PHASE CHANGES I N ENZYME SYSTEMS: AZOTASE ACTIVITY I N RELATION TO pH DEAN BURK
AND
HANS LINEWEAVER
Fertilizer and Fixed Nitrogen Investigations U n i t , Bureau of Chemistry and Soils, U.S. Department of Agriculture, Washington, D . C. Received August 22, 1033
The phase rule has seldom been employed in interpreting enzyme behavior. It represents, nevertheless, a relatively simple method of analysis that is often highly determinate. I t makes possible distinction between change in number or kind of phase and mere change in phase composition. This paper will present a phase rule analysis of the abrupt activity-pH function of the nitrogen-fixing enzyme system azotase.' General applications t o enzyme chemistry and kinetics, whether homogeneous (23,27,38) or heterogeneous (2, 7, 12, 13, 15, 16, 17, 18, 25, 34, 35, 37), will be indicated. Azotase will represent a fundamental type case. PHASE RULE ANALYSIS
OF USUAL ENZYME
ACTIVITY-pHFUNCTION
The influence of pH on enzyme reactions has been variously explained on some one of the bases that either the enzyme or the substrate is a weak acid or base and that activity is correlated with the concentration of undissociated molecules or posjtive or negative dissociated molecules, as the case may be (1, 11, 22, 26). The experimental activity-pH curves are 'Azotobacter possesses a highly specific enzyme system, azotase, capable of catalyzing the fixation of nitrogen gas a t ordinary temperatures and pressures. I t s properties are constant and characteristic, and have been described in detail elsewhere (6). In brief, no activity occurs below a critical concentration of hydroxyl ion of 10-8.03 iM (pH 5.97). Ca or Sr and $10 or V are required for its operation, being replaceable by no other elements. The Michaelis dissociation constant, Km,,, or nitrogen pressure a t half-maximum velocity, is 0.215 atmosphere. KmNland the pH limit a t 5.97 j=0.02 are not affected by any known factor, including concentration of calcium or strontium. Specific inhibition by hydrogen ion and oxalate is reversible and non-competitive. Finally, unpublished data indicate that the O/R potential (as imposed upon Azotobacter cells by various pressures of oxygen gas) must ordinarily be slightly but definitely lower for maximum azotase activity as compared to nitrate reduction, growth, or any other normal activity of Azotobacter. Nitrogen gas is ordinarily fixed by Azotobacter in intracellular form only, the amount being directly proportional to the amount of growth. The velocity of fixation becomes solely limited by the velocity of growth (generation time for cell division, or increase in cell mass) only when pH, nitrogen pressure, calcium concentration and O/R potential are all adjusted to values specifically optimal for azotase activity. 35
36
DEAN BURK AND HANS LINEWEAVER
very similar to dissociation or dissociation-residue curves. Further emphasis is lent by the fact that enzyme systems usually contain proteinlike components, and activity-pH curves likewise resemble the continuous pH functions of the physical properties of aqueous amino acids, polypeptides or proteins, via., solubility, viscosity, swelling, osmotic pressure, surface tension, alcohol number. The phases, or physically homogeneous regions, involved in enzyme activity are characterized at equilibrium by variability in chemical composition and constancy in number, without regard to quantity or form. The essential element in the concept of phase is characterization of the properties of each phase by a definite number of degrees of freedom, or parameters (14, 19, 20). At constant temperature and pressure the equilibrium concentrations and ratios of the individual components, dissociated and undissociated, of any one phase, alter continuously over the entire pH range. The number of components and phases remains constant. The simplest type of base-acid equilibrium, occurring in dilute aqueous solution within a single phase a t constant temperature and pressure, and first order with respect to all individual components, may be represented, in nomenclature resembling that of Bronsted and Guggenheim (4), by the equation B e A
+ OH-
(1)
where B and A are conjugate weak base and acid, differing in charge algebraically by one. Equation 1 defines a two-component, one-phase system that is trivariant, 2 = 2 - 1 2 = 3 degrees of since by the phase rule F = C - P freedom. The mass law dissociation constant contains all individual components:
+
KB = (A)(OH-)/(B)
+
(2)
Curve I, figure 1, and curve I, figure 2, illustrate graphically the very common function represented by equation 1. Percentage dissociation is plotted against pH and (OH-) respectively, and a value of (OH-) existing when the ratio (A)/(B) is unity is arbitrarily chosen as M . This value represents attainment of 50 per cent maximum activity in the azotase function. Curves 11, 111, and IV, figure 1, and curves 11, 111, and IV, figure 2, present the functions obtained when hydroxyl ion is involved in equation 1 to some number (equation 2, some power) moderately but not greatly different from one, viz., 1/2, 2, and 4. Plots against (OH-) as well as pH are given because although the latter are more common they are somewhat arbitrary and, in connection with equation 1, less direct (36). As approximations to these theoretical functions, curves V and VI, figures 1 and 2, show typical, reversible, enzyme activity-pH functions, viz.,
PHASE CHANGES I N ENZYME SYSTEMS
37
respiration and growth of Azotobacter (6), plotted upon a basis of percentage of maximum activity. The differences are of a secondary nature. (OH-) appears to be involved to a power not far from unity, indicating a relatively simple system. Clark (9) cites numerous references to similar biological pH-functions, enzymic and otherwise. These usual functions have been described as a basis for comparison wit.h the azotase function.
Curves I, 11, 111, IV, theoretical curves based on equations 1 and 2, with RB = and 1/2, 1,2, and 4 hydroxyl ions, respectively, involved. Curves V, VI, VII, respiration, growth (in nitrate) and nitrogen fixation (by azotase) in Azotobacter vinetandii, from data o f Burk, Lineweaver, and Horner (reference 6, figure 4). THE AZOTASE
ACTIVITY-pHFUNCTION
The unique activity-pH curve of aeotase is reproduced in curve VII, figure 1 (cf. also curve VII, figure 2). The velocity constant of nitrogen fixation is plotted upon the basis of percentage of maximum activity. The distinctive characteristics of the curve upon which the phase rule analysis will be based are as follows. (1). It approaches a critical threshold pH limit at zero activity in a
38
DEAN BURK AND HANS LINEWEAVER
manner concave downward, substantially perpendicular. The usual curves, plotted against pH as shown in figure 1, are S-shaped or double S-shaped (bell-shaped) , and approach the pH axis asymptotically (concave upward). No finite critical pH is involved, except in certain types of minima to be discussed later. In the plot against (OH-) the curves intersect the (OH-) axis at the origin.
FIG. 2. COMPARISON
OF
VARIOUS ACTIVITY-(OH-) FUNCTIONS
Curves I, 11,111,IV, VIII, IX, theoretical curves based on equations 1 and 2, with and 1/2, 1, 2, 4, 16 and 24 hydroxyl ions, respectively, involved. Curves K, = V, VI, VII, respiration, growth (in nitrate) and nitrogen fixation (by azotase) in Azotobacter, from data of Burk, Lineweaver, and Horner (reference 6, figure 4).
(2). The azotase function is reversible over an indefinitely extended period of time; this is true even considerably below the pH of zero activity, down to pH 5.0. A true thermodynamic equilibrium is therefore involved, approachable from either side of pH 5.97. The usual functions generally show irreversible inactivation in a few minutes or hours a t a pH where activity is still 20 per cent of maximum (curve 111,figure 3). (3). The pH limit is a characteristic constant, and has not been observed so far to be changeable beyond f0.05 pH unit a t most, if a t all. Usual
PHABE CHANGES IN ENZYME SYSTEMS
39
functions may often be greatly shifted along the pH axis by various factors. An excellent example is the shifting of the oxygen-hemocyanin dissociation constant one and one-half pH units by 0.5 M sodium chloride (figure 3, curves I, IA), or similarly that of oxygen-hemoglobin by various salts
PH Fxa. 3. COMPARISON OF SPECIAL pH FUNCTIOKS OBTAINEDBY VARIOUS INVESTIQATORS Curves I and Ia, oxygen affinity constant of hemocyanin of Busycon canaliculatum, in presence and absence of 0.5 M sodium chloride, respectively, from data of Redfield and Ingalls (reference 31, figures 3 and 4; a = io50 X 7.5 mm. mercury). Curve 11, relative rate of respiration of Sarcina lutea, from data of Rubenstein (reference 32, figure 6). Curve 111, sedimentation velocity of hemocyanin of Helix pomata, from data of Svedberg and Heyroth (reference 33, figure 5; a = sedimentation velocity X 8.22 X 10l2cm. per second. Curves I V and IVa, relative concentration of ionized gelatin salt and relative rate of hydrolysis by pepsin (acid to isoelectric point) or trypsin (alkaline to isoelectric point), respectively, from data of Northrup (reference 26, figures 4 and 5). Curve 17, relative activity of azotase, from data of Burk, Lineweaver, and Horner (reference 6, figure 4).
(reference 3, figure 191, p. 621). Daniel (10) changed the isoelectric point of gelatin over one pH unit by varying alcohol concentration up to 60 per cent. (4). The azotase curve shows tremendous molal buffering capacity over
40
DEAN BURK AND HhNS LlNEWEAVER
the pH range involved, 5.97 =k 0.02 and 6.37 f 0.02 (curve VII, figure 1). A change in activity from 0 to 100 (&2) per cent takes place in 0.4 pH unit. Usual enzyme curves require at least one and generally several pH units for only 95 per cent change. Many observations exist in the literature to the effect that a certain biological process has a characteristic pH limit. Thus Clark (8) showed that certain strains of B. coli invariably stopped growing when a pH limit of 4.8 was attained. In cases of this sort, however, the data rarely indicate the manner of reversible approach to the pH axis, especially when very close. For example, in curve 11, figure 3, it is suggested that the dotted portion represents a certain amount of irreversible pH effect and that the reversible curve really becomes asymptotic as in the alkaline region. PHASE RULE ANALYSIS OF AXOTASE
ACTIVITY-pHFUNCTION
So far as the writers are aware there is only one interpretation, based, namely, on the phase rule, which is consistent with all four of the abovecited characteristics of the reversible reaction between hydroxyl ion and the inactive azotase residue: AOH- e AH+
+ OH-
(3)
where AO*- and AH- are the active and inactive forms of the grouping in azotase specifically influenced by pH. The charges on AOH-and AH+may be positive, zero, or negative, but differ algebraically by the number of hydroxyl ions involved, presumably one (see later), Equation 3 and curve VII, figure 1, describe a two-component system which is univariant under ordinary experimental conditions, where temperature, pressure, and total cellular azotase concentration (AOH-and AH+) are held constant, and the state of the system is defined by the hydroxyl ion concentration of the external medium, no AoH- existing below about pH 5.97, no AH- existing above this value. According to the phase rule the number of phases existing when the system is in equilibrium a t pH 5.97 is three, thus: P = C - F 2 = 2 - 1 2 = 3. One phase, containing the hydroxyl ion, is aqueous, and the other two, consisting of AOH-and AH+, respectively, are therefore non-aqueous, either liquid, solid, or surface phases. It is assumed for the present that curve VII, figure 1, is strictly perpendicular and that the two non-aqueous phases are therefore pure components or compounds of fixed composition. The possibility that AOH-varies somewhat in composition between pH 5.97 and 6.37 will be considered shortly. Since in heterogeneous equilibrium the absolute mass or quantity of one phase does not influence the composition of another phase, (AOH-) and (AH+)do not appear in the mass law dissociation constant:
+
+
K
=
(OH-) =
10-8.03
(4)
PHASE CHANGES IN ENZYME SYSTEMS
41
In view of the equilibrium (H+)(OH-)/(H,O) in the aqueous phase, equations 3 and 4 might be written, so far as available experiments decide, AH+(non-aq)
K‘
~
=
AoH-(non-aq) -I- H+(aq)
(3‘)
(H+) =
(4’)
10-6.91
This ambiguity occurs commonly in base-acid equilibria and must be resolved by independent evidence (reference 9, 2nd ed., 1925, pp. 29,306), e.g., migration experiments. Alteration of K in equation 4 (or K’ in 4’) to an extent minute or otherwise, although unobserved so far, is theoretically possible under the phase rule, as a function of temperature, total pressure, or the chemical composition of AoH-,
Comparable equilibria The heterogeneous equilibrium of equations 3 and 4 is comparable to well-known univariant gas-solid equilibria involving salt hydration. Thus, with, e.g., anhydrous copper sulfate and water vapor, no hydrate is formed a t constant and ordinary temperatures until a certain critical water vapor pressure is reached, about 4.5 mm. This is the dissociation pressure of the monohydrate, a t which point the anhydrous salt is all converted into the new compound, the monohydrate, before further rise in the equilibrium vapor pressure may occur, two solid phases (three altogether) existing during the meantime.2 The equations representing these phenomena of critical phase change, corresponding to equations 3 and 4, are: CuSOe*HzO(s)
+
CUSO~(S) HzO(g)
Kdlss. = (HzO) = 4.5 mm. a t 50°C.
+
(5) (6)
+
Here F = C - P 2 =2-3 2 = 1. In the system solid mono- and di-calcium phosphates in aqueous equilibrium at constant temperature and pressure at a given pH, the slightest change of pH in either direction results in the complete conversion of one solid to the other. This system is perhaps more analogous to the azotase system than salt hydration in view of the nature of the independent variable (pH) and the known r81e of calcium In Bayliss’ phase rule analysis of the system hemoglobin-oxyhemoglobinoxygen (reference 3, p. 617, last paragraph) three phases and two components were assigned in the equation F = C - P 2 = 2 - 3 2 = 1, and it appeared therefore that the system was formally comparable to the univariant system CaCOs (s)-CaO(s) -COz(g) (or, similarly, the case of salt hydration illustrated). This was taken t o be anomalous inasmuch as bivariance was observed experimentally. However, from the nature of the dissociation curves (reference 3, pp. 620, 621) oxygen combines with hemoglobin at all pressures and hence hemoglobin and oxyhemoglobin occur in one and the same composition-varying phase, so that F = 2 - 2 2 = 2. This leaves no basis for the alternatives of either the existence of three components, or non-applicability of the phase rule to microheterogeneous systems.
+
+
+
42
DEAN BURK AND HANS LINEWEAVER
in fixation. Amylase activity apparently involves an essential organic calcium component also (24).
The pH region 6.97 to 6.37 The azotase function appears to require some 0.4 pH unit to change reversibly from 0 to 100 per cent activity. Slight non-homogeneity of phase may be involved ; it is well-known that even under equilibrium conditions the vapor pressure of liquids depends slightly upon the size of the droplets; the solubility of solids upon the size of the particles; the melting point withiout decomposition may vary a perceptible fraction of a degree; surfaces may depart somewhat from complete homogeneity, varying perhaps in curvature; and secondary factors ordinarily neglected may affect certain phase rule applications. Mathematically considered, the magnitude of the region of phase change depends upon the phase spaces involved, in the sense employed in statistical mechanics. Zero velocity at pH 5.97 represents in any case complete conversion of AoH- to AH*, and the attainment of maximum velocity above pH 6.37 complete conversion of AH7 t o AOH-,within experimental error. It is scarcely possible that AH+(non-aq)
and A’oH-(non-aq)
+
+ OH- e A’OH-(non-aq);phase change, pH 5.97 e AOH-(non-aq);non-aqueous
TZO~I-
(7)
solution, pH 5.97 t o 6.37 (8) L
where AH+ is converted at pH 5.97 into a new but inactive non-aqueous phase, AfOH-, which becomes active upon further combination with, or solution of, aqueous OH- ions over the region t o pH 6.37, when all A’OHis converted into completely active AoH-. It is evident, comparing the upper portions of curve VII, figure 2, and curves IV or VIII, that the value of n in equation 7 must be much larger than in the usual enzyme dissociation, and, moreover, for the portion below 50 per cent activity that curve VI1 does not represent merely dissociation with some large power of n. If one plots the logarithm of the ratio of the concentrations of undissociated and dissociated molecules of an electrolyte against pH a line is obtained whose slope represents n, the number of hydroxyl ions involved in the dissociation. Such a plot of the azotase function does not yield a uniformly straight line but one which varies continuously, indicating that n varies. Between 6.3 and 6.15 n appears to possess a fairly constant value of about 6, but at pH 6.0, where activity is only about 25 per cent of maximum, it becomes 12, at 5.98, 31, and a t 5.97 substantially infinite. PHASE CHANCE ALTERNATIVES
A curve at relatively low activities, lying between curves VI11 and IX, figure 2 ( n = 16 and 24, respectively), would cross curve VI1 within experi-
PHASE CHANGES IN ENZYME SYSTEMS
43
mental error of measurement of zero activity (about 1per cent of maximum, where AH+/AOH- = 100). The azotase pH limit 5.97 might thus be explained homogeneously, AOH- e AH+
K”
=
+ 20 OH-
(OH-)zo(A~+)/(A~~-)
except for there being no chemical precedent for a molecule with some twenty (basic) groups titratable a t the same pH. (The problems of limit (equation 9) and transition range (equation 7), each involving large values of n, are to be clearly distinguished.) Similarly, AoI-I-and A H + might differ greatly in molecular weight.
Most properties of a molecule must be considered quantitatively as properties of the whole molecule and not as the sum of the properties of the various composing groups or atoms. It is thus conceivable that the molecule within the azotase system specifically affected by OH- is active only when possessed of a minimum molecular weight. Here again, however, numerous groups all dissociating reversibly a t approximately pH 6.0 would have to be involved, for which there is no chemical precedent. Svedberg and Heyroth (33) showed that the sedimentation velocity of hemocyanin from Helix pomatia decreases about tenfold between pH 4.8 and 3.8 (curve 111, figure 3) and is accompanied by a roughly parallel decrease in molecular weight. Actually, however, the curve is reversible only in the earliest stages at the higher pH values; several hours exposure at 3.4 results in 25 to 75 per cent permanent change. Certain properties of ampholytes, electric charge and cataphoretic or membrane potential, approach abrupt minima substantially linearly as a function of pH, as illustrated in curve IV, figure 3, for gelatin. In the case of hemoglobin the electric charge involved decreases reversibly to zero between pH 8.4 and the isoelectric point 6.8, where it presumably changes abruptly to positive (26). Compared to curve VII, figure 1, however, such curves extend over a much greater pH range and do not appear capable of offering an alternative explanation for the assigned phase change in azotase, although they may represent accompanying phenomena. Moreover, the corresponding enzyme activity curves, e.g. curve IVa, figure 3, approach their minima concaved upward in the normal continuous manner. DISCUSSION
The phase rule involves great generality and formality in one sense, but also high specificity, as a means of classifying a great variety of type reac-
44
DEAN BURK AND HANS LINEWEAVER
tions, homogeneous or heterogeneous. It makes possible distinction between change in number or kind of phase and mere change in phase composition. The use of phase rule analysis will quite possibly be imperative3 in certain cases of enzyme reaction velocity or enzyme stability where inhibitors, accelerators, carriers, and substrates sometimes appear to act only above certain critical limiting concentrations. Thus Quastel and Whetham (29) find for certain dehydrogenases the equation v = k log (SIC) where the velocity v = 0 when substrate concentration S = critical concentration C ; by phase rule analysis there would appear to be a bivariant twocomponent, two-phase system, with an inactive non-aqueous phase invariant in composition occurring below the critical concentration and an active substrate-solution phase above it (cf. equations 7, 8). In the case of nitrogen fixation, quite possibly the very nature of the reaction involved accounts for the phase change requirement. The dissociation energy of the nitrogen molecule is some 84 volts or more (200,000 calories). This is enormously greater than the heats of activation of most enzymic reactions, which are rarely more than 10,000 to 20,000 calories. Generally considered, heterogeneous catalysis is much more effective than homogeneous catalysis in causing unusually unreactive molecules to react. Cannan (7) has reviewed the evidence for the view that the catalytic action of enzymes is restricted to certain surface areas. Quastel’s (28, 30) modified electric field theory of dehydrogenase activity and enzyme specificity provides for surface differentiation into specific areas or regions of unequal activity. Langmuir (19) has recently developed a detailed extension of the phase rule to include surfaces of the most varied types, active and inactive, in which a surface may consist of several phases, differing in structure or composition, but not size or shape. The phases may thus be submicroscopic, as well as microscopic or macroscopic as in ordinary phase rule applications. This point is important in view of the fact that the Azotobacter cell is only about 2000 A.U. in diameter and the a However, McBain (21), in common with Loeb, Sorensen, Perrin, Pauli, and Smoluchowski, holds that by phase rule a solution of reversible colloid, no matter how complicated, may be considered to behave toward external equilibria as a single phase. Buchner ( 5 ) concludes that while a colloidal solution may be regarded as either a one- or two- (or more) phase system, microheterogeneous systems in general seldom involve the formation of new phases and hence that the concept of phase will rarely be useful in connection therewith. He reviews various opinions on the nature of the concept phase and, while agreeing that heterogeneity may be considered relative and not sbsolute (depending upon the smallness of particles and roughness of observation), inclines t o the single phase view. On the other hand, the three-phase system azotase indicated in this paper throws new light on the problem, and strengthens the view that enzyme systems may consist of more than one phase, and that for some enzymes equation 1 might represent a two-component, twophase, bivariant system rather than a two-component, one-phase, trivariant system.
PHASE CHANGES IN ENZYME SYSTEMS
45
enzyme systems within it of course very much smaller. It is not necessary, in fact, that the AoH- and A H + phases consist of more than some several hundred molecules, enough to sustain the statistically based, thermodynamic equilibrium observed experimentally. SUMMARY
1. Azotase (nitrogen-fixing) activity in Azotobacter varies with pH abruptly. A characteristic zero limit a t 5.97 is approached reversibly and perpendicularly. Phase rule analysis implicates a two-component heterogeneous system with three phases in equilibrium at the critical pH: aqueous, active non-aqueous, and inactive non-aqueous. The active (basic) component exists above the critical pH, the inactive (acidic) one below. Slight phase non-homogeneity may occur between pH 5.97 and 6.37. Interpretations of the abrupt pH function, alternative to phase change, such as normal acid-base dissociation, large molecular weight change, multiple basicity, and minimal charge or potential difference have been discarded as inconsistent with one or more characteristics of the reaction. 2. Phase rule applications to microheterogeneous systems, surfaces, and problems of general enzyme reaction velocity and stability have been briefly indicated. REFERENCES
(1) ARRHEWITJS,S. : Quantitative Laws in Biological Chemistry. Blackie and Sons, London (1915). (2) BAYLISS,‘CVM. : The Nature of Enzyme Action, 4th edition. Longmans, Green and Co., London (1919). (3) BAYLISS,WM.: Principles of General Physiology. Longmans, Green and Co., London (1924). (4) BRONSTED,J. N., AND GUGGENHEIM, E. A.: J. Am. Chem. SOC.49, 2554 (1927). (5) BUCHNER, E. H. : Colloid Chemistry, Chap. 4, Vol. I (Alexander). The Chemical Catalog Co., New York (1926). (6) BURK,D., LINEWEAYER, H., AND HORXER,C. K.: J. Bwt., in press. Cf. also: BTJRK, D.: Chapter “Azotase and Nitrogenase in Azotobacter” in Ergebnisse der Enzymforschung by F. F. Nord and R. Weidenhagen, Vol. 111. In press, Akademische Verlagsgesellschaft, Leipzig (1934). (7) CANNAN,R. K.: Colloid Chemistry, Chap. 10, Vol. I1 (Alexander). The Chemical Catalog Co., New York (1928). (8) CLARK,W. M.: J. Biol. Chem. 22, 87 (1915). (9) CLARK,W. M.: The Determination of Hydrogen Ions. Williams & Wilkins, Baltimore (1920 et seq.). (10) DANIEL,J.: J. Gen. Physiol. 16, 457 (1933). (11) EULER, H.: Z. physiol. Chem. 61, 213 (1907). (12) FISCHGOLD, H., AND AMMON,R.: Biochem. Z. 247,338 (1932). (13) FODOR, A. : Das Fermentproblem, 2nd edition. Steinkopff, Dresden (1929). (14) GIBBS,J. W.: Am. J. Sei. 111, 16,446 (1878). (15) HALDANE, J. B. S. : Enzymes. Longmans, Green and Co., London (1930). (16) HEDIN,S. G.: Z. physiol. Chem. 164,252 (1926).
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DEAN BURK AND HANS LINEWEAVER
(17) HITCHCOCK, D. I.: J. Am. Chem. SOC.48,2870 (1926). (18) KUHN, R.: Die Fermente (Oppenheimer-Kuhn), p. 183. Thieme, Leipzig (1925). (19) LANGMUIR, I.: J. Chem. Physics 1 , 3 (1933). (20) LEWIS,G. N., AND RANDALL, M.: Thermodynamics, Chap. 2. McGraw-Hill Book Co., New York (1923). (21) MCBAIN,J.: Colloid Chemistry, Chap. 5, Vol. I (Alexander). The Chemical Catalog Co., New York (1926). (22) MICHAELIS, L. : Die Wasserstoffionenkonzentration. Springer, Berlin (1914). (23) MICHAELIS, L., AND MENTEN,W. L.: Biochem. Z. 49,333 (1913). (24) NAKAMURA, H . : J. SOC.Chem. Ind. Japan 34, Suppl. Bind., p. 16 (1931). (25) NELSON,J. M., AND VOSBURGH, W. C.: J. Am. Chem. SOC.39,790 (1917). (26) NORTHRUP, J. H. : J. Gen. Physiol. 6, 263 (1922). J. H.: J. Gen. Physiol. 16, 295 (1932). (27) NORTHRUP, (28) QUASTEL,J. H.: Biochem. J. 20,166 (1926). J. H., AND WHETHAM, M, D.: Biochem. J. 19,520 (1925). (29) QUASTEL, (30) QUASTEL, J. H., AND WOOLDRIDGE, W.R.: Biochem. J. 21, 148, 1224 (1927). (81) REDFIELD, A. C., AND INGALLS, E. N. : J. Cell. Comp. Physiol. 1, 253 (1932). (32) RUBENSTEIN, B. B.: J. Cell. Comp. Physiol. 2,27 (1933). (33) SVEDBERG, T., AND HEYROTH, F. F.: J. Am. Chem. Soc. 61,550 (1929). (34) WEIDENHAGEN, R., AND LANDT,E.: Ver. deut. Zuckerind. 80,25 (1930). (35) WESTENBRINK, H. G. K.: Arch. n6erland. physiol. 16, 538 (1930). (36) WHERRY,E. T.: Colloid Chemistry, Chap. 10, Vol. I1 (Alexander). The Chemical Catalog Co., New York (1928). (37) WHITE,T. A.: J. Am. Chem. SOC.66, 556 (1932). (38) WILLSTATTER, R.: Ber. 66,3601 (1922).
z.
