store up free energy potentially as cell material or use the energy by recombustion. I n the latter case no chemical change would be evident. In the former case, in addition to the chemical change involved in the cell material appearing, a certain amount of "ordinary" oxygen would have appeared which would not react with hydrogen. What the efficiency of 100% indicates is that the amount of COz actually reduced is not greater than that permitted by the free energy of oxidation of hydrogen after all extraneous but perfectly clearcut losses of hydrogen (in this instance by indirect reaction with oxygen) have been accounted for. In other words, no reaction such as CO? H2O = CHzO 0 2 has taken place spontaneously. Had it occurred the experimental ratio would have sunk below ,966. We must conclude from the fact that the observed second law efficiency is t o o ' ; either that ( I ) the second law is not transgressed, or that ( 2 ) another chemical reaction (in the case under discussion one involving hydrogen) occurs in such a manner as to be exactly compensating with respect to both sign and magnitude. The latter possibility, which would involve reduction by hydrogen of the inorganic salts or the production of highly hydrogenated gaseous organic compounds, was not observed to take place. tThe free energy required in concentrating the salts from the culture medium into the cells would be negligible, calculations indicating that probably .I?:, a t most, of the free energy of CO2-reduction would be involved, in such a direction, if at all, as to increase the efficiency from 100.4';. to 100.jc;, There are a number of other similar very minor factors involved such as changes in surface tension, pellicle formation, etc.
+
+
440
DEAN BURK
of carbon dioxide is exactly 105140cals. per mol, whereas a value even two or three per cent different is conceivable. I n any case, there can be no question but that the reaction is highly reversible and that an enormous difference obtains between the maximum machine efficiency and the second law effi7 ~ 100.47,. This difference, ciency, namely, a difference of between ~ 8 . 4and it may be stated again, is owing to the energy required to produce a given weight of dry matter (see Buchanan and Fulmer, I I ~ ) .
TABLE I Ratio of Gases consumed by Bacillus pycnoticus. (From Ruhland). Column Exp. No.
I
2
H?
0:
2
137.82
3 4 15 I9
111 . 4 8
52.75 44.72 39.06 4 1 . '5
89,48 87.92 91.21 103 . 2 0
22
28
Total Average Relative
39.39 10.58
5 6 7 4 HdCOz Hz/OZ OzC02 (H2-202)/2CO2
16.90
8.15
2.63
10.40
10.72
2.50
6.20
14.42
2.29
3.12 4.30 6.30
3 .oo
29.31
5.30 13.IO
17.20
2.14 2.24 2.62
13.7 7.68 3.01
,937 ,924 ,932
2.79 2.78 2.78 2.78 2.78
2.45
,969 1.098 ,932 ,962 ,947
2.56
3.40
7.88 6.84
40.71
4.31 10.89 17 . O I
94.93 225.34
34.12 81.38
'3.87 33.04
7.84 6.6j 6.85 6 .83
1:169.22
455.21 41.38 3.40
134.02 I 2 .I8
8.71
29.51 85.20 113 .13
29 30 31 32
40.71
3
coz*
106.29 8.71
* This refers to the
30.64
2.82
2.39 2.46 2.46
,956 1.060 ,916
.966*.012
I
C in the cells; Le., reduced CO:.
Indeed, a n independent roughly quantitative demonstration of the operation of the second law might be based upon the dry matter requirement of B. pycnoticus. I n the case of most bacteria and yeasts, etc., deriving their metabolic energy from respiration, three to six grams of glucose (or about 1 2 0 0 0 to 24000 cals. of free energy) are required under the most favorable conditions to produce one gram of dry matter. The figures in Table I Column 6 show that these limits quite neatly cover the requirements of B. pycnoticus, which, of course, likewise obtains its energy of growth directly from respiration quite comparably to the bacteria and yeasts. In other words, since the machine efficiency is 2 9 $ $ , 2 9 7 I cc. of reduced C0.r are required to produce 29 cc. of stored reduced carbon dioxide, or 2 9 7 1 grams of sugar are required to produce approximately 2 9 grams of hydrogen bacteria, or a ratio of 3.4, which agrees with the best values derived from Column 6, ivhere ( 0 2 :
+
+
REVERSIBILITY AXD THE SECOND LAW O F THERMODYNAMICS
CO,)
+
441
+
CO, = 2.4 I = 3.4, showing that the inefficiency of the bacteria considered as a machine for storing reduced COZ is entirely taken care of by its normal metabolic needs as judged by the needs of comparable organisms, and hence that the reversibility of the hydrogen-carbon dioxide reaction must be fairly high. Conforming to this view, the reason why the other known types of autotrophic bacteria all have much lower machine efficiencies ( I I , p. 104) is with little doubt owing to the fact that they also require much more energy to produce a given weight of dry matter. I t must be remembered in regard to the experimental data that the probable error of the mean, i . O I Z , is quite small in view of the facts that in the different experiments the H2 consumed varied 8-fold ( 2 2 5 to 29 cc.); 02 consumed 8-fold (81 to I O cc.); organic carbon produced 11-fold (33 to 3 cc.); initial pH from 7 . 5 to 6.5; duration 11-fold ( 3 4 to 3 days); ratio of H2 to O2 used 2.79 to 2 . 1 4 ; ratio of H, used to COZreduced 4-fold (29.1 to 6 . 6 ) ; and the rate of growth (final amount of organic matter produced per total time) 58-fold ( 5 . 2 to .09 cc. of organic C from CO, per day), as is shown for the most part by Table I. This shows that the wide variations in the ratio of total hydrogen to total carbon dioxide as given in Table I Column 4 are owing to variations in conditions of cell metabolism processes and not to variations in conditions of the efficiency or reversibility of the isolated coupled reaction of hydrogen oxidation-carbon dioxide reduction. Attention should be drawn to the fact that the theoretical ratio based upon standard rather than actual free energies (as given in Equations 4 and jl), uncorrectcd by the factor ,931, is .990, not greatly different from .970; also to the fact that were the experimental ratio calculated from the five best expkriments where the highest machine efficiencies were obtained (i.e., Kos. 28-32 where the ratio of H, to CO? was only about 7 to 8) it would be ,968 i , 0 2 0 , or little different from .966 , 0 1 2except for anincreased probable error. Finally, additional support for the second law is to be found in the opportune circumstance that the theoretical ratio is much smaller when based upon heats of reaction rather than upon free energies. The heats of reaction corresponding to Equations 3 and j are ( 2 X -68270) and 112300. Hence
*
z X
(KO.of mol9 H p needed) (No. of mols COZreduced)
-
112300 X ,931 = , 7 6 2 . 2 x 68270
I n other words, if the entropy considerations of the second law be neglected, then, on the basis of heats of reaction, the biological machine could use (.970--.762),!.970, or 2 2 % less cc. of Hz per cc. of COz consumed than calculated previously. We see, however, that the observed ratio is not significantly less than the minimum allowed by the second law, and hence the actuality of the latter’s operation is somewhat strikingly indicated. Here is a n interesting refutation of the Thomsen-Berthelot principle supplied by experimental observations on a living process rather than by a priori generalizations such as those of Guldberg and Waage, etc.
Summarizing,* we may say that it has been shown to within an accuracy of about 1~7; that ( I ) the second law of thermodynamics operates during the reduction of carbon dioxide by hydrogen, ** granting the one assumption regarding the exact free energy of reduction of carbon dioxide, and ( 2 ) the reversibility is one hundred per cent Ii,e.] :ill the consumed H?reacts with CO? and none of the free energy of the isolated reaction is irreversibly converted into heat), granting further that the writer has given sufficient proof that the oxygen consumption is totally accounted for by respiration. There seems to be no reason t o supporp that both the assumption in the first case and the proof in the second case do not hold rather exactly. I n any event it is hardly conceivable that they are quantitntively inexact to such an extent as to affect the order of accurncy to more than a few per cent, possibly ten per cent,’ rather than one per cent 3s stared. Icven so, an experimental accuracy of to within I O ( in the>determination of the operation of the second law is far better than obtain? in the cases of other known comparable coupled biological reactions involving large amounts of free energy. *It may be well now to briefly summarize the chief experimental data. ( I ) and ( z ) , the hydrogen and carbon dioxide consumptions are known, which permit calculation of the machine free energy efficiency. (3), the oxygen consumption is known, which permits calculations of the second law free energy efficiency by correcting for the irrelevant losses of simultaneous extraneous metabolism. (4),hTdrogen does not react with ordinary oxygen, which indicates high reversihility. ( j ) ,the difference between the machine and second law efficiency is confirmed as to order of magnitude by the probable free energy requirement of dry matter formation. I n addition (6), it is to be ohserved that the chemical free energy of the hydrogen oxidation can be transferred consequentially only into either chemical free energy in reduced CO? compounds, or into heat. **It is possibly an interesting observation that particularized proof of the second law for animate nature as given here is about a century less advanced temporally than particularized proof of the first law for inanimate nature. It is, of course, just one hundred years since Carnot first stated that the quantity of energy (motive power) in nature is invariable and i w l e s i i u c f i b l e , however much it may be changed from one form into another, and determined the mechanical equivalent of heat, some fifteen years before Sequin, Mayer and Joule. Although Rumford determined the mechanical equivalent of heat about 1798 to within twenty per cent of the correct value. he apparently did not correlate this with the idea of the zndestrurtibility of energy, whirh is the essence of the f m t law as announced bv Carnot, and a little later by Mayer, Grove, Helmholtz, Joule, Colding, and others. The equality, as distinguished from the proportionality (or some other function), between heat and work appears to have escaped conreption and particularized proof until the later vears of Carnot’s life. Kewton’s Querl- 30 “Are not gross Bodies and Light convertible &to one another?”can hardly be consid&ed an anticipation of either of the laws of Conservation of Energy or of Mass, since neither the query nor the discussion following it imply a quantitative (as distinguished from a qualitative) convertibility, which, again, is the essence of these laws, just as by the Atomic Theory is meant Dalton’s quantitative demonstration. Kewton (Opticks, 2nd Ed., 1718, p. 373) unconsciously portrays the conception of the destructibility of energy maintained for centuries previous to the last one in his statements, “there is not always the same quantity of Motion in the IVorld-Motion is alwavs upon the Decay-if two equal Bodies meet directly in D U C U O they will lose all their hlotcon (if elastic they will lose all but what they recover from their Elasticity) . . .”. While these clauses are possibly true, there is no implication that the lost motion is quantitatively converted into something else; it has been considered destroyed. For the same reason it can hardly be said that the Second Law is anticipated by the second very suggestive clause quoted, nor by the similar one (p. 3 7 j ) , “the variety of Motion in the Korld is always decreasing”. Unusefulness is very different from total destruction. For an excellent historical review of n-ork on the first and second laws between the years 1830-1880 see Planck “ D a s Princip der Erhaltung der Energie” (1921). tSee previous remarks concerning the energy requirement of growth. The growth energy must be derived from the reaction between oxygen and organic matter, i.e., from respiration, and it has been shown that in the case of H . pycwfictcs the oxygen consumption no more than covers the approximate growth energy requirement, Le., little or none is directly available for direct oxidation of hydrogen. See also footnote, page 436.
.
REVERSIBILITT A S D THE S E C O S D L.iW O F THERMODT?iA?,fICS
443
Autotrophic Methane Oxidation The methane-oxidizing organisms are very similar to the hydrogenoxidizing organisms, being facultatively heterotrophic and apparently yielding, under autotrophic conditions, fairly high machine free energy efficiencies as large as 307'( I I ) . If the available data ( I ja) be taken literally the second law is not obeyed, however. I n one experiment (in which the organisms were grown in a n inorganic medium containing ammonium salts as a source of nitrogen and in an atmosphere of one part, of methane to two parts of air), 2 2 j cc. of methane and 148.7 cc. of oxygen were consumed, producing 99 cc. of C O , and an unmeasured amount of organic carbon, according to the equation : z z j CH1 1 1 8 . j 0, = 99 CO? 126 CH?,O, x' HIO (IO)
+
+
+
where x, x', and y are unknown constants, (x+x') = 2 2 j , and the value 126 has been derived from ( 2 2 5 - 9 9 ' ) . S o w 99 cc. CO?correspond to 99 cc. 02, leaving only (118.j-99) or 1 9 . j cc. O?to have formed both the water and organic matter. If no water were formed, the organic matter would have the formula (with respect to C,H, 0, neglecting S, Y, P etc.) Ci?6H900099.i, or approximately CjH360i. If any water were formed the organic matter would still possess closely the same degree of reduction with respect to the valence of carbon. Such formulas, or degrees of reduction, while not experimentally disproven, are not only practically inconceivable, physiologically, but correspond t o a second law efficiency of about 1 7 0 2 , ~if it be assumed, as in the case of other bacteria, that the degree of reduction of carbon corresponds to glucose or thereabouts. Either the second law has really been transgressed or some unobserved reaction has taken place, probably a gaseous one involving H,,S?,C'O, etc. The production of hydrogen gas, or its incorrect estimation as methane could entirely account for the discrepancy, not to mention, of course, sheer mistakes in determining oxygen and carbon dioxide or the undetected appearance of hydrocarbons such as CzHs, etc. The rather meager data on methane bacteria are discussed here not so much with respect to proof or disproof of the second law, but to show how, granting the applicability 1 Even considering no water formed in Equation ( I O ) we have, after neglecting the respiration C 0 2formed which yielded only heat energy, 126 CHa 49.7 0 2 26.6 HzO = I26 CHiO 152.6 H ? (11) I n other words, some of the oxygen used to oxidize the methane to CH?O is not atmospheric gaseous oxygen b u t must be considered as derived from bound oxygen, as in water, at no expense of energy and therefore contrary to the second law. Without troubling to distinguish between standard and actual free energies, Equation ( I I ) may be split into two components I26 CHI 126 02 = 126 CHzO 126 H20; AF' (126 X -80700) (12) 49.7 0 2 152.6 HzO = 126 02 I j2.6 H I ; bF" = ( I j 2 . 6 X 113120) (13) yielding a second law free energy efficiency of (152.6X 113120)/(126X 8ojoo), or 170'1~. Theincreaseof 707~oover~oo';isowingtothefact that ((152.6X 113120)- (126 X 80700)) 126, or 56200 cal. of heat energy in the environment are employed contrary to the second law in changing a mol of C H I and H20 t o CHlO and H2.
+
+ +
+
+
+ +
7
444
DEAN BURK
of the latter, the second law efficiency calculations may be very useful in detecting impossible, improbable, or incomplete experimental biological data.’ I n the only other experiment performed by Sohngen for which data are given, 161 cc. CH? and 193 cc. 0 2 were consumed and 90.8 cc. of CO, were formed, yielding a second law efficiency very much less than one hundred per cent. Here, as may be shown, far too much oxygen is consumed, unless the organic material formed be assumed to correspond to an average degree of oxidation of practically HCOOH instead of C’H& ( m e n with no H, being produced), which circumstance, while no! inconceivable, is most improbable. The machine efficiencies for both experiments were respectively 33.8 and 2 5 . 8 5 x (11); yet, because they take no account of oxygen consumption, they give no inkling that [granting the second law) the data are incomplete as they stand, if not incorrect. This point is especially intereqting when i t is considered that the two experiments are unsatisfactory in opposite directions.
TABLE I1 Effect of Initial pH upon Hydrogen Consumption (From liuhland). Exp. No.
Length of Exp. (days)
I T P Consumed (CC.)
Initial pH
25
3
. ) , and failed to indicate that the efficiency they obtained \cas not to he compared with the efficiencies for autotrophic processes where, so far as the writer is aware, the efficiencies given in the literature have always been machine and not second law efficiencies. For example, the nitrate-ammonia second law efficiency of 3 2 5 is not to he compared with the machine efficiency of nitrification found by Meyerhof ( 2 0 ) to he 6 7 .
D E A S BURK
446
0
N
ow
0
t i 3
lo
-
N
rn-a 3
0
-
cc
G * i 3 ' N h N
h
" i
0
0
0
0
3 0 i c c ,
N
-,
.
h C
N
O
0
O
N
*
ccrn
N
v, N II-
",
*
PI
w
0
0
0 : -
0
t . I
.
ew
-
,
ts 0 . .
- - -
e-rn
4
w
-?IC'
- ? O h
m - 4 0
N
"
N
-
N
"lorn
o o w - , c
REVERSIBILITY AND THE SECOND LAW O F THERMODYPU‘AMICS
447
Column 2 ) by the third hour (when the maximum efficiencies are obtained) to about normal so that the correction is probably unnecessary (but see later discussion). I t is obvious that the second law is obeyed so far as ammonia production is concerned, since the second law efficiency is considerably less than 1ooc7;.* I t is practically impossible to derive any satisfactory proof of the second law in the case of nitrate reduction as a whole, as will now be shown. Too many assumptions would be involved, in the absence of experimental data. The chief difficulty lies in the fact that Warburg and Xegelein give no data to show that the ammonia produced under optimum conditions of efficiency corresponds stoichiometrically with the nitrate disappearing (nor did they analyze the cells for increase in organic nitrogen). Such determinations would be very difficult to carry out, of course, since it would mean measuring decreases of roughly IO-^ to IO-^ mols out of IO-l mols of nitrate per liter of * T h e writer would venture to suggest a means of predicting the probable maximum second law efficiencies to be expected in cases of isolated coupled reactions, making the assumption, of course, that the second law holds. In the case of nitrate reduction, we have, approximately, H+ HNOl H20 = KH+, 2 0 2 ; A F = 68000 XO. XCHvO = XCOI XHIO: A F = - X I I ~ O O O where with perfect reversibilitv X ;odd equal 68000/11~000,or .59. It will be observed, however, that experimentally ‘the mechanism proceeds corresponding to X equals at least 2, the least number of oxygen molecules in the equation requiring energy. Similarly, in the case of hydrogen oxidation we have approximately, COn .93 HZO = 1/6CHi.mO I.93/2 02; A F = 105140 A F = - X 108460 X Oz 2X Hz = ZXHzO; where the perfect reversibility X would equal 1og1 0/108460 = .97 and again it will be observed that experimentally X actually equals a t feast .97, the least number of oxygen molecules in the equation requiring energy. I n other words, in both cases, the maximum amount of free energy-yielding reaction taking place is possibly determined not only by the amount of free energy demanded in the free energy-requiring process in accordance with the second law, hut also by the stoichiometry of the latter. Expressed in more strictly chemical terms, all the incidental compound produced in the free energy-requiring reaction (in the above particular cases oxygen) must, by virtue of the mechanism chosen by the organism, be consumed in the free energyyielding reaction. This “biochemical reversibility principle” stands in much the same relation to the second law as the second law does to the first, namely, as conditioning the convertibility of energy from one form into another, and states that of the free energy available in the free energy-yielding reaction of a coupled reaction taking place in a biological system only a fraction of this is available under biological conditions, the loss of availability being determined by stoichiometric considerations. The greater the free energy of the free energyrequiring reaction in proportion to the free energy of the properly stoichiometric free energy-yielding reaction, the greater will be the maximum reversibility and second law efficiency, up to 1005. An analogous. but not in all respects similar principle is employed by Warburg in explaining the varying efficiencies of different wave lengths of visible light in the photosynthetic reduction of carbon dioxide, where Noh” grows proportionally to v, while U, the energy required remains constant, 60 that the efficiency must vary with wave length. \%Me the “biochemical reversibility principle” has been proposed upon the experimental basis of only two cases, it is to be observed that the two cases present R-idely different reversibilities (namely 32 and 100 per cent), which is in favor of the principle. It is not anticipated that invariable applicability will necessarily obtain. The word principle has been used in the sense of being a generalization of experience applying in a number of cases, in distinction t o the word law, which is a relation of phenomena invariable under given conditions. Without going into detail it may be stated that according to this principle the reversibilities of isolated autotrophic reductions of carbon dioxide should approximate perfection, whereas the reversibilities of heterotrophic consumptions of organic carbon compounds should usually be fairly low Le., o - 5oyc, and, so far as is known, this is the case.
++
+ +
++
+
+
448
DEAN BURX
solution. Without either this information or calorimetric measurements (see later) it is impossible to properly account for the (100 - 3 2 % ) , or 68’%, efficiency loss, Le., to know whether the loss can be explained upon the basis of other reduction products (involving storage of chemical free energy) or heat evolution; we know the second law efficiency of ammonia production but not of nitrate reduction as a whole (Le., reduction to ammonia and other nitrogenous compounds). I t was shown that normally no appreciable amount of ammonia is to be found inside the cells, and that KO, Nz, and KO2 were not produced. The possibility of numerous other likely intermediate nitrogen compounds was, however, not experimentally excluded (i,e., by chemical analysis) and there can be no question that during the first hour or two of ammonia production part of the reduction products do not appear as ammonia but are built into the cell tissue (Table 111, Protokolle 1 2 , 1 3 , 14), since it was shown that cells which had been previously starved for nitrate and then placed in nitrate solution at pH z gave high respiratory quotients of 1 . 7 etc., without, however, producing ammonia (19, Protokolle 16, I 7 ) . The total extra cellular ammonia nitrogen content never rose much above 5 X 1 o - W whereas the concentration of organic cell nitrogen in algal cultures may attain values one thousand times as great. Judging from this evidently small percentage of nitrogen appearing as ammonia, it is possible therefore that even under conditions of maximum observed efficiency there are nitrate-reduction products which do not appear as ammonia but disappear in assimilation, the observed concentrations of ammonia merely representing balances between ammonia production and assimilation. Now the aforementioned decrease in rate of oxygen consumption to normal by three hours might have occurred because the organisms were able to make some such reaction as Equation 7 take place spontaneously without any corresponding expenditure of energy upon their part; the oxygen given out by such a reaction would tend to lower the observed rate of oxygen consumption (the decrease might be owing, of course, to any number of factors, such as decreasing concentration of respirable carbohydrate, lowered vitality of the cells, etc.). I t should be pointed out also that the oxygen consumption continues to decrease to values much below normal (19, Table 19). On account of the unknown reason for both the initial increase and the subsequent marked decrease in rate of oxygen consumption, it is therefore unfortunately true that until it can be shown that the nitrate disappearing corresponds stoichiometrically either with the ammonia appearing or other reduction products of nitrate the possibility exists that the second law does not operate in nitrate reduction a> a whole. Still another possible difficulty arises from the fact that no efficiency data are available for periods of time later than the third hour, a t which period the efficiency is increasing a t a marked rate; indeed not only the first differential but also the second differential of efficiency with respect to time is increasing (Table 111, Protokolle 1 3 and 14, Column 1 2 ) . It is true that the decrease in oxygen consumption after three hours may explain how the
RETERSIBILITY AND THE SECOND LAW O F THERMODYNAMICS
449
efficiency might increase aft,er three hours, as it promises to do; Le., after three hours the reaction may not take place according to H N 0 3 + H 2 0 + z 16(C8H1206) =NH4++zCO?- 1 6 2 0 0 0 cal. (heat,seebelowj (8) Some of the oxygen may then appear as gas, causing the observed decrease in rate of oxygen consumption, rather than reacting with carbon in carbohydrate. This explanation involves a sudden change of mechanism a t the point where a 32% second law efficiency is attained and is therefore improbable. Varburg and Xegelein offer an explanation for the increase of oxygen consumption when the cells are placed in the nitrate mixture at pH 2 , but they take no note of t,he difficulties offered by the subsequent decrease, nor the difficulties presented by the promised increased efficiency after the third hour. The possibilities that either (1) some of the extracellular ammonia after the third hour is derived from breakdown of cell organic nitrogen (Le., ammonification) or ( 2 ) the carbon oxidized corresponds to a reduction stage considerably different from that in carbohydrate, do not seem very probable, but must' also be taken into considerat'ion. It is to be observed that the uncertainty in regard to proof of the second law consequent upon not knowing the stoichiometric relations in the case of nitrate reduction does not obtain correspondingly in the case of carbon dioxide reduction by hydrogen. Here, even if it had been true t,hat the reversibility was not IOO%, (Le., that some hydrogen reacted directly rather than indirectly with oxygen to form water), the proof of the second law would have been in no way affected since all the reactants of the then irreversible reaction, hydrogen and oxygen, would have nevertheless been accounted for, having disappeared in the ratio 2 :I as in water (see also footnote p. 439). h fair approximation to proof of the applicability of the second law might be obtained from calorimetric measurements, Le., it might' be possible to show that the difference between 3 ~ and 7 ~1007~ could be accounted for entirely as heat, providing ammonia was the only nitrogenous reduction product of nitrate. According to Equation (a), all of the oxygen given out according to Equation ( 7 ) has reacted according to Equation (5) (taking place in the reverse direction however), and that of the approximately 230000 cal. available per 2 0 2 only 68000 cal. have been converted into chemical work, the rest, about 1 6 2 0 0 0 cal., appearing as heat. The measurement of this 162000 cal. has not been carried out calorimetrically, as yet however.' I Meyerhof (20) performed a somewhat similar ex eriment in the case of autotrophic nitrification for the reaction NO2 b 0 2 = NO8. Tge machine e5ciency as determined chemically was about 6y0,and Meyerhof found as the average of a series of calorimetric experiments that the heat given off per mol of nitrate formed actually corresponded to about (100-6) or 94% of that given by the heat of reaction. Owing to the small efficiency yield, and the accuracy of calorimetric determinations in general, and, indeed, a number of other experimental uncertainties, this proof of the second law can not be considered ,rery accurate, altho it is possibly as accurate as for any comparable coupled reaction case apart from autotrophic hydrogen oxidation. The calorimetric measurements in the nitrification case correspond to t8heoxygen consumption measurements in the hydrogen oxidation case; they determine directly or indirectly the metabolic ener y The nitrification case really presents a much better demonstration of the fist law t%an the second, since all but approximately 5 % of the chemical energy was converted into, and obtained as, heat, as required. Here it is not determining a quantity as a small difference hetween two large quantities, but rather comparing two large and nearly equal quantitiab.
+
450
DEAK BURK
Summarizing, me see that in the nitrate-ammonia reaction it is possible to calculate both the machine and second law free energy efficiencies (and therefore the reversibility and the applicability of the second law) as in the case of autotrophic hydrogen oxidation, but, owing to lack of certain data (Le., data accounting for the difference between the maximum observed ) , is as yet imsecond law free energy efficiency and an efficiency of I O O ~ ~ it possible to test the applicability of the second law of thermodynamics t o nitrate reduction as a whole. It has been found again that a large difference (about 3-fold) obtains between the two types of efficiencies. I n other cases to be mentioned below such large differences will not alxays exist. The Reversibility of Other Coupled Reactions a. Partially Reversible Reactions The non-reconversion of the potential energy of tension in isometric muscular contraction presents a case where the second law free energy is zero; where, so far as is known (see 1 3 , p. 167) the process under anaerobic conditions is totally irreversible, all of the tension energy being converted into heat, rather than some being used to condense lactic acid back into a hexose, or into glycogen. The anaerobic reconversion of lactic acid into glycogen is partially reversible, generally twice as much energy being consumed as required under ideal conditions, Le., the second law efficiency is only about jo?:. That is t o say, when lactate is added to muscle in Ringer’s solution, four to six molecules of lactate are reconverted per molecule of lactate burned to carbon dioxide, whereas according to the free energies involved about ten reconverted molecules are possible under perfectly reversible conditions. The maximum second law free energy efficiency of aerobic muscular contraction (mechanical work done)/ (chemical free energy consumed) is only about I j to 2 5 % (13), and according to the latest data of Hartree and Hill ( z j) the second law efficiency of anaerobic human arm muscle contraction reaches a maximum of about only fifty per cent, in the case of frog sartorius muscle contraction, thirty per cent. In the cases of the partially reversible reactions mentioned in this section, the machine efficiencies are practically as large as the second law efficiencies owing to the fact that the resting metabolism of the muscle is very small compared to the coupled reactions it carries out. This will also be true of other coupled reactions carried out by multicellular organisms, because the ordinary metabolic chemical energy liberated is much more organized and disciplined to subserve function. Brown ( 2 4 ) has shown, for example, that the “maintenance” metabolism of man is some IOO times as small as that of yeast per units of weight and time. If the latest conclusion of Hartree and Hill ( 2 6 ) be accepted that the isometric relaxation heat remesents the maximum mechanical work capable
REVERSIBILITY AND THE SECOND LAW O F THERMODYSAMICS
4:
I
of being performed by a twitched frog sartorius muscle under anaerobic conditions, then the second law efficiency (mechanical work)/(mechanical work relaxation heat when work is done) = (mechanical work),’(isometric relaxation heat) may apparently reach the high value of 71% ( 2 6 , Table 11). Even under tetanic conditions (i.e., where the stimulus is continued for some time, . 2 to .1 of a second), the corresponding second law efficiency attains values approximating 505( 2 6 , Table IV, (d)/(d+f) ). The main thermodynamic work which microorganisms perform is that of growth.* Brown ( 2 4 ) has shown that when yeast is maintained a t a concentration sufficient to prevent reproduction, the heat given off per gram of maltose fermented is 1 2j cal., whereas when growth is allowed to take place only 8.jC; less heat is given off, 111.4 cal. It is likely that relatively little of this 114.1 cal. is necessary for true maintenance energy, since similar yeast juice containing no intact cells would give about the same value. Brown’s findings confirm the view that the breakdown of carbohydrates, etc., by unicellular microorganisms is often if not usually conditioned chiefly by the concentration and activity of the cell enzymes necessary therefor and the concentration of carbohydrate, independently of whether the organisms are able to take advantage of the energy liberated. Wasted heat, as illustrated in the work of Brown, is chiefly the result of uncontrolled enzymes acting on an appropriate substrate, the organisms possessing no mechanism, as do multicellular organisms, for closely regulating the amount, of substrate in contact with cell enzymes, and correlating most of the energy liberated with some vital function requiring free energy. The free energy efficiency of growth obtained by Brown (about 8.jyc),it may be mentioned, is somewhat less than maximum values usually reported for yeasts, fungi, bacteria, etc., where, as has already been pointed out in discussing the amount of sugar required to produce a given weight of dry matter, the maximum efficiencies vary from about’ I j to 3 0 $ .
+
In all these partially reversible reactions just discussed the same kind of difficulties in the way of proving the second law with regard to the processes involving the energy not appearing as work in the primary process obtains as in the case of nitrate reduction-too many assumptions become involved in the absence of all the necessary experimental data, which, it may be added, is often difficult or impossible to obtain. There is generally at least one unknown too many. We see how every much more difficult it is to prove the * Angerer ( 2 2 ) and Ludwig (23) have shown that an inconsequential fraction of the metabolic energy of motile microorganisms is accounted for by motility, in the neighborhood of 0.1 per cent. Considering the relative amounts of energy involved in motility and Brownian movement by a single microorganism one might doubt that, although some organisms may be able to disobey the second law by in some manner converting the heat energy of Brownian movement into work, the amount of work so accomplished and gained would be significantly appreciable.
452
D E A S BURK
second law in heterotrophic rather than in the less complicated autotrophic coupled reactions.* b. Highly Reversible Reactions. There are a number of reactions occurring in biological systems which are highly reversible : chemical equilibria such as reactions between ( I ) haemoglobin and oxygen, ( 2 ) haemoglobin and methaemoglobin, (3) the respiration enzyme and oxygen, (4) the respiration enzyme and carbon monoxide, (j) hermidin and cyanohermidin, (6) reduced and oxidized echinochrome, ( 7:’ ordinary and active glucose ( 2 I ) , (8) hydrogen ion buffer systems, ( g j nitrogen gas and an initially fixed form (IS), and ( I O ) succinic acid and methylene blue to give fumaric acid and leuco-methylene blue. Most of these reactions take place under approximately equilibrium conditions** and their free energy changes are consequently practically zero. I t is also true that a number (i.e., ( I ) , ( z ) , etc.) are not coupled reactions in the sense used in this paper, since they do not involve a free energy storing process but only a heat change; in the case of hydrogen oxidation, for example, if hydrogen reacts with carbon dioxide, free energy is stored as carbohydrate (etc.) produced, and the reaction is coupled, whereas if hydrogen reacts directly with oxygen and the energy is given off as heat, no free energy is stored, and the reaction is not considered as coupled. Chemical free energy is considered as “stored” when the chemical substance or substances formed are still out of practical equilibrium with the environment :in the bacterial case, oxygen, Le., carbohydrate would be out of equilibrium with oxygen, water, however, practically in equilibrium with oxygen).
* If one were to set out to look for cases where the second law might not be obeyed in biological systems the most likely field, a priori, would lie in reactions involving small amounts of free energy, i.e., carbohydrate and protein hydrolytic equilibria, etc. A small shift in position of the equilibrium point would require little energy but could result in a large chemical change relatively easily detected. The di5culty of excluding extraneous free energy reactions would be greater, of course. Donnan’s statement quoted previously was made with reference to systems of dimensions of the order of 1 0 - l ~ccm., or less; so that in order to consider a series of such systems amounting to macroscopic dimensions, it requires one additional logical step to suppose that the infra-microscopic systems might all fluctuate together simultaneously in such a manner that the second law would no longer be applicable to the macroscopic system as a whole. This logical step would, indeed, be the real ieaue awaiting test, since, beyond question, if the size of any one system is made small enough the second law as classically stated by Clausius could not apply. The utilisation of fluctuations in the organized, non-random, and extensive manner indicated is to be claeaed as true perpetual motion of the second kind, whereas the occasional fixation of random fluctuations of the type indicated by Donnan would not necessarily involve such an implication, since compensation would in the long run probably take place. ** Although one can conclude from the fact that when equilibrium conditions exist the reversibility is very high or practically perfect, it doas not follow, or course, that the second law is necessarily operating, since the biological machine (Le., the organisms) may have shifted the equilibrium point without corresponding expenditure of energy upon its part. So far aa the writer knowe, there are no case8 as yet where it has been shown that the equilibrium point is the same both in and out of the biological system, a t least with any desirable degree of accuracy.
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The second law efficiency of the photosynthetic process in plants whereby C o nis reduced to sugar may attain fairly high values. Thus in the simplest case as studied by Warburg and his co-workers, where all the incident light energy is absorbed by the photosynthesizing machine (Chlorella) a maximum efficiency of about 6 0 7 is obtainable. An accounting for the remaining unutilized 40% of the energy as heat (or possibly, in part, as other chemical energy) has not been made and it is conceivable (so far as present experiments may decide), although not probable, that the second law is not observed in some other reaction occurring simultaneously with sugar formation and that heat is being absorbed from the environment in addition to the radiation absorbed and that required by the second law. If the photosynthesizing process be considered from the standpoint of mechanism t o form glucose and hydrogen peroxide, first, and then later glucose and oxygen, the second law efficiency of this first reaction considered as an isolated step, may approximate 1007.The final physiologically necessary change of hydrogen peroxide to oxygen and water would account for the subsequent loss of efficiency in the overall process. Thus we see that in biochemical reactions there is a continuous range of reversibility between practically roo and o per cents. In no case is perpetual motion of the second kind indicated.
Discussion It has been shown that the numerous existing published efficiency data on certain autotrophic and other coupled processes often fail both ( I ) to test the applicability of the second law of thermodynamics to such processes, except in the crudest manner, and ( 2 ) to measure the reversibility of each of the processes per se apart from accompanying but extraneous, unrelated, normal metabolic processes of the microorganisms. I t might be argued, in connection with the latter objection, that since these extraneous processes have always accompanied the coupled reactions, calculations correcting the machine efficiencies ii.e., the second law efficiencies as defined by the writer) are without point. However, this circumstance may not be true in the future. Indeed, attempts are being made to isolate important coupled reactions, so that if success should attend these efforts, then the extracellular efficiency will be the second law efficiency, and the machine efficiency will then, in turn, be without point. The problem is very real, and the determination of the second law rather than the machine efficiencies very necessary, therefore, regarding what would be the efficiency of a coupled process if it were isolated from the cells and carried on independently, and accordingly the title of this paper has been made to read “coupled reactions in biological systems” rather than “coupled biological reactions.” I n the case of nitrogen fixation, for example, the machine efficiency is only about one per cent, whereas the second law
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efficiency is fifty to one hundred times this value (IS), and there is good reason to believe that the process of fixation per se might be isolated and carried on independently of the organisms. No implication is intended, of course, that isolated coupled reactions will necessarily give exactly the same second law efficiency as when unisolated.
Summary I t has been the task of this paper to indicate the extent to which the applicability of the second law of thermodynamics to life processes has so far received direct experimental support. It is pointed out that, in general, critical data do not obtain. I.
2. The applicability of the law to autotrophic reduction of carbon dioxide by hydrogen has been shown to obtain very accurately to within an order of about one per cent, in the case of Bacillus pycnoticus Ruhland.
3 . The reversibility of autotrophic reduction of carbon dioxide by hydro~~ the extraneous energy consumed gen is practically perfect, I O O i. 1 . 2 7 when in the metabolic processes of the organisms is corrected for.
4. The reversibilities of the more important known coupled biological reactions have been described and summarized. Few, if any, attain 100% as in the carbon dioxide-hydrogen case. 5 . It is shown that with respect to the possible thermodynamic free energy efficiencies of coupled reactions occurring in biological systems two fundamentally different types obtain: those in which the work done in any given reaction is compared to the total free energy dissipated by that reaction, and those in which the work done in any given reaction is compared to the total free energy dissipated by the organisms in carrying out all their life processes. The former has been termed the second law free energy efficiency and the latter the machine free energy efficiency. 6 . The hydrogen bacteria cpnstitute one of the few cases, if not the only case, where, with respect to the entire life processes of an organism, it has been possible experimentally to account for all the free energy consumed, with an order of one per cent, i.e., where it has been possible to draw a complete free energy balance sheet between the total free energy shown to have been utilized or dissipated by the organism and that known to have been consumed by the organism.
For reading the manuscript and offering criticism, the writer is indebted to Professor R. C. Tolman, Professor L. Michaelis, Professor E. I. Fulmer, Dr. F. G. Cottrell, Mr. Hans Lineweaver, Dr. C. A. Ludwig, Dr. 0. R. JVulf, Dr. K.Wiebe, Dr. R . Milner, and Dr. F. E. Allison. Bureaii of Chemistry and soils, IVashinglo?a, D. C.,
June 28, 1980.
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References ’Thornson: Proc. Roy. Soc. Edin., March 1 7 (1851). Grove: “ T h e Correlation and Consemation of Forces,” by E. L. Youmans: 82 (186j). 3 Wand: Karl’s Repertorium der Exp. Physik, 4, 390-400 (1868). Helmholtz: Sitxungsber. Akad. Wiss. Berlin, 1882, 34. Parker: Proc. Phil. SOC.Camb., 1892, Oct., 6. Parker: “Thermodynamics”, 123 (1894). ’ A . V. Hill: J. Physiol., 46, 469 (1913); Nature, 113, 8j9, 1924. a Lewis and Randall: “Thermodynamics”, Chap. I O and I I (1923). Guye: “Physico-Chemical Evolution” (1925). l o Lewis: “ T h e Anatomy of Science”, Chap. 6. Baas-Becking and Parks: Physiol. Rev., 7, 8 j (1927). l l a Buchanan and Fulmer: “ T h e Physiology and Biochemistry of Bficteria”, 3, 185, lines 1-4 (1930). Donnan: J. Gen. Physiol., 8, 688 (1927). Burk: Proc. Roy. Soc., 104 B, I 53 (1929). 1 3 8 Watson: Science 72, 220 (1930). l4 Thomson: Trans. Roy. SOC.Edin., 16, 541 (1849). l5 Helmholtz: “Eeber die FVechseln
