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Equilibrium and Nonequilibrium in the Glycolysis System.

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Equilibrium and Nonequilibrium in the Glycolysis System [*]
BY PROF. DR. TH. BUCHER AND CAND. MED. W. RUSSMANN
INSTITUT FOR PHYSIOLOGISCHE CHEMIE
DER UNIVERSITAT MARBURG/LAHN (GERMANY)
Dedicated in gratitude and admiration to Otto Warburg on the occaPion of hir 80th birthday
The relationship between the metabolic throughput within the network of energy-firrnishing
rnetabolisni and the deviation of its composite reacting units from equilibrium is discussed
Measurements hale been made of the steady-state relaxation times, and, following a suggestion by Alberfy, their application is described. The results confirm and extend the concepts
of intracellular redox relationships which the authors’ research group outlined five years ago
in this journal. The maximum difference between the redox potentials of the factatejpyruvate and of the DPNIDPNH systems was calculated to be 2 mV. Deviations of the GCglycerophosphate/dihydroxyacetonephosphate system measured in vivo are correlated
with the rate of flow in the glycerophosphate cycle.
1. Ordering of Nonequilibria
(The principle of opposing changes of potential differences)
The phenomenon of continuous nonequilibrium in living
matter is an old problem in the philosophy of nature. A
quantitative exploration was started by Liebig’s “law of
minimum” and by Blackman’s concept of the “limiting
factor”. Especially Blackman’s statement “ . . .the rate
of a process is limited by the pace of the slowest factor”
[I] as well as consecutively coined terms like “ratelimiting reaction” [ 2 , 3 ] “master reaction” [4,5],“pacemaker” [6], “bottle-neck”, etc. not only describe but
also require a formal and quantitative arrangement of
nonequilibria within the living material.
The main point in this connection may well be illustrated
by comparing wild and controlled streaming of a river.
Figure l a represents an uncontrolled waterway, in which
the total gradient is distributed approximately equally
among the various section along the flow line. The same
flow may be tamed by constructing flood gates; the
river is thus divided into reservoir - or backwater and waterfall sections (Fig. Ib). The greater crosssectional area of the water in the dammed up zone offers
less resistance to flow and thus compensates for the
minute gradients existing in the river before the dam.
_
_
~
~
_
[*I This article is based in part on the manuscripts of lectures
presented to the meetings of the Gesellschaft fur Physiologische
Chemie in Berlin, autumn 1959, and the Belgian Society for Biological Chemistry in Louvain, spring 1962. The work described
was supported by the special Program on “Experimental Cell
Reszarch ”of the Deutsche Forschungsgemeinschaft.
[ l ] F. F. Blackman, Ann. Bot. (London) 19,281 (1905).
[2] A. Piitter, 2. allg. Physiol. 16, 574 (1914).
[3] H. Holzer in: Biologie und Wirkung derFermente, 4. Colloquium der Gesellschaft fur physiologischc Chemie. Springer,
Berlin-Gottingen-Heidelberg 1953, in particular p. 89.
[4] A . C.Eurton, J . cell. comp. Physiol. 9, 1 (1936); 14,327 (1939).
[5] H . L. Booij and H . P. Wolvekarnp, Bibliotheca biotheoretica
(Leiden) I , 145 (1944).
[6] H . A. Krebs and H . L. Kornberx, Ergebn. Physiol., biol. Chem.
exp. Pharmakol. 49,212 (1957).
426
Michaelis used a similar model (locks regulating a waterway) in describing redox pathways [7]. From the organizational point of view, the ordering of nonequilibria
produced by regulation of the waterway has three effects:
it facilitates control of the levels and of the rate of flow
L
/aI
Null
Flow rate
ICi
Fig. 1. Scbematk representation of (a) a n unregulated waterway.
(h) a regulated stream, and (c) the changes in the potential gradient a t
increasing rates of flow (throughput)
and it concentrates the capacity of the system to do usef u l work. To regulate the rate of flow of water or, more
generally spoken, to regulate the throughput of matter
within the system, the “flaod gate” need only be raised
or lowered.
As the throughput increases, the gradients undergo a
characteristic change, as shown by the dashed lines in
Figure I b. The rate-controlling factor, i. e. the potential
drop at the “flood gate”, decreases, while at the same
time the potential difference between the two ends of
the reservoir increases. This is indicated graphically in
Figure Ic. This principle of opposing changes in potential
differences is always encountered when a waterway (or
a metabolic chain) is subdivided by “flood gates” (or
limiting steps). It can help us in locating such limiting
steps and their controlling factors.
~
____
[7] L. Miehnelis: Oxydations-Reduktionspotentiale mit besonderer Berucksichtigung ihrer physiologischen Bedeutung. 2nd
Edit. Springer, Berlin-Gottingen-Heidelberg 1933.
Angrw. Cliem. intertml.
Edit. 1 Vol. 3 (1964)
1 No. 6
2. An Example
(Metabolic patterns of skeletal muscle)
Tissues in which the metabolic rate can change considerably and at short notice as a function of the activity of
the system provide a fairly simple object on which to test
surements. If we want to interpret them via the model of
the regulated river, we must first calculate ratios Qf the
“levels” (see [40a]) of the metabolites [lo, 111 and compare these ratios with the known (apparent) equilibrium
constants. By convention, the levels of the reaction products are placed in the numerators of the ratios. Eyuilibrium constants are also presented in the Figure. These can
GLYCEROPHOSPHATECYCLE
Glycerdl-1-P
Fructose- 1 6 - diP
Lactate
and
Pyruvate
;
~
ATP
EMBDEN-MEYERHOF
PATHWAY
Fig. 2. Schematic diagram of the interrelationships in carbohydrate metabolism [*]
the above principle. Voluntary skeletal muscle is an example. In it, the rate of energy-releasing metabolism can
increase by several orders of magnitude, especially in the
Enibden - Meyerhof glycolytic reaction chain (Fig. 2).
Recently, Hohovst et al. [8,9] studied the changes in the
metabolite pattern of the Embden-Meyerhof pathway of
rat abdominal wall muscle when the latter went into
tetanic contraction. Figure 3 shows some of these mea-
[*I T h e following abbreviations are used in this paper:
= aldolase
ALD
= adenosine diphosphate
ADP
= adenosine triphosphate
ATP
= dihydroxyacetone phosphate
DAP
DPN
= diphosphopyridine nucleotide
D P N H = reduced D P N
EN
= enolase
FDP
= fructose-1,6-diphosphate
F6P
= fructose-6-phosphate
F 6 P K = phosphohexokinase (6-phosphofructokinase)
= glyceraldehyde-3-phosphate
GAP
G A P D H = phosphoglyceraldehyde dehydrogenase
= glycerol- 1-phosphate dehydrogenase
G DH
a-GP
= glycerol- I-phosphate (a-glycerophosphate)
= glucose-6-phosphate
G6P
= phosphoglyceric mutase
GPM
a-GPOX = glycerol-1-phosphate oxidase
HIM
phosphohexose isomerase
Lac
= lactate
LDH
= lactic dehydrogenase
M D H = malic dehydrogenase
= inorganic phosphate
P
PEP
= phosphoenolpyruvate
PGK
phosphoglycerokinase (ATP phosphoglyceric
transphosphorylase)
= phosphoglyceric acid (glycerate phosphate)
PGA
PK
=- pyruvate phosphokinase
:; pyruvate
Pyr
TIM
= triosephosphate isomerase
[8] H . 1. Hohorst, M . Reirn, and H . Bnrtels, Biochem. biophys.
Res. Commun. 7, 137, 142 (1962).
[9] H . J . Hohorst in P . Karlson: Funktioneile und morphologische Organisation der Zelle. Springer, Berlin-Gottingeii-Heidelberg 1963.
be found without difficulty for most pairs of metabolites, since they belong to two-component reactions [I21
(see [*I on p. 431). However, a special assumption
Muscle relaxed
Muscle in letanic
,1’
017 1 2 1 0 ~ L 1
I
FOP
035
3-PGA
I
0 3 6 10 501
PLP
0 0 4 8 10 0461 P E P
I
GAP
~
GAP
2-=
5
A n g r w . Chrin. iiitcriuit. Edit. 1 Vol. 3 (1964)
No. 6
Fig. 3. Metabolite levels in rat abdominal imscle [8,91.
For the analytical method, see [ill. Ratios calculated from metabolite
levels are included between metabolite pairs. while (apparent) equilibrium
constants [16] are in parentheses. In the case of phosphohexokinase
ratios [see Equation (a), p. 4281, the [ATPl/[ADPl ratio was calculated
from the levels of creatine phosphate (CP) and Creatine ( C ) :
(ATPI/[ADP] = 10 i (CP}/{C).
[FDPI/[F6P1 = Kapp : [ ~ T P l / [ A ~ P
=] 10 < lo3
- -
i{CP}/{C}.
~~
[lo] Th. Biicher and M.K/ingenberg, Angew.Chem.70,552 (1958).
[ I I ] H.1. Hohorst, F. H . Kreurz, and Th. Biicher, Biochem. 2 . 3 3 2 ,
18 (1959).
[I21 Th. Biicher, Pure appl. Chem. 6, 209 (1963).
427
must be made for the pair F6P/FDP (see legend to
Fig. 3), since it is part of a four-partner reaction.
Comparison of the ratios of the steady-state metabolite
levels with the equilibrium constants reveals two facts :
1. The ratios can be classified into two categories : the
first contains ratios which are of the same order of magnitude as the equilibrium constants ; here the difference
of potentials is small. In the second case (F6P/FDP),
there is considerable difference between the two; there
exists a considerable drop of potential.
2. As a consequence of the transition from the quiescent
to the active state of the muscle, ratios of the first category show a decrease, while those of the second category
show an increase (F6P/FDP by a factor of 4).
Employing the concepts developed in Section 1, it is
obvious that the following reaction which is catalysed
by the enzyme phosphofructokinase (see also Figure 2 ) :
Fructose-6-phosphate + ATP
F 6 PK
Fructose-l,6-diphosphate ADP
11
+
is a limiting step. We can attribute the other metabolite
pairs to the sections with a low gradient of the chemical
potential.
In a somewhat similar fashion, Holzer and HoNdorf[13]
defined “rate-controlling reactions” and “equilibrium reactions” (hexose monophosphate isomerase, aldolase, triose
phosphate isomerase, alcohol dehydrogenase) for the fermentation process in yeast. Hess [I41 divides the complete
sequence of metabolites of glycolysis in Ehrlich ascites tumors
into three groups of “quasi-equilibrium intermediates”,
separated or controlled by “quasi-irreversible’’ reactions :
phosphohexokinase, phosphoglyceric kinase, a n d pyruvic
phosphokinase. His values and those of Munn et al. [15],
who also performed pioneer work on the dynamics of the
metabolite pattern, are shown in Table 1 .
Table 1. Ratios of metabolite levels in various cells. Apparent equilibrium constants Kapp [I61 are given in parentheses in the first column.
Yeast [15]
G6PIF6P
(0.43)
3-PGAI2-PGA
(0.17)
2-PGA/PEP
(3.0)
0.33
1
I
Ascites
tumor 1141
I
0.43
0.12
~
3.0
0.30
n
1
L
=
Vs,RTln --
(1)
1
where Kapp = the thermodynamic equiiibrium constant, see Equation(21,
and
0.30
3. Limiting Steps
(Energetics and Definitions)
It has already been mentioned that organization of a
system into “low-gradient’’ sections with an intervening potential drop “concentrates” its ability to do
[13] H . Holzer and A . Holldorf in W . Ruhland: Handbuch der
Pflanzenphysiologie. Springer, Berlin-Gottingen-Heidelberg
1906, Vol. XII/l.
[I41 B . Hess in P . Karlson: Funktionelle und morphologische Organisation der Zelle. Springer, Berlin-Gottingen-Heidelberg 1963.
[ 151 P. F. E. Mann, W . E. Trevelyan, and J. S . Harrison in: Recent
Studies in Yeast and their Significance in Industry. Society of
Chemical Industry, London 1958, in particular p. 68.
[I61 K. Burton, Ergebn. Physiol., biol. Chem. exp. Pharmakol.
49, 275 (1957).
428
The phosphofructokinase reaction, the limiting step
in the section of the Embden-Meyerhof pathway treated
in Figure 3, is not a power plant, i. e. it does not produce
energy for the cycle, It is thus a direct controlling step.
As such, it transforms a cmsiderable quantity of free
energy into heat. This is analogous to the problem of
maintaining pressure in a leaky vessel. Maintenance of
a steady nonequilibrium in such a chain of reactions is
accompanied by a continuous transformation of free
energy into heat [19,20]. The work per unit of time per
unit of volume required, which is represented by L in
Equation (l), is proportional to the metaboZic throughput
VSt (molarity per unit of time) and to the potential
difference (deviation from equilibrium [*I).
Kapp
0.38
1.6
However, an ideally functioning power plant can
also act as an indirect controlling factor in the system, for the resistance it offers depends upon the output
it produces. Since it is coupled to the process which
utilizes the free energy of the system, the controlling nonequilibrium is shifted towards the energy-consuming
process. Such relationships are of fundamental importance in the control of energy-supplying metabolism via
the cyclic participation of phosphate. In this sense, the
(‘cross-over’’ theorem of Chance [ 181 may be regarded
as a special case of the principle outlined above of opposing directions of changes in the potential gradients
that is applicable to the region of indirect controlling
factors.
Skeletal muscle [71
Rest
Work
0.23
0.45
useful work: metabolic “power-plants’’ can only be
located within a range involving a drastic drop of
potential. At the same time, it should be kept in mind
that the production of a maximum amount of useful
work destroys the nonequilibrium and thus removes
the possibility of control. The variability and controllability of a system require that at least one unidirectional step (nonequilibrium) is involved [17].
r
P
“mass-action ratio” of nonequilibrium, see Equation (4).
The continuous loss of free energy is small in those
parts of the reaction chain where the potential differences and hence the deviations from equilibrium are
small, but is large in the phosphofructokinase reaction.
This is the energy price which the system must pay
for its ability to vary its throughput.
Equation (1) follows from the thermodynamic definition
of equilibrium and nonequilibrium. It is known that at
equilibrium, the work which the system is capable of
[ 171 H. Mirtelsfaedt: Regelungsvorgange in der Biologie, Beihefte zur Regelungstechnik. R. Oldenbourg, Miinchen 1956.
[*] In r / K a p p is approximated by I’/Kapp-l in the neighborhood
of F/Kapp= 1. Terms like r/Kapp,;l may serve also as expressions for the deviation of the mass-action ratio” from
equilibrium in the treatment of the “small-deviation” sections
of the metabolic pathway.
[I81 B. Chance and G . R . Williams, Adv. Enzymol. 17, 65 (1956).
[I91 W. Kuhn, Ergebn. Enzymol. 5 , 1 (1936); Angew. Chem. 48,
215 (1936).
[20] L. v. Bertalanffy: Biophysik des FlieBgleichgewichts. Sammlung Vieweg, Braunschweig 1953.
Angew. Chem. internat. Edit.
I
Vol. 3 (1964) No. 6
doing is zero, while the entropy reaches a maximum
(dS = 0). In this sense, equilibrium is a static condition. The observed concentrations or, to be exact,
the activities of the reaction partners obey the law
of mass action.
[PI rQ1-
Kapp = _ _ - ~
[A][B].”
5 . Metabolite Patterns at Rest and during Activity
Nonequilibria can be “stationary”, “nonstationary”, or
“steady” [*I. The stationary-state nonequilibrium is also
called “flow-equilibrium” [20a].
4. Pacemakers
Krebs and Kornberg [6] wrote the following about the
pacemaker reaction: “There is a general principle which
may guide the search for pacemakers. As pacemakers
are reactions of variable rate, the level of substrate concentration of the pacemaker must vary inversely with the
rate: it must increase when the reaction rate decreases.”
In view of this definition, can the phosphohexokinase
reaction be classified as a pacemaker reaction? It can be
seen in Figure 3 that the metabolite levels of both F6P
and FDP i n c r e a s e with the flow rate. Thus, the change
produced is opposite to that required by Krebs and Kornberg for a “pacemaker”. Actually, this phenomenon is
caused by other limiting reactions taking place upstream
from the metabolic sequence in question, viz. by the phosphorylase reaction and the glucokinase reaction. In
particular, activation of phosphorylase causes the instantaneous discharge of glucose phosphates from the
glycogen reservoir [21-231. This can also be seen in
Figure 3.
The above facts also explain why the phosphofructokinase reaction has been omitted from consideration in
so many articles on regulation of glycolysis.
Although we cannot enter here into a detailed discussion
of some recent findings concerning the functions and
~[ * ] T h e term “stationary state” applies to a compound in a
reaction sequence where there is a continuous and constant
supply o f substrate from a n infinite reservoir, while “steady
state” applies to a compound during a prolonged period of
transition. In a muscle a t rest the metabolites are in a “stationary state”. After stimulation for reversible contraction the
metabolites can be considered to be in the “steady state” [20al.
[20a] R . Estabrook, personal communication.
[21] C. F. Cori in 0 . H . Gaebler: Enzymes, Units of Biochemical
Structure and Function. Henry Ford Hospital International
Svmuosium. Academic Press. New York 1956. D. 573.
[221 C. F. Cori: Currents in Biochemical Research. Interscience,
New York 1956, p. 198.
[231 W . H . Danforfh, E. Helmreich, and C. F. Cori, Proc. nat.
Acad. Sci. USA 48, 1191 (1962).
[24] H. A. Lardy and R . E. Parks ir. in 0 . H . Gaebler: Enzymes,
Units of Bioloaical Structure and Function. Henry Ford HosDital
International Symposium. Academic Press, New York i956,
p. 584.
[2S] T . E. Mansour and J . M . Mansour, J . biol. Chemistry 237,
629 (1962).
1261 J . V. Passonneau and H . 0 . Lowry, Biochem. biophys. Res.
Comrnun. 7, I0 (1 962).
-
1
A n g c w . Chem. internat. Edit.
mechanism of this reaction [10,24-271, it is worthwhile
calling attention to the advantages of analyzing processes in terms of relative rather than absolute changes
in metabolite levels.
I
/
VoI. 3 (1964)
.
No. 6
(The principle of functional readiness)
In principle, a single controlling step is sufficient for
control of any metabolic chain [4,5]. However, as
has just been discussed, glycolysis in muscle involves
several limiting reactions. Since we are dealing with
a biological system, it is permissible to inquire about
the purpose of this greater complexity.
Our problem may be considered in terms of the need
for reversibility of the metabolic flow. Since the free
energy is stored in standardized quantities as “highenergy” phosphate compounds and since chemical
potential is consumed in this form, energetically practicable sections must be present, just as series of locks are
usually needed between the higher and lower levels of a
canal.
Another aspect of the problem which has received even
less attention [12,27] is “functional readiness”. In the
metabolic organization, the entry of new substrate
molecules into the glycolytic pathway is controlled by
the pathway’s output. The existence of this coupling
means that, after disappearance of intermediate metabolites, the flow through the pathway can be restored to
a steady state only after a long induction period. In fermentation research, this well-known phenomenon is called “Angarung”. However, in rapidly responding tissues,
such as skeletal muscle, the power output and consequently the metabolic throughput may change within
a fraction of a second. Here not only well-filled energy
reservoirs are required, but also a preparation of the
metabolite pattern at rest counteracting any depletion
of intermediate levels.
In the two sections of Figure 3, the throughput differs by
at least a factor Of loo. In view Of this, any changes Observed in the pattern of the metabdite levels, and
especially any changes in their relltive proportions,
must be ‘Onsidered
as
This Phenomenon becomes meaningful when considered in terms
of physiolsgical
requirements far functional reidiness.
. ~
~readiness produced
~
by
~ homeostasis
~ oj-ceilu[ar
i
rnetabo/ite ratios necessitates the interaction of several
controlling reactions. Approximately one-third of the
metabolite levels is controlled bv these reactions.
is s~lown impressively in ~i~~~~ 3, the other twothirds of the levels approach (and are controlled by)
equilibrium. It is with this second fraction of metabdite
levels that we shall deal in the following Sections.
[27] Th. Biicher in: 7 . Symposium der Deutschen Gesellschaft fur
Endokrinologie. Springer, Berlin-Gottingen-Heidelberg 1961,
p. 129.
429
~
6. Metabolic Throughput and Deviation
from Equilibrium
With Kanp
Let us imagine that one of the reacting units in a metabolic pathway (i. e. the reactants and the catalytic agent)
were momentarily separated from the rest of the active
pathway. Just before the separation our reaction, as a
link in a metabolic chain, is deviated from equilibriunz
to a certain extent, which is a function of the throughput
within the pathway. The isolated reaction would then
immediately tend to attain a state of equilibrium. The
i n i t i a l r a t e (molarity per unit of time) of this r e l a x a t i o n p r o c e s s would be equal t o the throughput
mentioned.
~
[?]/[A] we obtain:
or
or
or
As a n example, let us assume that the enolase reaction
system
2-Phosphoglycerate
T=E;d;~L Phosphoenolpyruvate + HzO
(b)
has been isolated from the metabolic sequence of the
working muscle, shown in Figures 2 and 3 (i.e. we
isolate the metabolite, the enzyme, and the activating
Mg2 +).
In the first part of the enolase experiment (left part of
Fig. 4, open circles) this type of kinetics appears
straight on from the start (addition of enzyme). If
equilibrium is again disturbed by addition of a small
amount of metabolite to the system, then the process of
relaxation is repeated (full circles in Fig. 4).
I
1
A F.8 059
Fig. 4. Attainment of the equilibrium
2-Phosphogfycerate S Phosphoenolpyruvate
i n the enolase reaction. T h e reaction starts (on the left) following
addition of 4.6 units [34a] of enolase from rabbit muscle [341. Extinction registered a t 240 m y (light path: 1 cm) on a Beckmann DKI
instrument. 100 m M imidazole buffer, 0.8 m M MgS04, p H 6.8, 37 ‘ C .
In addition a semi-logarithmic plot of the measurements (0 and 0 ) is
shown, applying corrections for the dilution o n addition of substrate.
AE = Change in extinction
As Warburg and Christian have shown [28], the reaction proceeds to equilibrium by a first-order process.
Therefore, the reaction rate is always proportional
to the deviation A[A], of the substrate concentration
from the equilibrium value:
where (A], [PI = arbitrary concentrations of substrate and product
and
[TI, [PI = concentrations a t
apparent equilibrium
4 [ A l = I A l - [ ~ l = deviation of the substrate concentration from
equilibrium V8al as in:
1‘ = “1
- A[AI)I([AI
+
A[Al)
(4)
~
[28] 0.Warburg and W. Chrisfinn, Biochem. Z. 3I0, 384 (1941).
430
The relaxation time [30a] :ss, the rzciprocal of the constant k of the monomolecular reaction
is the time during which the deviation decreases to the
e-th part of the initial value. This is also evident from
the semi-logarithmic plot in Fig. 4.
Employing the concept developed at the beginning of
this Section we replace A[AIt in Equation (3) by A[A],,,
-
[28a] In a previous article [29], we designated the ratio of concentrations in the mass action equilibrium with Q and in the
nonequilibrium with Q. We shall now use Kapp for the former and the symbol
which has been previously introduced
by W’. Kuhn [19], for the latter. This is done to avoid confusion
with the efficient system of notation, developed by Cleland for
enzyme kinetics [301. In that system, [Q] is the concentration of a
second product, see Equation (14).
[29] H . Schirncrssek, 6.Kndenbnch, W . RuJhanrz, and Th. Buchcr
in G . Weber: Advances in Enzyme Regulation. Pergamon Press,
London 1963, Vol. 1, p. 103.
[30] W . W . Clelcind, Biochim. biophysica Acta 67, 104 (1963).
[30a] The relaxation time cssis understood to be the relaxation
time of the enzymic steady state, defined from the point of view
of enzyme kinetics. In this case, the notation of Hnnzmes and
A h e r t y [31] has been used.
r,
Atigew. Cliewi. interiicit. Etht. [ Vol. 3 (1964)
1 No. 6
the deviation of any reaction in the stationary or even
in the steady state of a metabolic sequence, and
- d(A‘A1) by its metabolic throughput Vst. This yields
it is also valid that
dt
VSt = k A[AIs, =
A [Alst
~
--
-
[molarity per unit of time]
(6)
TSS
By using the “Haldane-Alberty relationship” [32]
from which it can be seen that there is a simple relationship between the deviation and the metabolic throughput. This relationship is due to the pioneering work of
Albevry and his research group [32], who pointed out
that Equation (6) is analogous to Ohm’s law:
current
we obtain
V,
- pofe~i~iaiJresis~ance
In conformity with the relaxation concept itself, Equation (6) is valid only for small deviations from equilibrium. However, it stil! may be used in practice because
fortunately a large number of enzymatically catalysed
reactions approach first-order kinetics, even at quite
large deviations from equilibrium. Processes which obey
this relationship include not only the enolase reaction,
which we have used as an example, but also such reactions as the complicated test system of phosphoglyceric
kinase [33] (see also Fig. 9).
Figure 5 summarizes the relaxation measurements
made with the enzyme enolase (crystallized from
rabbit muscle [34]). Values rneasL :d in the experiment discussed above (Fig. 4) are marked with a “plus”
01
7. T,, of the Two-Partner Reaction [*I
(Enolase system)
0 01
I n conformance with the method of Hummes and Alberfy
[31], we can d e r i v e the r e l a x a t i o n of an enzymatic reaction from the general equation for the rate of reaction. This
genera1 equation is obtained from the Michealis-Haldane
theory by assuming steady-state concentrations of the intermediate enzyme-substrate or enzyme-product complexes.
We shall use the nomenclature developed by Clelund [30], see
Equations (1)-(3).
Ka, K b
01
02
Fig. 5. Enolase reaction: Relaxation timexunits of enzyme per unit
volume (ordinate) versus equilibrium concentration of phosphoenolpyruvate (abscissa). The “plus” signs mark the values obtained in the
experiments represented in Figure 4. Constants for the regression line,
see text [Equation (11)):
Ordinate: rss.Vl [mmole/ll.
Abscissa: [PEP] [mmole/ll.
sign. It can be seen that the relaxation time is a function
of the enzymatic acitivty used (established from the rate
of the forward reaction VI [enzyme units [34a] per ml])
and of the metabolite concentrations at equilibrium. By
analogy to Equation (lo), the regression line is given by
Equation (1 1):
Michaelis constants
V,, V2 = maximum velocities of forward and back reactions.
From Equation (4) [A] = [A] + A[Al and [PI
When A[A] @[A], [PI, it follows that
T , ~ . V ,=
=
[PI-AlA].
0.0056 [PEP] + 0.01 [pmole/I]
( I I)
where V1 = enzyme units per mi [34al.
To apply these relationships according to the concept outlined
in Section 6 and according to the measurements on muscle
described in Section 2, we can convert Equations (4) to
Since it also applies that
In this equation, is the “mass-action ratio” in steddy-state
nonequilibriurn [see Equations (1) and (4)) The factor A[A],t
(3)
[ * ] Reaction involving a single substrate and a single product,
see [12].
I311 G. G. Hammes and R . A . A l b e r f y , J. Amer. chem. SOC.82,
1564 (1960).
Arrgew. Chem. ititerncit. Edit. ! Vol. 3 (1964) N o . 6
[32] R . A . AIberty, 3. Amer. chem. Soc. 7.5, 1928 (1953).
[33] Th. Biicher, Biochim. biophysica Acta I, 292 (1947).
[34] R . Czok and Th. Biicher, Adv. Protein Chem. 15,315 (1960).
[34a] One enzyme unit corresponds to the conversion of one
wmole of substrate per hour in a standard test [35] at the temperature of the relaxation experiment.
43 1
has already been defined in connection with Equation (6). We
can substitute the relationship given in Equation (4a) for
A[A],t in Equation (6), a n d obtain:
8. Four-Partner Reaction [*I Near Equilibrium
(Lactate/pyruvate and the extramitochondrial
DPNH/DPN system)
The treatment of symmetrical f our-component reactions
To obtain the relaxation time of the tissue enzyme, the
value measured in vifro is divided by the ratio [enzyme
units in tissue]/[enzyme units in the relaxation experiment] (see also [34a]). To obtain these data, the
enolase localized in the muscle is exhaustively exextracted and tested under the same conditions (30000
units/g fresh weight at 37 "C)as described for obtaining
V1 in the relaxation experiment (4-10 units/ml). Thus,
we dare to assume that the enzyme molecule behaves
in the same way in a dilute, homogeneous solution as it
does in its cellular environment where it is present at a
concentration which is many hundred times higher. With
this assumption we obtain
It is with this assumption that the relationships between
the rate of flow in glycolysis in rat abdominal wall muscle
at work (see Fig. 3) and the deviation of the enolase
reaction from equilibrium are presented in Figure 6 for
different equilibrium concentrations of phosphoenolpyruvate. Actually the glycolytic throughput (VSJ
determined indirectly from the diagram (Fig. 6) using
the deviations (r/Kapp)measured in the organ (about
0.8, see Table 1) is of the same order of magnitude as
the directly me-sured glycslytic throughput (formation
of lactate in .vifu): about 5 mmoles per gram of fresh
tissue per hour.
A+B
+
P + Q
is considerably more difficult than that of two-component reactions. However, such processes are important,
because the action of c o u p l i n g n u c l e o t i d e s in intermediary metabolism usualIy takes place via four-component reactions. Therefore, four-component reactions
provide information on the state of the coupling nucleotide systems. This information sometimes cannot be
obtained in any other way [10,11,36]. From the definition of equilibrium, the potential difference between two
opposing compounds ( e . g . lactate and pyruvate, see
Equation (c) below) is numerically equal (but of opposite sign) to that of the other pair (e.g. DPNH and
DPN). Thus the redox potential of the DPNH/DPN
system can be calculated from the concentration ratios
of the appropriate pair of metabolites if the deviation
from equilibrium may be neglected.
Five years ago, we used our own observations and those
made by the groups of Lynen and HoOer [36] to derive
some conclusions, applicable to cell physiology, about
the redox state of the extramifuchondrial pyridine nucleotides in the liver [lo]. Our evidence that equilibrium
is a sufficient approximation for the treatment of the
lactic dehydrogenase system was based on the good
Pyruvate
+ DPNH + H +
T
y
=
=
2 Lactate + DPN
Lactic dehydrogenase
(c)
agreement between redox potentials of three DPNspecific extramitochondrial substrate pairs in resting
liver [ I l l . In the meantime, Huhorsf et al. have shown
that this agreement between the redox potentials
continues even if the absolute values change, either
by cuttin2 off the blood supply (ischemia) [37] or
by the influence of the diet or the endocrine situation [38].
Schimassek has been able to obtain new evidence by continuing his p e r f u s i o n experiments on rat liver. using a
synthetic medium (see note [a] in Table 3) in a closedcircuit, extracorpxeal circulation [39,40]. The p x sibility of loss of the nascent lactate into metabolizing
regions outside the liver is excluded under these conditions. Since there are no opportunities worth men_
2
-
[*I A (symmetrical) four-partner reaction involves two substrates
@I;]
Fig. 6. Relationship between the rate of flow (current density) of
glycolysis in muscle (ordinate) and the noneqiiilibriuni of the enolase
reaction (abscissa) [Equation (13)l.
(V,)tissue = 3 0 r lo3 units per g fresh weight; 37 "C
( T ~ ~ - V , )obtained
~ , ~ . from Figure 5.
Curve ( I ) : [PI = 56 mvmole/g fresh weight.
Curve (2): [PI = 28 mvmole/g fresh weight.
Curve (3): [PI = 14 rngmole/g fresh weight.
Ordinate: Vst [rnmolej:i/g fresh weight].
Abscissa: upper scale: l'/Kapp.
Kappl
lower scale: KKapplI') -11/[1
+
43 2
and two products.
[35] Th. Biicher, D. Pette, and W . Luh in Hoppe-Seyler-Thierfelder: Handbuch der physiologisch-chemischen Analyse. Springer,
Berlin-Gottingen-Heidelberg, in the press.
[36] H. Holzer, C . Schulze, and F. L.vnen, Biochem. Z. 328, 252
( I95 6).
[37] H . J . Hohorst, F. H . Kreutr, and M . Reim, Biochem. biophys.
Res. Commun. 4 , 159 (1961).
[38] H . J . Hohorst, F. H . Kreutz, M . Reinr, and H . Hubener, Biochem. biophys. Res. Commun. 4, 163 (1961); E. Kirsten, R.
Kirsten, H. J . Hohorst, and Th. Biirher, ibid. 4 , 169 (1961).
[39] H . Srhimassek, Life Sciences 1, 629, 635 (1962).
[40] H . Schimassek, Biochem. Z . 336, 460, 4 6 8 (1963).
Angew. Chem. internat. Edit. 1 Vol. 3 (1964)
/ No. 6
tioning for utilizing lactate in the region of the liver
parenchyma without the participation of lactic dehydrogenase, the lactate/pyruvate system is thus on a
blind alley.
When in the perfusion changes occur of oxygen supply
(Fig. 7), or when lactate is added [40], the observed
adaptability of the system is indicative of its dynamic
characteristics. In this case, the isolated organ produces roughly the same concentrations and redox ratios
as those found in blood plasma, even though the volume
of the perfusion system is considerably larger (100 ml as
compared to 10- 15 nil of blood).
(Table 2). Lynen’s postulate [41] “that the calculation of
absolute concentrations from analytical data is meaningless if the cell structure is destroyed to obtain them” does
not hold in this case. On the contrary, the conditions described in Schimassek’s system permit completely objective and meaningul correlation of the absolute levels
of metabolites with cellular concentrations which can be
evaluated thermodynamically.
Thus, the redox potential calculated from cellular levels
is thermodynamically valid, and Schimassek’s experiments deserve special consideration because of the
fundamental significance of the redox potential in the
T
,
,
\
TI
I
T
T
I
I
I
I
I
I
k;Ol
19$
I
I
I
121 Ll
I
il? 71
I
I
I
I
I
I
I
L
t
I
I
I
11L21
1
~
0
rn
110’
78
I
1
I
I
I
30
60
90
120
150
Fig. 7 . Perfusion of isolated rat liver with synthetic “blood” (see note
[a] in Table 3) in a closed circuit [39,401. Ordinate: Concentrations of
lactate (above) and pyruvate (below) in the medium at various rates of
perfusion. Concentration ratios in parentheses. At rates of flow CI I ,
the oxygen consumption of the tissue (200yatom/g/h) is not completely
accounted for. The high quotient at the start of the experiment is a
result of the ischemia of the organ during its transfer to the artificial
circuit.
The metabolite levels (see [40a]) in the perfused liver a t the end of the
experiment are shown on the right: ({a-GP}/{DAP})x ({Pyruvate}/{Lactate)) = 0.59 (cf. Table 4).
The figures above the profile diagram at the bottom of the section on the
left indicate the rates of flow in ml/m;n per 3 of liver.
Ordinate: Concentration [!imole/ll or level [vmolelkg fresh weight].
Abscissa: Time [min].
Furthermore, it follows from these experiments that
there is agreement between the levels [40a] of metabolites found in the cells by tissue analysis and
the concentrations measured in the p e r f u s i o n f l u i d
Table 2. Perfusion of isolated liver In closed system. Metabolite levels
in the tissue (corrected for the content of medium and interstitial fluid)
and in the medium after three hours’ perfusion under standard
conditions [40].
Lactate
Pyruvate
3.5
0.37
3.5
0.33
Lactate/Pyruvate
9.5
10.5
extramitochondrial DPNH/DPN system. In the section
which follows we shall present further (kinetic) evidence
to show that the lactate/pyruvate system is a useful indicator of this potential.
In studies, of which we were unaware when writing previous papers, Huckabee [42] demonstrated the following
in man and in animal experiments: it is the lactate/
pyruvate ratio and not the change in the lactate level of
plasma which is relevant for detection of an oxygen
deficiency in cells. He was able to produce large fluctuations in the lactate level without affecting the lactate/
pyruvate ratio by injecting either the metabolites or bicarbonate and by hyperventilation. This offers a close
analogy to the perfusion experiments described above.
Table 3. Effect of various perfusion conditions on the lactatelpyruvate
ratio in the liver and in perfusion medium (401.
Perfusion conditions
~~
{Lactate}
Medium
[Lactate]
{Pyruvate}
[Pyruvatel
~
Homologous blood
Synthetic medium [a]
Control
Reduced perfusion rate
Addition of prednisolone
(perlusion rate normal)
9.6
8.0
10
10
25
26
17.7
18.2
[a] Tyrode solution, serum albumin, cattle erythrocytes [391.
This aspect is expanded in Table 3. The Table demonstrates the effects of regulatory mechanisms on the redox
potential in the extramitochondrial, DPN-specific area
[41] F. Lynen in: Proceedings of the International Symposium
o n Enzyme Chemistry, Tokyo and Kyoto 1957. Pergamon Press,
London 1958, in particular p. 28.
[42] W. Hiickabee, J . clin. Invest. 37, 244, 255, 264 (195s).
Aiigew. Cheni. interitat. Edit. / Vul. 3 (1964) / No. 6
433
in an extracorporeal system, as has already been partially
done by Hohorst et al. 1381 in animal experiments.
The agreement between the redox potentials in tissue and
plasma leads us to conclude that the interstitial fluid and
blood plasma are to a certain extent, “common-level reservoires” of the extrarnitochondrial lactic dehydrogenase system of the cells of an organ and, in the final analysis, of any organ [lo] (Fig. 8). Klingenberg [43] recently
-
the evaluation of results arise from the much more complicated enzyme mechanisms and the larger number of
reactants.
‘c
0 0027mM DPNH
i
t 0031
=
tarale + NHl
Malale
~~
Oxalo~celatelmllcl
Lactate
Glycerol - tP+
acetone P
0 - R - HydrOxy- +Acetoacebulyryl-CoA
lql-COA
a-Keloglu-.
tarate + NH3
I-D-Hydroxybutyrate
q-250
tactate+
Iml
Pyruvate
[a-GPl=0996rnM
[OPNI :0996mM
t-A- Hydraxy- *Aceto-
-
DPN
1
Y
0
m
i 0.214
1
Dihydroxyacetone phosphate f D P N H $- Hf
acetate
It
+.
- 300
lmllci
ja32781
Fig. 8. On the coordination of cellular redox potentials by the blood
plasma. Left: Mid-potentials I43al of cellular redox systems at p H 7 and
37 “ C . Right: Potentials (Tst” potentials 1101) of the redox systems in
blood plasma T h e systems of the extramitochondrial region (marked
b i t h (c). c-region [10,52]) of cells (left) are coupled via the lactatel
pyruvate system (right) 7 he homeostasis of this ootential forms the
basis for the redox variation in DPN-dependent systems in the extramitochondria1 region. .4nalogous disciissions of the mito:hondrial
(in:-systems f o r the p-hydroxybutyrate/acctoacetate pair in plasma can
be found in I431 and 144-461.
*INHA]in nimole/l.
The special case i n which one of the metabolite concentrations remains constant and the concentrations of two
other reactants are adjusted in such a way that they are
large in comparison to the deviation A[A], (see Equa10.;
i
i
Reaction
As the experiment represented in Fig. 9 shows, measurement of the relaxation times in a four-component reaction does not involve much greater difficulties in the optical assay than the measurement of two-component reactions. The difficulties mentioned above with regard to
[43] M . K h g e n b e r g and H . v. Hafen, Biochem. Z. 337, I20 (1963).
[43a] M . Kfingenberg and Th. Biicher, Annual Rev. Biochem. 29,
669 (1960).
[44] P . Borst in: Proceedings of the Fifth International Congress
of Biochemistry, Moscow 1961. Pergamon Press, London 1963,
Vol. 11, in particular p. 233.
[45] P. Borst in Th. Biicher: Redoxfunktionen cytoplasmatischer
Strukturen, Symposium, Vienna 1962. Wiener Medirinische Akademie fur Arztliche Fortbildung. Vienna 1962, in particular p.189.
[46] P . Borst in P . Karlson: Funktionelle und Morphologische
Organisation der Zelle. Springer, Berlin- Gottingen -Heidelberg
1963.
(d)
measured by a n optical assay. The reaction starts (on the left) on addition
of 36 units/ml of G D H from rabbit muscle [34J. Measurements were
made a t 334 mw (light path: 4 cm) on a n Eppendorf Photometer. Scale
expanded 4 x before addition of a small amount of D P N H . KHzP04I
K L H P 0 4 buffer, ionic strength w = 200 mM, p H 6.88, 37°C. The
dashed curve indicates the decrease in the concentration of dihydroxyacetone phosphate; this was calculated on the assumption that
ADAP = ADPNH.
9. The Deviation Kapp/F-lof the Four-Partner
(Indicator error at the indirect
determination of the DPN/DPNH-potential)
GDH
~-Glycerol-l-phosphate D P N
extended this hypothesis to the coupling of mitochondrial compartments with the $-hydroxybutyrate/acetoacetate system (see also [45,46]).
434
r
+
6rn1n
<
x
4
Fig. 9. Attainment of the equilibrium and relaxation (after addition of
D P N H ) of the glycerophosphate dehydrogenase reaction
+Aceloacetale lmt
butyrale
OPNH
A€
lc1
ici
Pyruvate
Dihydroxy
Glutamate-
GT’
.*’
36 units
i
f
3Osec
I
r
i.\
’?
60
IT,,
120 sec 180
Vlle,p=Tss 6 6units=OlL[hours units1
‘I””
[a-GPI 359 pM -1 ~ 0 1 7 162 ; M I
A € = - 0 025
4
Fig. 10. Relaxation of the glycerophosphate dehydrogenase reaction
after addition of enough malic dehydrogenase (as D P N H hindin:
protein) to buffer the DPNH. T h e reaction starts (at the bottom) on
addition of 7 units of enzyme per nil in accordance with Figure 9. Measurements at 334 mu (light path: 2 cm) with a n Eprendorf Photometer
[46b]; Scale expansion 4r ; K phosphate bnffer, ionic strerizth w =
60 m M ; 0.7 m M EDTA; pH 7.2; 25°C. Addition of 20 ~ r n o l e s / lof
malic dehydrogenase (36x lO‘g/mole) results in a n uaspecific increase
i n the extinction. [ Z D P N H ] = free D P N H
D P N H linked t o M D H .
+
Angew. Cheni. internut. Edit.
Vol. 3 (1964)
No. 6
tion (3) on p. 430) is feasible from the experimental
standpoint. It is also justified from the standpoint of
cell physiology, provided steady-state metabolism exists
in the tissues. Such a n arrangement, in which the numerical values were chosen in conformity with cellular
ratios, is presented in Figure 10.
The departure from equilibrium is produced by addition
of a D P N H - b i n d i n g p r o t e i n (dialysed malic dehydrogenase [46a] in a buffering concentration). The
MDH protein binds 1 mole of D P N H per 36x lO3g. The
dissociation constant was determined by fluorimetric titration with DPNH in the presence of DPN, a-GP, and
DAP.
Equation ( 1 7), obtained by making these simplifying assumptions, is evaluated in Figure 1 1 as a function of the
relaxation times mentioned above of the DPN-specific
dehydrogenases.The relationship between the rate of flow
VStand the maximuni enzymatic activity V 1 of the tissue
is plotted on the ordinate. Thus, the curve can be used
for evaluating therelationships existing in various tissues.
However, it should be kept in mind that ( T ~ ~ . was
V ~ ) ~ ~ ~
measured only with glycerophosphate and lactic dehydrogenases from skeletal muscle of rabbit.
Brain,
lltghl muscle
liver
hyper:
thyroid
Titration also showed that the rate a t which the MDHDPNH complex is formed does not produce any appreciable error in the results. The reaction was followed at
334 mp, roughly a t a n isosbestic point [47]. Relaxation
times measured at 25 "C and based o n one enzyme unit
per ml were roughly identical for lactic and glycerophosphate dehydrogenases from rabbit muscle [34,46b]. In a
large number of experiments, they ranged from 0.12 t o
0.25 h/unit/ml. There was interference due to the superposition of a small but constant background decrease in
extinction of unknown cause on the observed variation
in extinction.With the large scale expansion required, accurate determination of the absolute values was thus
difficult.
If, in analogy to Equation (4), we set up an equation for the
symmetrical four-component reaction:
then, assuming that [A] = const. (A = DPNH)
z
z
Heart
-+
005
Thigh muscle-
Liver
normal
hypo=
thyroid
-
0
1
09
08
r/Kapp O 7
Id32111j
Fig. 1 I . Relationships between the rate of flow and the deviation of the
mass-action ratio Kapp/l--l in the lactic dehydrogenase reaction ( I ) and
in the glycerophosphate dehydrogenase reaction (2) [Equation (1711.
-
Curve ( I ) :
[Bl
-
= 0.3 mmole/l.
Curve (2): [B] = 0.04 mmole/l.
(Tss.V,)enp = 0.15 mmoleil.
Ordinate: VstjV,.
Abscissa: upper scale: (Kapp/r)-l.
lower scale: r/Kapp.
The arrows on the ordinate indicate the proportions of the enzymatic
activity of a-GPOX and GDH (cF. Table5, Column 5 ) in rat tissues
and in the flight muscle of thd locust.
The straight line with the greater slope (Curve I), corresponding t o a pyruvate concentration of 0.3 mmole/l, is
the one pertinent to the discussion of the lactic dehydrogenase system, which follows below, whereas the
discussion of the glycerophosphate system is given in
the last paragraph.
l+-
[BI
If we also assume
(where B = pyruvate or dihydroxyacetone phosphate), then
Equation (15) can be simplified to
By using Equations ( 6 ) , (12), and (16), we obtain
which is analogous to Equation (13).
__
Dr. H . U . Eergmeyer of C. F. Boehringer
GmbH., Biochemical Division, Tutzing (Germany),
tor the malic dehydrogenase.
[46a] We wish to t h a n k
u. Soehne
[46b] C . Beisenherr, H . J. Boltre, Th. Biicher. R . Czok. K . H .
Garbade, 4. Meyer-Arendt, and G . Pfleiderer, 2. Naturforsch.
86, 555 (1953).
[47] A . Pfleiderer and E. Hohnholr, Biochem. Z. 331, 245 (1959).
Angew. Chem. internat. Edit. / Vol. 3 (1964)
-.-
/ No. 6
The activity of the lactic dehydrogenase extracted from
I g of rat liver (fresh weight) and tested in vitro, was
30-40 mlnole/h at 37°C. This is the maximum value
which can be assigned t o (Vl)tissue.The minimum value
was calculated t o be 1.7 mmole/g fresh weight/h, using
the value for l a c t a t e f o r m a t i o n in the o r g a n at the
onset of ischemia (Table 4, Column 7). The actual value
of (Vl)tissue is probably closer t o the upper limit.
As far as the metabolic throughput VSt (lactate +
pyruvate) is concerned, it can be stated that it must be
considerably less than the maximum respiration value
in the organ. The maximum respiratory value in rat
liver is 0.6 x 10-3 atoms of oxygen per g fresh weight
per hour. This value also agrees with the conversion of
energy-rich p h s p h a t e (2x 10-3 atoms/g fresh weight/h)
estimated from the ischemia experiments.
The ratio of the maximum value of the metabolic
throughput t o the minimum (Vl)tissue, i . r . the upper
435
limiting value, is
From Fig. 11, Curve 1, this corresponds to a maximum
mass-action ratio deviation of 15 % (see also [*I on
p. 428).
“central complexes”. To simplify the calculations and
for the sake of greater lucidity, we used an ordered
sequence for the formation of transitory complexes,
according to the following scheme which was introduced
by Cleland (“ordered BiBi”) [ * J :
(5)
=0.85.
pyi.-lac.
Since T~~is independent of the direction of the deviation,
the calculated value of 15 % is valid for both the forward
and the reverse reaction. The deviation from the massaction ratio is proportional to the potential difference
Our calculation gives a maximum value for the deviation
of the redox potential of the DPNH/DPN system from
that of the lactate/pyruvate system at the site where the
lactic dehydrogenase is operative. Even under extreme
conditions, the actual physiological deviation is considerably smaller since the actual rates of flow are very
likely to be smaller and, above all, since the actual
(Vl)tissuemust be assumed to be considerably larger than
the value used in the calculation.
These calculations close the ring of evidence around the
status of the lactatelpyruvate system in the liver with regard to its use as an indicator for the redox potential of
the extramitochondrial DPNiDPNH system. They also
show that the indicator error can be neglected.
K Vi [PI K p V i [QI
Vi [PI [QI
+L-+--+-Kapp
Kapp
Kiq
( T ~calculated
~ ,
and experimental)
Enzymatic catalysis of the reaction A + B + P + Q can
proceed via several conceivable mechanisms. These were
discussed by Bloomfield et al. [48]and Cleland [30].As
far as the mechanism of the reaction catalysed by glycerophosphate dehydrogenase (von Euler-Bsranowski
enzyme, see also Fig. 2, top right) is concerned, it can
Dihydroxyacetone phosphate
11
GDH
r-Glycerol-1-phosphate
+ DPNH + H+
+ DPN
(d)
+--K,Vi [A1[PI
Kia Kapp
Vi P I [PI [QI
Vz [A1P I [PI
KaVz[Bl [QI
+ ---+
10. Glycerophosphate Dehydrogenase
Kapp
Kip
KibKapp
K, etc. = Michaelis constants (e. g. [Bl saturating,
[PI and [QI at zero concentration)
V, = maximum velocity ([A] and [Bl saturating,
[PI and [Q] at zero concentration)
Vz in analogy to V1 for the reverse reaction
Kia etc. = inhibition constants (dissociation constants of EA etc.)
All constants are in [ ~ m o l e / l l .
The value of T~~ was obtained by applying a modification of
the method of Hnmmes and Albert)), which is analogous t o
that used for the two-component reaction (see page 431).
<
El
[A], [B], [PI,
and applying the
Assuming that A A
very useful “Haldane” relationships given by Clelund (see
1301, page 128), we obtain:
+--
-
[A1
+ [El +K-- [PI + [Ql
~
eq
be deduced from
titrations that DPNH and
DPN react directly with the protein of the enzyme. Our
mechanism, which was selected only f o r a p p r o x i m a t e
c a l c u l a t i o n s * is
by the
[48l V. Bloomfield, L. Peller, and R . A. Alberty, J. Arner. chern.
SOC. 84, 4365,4361,4375 (1962).
436
~~
- __
[*I This graphic descrlption of the reaction sequence should be
read from left to right. The enzyme IS represented by the
horizontal line. The f r e e substrates (A, B,:..) and products
(P, Q,...) lie above it and the transitory complexes beneath. The
central complexes (EAB) and (EPO) are characterized by the
fact that they do not participate in- birnolecular reactions- with
substrates or products, but can only undergo (monomolecular)
cleavage or isomerization.
Angew. Chem. internat. Edit.
Vol. 3 (1964) / No. 6
[a,
If
El, and [A], [B] are constant, then T ~ ~ .canV ~be
expressed as a function of
:
[s]
In view of these discrepancies, it would be advisable, at
the present state of the theory, to measure relaxation
times directly and not to calculate them by using Michaelis constants (cf. [14]). The adoption of T~~as a parameter in mathematical models should prove to be advantageous for the same reason.
If we substitute the kinetic constants obtained in the approximation experiments using the method of Florini and Vestling
[48a] and by fluorimetric titration (see Table 4), and if
11. The Glycerophosphate Cycle
we consider that the terms containing K i b and K i p are suffi-
ciently small to be neglected, then, when
It can be seen that the relaxation time increases with decreasing equilibrium concentrations of [DAP]. The graph of
the function resembles a hyperbola.
~
Table 4. Kinetic constants.
Measurzd by
the method of
Florini and Vestling
Fluorimetry
V,
Kia = 0.01 +mole/l
Kiq = 2.8 pmolell
3.8 mmolell/h
V2 = 0.8 mmole/l/h
Ka = 2 pmole/l
Kd = 30 pmole/l
Kp = 530 pmole/l
Kq = 980 pmole/l
=
25 OC,50 mmole/l of triethanolamine/HCl buffer,
5 mmole/l of EDTA, pH 7.5, Kapp = 2.5X lo4
Our measurements (Fig. 12) on the relationship between T ~ ~ and
. V ~
the equilibrium concentration of dihydroxyacetone phosphate are in agreement with the
theory cited above insofar as there is a large variation in
T ~ ~ in
. Vthe
~ range of low [DYA] concentrations. The
shape of the curve also resembles that described by
Equation (20). However, the numerical values of T ~ , , . V ~
calculated from Equation (20) are much higher than the
experimental values.
113271il
20
LO
The glycerophosphate/dihydroxyacetonephosphate system cannot be treated in the same manner as the lactate/
pyruvate system (see Section 9) without introducing
some further considerations. First, the cellular activity
of GDH is lower by at least one order of magnitude
(Table 5, Column 3) than that of LDH (except in the
flight muscles of insects [49,50,52]J. Second, in conformance with Equation (17), V s t / V 1 is a function of
[B]. However, [B], the metabolite concentration, in the
glycerophosphate system is considerably lower than
that in the lactate system.
Third, the glycerophosphate system is not isolated in a
“blind alley”, but oscillates between and is coupled with
two different redox systems. In the glycerophosphate
cycle (Fig. 2, top right), it is coupled to the extramitochondrial DPNH/DPN system via extramitochondrial
glycerophosphate dehydrogenase ; in the same cycle, it
is coupled to the respiratory cycle via glycerophosphate
oxidase (the Meyerhof-Green enzyme). The mitochoadrial reaction, which is unidirectional under aerobic
conditions, is the controlling reaction.
Another fact that is also of functional importance is the
redox potential of the extramitochondrial DPNH/DPN
system, which is considerably more positive (about
80 mV [10,43a-46]) than the mid-potential (Fig. 8).
This’is indicated by the potential of the lactate/pyruvate
system (see Sections 8 and 9).
We have already discussed in previous articles the
differences between the redox potentials of the lactate
and glycerophosphate systems, in connection with the
glycerophosphate cycle [10,49,50]. In order to make use
of the more extensive information now available, we
have marked the ratios found in various tissues (see
Table 5, Column 5 ) for the activities of glycerophosphate oxidase and glycerophosphate dehydrogenase by
arrows at the ordinate of Figure 11 (Vst/Vl). We assume here that VSt is proportional to the activity level
of the controlling mitochondria1 enzyme and that
(Vl)tissue is proportional to the activity level of the extramitochondrial enzyme.
60
Fig. 12. Glycerophosphate dehydrogenase Beaction.
Relaxation timex enzyme units per unit volume (ordinat$) versus
equilibrium concentration of dihydroxyacetone phosphate (abscissa).
[49] E. Zebe, A . Delbriick, and Th. Biicher, Biochem.
(1959); Ber. Physiol. 189, 115 (1957).
Experiment9 of the type indicated in Figure 9 ([DAP]x[DPNH]
approximate!>, constan:), hut at pH 7.2 with an ionic strength 9 = 0.1
m M . The “plus” sign corresponds to the experiment reproduced i n
Figure 10.
S.-Ber.Ges.Beforderung ges. Naturwiss. Marburg 8 5 , 383 (1963).
1511 Y . P . Lee and H . A . Lardy, Fed. Proc. 20, 224 (1961); Y. P .
Lee, A . E. Takemori, and H . A . Lardy, J. biol. Chemistry 234, 305
Ordinate: r s s . V ~ [mmole/l].
(1959)
__
~ _ _
[DG[~irnole/l].
2.331,
254
[50] Th. Biicher, “Redoxbeziehungen des r-Glycerophosphats”,
[5la].
[48a] R . Florini and C. S. Vestling, Biochim. biophysica Acta 2 5 ,
[5la]Inadvertently the second paper in ref. [51] was not quoted
in our previous publications [12] and [29].
(521 A . Delbriick, E. Zebc, and Th. Biicher, Biochem. 2. 3 3 1 , 2 1 3
755 (1957).
(1959).
Abscissa:
Angew. Chem. internat. Edit.
Vol. 3 (1964)
/ No.6
437
2
1
5
[bl
G-GPOX
___
Organ
[f*mole/h/g fresh weight)
[I1
6
GDH
{a-GP) {Pyr}
y
10'
__.-
CDAP)
{Lac)
1700
74
36
49
0.1 I [ c ]
(0.17) [kl
Heart (rat)
26 000
236
13
5.6
0.11 [dl
( 0 . 2 ) [kl
Heart (dog)
18000
670
34 [a1
5.1
0.1 [el
Skeletal muscle
(rat)
30000
2600
90
3.5
24000 [h]
14000
16000 [hl
2200 [hl
2300
2800 [hl
Brain (rat) [ml
Liver.
hyperthyreoid
normal
hypolhyreoid
1
190 [il
15 [il
1 [I1
86
0.6
0.04
0.23 [f]
(0.46) Ikl
7
Metabolic throughput in v i r o
lactate
dycerophosphate
formation
formation
[&mole/h/gfresh weight]
I
240 [el
36
9200[f]
640
0.9 [gl
[c] From measurements of W. Wesemann and H. .I. Hohorsf [91
Id] From measurements of Th. Biicher and C . H o m a n n [lo].
[el F r o m measurements of M. Klarwein et al. [581.
[hl From unpublished nieasurements of H . Mirzkat and G. Rassner,
cf. 1601. T h e significance of the deviation f r o m normal values was not
statistically confirmed.
[il From measurements of B. Kadenbach and H . Brandilir [59].
[ kl Ratios in parentheses are based on the plasma value [Z.ac]/[Pyr] =lo.
[f] From measurenients of H. J . Hohorsf et al. [8,9,211.
[g] From measurements of H. Schimassek [291.
[I1 [?-GPl~[P~rl/[DAP]~[Lacl
= 0.8.
[mlCompare also [531.
Curve 2 of Figure 1 1 describes the system under consideration. Sections of the abscissa corresponding to the
arrows opposite the ordinate would lead us to anticipate
considerable deviations of r/Kapp-l in s x n e cases. That
such deviations do indeed exist and that their interpretation can be correlated with the chain of reasoning presented here, will now be shown using liver as an
example [29].
If the measured values given at the bottom of Column 6
in Table 5 are inserted, p/Kappin the hypothyroid state
becomes 1.1, in the normal state 0.8, and in the hyperthyroid state 0.4.Sections of the abscissa corresponding
to the arrows on the ordinate in Figure 11 represent
smaller deviations. Thus, for the hypothyroid state, we
obtain from the graph: r / K a p p= 0.76.
[a] From unpublished measurements of D . P e f t e .
[bl From unpublished measurements of B. Kadenbach.
L a d y and coworkers discovered that the cellular activity of mitochondria1 glycerophosphate oxidase is
governed by the inductive action of the thyroid hormone
[51]. The hormone does not affect the activity of the
extramitochondrial enzyme. In fact, the ratio x-GPOX/
G D H can be varied over a range of two orders of
magnitude by feeding or withdrawing the thyroid
hormone (Table 5, bottom of Column 5).
In order to demonstrate deviations in the metabolite
ratio {a-GP}/{DAP},we may use the {Lac}/{Pyr}ratio as
an indicator for the redox potential of the extramitochondrial DPNHiDPN system (see Section 9). When the two
DPN-specific systems are at equilibrium
Lactate
+ Dihydroxyacetone phosphate
Pyruvate
11, LDH + G D H + D P N I D P N H
+ Glycerol-1-phosphate
then we have in our ionic medium
[or-GP][Pyr]
z
_
:
~
= 0.8
[DAP] [Lac]
and, therefore,
'I
~_
Kapp
438
1 ~
{E-GP}
{Pyr}
_
-- - -~
0.8 {DAP}{Lac}
At the present state of these techniques, exact numerical
agreement between the values predicted by reconstruction experiments and those measured in the organ could
only be accidental. However, even an agreement between mere trends, which can be seen from examination
of Figure 1 1 and Table 5, is already convincing evidence
for the existence of the glycerophosphate cycle in vivo
in rat liver. Besides, it should be noted that with the
characterization and localization of the enzymes (see
review in [SO]) and with the measurement of the ratios
listed in Table 5 , we have gathered all the evidence
which could be obtained in vitro to contribute to a
demonstration of the existence of the glycerophosphate
cycle. Irrespective of whether the results are positive
[53-561 or negative [57], reconstruction experiments
with homogenate fractions or isolated mitochondria
[53] B. Sacktor and L . Packer, J. Neurochem. 9, 371 (1962).
[54] E . J . Ciaccio and D. L . Keller, Fed. Proc. 19, 34 (1960).
I551 P . Borst, Biochim. biophysica Acta 57, 256 (1962).
[56] B. Sncktor and A. Dick, J . biol. Chemistry 237, 3259 (1962).
[57] R . ffedmrm,E. M . Suranyi, R.Luff,and L . Ernster, Biochem.
biophys. Res. Commun. 8 , 314 (1962).
[58] M . Klarwein, W . Lamprecht, and E. Lolimnnn, Hoppe-Seylers
Z. physiol. Chem. 328, 41 (1962).
[59] B. Kadenbnch, H . Brandnu, and Th. Biiclier, Enzymologia
biol. clin., in the press.
[60] J . R . Tata, L . Emster, 0 .Lindberg, E. Arrhenius, S . Pedersen,
and R. Hednzan, Biochem. J. 86, 408 (1963).
Angew. Clicm. interntit. Edit.
/
Vol. 3 (1964)
No. 6
and GDH cannot yield more significant data than
those obtained from the measurement of kinetic constants of the enzymes.
hydroxyacetone phosphate systems are not to be anticipated even if the liver is in a normal state. In this respect, we have to correct o u r previous statements [ 10,111.
As shown by the data and discussion of this Section, the
oc-glycerophcsphate/dihydroxyacetone phosphate systern departs considerably from equilibrium even at low
rates of flow. Exact agreement between the redox potentials for the lactate/pyruvate and x-glycerophosphate/di-
We thank Prof. R. Estabrook and Prof. L. Krampitz for
reading and improving the English manuscriprt.
[A 327/148 IE]
Received, August 20th, 1963
Publication deferred until now at the authors' request
German version: Angew. Chem. 75, 881 (1963)
Translated by scripta technica, New York.
COMMUNICATIONS
Synthesis of 6-[(D-a-Amino-a-phenylacetyl)amino]penicillanic Acid Using P-Dicarbonyl Compounds
as Amino-Protecting Groups
By Prof. Dr. E. Dane [ I ] and Dipl.-Chem. T. Dockner
Institut fur Organische Chemie
der Universitat Munchen (Germany)
Dojde et al. [2] prepared 6-[(~-a-amino-cc-phenylacetyl)amino]penicillanic acid [ampicillin, ( 3 ) ] , in the following
way:
in chloroform of the triethylammonium salt (2), X(3 =
[HN(C,H,),]@. The oily products remaining after evaporation were taken up in NaHC03 solution. The p H was
gradually brought to 2 by addition of 1 N HC1 with stirring.
This precipitated the compound formed from (4a), 6-[a(benzoylacetonylamino) - cc - phenylacetylamino]penicillanic
acid, m.p. 138-147'C, yield 63 %. The protecting group
was split off by passing CO2 into a solution of the compound
in chloroform covered with water. We did not isolate the
N-protected compounds from (46) and ( 4 c) . The protecting
groups were split off in the acid solution. After extraction
with ether, the pH of the aqueous phase was adjusted to
5 with NaHCO3 solution. The solution was then concentrated
by evaporation, and (3) crystallized out at 4°C. The yield
based on (2), X@= He, was 50-60 %,. Microbiological tests
showed that the compound obtained from (4c) had the
characteristic activity against E. coli.
Received, January 31st, 19/54
[Z 678/503 IE]
German version: Angew. Chem. 76, 342 (1964)
[l] We wish to thank the Fonds der Chemischen Industrie and
Farbenfabriken Bayer A.G. for supporting this work.
121 F. P . Doyle, G . R. Fosker, J. H , C . Nuyler, and H . Smith, .1.
chem. SOC.(London) 1962, 1440.
[3] E. Dane, F. Drees, P. Konrad, and T. Dockner, Angew. Chem.
74, 873 (1962); Angew. Chem. internat. Edit. I , 658 (1962); German Patent 1143516 (April 27th, 1961) and foreign patents,
Farbenfabriken Bayer A.G., inventors: E . Dane, F. Drees, and
P. Konrad.
The catalytic hydrogenation required for removal of the
protecting group does, however, not proceed satisfactorily
because of the S-content of the compound.
We have found that it is also possible to use j?-dicarbonyl
compounds as amino-protecting groups in the synthesis of
(3) P I .
~-a-Amino-a-phenylacetic acid dissolved in methanolic
KOH reacts with benzoylacetone, acetylacetone, and ethyl
acetoacetate to give the potassium salts (4u) to (4r). The
formation of (4a) requires heating at 60°C for some hours.
The reaction with acetylacetone takes some hours at room
temperature, acetoacetic ester reacts when the solution is
warmed briefly.
CsH5- CH - C OzK
H3C
YN'H
'
,c.cGo
H
I
R
R
Decomp.
Yield
temp. I "C1 1%I
(4a)
CsHc
231-234
95
(.lbl
CH3
222-224
80
229-233
84
( 4 ~ ) COICIHS
The potassium salts (4a)-(4c) were treated with pivaloyl
chloride in tetrahydrofuran at -5 t o -1OOC [(&I, (4b) in
suspension, (4c) in solution] giving the corresponding mixed
anhydrides. T o the anhydride solution was added a solution
Angew. Chem. internat. Edit.
1 Vat. 3 (1964) 1 No. 6
Selective Hydrolysis of Pyrophosphate Bonds
in Polynucleotides
By Dr. H. Schaller
Institute for Enzyme Research, University of Wisconsin,
Madison, Wis. (U.S.A.) and Max-Planck-lnstitut
fur Virusforschung, Tubingen (Germany)
Dinucleoside pyrophosphates ( l a ) can be split to 2 moles of
mononucleotide (Su) by reaction with dicyclohexylcarbodiimide (DCC) and 2-cyanoethanol (2) and alkaline hydrolysis
of the phosphoric acid di- and tri-esters, (30) and (4n),
formed [I].
This method is also suitable for the selective hydrolysis of
pyrophosphate bonds in polynucleotides ( I b ) , as they are
found at the end of a polymerization with DCC [2] or
similar reagents. The doubly esterified phosphate groups i n
the polynucleotide chain are partly also esterified, but are
recovered unchanged on treatment with alkali, since the $elimination of the cyanoethyl group from the triester proceeds very rapidly [I].
T o a polymerization mixture of thymidylic acid (2 mmoles)
with DCC (4 mmoles) in dimethylformamide (0.9 ml) and
pyridine (0.1 mi), 20 mmoles of (2) and 5 mmoles of DCC
439
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