1046
BIOCHEMICAL SOCIETY TRANSACTIONS
Reversible (Near-Equilibrium) Reactions and Substrate Cycles
BERNARD CRABTREE
Department of Animal Physiology and Nutrition, University of Lee&,
Vicarage Terrace,Leeds LS5 4HL, U.K.
Many metabolic reactions are very close to equilibrium in uiuo (see Rolleston, 1972;
Newsholme & Start, 1973). For such reactions the rate of conversion of the products into
substrates (reverse process) is similar to the rate of conversion of substrates into products
(forward process), and both rates are much greater than the net flux through the reaction:
thus, as the following reaction approaches equilibrium,
-
-
c1
S
e
.
P
m
(net flux= J),
the rate of the forward process (uf) becomes similar to that of the reverse process (ur), with
both uf and or much greater than the net flux, J (= ur-ur). At equilibrium uf = ur and
J = 0. Such near-equilibrium (or reversible) reactions are very sensitive to their substrates and/or products (Newsholme & Crabtree, 1973, 1976) and, in this respect, are
analogous to a substrate cycle, with vf and or as analogues of the forward and reverse
reactions of the cycle, respectively:
-
Uf
S
= P -
(J)
Or
Reversible reaction
- s
p
W
-
(J)
C
Substrate cycle
Consequently the functions describing the intrinsic sensitivity of the reversible reaction
to S and P are analogous to those for the intrinsic sensitivity of the cycle to S and P.
These functions have been derived previously and are as follows (Newsholme &
Crabtree, 1976).
For the cycle (assuming linear responses of F or C to S or P,respectively),
JredSIrel = 1 + (
0
Jrc~/[Plre~
= - C/J
thus, for the reversible reaction (assuming linear responses to S and P),since or = C,
Jre~/[Slrc~= 1 + (ur/J)
= Uf/J
J r e ~ / P l r e=
~
- 4J
= -[(or/J)
- 11
(The subscript, rel, denotes a relative change: see Newsholme & Crabtree, 1976;
Crabtree, 1976.)
The function uf/J is termed the reversibility, R, of the reaction (Newsholme &
Crabtree, 1976), so that:
Jre~/[Slre~=
R
Jre~IP’lre~
=4
R - 1)
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565th MEETING, STIRLING
1047
The value of R increases from unity, when vf = J and the reaction is unidirectional (i.e.
irreversible), to very large values as the reaction approaches equilibrium; thus, as the
reaction approaches equilibrium (i.e. as R increases) the magnitude of the intrinsic sensitivity to S and P also increases, in agreement with earlier conclusions (Newsholme &
Crabtree, 1973). R is related to the more usual function for displacement from equilibrium, K/T (where K is the equilibrium constant and r the ‘mass-action ratio’; see
Rolleston, 19721, by the equation:
(Newsholme & Crabtree, 1976). Some values of R, as a function of K / r , are given in
Appendix 1 of Newsholme & Crabtree (1976): they show that R (and hence the sensitivity
conferred by a reversible reaction) is very large only when K/T lies between unity (i.e.
equilibrium) and 5, i.e. when the reaction is extremely close to equilibrium.
Restriction of reversible-reaction-sensitivity to substrates andproducts
A substrate cycle increases the sensitivity of the net flux to any effector of the forward
and/or reverse reaction (Crabtree, 1976), whereas the reversibility of a reaction only
increases the sensitivity to its substrates and/orproducts (i.e. ‘mass-action’ effectors). This
is because an effector which does not participate in the reaction must act by changing the
activity of the catalyst (enzyme) and therefore cannot alter the rate of one process
(vf or v,) without altering the rate of the other. Moreover, since a catalyst does not affect
the equilibrium constant, K, and since [S], [PI and hence r ( = [ P ] / [ S ] ) are assumed to
remain constant when calculating the intrinsic sensitivity to a non-mass-action effector
(see Crabtree, 1976), the ratio KIT is constant under these conditions. Now KIT = vf/v,
(see Newsholme & Crabtree, 1976), so that vf/vl remains constant for the intrinsic
response to a non-mass-action effector : thus :
J = Vf-V1
=vf-k.vf,
where k (= vI/vf) is a constant, so that:
J = vr(1- k).
Consequently, in this situation J is directly proportional to vIand the intrinsic sensitivity,
Jrcl/(uf)rcl,is unity: there is no effect of the reversibility, and the response is as if the
reaction were completely irreversible (i.e. as if R = 1). n h e reason why the reversibility,
R, affects the response of a reaction to its mass-action effectors is that these effectors, by
participating in the reaction, can alter the rate of one process (vr or v,) independently of
the other.]
These results imply that, if a reaction is very close to equilibrium in vivo (i.e. R is large),
the sensitivities to non-mass-action effectors may be insignificant compared with those
to substrates and products. Moreover, the sensitivities of any effects of the substrates and
products on the catalyst of such near-equilibrium reactions (e.g. substrate inhibition)
may also be insignificant compared with the mass-action effect, since only the latter is
increased by R. These points must be appreciated when extrapolating the kinetics of a
reaction in vitro, where it is usually studied as an irreversible reaction, to the kinetics
in vivo, where it may be close to equilibrium. Under the former conditions the sensitivities
of the mass-action effects and effects on the catalyst may be similar, and this could lead
to an overestimation of the importance of the latter effects if the reversibility in vivo is not
considered.
Crabtree, B. (1976) Biochern. SOC.Trans. 4,999-1002
Newsholme, E. A. & Crabtree, B. (1973)Symp. SOC.Exp. Biol. 27,429-460
Newsholme, E. A. & Crabtree, B. (1976) Biochern. SOC.Symp. 41,61-110
Vol. 4
1048
BIOCHEMICAL SOCIETY TRANSACTIONS
Newsholme, E. A. & Start, C. (1973) Regulation in Metabolism, John Wiley and Sons, London,
Sydney and Toronto
Rolleston, F. S . (1972) Cur. Top. Cell. Regul. 5,47-75
The Hormonal Control of Pyruvate Kinase Activity and of
Gluconeogenesis in Isolated Hepatocytes
JUAN E. FELfU, LOUIS HUE and HENRI-GBRY HERS
Laboratoire de Chimie Physiologique, Universite' Catholique de Louvain and
International Institute of Cellular and Molecular Pathology, UCL-75.39,
avenue H@pocrate 75, B-1200 Bruxelles, Belgium
Effects of Tryptophan on Gluconeogenesis in the Rat and the Guinea Pig
KEITH R. F. ELLIOTT, CHRISTOPHER I. POGSON and
STEPHEN A. SMITH
Biological Laboratory, University of Kent, Canterbury, Kent CT2 7NJ, U.K.
The effect of tryptophan on gluconeogenesis in the isolated perfused rat liver was initially demonstrated in Lardy's laboratory (Venezialeet al., 1967). Significant differences
in the regulation of hepatic gluconeogenesis exist between the rat and the guinea pig.
Addition of fatty acids causes an increase in the rate of glucose production from lactate
by the perfused rat liver, whereas a decrease occurs with the guinea pig (Arinze et al.,
1973).The intracellular distributionof phosphoenolpyruvatecarboxykinase(EC4.1.1.32)
differs between the livers of the two species, being approx. 90 % cytosolic and 10% mitochondria] in the rat, whereas in the guinea pig a substantial proportion is mitochondrial.
We have investigated the effects of tryptophan on gluconeogenesis in isolated liver
cells prepared from both species by the collagenase perfusion technique (Elliott et al.,
1976).
Isolated liver parenchymal cells (60-80mg dry wt.) prepared from 48h-starved animals were incubated in 15ml of Krebs-Henseleit bicarbonate buffer supplemented with
2 % bovine serum albumin and containing lOrnr+L-lactate. The incubation vessels were
shaken at 100cycles/min in Dubnoff-type shaking water baths at 37°C. Cell and incubation-medium fractions were obtained by means of a separatingcentrifuge tube (Hems
et d.,1975) at various times after the addition of O.Sm~-~-tryptophan.
Glucose and
other metabolites in the cellular and incubation-medium fractions were assayed by
standard techniques.
In rat liver cells 0.5m~-~-tryptophan
is a potent inhibitor of gluconeogenesis from
lactate, decreasing the rate to approx. 10% of that of the control without L-tryptophan.
n e half-maximal effective concentration is 0.1 m,close to that normally present in
plasma. The inhibition is accompanied by a change in the intracellular 8-hydroxybutyratelacetoacetateratio, indicating a shift towards a more reduced mitochondrial redox
state. Large increases over the control values of intracellular malate and aspartate (3fold) occur, together with smaller increases in 8-hydroxybutyrate (2-fold), citrate and
2-oxoglutarate (1.5-fold). After 20 min incubation with L-tryptophan the intracellular
phosphoenolpyruvate content falls to less than 10% of the control value. There is no
change in the phosphorylation state of the adenine nucleotides nor in the cytosolic redox
state as indicated by the intracellular lactate/pyruvateratio.
In the guinea-pig liver cells 0.5 m-L-tryptophan does not inhibit glucose production
from l0mM-L-lactate.No significant differences in intracellular metabolites were found
between the L-tryptophan-treated and control cells.
Parallel experiments using rat hepatocytes showed that 0.5 rn-L-tryptophan also
inhibits glucose production from 10mM-pyruvate, -propionate, -L-serine, -L-alanine,
+proline and +glutatnine but not from lorn-glycerol or -D-fructose.
1976