J. theor. Biol. (1996) 182, 437–447
Triosephosphate Isomerase Deficiency: Predictions and Facts*
F O,† B G. V́,† S H́,‡ M H́‡
 J O́†§
†Institute of Enzymology, Biological Research Center, Hungarian Academy of Sciences,
Budapest, H-1518, P.O. Box 7, Hungary and the ‡National Institute of Haematology,
Blood Transfusion and Immunology, Budapest. H-1113, Daróczi út 24, Hungary
Deficiencies in around 20 enzymes, associated with widely different degrees of severity and complexity,
have been identified for human erythrocytes. The fact that glycolysis is crucial for erythrocyte function
is reflected by the large number of inherited glycolytic enzymopathies. Triosephosphate isomerase (TPI)
deficiency, a rare autosomal disease, is usually associated with nonspherocytic hemolytic anemia,
progressive neurologic dysfunction, and death in childhood. The two affected Hungarian brothers
studied by us have less than 3% TPI activity and enormously (30–50-fold) increased dihydroxyacetone
phosphate (DHAP) concentration in their erythrocytes.
The well-established concept of the metabolic control theory was used to test the contribution of TPI
and some related enzymes to the control of a relevant segment of the glycolytic pathway in normal and
deficient cells. Deviation indices, DEJ = (DJ/DE) E r/J r, which give a good estimation of flux control
coefficients using a single large change in enzyme activity, were determined from the fluxes in the absence
and presence of exogeneous enzymes. We found that PFK and aldolase are the enzymes that
predominantly control the flux, however, the quantitative values depend extensively on the pH: DEJ
values are 0.85 and 0.14 at pH 8.0 and 0.33 and 0.67 at pH 7.2 for aldolase and PFK, respectively.
Neither the flux rates nor the capacities of the enzymes seem to be significantly different in normal and
TPI deficient cells.
There is a discrepancy between DHAP levels and TPI activities in the deficient cells. In contrast to
the experimental data the theoretical calculations predict elevation in DHAP level at lower than 0.1%
of the normal value of TPI activity. Several possibilities suggested fail to explain this discrepancy.
Specific associations of glycolytic enzymes to band-3 membrane proteins with their concomitant
inactivation have been demonstrated. We propose that the microcompartmentation of TPI that could
further decrease the reduced isomerase activity of the deficient cells, is responsible for the high DHAP
level.
7 1996 Academic Press Limited
erythrocytes have been identified and it has also long
been recognized that the rates of all the metabolic
processes of the cell depend on the properties of the
enzymes that catalyse each of the required reactions,
the number and quality of enzyme molecules present,
the temperature and the concentration of substrates,
cofactors, activators, inhibitors and the pH within the
cell. Attempts have been made to construct computer
models that simulate this network of reactions in the
red cell (Heinrich et al., 1977; Heinrich & Rapoport,
1974; Rapoport et al., 1974). The glycolytic flux was
Glycolysis in the Red Blood Cell
The mature red cell has to depend almost solely on
anaerobic glycolysis to produce the energy required
for its functions (cf. Fig. 1). The process of extracting
energy from glucose and the utilization of this energy
is carried out by a large number of enzymes. The
pathways of energy and redox metabolism of
* This paper is dedicated to the memory of Henrik Kacser.
§ Author to whom correspondence should be addressed.
E-mail: ovadi.enzim.hu
0022–5193/96/190437 + 11 $25.00/0
437
7 1996 Academic Press Limited
438
.  E T A L .
found to be controlled by hexokinase (HK) and
phosphofructokinase (PFK). The control strengths
for the HK and PFK were calculated to be 0.69–0.73
and 0.31–0.27 at pH 7.2 and 0.87–0.90 and 0.13–0.1
at pH 8.2, respectively (Rapoport et al., 1974). The
model was appropriate to describe the glycolytic flux
using kinetic parameters determined in diluted
systems with isolated enzymes. In addition, it
describes the time courses of changes in concentrations of glycolytic intermediates following changes
in substrate concentrations (Schauer et al., 1981), and
on other effects [for references see Keleti & Ovádi
(1988)]. Additional experiments from other laboratories which demonstrate the regulation of glycolysis
through the change of energy charge by affecting the
activity of PFK and pyruvate kinase (Yoshino &
Murakami, 1985) or PFK by ATP and/or HK by
glucose 6-phosphate (Ataullakhanov et al., 1981;
Meléndez-Hevia et al., 1984) and of PFK and fructose 1,6-bisphosphatase by fructose 2,6-bisphosphate
(Hers & Van Schaftingen, 1982) are also consistent
with the model. These analyses suggest that ATP
concentration is kept constant in the cell by a
mechanism in which 2,3-bisphosphoglycerate by-pass
acts as an ‘‘energy buffer’’ (cf. Fig. 1), it acts as energy
source and ATP change is buffered by variations in
the accumulation rate of fructose 1,6-bisphosphate
and triose phosphate.
The role of PFK in the control of red cell glycolysis
has been extensively discussed (Boscá & Corredor,
1984; Fell, 1984). The published data suggest the
importance of PFK in the control of erythrocyte
glycolysis; however, its control depends on the type of
cells which have various PFK isoforms. For example,
in tumor cells or in yeast, a relatively high ratio of
fructose-1,6-bisphosphate to fructose-6-bisphosphate
was found indicating that PFK was not rate-limiting
under glucose utilizing steady-state conditions. Therefore, the contribution of the enzymes to the control
of glycolytic flux is varied by a number of effects
including isoforms and cellular conditions.
Compartmentation of Glycolytic Enzymes:
New Concept
The mathematical models including the recent ones
have ignored the experimental observations that
certain glycolytic enzymes associate with the erythrocyte membrane and these specific associations alter
their catalytic properties. For example, convincing
studies with PFK indicated that the activity curve
shifts from a sigmoidal shape to a rectangular hyperbola on binding of the enzyme to the erythrocyte
membrane (Karadsheh & Uyeda, 1977). Up to now
several experiments using a variety of techniques
indicated isotonic binding of glycolytic enzymes.
Activity of glyceraldehyde-3-phosphate dehydrogenase (GAPD) in vivo was measured by using 1H
NMR to monitor non-invasively a couple 1H2H
exchange reactions in which the enzyme was involved
(Brindle et al., 1982). The study showed that the
enzyme was totally inhibited when bound to the band
3 membrane protein of erythrocytes. In a series of
studies Steck and his co-workers have demonstrated
that glycolytic enzymes bind specifically to the acidic
N-terminal region of human erythrocyte band 3
(Jenkins et al., 1985; Tsai et al., 1982). From these
enzymes aldolase and GAPD effectively compete with
PFK for binding to band 3 protein and release the
bound PFK (Higashi et al., 1979). More recently, a
rigorous test was developed providing direct evidence
for control of glycolysis by binding to the cytoplasmic
extension of the anion transporter, band 3 protein
in vivo. The glycolytic flux was found to be modulated
over 30-fold by controlling the availability of
glycolytic enzyme binding sites at extreme N terminus
of the anion transporter, band 3 (Low et al., 1993).
By regulating the occupancy of the enzyme binding
site at the N terminus of the anion transporter, the cell
has the potential to adjust its glycolytic flux over a
wide range.
The role of the isoenzyme-specific interactions in
the regulation of glycolysis in various tissues has been
extensively emphasized (for review see Ovádi, 1995).
The presence of isoenzymes in several metabolic
steps can keep multiple pools of intermediates by
isoenzyme-isoenzyme associations as demonstrated
for conversion of glucose-6-phosphate to pyruvate or
glycogen via glycolytic or gluconeogenic pathways
(Ureta, 1978, 1991).
Recently we provided evidence that the different
isoforms of brain PFK exhibited different affinity
towards MAP-containing microtubules (Vértessy
et al. 1996). C-type PFK that predominantly occurs
in brain and tumor cells has much lower affinity to
MTs than M-type has. The muscle type PFK under
identical conditions binds to MTs while the binding
of C isoform is not significant. The binding of muscle
enzyme reduces the overall activity of the kinase since
the inactive dissociated form of the enzyme associates
with MTs. This finding may have physiological relevance and it may partly explain the high uncontrolled
glycolytic rate in tumor cells.
The data available about binding of glycolytic
enzymes to microtubule suggest that the glycolytic
enzymes with high isoelectric point bind to the acidic
C-terminal ‘‘tail’’ of a subunit of tubulin (Carr &
Knull, 1993; Itin et al., 1993; Volker & Knull, 1993).
     
439
GLUCOSE
ATP
*Hexokinase
ADP
G6P
*Glucosephosphate
isomerase
F6P
ATP
*Phosphofructokinase
ADP
FDP
*Aldolase
DHAP
*Triosephosphate
isomerase
GAP
Pi
NAD
Glyceraldehyde-3phosphate
dehydrogenase
NADH
1,3-DPG
*Diphosphoglycerate
mutase
ADP
*Phosphoglycerate
kinase
2,3-DPG
Pi
*Diphosphoglycerate
phosphatase
ATP
3PG
*Phosphoglycerate
mutase
2PG
*Enolase
PEP
ADP
ATP
*Pyruvate kinase
PYRUVATE
NADH
*Lactate dehydrogenase
+
NAD
LACTATE
F. 1. The glycolytic pathway in human erythrocytes. Enzymes whose deficiency have been demonstrated are indicated by an asterisk. For
simplicity all reactions are denoted with single arrows. The portions of glycolysis studied in this paper are indicated by solid or dotted lines.
.  E T A L .
440
This C-terminal binding domain of a tubulin shares
many properties with the N-terminal binding domain
of human erythrocyte band 3 including sequence
homology (Knull & Walsh, 1992). Since it has been
demonstrated that glycolytic enzymes specifically
bind to the acidic N-terminal region of band-3
membrane protein in RBC, it appears, therefore, that
the binding of glycolytic enzymes to domains of
either MTs or red cell membrane is highly specific and
it produces similar functional consequences. These
macromolecular associations have yet to be taken
into account in order to understand the regulation of
energy production in the RBC and the molecular
alterations of diseases caused by inherited or acquired
enzyme deficiency.
Enzyme Deficiency
Extensive evidence indicates that the metabolism of
cells can be impaired if the activity of only one of the
participating enzymes is altered by spontaneous
mutations (inherited or acquired enzymopathies) or
by the administration of toxic drugs or for any other
reason (Schuster & Holzhütter, 1995). The fact that
glycolysis is crucial for RBC function is reflected by
the large number of inherited glycolytic enzymopathies found to result in hemolysis or other aberrations (Tanaka & Zerez, 1990). Based on the energy
dependence of mature erythrocytes on glycolysis, the
depletion of ATP has been proposed to be the cause
of the shortened life span in deficiencies of the
glycolytic enzymes (Valentine et al., 1984). However,
low red cell ATP levels are not invariably associated
with loss of viability, and circulating ATP levels are
not necessarily diminished in patients with glycolytic
enzymopathies (Beutler, 1980).
For human erythrocytes, deficiencies of about 20
enzymes, associated with widely different degrees of
severity and complexity have been identified so far
(Fuji & Miwa, 1990; Valentine & Paglia, 1984).
Nevertheless, quantitative relationships between the
degree of enzyme deficiency and the extent of
metabolic dysfunction are very difficult to establish
experimentally. For most enzymopathies, the experimental and clinical observations can be satisfactorily
rationalized by the computational results [Schuster &
Holzhütter (1995) and references therein]. The models
for the main metabolic pathways of the human
erythrocyte were successfully employed to describe
stationary and time-dependent metabolic states of the
cells under normal physiological conditions as well as
in the presence of enzyme deficiencies. Recently a
mathematical model was evaluated for predicting the
metabolic effect of large-scale enzyme activity alter-
ations. This model was applied for study of enzyme
deficiencies of RBCs (Schuster & Holzhütter, 1995).
Triosephosphate isomerase (TPI) deficiency is a
rate autosomal disease. There are only some 30 cases
reported so far [Hollán et al., (1993) and references
therein]. Although several isoenzymes have been
identified in normal tissues, none of them have been
observed to be specifically associated with a functionally deficient state. Clinically significant TPI
deficiency is usually associated with non-spherocytic
hemolytic anemia, progressive neurologic dysfunction, and death in childhood (Hollán et al., 1993).
TPI, notable for its high catalytic efficiency,
enhances the movement of a single proton to interconvert DHAP and GAP in glycolysis and gluconeogenesis by a factor of about 1010 (Nickbarg &
Knowles, 1988). The rate of catalysis is diffusion
limited (Rose et al., 1990), and the equilibrium
favours the formation of DHAP by 20:1 (Lolis &
Petsko, 1990). In fact, in the erythrocyte the most
striking metabolic abnormality is the 20- to 60-fold
increase in the concentration of DHAP, the substrate
for the enzyme, suggestive of an almost complete
metabolic block at this step (Valentine & Paglia,
1984). Therefore, the disease could be a consequence
of an increased concentration of DHAP. Little or
no modifications occur in the levels of ATP and
2,3-diphosphoglycerate (Hollán et al., 1993).
In Hungary a 13-year-old boy (B.J. Jr.) with
congenital hemolytic anemia and hyperkinetic torsion
dyskinesia was found to have severe TPI deficiency
(cf. Table 1). One of his two brothers, (A.J.), a
23-year-old amateur wrestler has hemolytic anemia as
well, but no neurological signs or symptoms. Both are
compound heterozygotes and have equally less than
3% TPI activity in their red cells. Both parents and
a third brother are healthy heterozygote carriers
of the defect. The main characteristics of the
TPI-deficient Hungarian family are summarized in
Table 1. A.J. represents a unique phenotype from the
point of view that all published homozygotes and
compound heterozygotes had severe neurological
alterations from infancy or early childhood. In
contrast to the two affected Hungarian brothers,
apart from one patient (Harris et al., 1970), all
compound heterozygotes died under the age of 6
years. The dramatic decrease of TPI activity occurs
during the time course of biological evolution due
to spontaneous mutations affecting the amino acid
sequence, and, thus, the spatial arrangement of
enzyme molecules. The Hungarian family is characterized by two mutations: one is mis-sense mutation
within codon 240 (Chang et al., 1993). The other
mutation has been recently localized (Hollán et al.,
0
+++
0
0
0
0
0
+
+
0
0
0
Neurologic
disordera
44
71
pearly white
pearly white
NT
yellow gel-like
546 2 35
NT
pearly white
pink
20–27
854 2 1
None
Partial
Partial
Total
None
Total
DHAP level Characteristics of
TPI
nmol/ml RBC isolated ghosts thermolabilitya
NT
NT
NT
NT
745a
436a
644a
11.1 2 2.1
12.3 2 3.5
40.0 2 1.7
1051–1842
31.5 2 1.0
NT
NT
NT
NT
3.2 2 0.9
3.3 2 0.2
Enzyme activity (Vmax ) U/g hemoglobin
TPI
PFK
Aldolase
DHAP level in whole blood was determined as in (Hollán et al., 1993). Enzyme activities were measured according to (Beutler et al., 1977). TPI activity was
measured with GAP as a substrate. Ghosts were prepared according to (Vértessy & Steck, 1989). NT, not tested; a, data taken from (Hollán et al., 1993).
Normal
Propositus
(B.J. Jr.)
Brother
(A.J.)
Brother
(T.J.)
Mother
(Mrs. B.J.)
Father
(B.J.)
Hemolytic
anemiaa
T 1
Characteristic features in the members of the TPI deficient family
     
441
.  E T A L .
unpublished). The modified TPI termed ‘‘deficient’’
has a slightly higher Michaelis constant for DHAP
but normal Michaelis constant for GAP. The mutant
enzyme is heat unstable and has slower electrophoretic mobility as compared with the normal enzyme
(Hollán et al., 1993). In spite of the considerable
amount of knowledge accumulated about this rare
genetic defect, the pathomechanism of both the
hemolytic anemia and the neurological symptoms is
still obscure.
30
[NADH] (µM)
442
20
Control
PFK
TPI
Aldolase
10
0
2
4
6
Time (min)
8
10
Flux Studies in Normal and TPI Deficient
Hemolysates
30
[NADH] (µM)
In the cases where clinically manifested TPI defect
was identified the TPI activities in erythrocytes
varied between 1.6–28% of the normal value. In most
cases (from 28 diseased persons) the TPI activity was
less than 20.0% (Eber et al., 1991). The two affected
Hungarian brothers have less than 3% activity in
their RBCs (cf. Table 1). Since the activity of TPI is
the highest of any glycolytic enzyme in RBCs, it has
virtually no control property in normal cells and thus
one can ask whether the reduced TPI occurring in
deficient cells is able to sustain the normal glycolytic
flux to produce the appropriate energy for red cell
functions.
The influence of particular enzyme activities on the
flux of metabolites in a pathway can be estimated by
‘‘modulating’’ enzymes and measuring the response in
selected parts of the system. In this particular case we
analysed a relevant segment of glycolysis including
TPI and some related enzymes but not HK which is
known to be by far the enzyme of lowest capacity.
The well-established concept of the metabolic control
theory (Heinrich & Rapoport, 1974; Kacser & Burns,
1973) was used in our laboratory to test the
contribution of TPI to the control of the segments of
glycolytic pathway in TPI deficient cells in comparison to normal cells. In the first type of experiment
the basic flux of normal and TPI deficient cells were
analysed with excess Fru-6-P, Mg-ATP and NADH
as substrates (cf. Fig. 2). In this case the formation of
DHAP produced by the PFK/aldolase/TPI catalysed
consecutive reactions (Fig. 1) was monitored by
coupling them with GDH as auxiliary enzyme. In a
second type of experiment DHAP was an intermediate of the pathway and NADH produced in
equimolar amount with diphosphoglycerate, a
product of GAPD reaction (Fig. 1) was monitored in
the presence of excess Fru-6-P, Mg-ATP, NAD and
arsenate as substrates (Fig. 3). For these studies the
hemolysates of the isolated RBCs were used, prepared
as described in Hollán et al. (1993). The amount of
20
Control
PFK
Aldolase
10
TPI
0
2
4
6
Time (min)
8
10
F. 2. Fructose-6-phosphate conversion in the consecutive
reactions catalysed by PFK/aldolase/TPI in hemolyzed red blood
cells from a normal individual (upper panel) and from the
Propositus (B. J., Jr.) (lower panel). Packed red blood cells
(prepared from the washed isotonic red blood cell preparation by
a final centrifugation at 5000 g, 4°C, 20 min) were lysed by diluting
them fourfold into 10 mM Tris/HCl buffer, pH 8.0, containing
1 mM EDTA and 5 mM mercaptoethanol, followed by three cycles
of freezing in liquid N2 and thawing [c.f. Hollán et al. (1993)]. These
lysed cells were used as hemolyzate in 150-fold dilution. Exogenous
GDH was added to 0.06 mg ml-1 final concentration and flux
was measured by monitoring NADH consumption at 340 nm in
the presence of 1 mM MgATP and 25 mM NADH in 100 mM
Tris/HCl buffer, pH 8.0 at 25°C. The reaction was started by the
addition of 1 mM Fru-6-P. Exogenous enzymes PFK, aldolase or
TPI, where indicated, were added separately to the assays at
0.02 mg ml−1.
hemolysates (extracts) for the assays was limited by
their turbidities. Accordingly, the kinetics were
measured with 150-fold diluted hemolysates of the
normal and deficient cells, hemoglobin content of
which varied between 0.5 and 0.8 mg ml−1. As shown
in Fig. 3, in the second type of experiment in which
TPI catalyses the physiological DHAP 4 GAP
conversion the basic fluxes catalysed by endogenous
enzymes were very low. When DHAP was coupled
with exogeneous GDH as indicated in the first type of
experiment then the flux (NADH consumption) was
well-detectable (cf. Fig. 2) and it corresponded to
1.7 mM NADH min−1 (3.1 U g-1 hemoglobin). The
data were similar whether the extract of normal or
TPI deficient cell was tested. These observations
     
[NADH] (µM)
30
20
Aldolase
10
PFK
Control,
TPI
GAPD
0
2
4
6
Time (min)
8
10
30
[NADH] (µM)
Aldolase
20
10
GAPD, PFK
0
2
4
6
Time (min)
8
TPI
Control
10
F. 3. Fructose-6-phosphate conversion in the consecutive
reactions catalysed by PFK/aldolase/TPI/GAPD in hemolyzed
red blood cells from a normal individual (upper panel) and from
the Propositus (B. J., Jr.) (lower panel). Hemolyzates prepared as
described in Fig. 2 were used at 150-fold dilution in the cuvettes.
Flux was measured by monitoring NADH production at 340 nm
in the presence of 1 mM MgATP, 4 mM NAD, 10 mM sodium
arsenate in 100 mM Tris/HCl buffer, pH 8.0 at 25°C. The reaction
was started by the addition of 1 mM Fru-6-P. Exogenous enzymes
PFK, aldolase, TPI or GAPD, where indicated were added
separately to the assays at 0.02 mg ml−1.
indicate that although TPI activity of the deficient
cells is only 3% or even lower than the normal RBC,
the rate of DHAP formation is not limited by the TPI
activity occurring in the deficient cells.
To get additional data for the control role of TPI
in deficient cells exogeneous TPI was added to the
assays and the fluxes of both NADH consumption
(GDH coupled reaction) and NADH production
(in the presence of NAD and arsenate) were analysed.
As shown in Fig. 2, if DHAP was coupled by excess
exogeneous GDH (first type of experiment) then TPI
caused additional increase in the fluxes in both
normal and deficient cell hemolysates. This finding
indicates that TPI activity is not in enough excess as
compared to the activity of auxiliary enzyme, GDH.
When TPI catalysed the DHAP 4 GAP conversion
in the reaction sequence (second type of experiment)
which is approximately 20-fold lower than the
conversion rate of the reverse direction, a quite
443
substantial increase in TPI activity caused a marginal
increase in the flux catalysed by deficient cells (Fig. 3).
In the normal cells the addition of exogeneous TPI
did not alter the basic flux. The observation that in
the normal cell TPI virtually does not control
glycolysis is in agreement with the expectation. When
comparing the data of normal and deficient cells it can
be argued that TPI activities around the in vivo level
do not appear to limit significantly the hexose and
triosephosphate conversion, even in the deficient cells.
In additional experiments the concentrations of
PFK, aldolase and GAPD of hemolysates were
modulated by separate addition of the exogeneous
enzymes and the fluxes were analysed in extracts
from normal and deficient cells. The data from these
studies allowed us to compare the contributions of the
enzymes with the control of a segments of glycolysis,
where the significant control effect of HK can be disregarded. We compared the measure of the sensitivity
of fluxes to the change in the enzyme activity at PFK,
aldolase and GAPD catalysed steps. The results of
the titrations with excess activities of the enzymes are
shown in Figs. 2 and 3.
In one of his last papers, Henrik Kacser (Small &
Kacser, 1993) developed a method for unbranched
chains to estimate the response of metabolic systems
using a single large change in enzyme activities. A
deviation index, DEJ , (Small & Kacser, 1993) is introduced which gives a measure of the relative change in
a flux:
DEJ = (DJ/DE)E r/J r
where DJ is calculated from the fluxes measured in the
absence and presence of exogeneous enzymes; DE is
the difference of the activities (aldolase or PFK) of the
hemolysates before and after addition of exogeneous
enzymes. The ratio of enzyme activity/flux (Er/J r ) was
calculated at the ‘‘new point’’, after addition of
exogeneous enzymes: 4 U and 0.08 U for PFK and
aldolase, respectively. According to the experimental
data presented in Fig. 2 and Table 1. in the case of
the normal cells, at pH 8.0, DEJ values are 0.85 2 0.1
and 0.14 2 0.05 for aldolase and PFK catalysed reactions, respectively. Since there is a direct relationship
between the deviation indices and control coefficients
(Small & Kacser, 1993), it can be concluded from our
quantitative data that under our experimental conditions aldolase has more significant control on the flux
than PFK. A qualitatively similar result was observed
in the case of the TPI deficient cells. It has to be added
J
J
that the ratio of Daldolase
/DPFK
depends extensively on
the pH, it decreases from 5.7 to 0.5 by decreasing pH
from 8.0 to 7.2. These data suggest that aldolase and
PFK beside HK are important control enzymes of the
RBC glycolysis and that the control properties of the
enzymes extensively depend on the conditions.
In order to compare directly the endogenous
aldolase and PFK activities of the normal and
deficient cells the initial rates of the reactions were
measured in the hemolysates at substrate saturations
with excess auxiliary enzymes. As shown in Table 1.
the Vmax of aldolase is significantly lower than that
of PFK in both normal and deficient cells at pH 8.0,
that predicts lower capacity for aldolase than for PFK
during the glycolysis. Vmax values of TPI reaction
measured in normal and deficient hemolysates (cf.
Table 1) refer to GAP 4 DHAP conversion from
which Vmax values for the reverse direction can be
calculated assuming constant equilibrium, Kequ =
[DHAP]/[GAP] = 20, for both systems. This value
(50–90) for normal cell is still far above the Vmax values
of both aldolase and PFK, however, for propositus
(1.6) it becomes comparable with that of aldolase
which is the slowest enzyme of this segment. Although
from the Vmax values of the sequential enzymes must
not be directly concluded for the capacities of the
enzymes in the sequence, nevertheless, in the light of
the Vmax data it is not surprising that the exogeneous
TPI could enhance the flux to some extent in deficient
cell if the reaction was coupled with GAPD.
Why is the DHAP Level so High in the
Deficient Cells?
A distinctly elevated DHAP level was detected in
the erythrocytes of all patients with defective TPI
although the activity of the isomerase was varied
widely. The concentration of DHAP in erythrocytes
of the Hungarian family is also extensively increased
and it is extremely high in the two affected brothers
(cf. Table 1). The concentration of the GAP is
normal and, in addition, that of ATP and
2,3-diphosphate does not differ significantly from
that of normal cells (Hollán et al., 1993). Although
mathematically oriented, theoretical research has
predicted in many cases the metabolic changes caused
by changing the activity of a given enzyme in the
metabolism of RBC (Schuster & Holzhütter, 1995),
considerable discrepancies can be found in the DHAP
metabolism. According to the theoretical calculations
a few per cent of TPI activity from the normal value
should not result in any elevation in DHAP level
(cf. Fig. 4).
The TPI activity of the members of the Hungarian
family are lower than the normal values but different
from each other, thus, by determining the in vivo
DHAP concentrations in their blood (Hollán et al.,
1993), we were able to construct an experimental
Metabolite concentration (% normal value)
.  E T A L .
444
5000
4000
DHAP measured
3000
2000
1000
DHAP calculated
0
0.01
0
ATP
0.1
1
10
TPI Vmax (% normal activity)
100
F. 4. The dependence of stationary DHAP concentrations on
the activity (Vmax ) of TPI. TPI activity (in washed red blood cells)
and ATP and DHAP levels (in whole blood) were determined
according to Hollán et al. (1993). Solid circles represent ATP levels,
solid and open squares represent DHAP levels measured in the
present study or taken from Hollán et al. (1993), respectively. Solid
curves are theoretical curves computed by Schuster et al. (1995).
curve of DHAP concentration vs. TPI activity. This
curve is compared with the theoretical one computed
for a wide range of TPI activity (Schuster &
Holzhütter, 1995). As shown in Fig. 4, according to
the computation model the extensive reduction of
Vmax of TPI (to about 0.1% of the normal value)
results in only a two-fold elevation in the DHAP level.
In contrast to the theoretical predictions, a 45-fold
increase of DHAP concentration was measured at
about 3% of the normal TPI activity in the patient.
There are other examples that illustrate the discrepancy between DHAP level vs. TPI activity. For
example, in the case of a Turkish girl, DHAP
concentration is 18-fold normal while the TPI activity
was reduced to only 28% of the normal (Eber et al.,
1991). The ATP level determined in the RBCs
(Hollán et al., 1993) appears to be consistent with the
computed data (Schuster & Holzhütter, 1995) and
independent of the actual values of TPI activities
(cf. Fig. 4).
The possible explanations for the discrepancy of
DHAP level vs. TPI activity are summarized as
follows:
(1) The problem in obtaining experimental data
for mature erythrocytes in the case of severe enzyme
deficiencies originates from the fact that the
population of red cells may contain large amounts of
reticulocytes which generally have higher enzyme
activities as well as higher intermediate concentrations than mature erythrocytes (Piomelli & Seaman,
1993). The ratios of the erythrocytes which are near or
beyond the critical threshold of loosing cell integrity
     
445
and of reticulocytes are different in the normal and
the TPI deficient cells. However, the reticulocyte
contents of the patient and his compound heterozygote brother were only slightly elevated (3% vs. the
range of 0.8–1.0 per cent) (Hollán et al., 1993).
(2) The discrepancy for TPI deficiency may also
originate from the remarkable instability of almost all
abnormal enzyme variants (Tanaka & Zerez, 1990).
Unstable proteins may even be more degraded during
the experimental procedures and thus the activities
measured may not reflect the critical level of activities
causing cell damage.
(3) Comparing the results of computerized calculations (Schuster & Holzhütter, 1995) with measured
metabolite concentrations (cf. Fig. 4), discrepancies
may originate from differences between kinetic parameters determined in normal and deficient cells. In
fact, the KM of DHAP to the mutant TPI occurring
in deficient cells is higher than that of the normal,
while the KM of GAP is the same (Hollán et al., 1993).
The velocities of the DHAP 4 GAP conversion
catalysed by TPI in normal and deficient cells can
be calculated according to the Michaelis–Menten
equation:
levels and TPI activities may be due to the fact that a
number of yet unknown structural kinetic parameters
are not taken into consideration. One of these parameters is the specific association of glycolytic enzymes
to the N-terminus of band-3 membrane protein under
physiological conditions (Harrison et al., 1991;
Jenkins et al., 1985; Low et al., 1993; Rogalski et al.,
1989; Tsai et al., 1982). There are data that a
glycolytic enzyme complex from TPI to pyruvate
kinase is bound in vivo to the cytoplasmic domain
of band 3 (Fossel & Solomon, 1978). Due to these
specific associations some glycolytic enzymes are
inactivated, only the unbound enzymes exhibit
catalytic activities (Low et al., 1993). The binding of
the enzymes is reversible. Therefore, it seems to be a
plausible explanation for the discrepancy of TPI
activity and DHAP level that under in vivo conditions
the TPI activity in the deficient cells is further reduced
due to the binding of the isomerase to band 3 in the
red cell membrane or to other cytoplasmic enzymes.
Thus a decrease of TPI activity of deficient cells could
easily reach the limit value which is not able to ensure
the rapid equilibrium of the triosephosphates and
results in the enormous accumulation of DHAP.
norm
def
v norm Vmax
[DHAP]norm([DHAP]def + KM
)
def
norm
def =
def
norm
v
Vmax [DHAP] ([DHAP] + KM )
TPI Deficiency and Enzyme Compartmentation
The KM values are 1.5 mM for normal and 2.8 mM
and 3.0 mM for deficient TPIs from the two affected
brothers (Hollán et al., 1993). [DHAP] for normal
and deficient cells are given in Table 1. Vmax values
of the DHAP 4 GAP conversion for normal and
deficient TPIs were calculated from data presented
in Table 1 using the Halden relationship assuming
identical equilibrium constant for DHAP/GAP conversion catalysed by normal or mutant TPIs. The
ratios of the velocities of the normal and mutant TPI
catalysed reactions are 1.0 and 1.1 for B.J. Jr. and
A.J., respectively. The fact that these ratios correspond to the unity suggests that in deficient cells the
reduction of Vmax and increase of KM are compensated
by the elevation of DHAP concentration; thus TPI
may not limit the endogenous flux.
(4) In general, it is postulated that the steady-state
metabolite level is adjusted by its production/
conversion. DHAP is not an inert metabolite in cells
which are active in lipid synthesis, since it is an
essential precursor of ether lipids. However, there is
no lipid synthesis in mature red blood cells. In fact,
in the hemolysates we were not able to detect GDH
activity, which would be responsible for the DHAP
conversion to lipid synthesis (data not shown).
(5) Additional reason for discrepancies between
the measured and the theoretically postulated DHAP
It is a widely discussed issue that the low TPI
activity in deficient cells leads to a metabolic block in
the glycolytic pathway that results in an increased
concentration of DHAP in the erythrocytes. Nevertheless, the relationship between high DHAP levels
and increased hemolysis is unclear, since accumulation of this compound occurs in cases of diphosphoglycerate mutase deficiency without hemolysis (Rosa
et al., 1978). Also, there are no indications that
DHAP may inhibit regulatory enzymes by its
increased concentration (Eber et al., 1991).
The main objective of this study was to assess the
severity of cellular dysfunction associated with TPI
defect. Since there is no reliable model which describes the relation between TPI activity and DHAP
level characteristic for deficient cells we propose that
the microcompartmentation of TPI, which may or
may not be different in normal and TPI deficient cells,
could be responsible for the altered metabolism in the
deficient RBCs. Different binding affinity of normal
and mutant isomerase molecules to the red cell membranes may originate from differences in the tertiary
structure of the mutant enzyme as well as from
changes in membrane fluidity (Hollán et al., 1995).
Direct binding studies on this issue are in progress in
our laboratory. Concerning the physiological relevance of the computerized models for the RBC
.  E T A L .
446
metabolism we agree with the argument of Beutler
(1980) that ‘‘the usefulness of the models has been
limited by the fact that all the in vivo interactions are
still not entirely understood’’. In fact he referred to
interactions of enzymes with metabolites, allosteric
ligands etc. Now, in the light of recent data the
importance of the macromolecular interactions has
to be underlined. These regulatory mechanisms are
probably different in normal and deficient cells.
This work was supported by grants from the Hungarian
National Science Foundation, OTKA, T-5412, T-6349 and
T-17830 to J.O and F 017392 to B. G. V. We thank Emma
Hlavanda for her expert assistance.
REFERENCES
A, F. I., V, V. M., Z, A. M.,
P, A. V., P, O. V., K, B. N. &
E, L. I. (1981). The regulation of glycolysis in human
erythrocytes. The dependence of the glycolytic flux on the ATP
concentration. Eru. J. Biochem. 115, 359–365.
B, E. (1980). A commentary. Blood Cells. 6, 827–829.
B, E., B, K. G., K, J. C., L̈, G. W., R, B.
& V, W. N. (1977). International Committee for
Standardization in Haematology: recommended methods for
red-cell enzyme analysis. Br. J. Haematol. 35, 331–340.
B́, L. & C, C. (1984). Is phosphofructokinase the
rate-limiting step of glycolysis? Trends Biochem. Sci. 9, 372–373.
B, K. M., C, I. D. & S, R. J. (1982). A 1H
n.m.r. study of the kinetic properties expressed by glyceraldehyde
phosphate dehydrogenase in the intact human erythrocyte.
Biochem. J. 208, 583–592.
C, D. & K, H. (1993). Aldolase-tubulin interactions:
removal of tubulin C-terminals impairs interactions. Biochem.
Biophys. Res. Commun. 195, 289–293.
C, M.-L., A, P. J., W, X., H́, S., L A.
& M, L. E. (1993). Human triosephosphate isomerase
deficiency resulting from mutation of phe-240. Am. J. Hum.
Genet. 52, 1260–1269.
E, S. W., P, A., B, A., G, M., K,
W. K. G., K̈, J., M, R. & S̈, W. (1991).
Triosephosphate isomerase deficiency: haemolytic anaemia,
myopathy with altered mitochondria and mental retardation due
to a new variant with accelerated enzyme catabolism and
diminished specific activity. Eur. J. Pediatr. 150, 761–766.
F, D. A. (1984). Phosphofructokinase and glycolytic flux.
Trends Biochem. Sci. 9, 515–516.
F, E. T. & S, K. (1978). Ouabain-sensitive interaction
between human red cell membrane and glycolytic enzyme
complex in cytosol. Biochim. Biophys. Acta. 510, 99–111.
F, H., M, S. (1990) Recent progress in the molecular genetic
analysis of erythro-enzymopathy. Am. J. Hematol. 34, 301–310.
H, S. R., P, D. E., J, E. R., V, W. & K,
R. L. (1970). Triosephosphate isomerase deficiency in an adult.
Clin. Res. 18, 529–535.
H, M. L., R, R. A, P., G, R. L. &
L, P. S. (1991). Role of band 3 tyrosine phosphorylation
in the regulation of erythrocyte glycolysis. J. Biol. Chem. 266,
4106–4111.
H, R., R, S. M. & R, T. A. (1977).
Metabolic regulation and mathematical models. Prog. Biophys.
Mol. Biol. 32, 1–82.
H, R. & R, T. A. (1974). A linear steady-state
treatment of enzymatic chains. General properties, control and
effector strength. Eur. J. Biochem. 42, 89–95.
H, H.-G. & V S, E. (1982). Review article:
fructose 2,6-bisphosphate 2 years after its discovery. Biochem. J.
206, 1–12.
H, T., R, C. S. & U, K. (1979). The interaction
of phosphofructokinase with erythrocyte membrane. J. Biol.
Chem. 254, 9542–9550.
H́, S., F, H., H, A., H, K., K, H., M,
S., H, V., G, E. & I-K, M. (1993).
Hereditary triosephosphate isomerase (TPI) deficiency: two
severely affected brothers one with and one without neurological
symptoms. Hum. Genet. 92, 486–490.
H́, S., D, I., S́, L., H́, M., M́, M.,
H́, V. & F, T. (1995). Erythrocyte lipids in
triose-phosphate isomerase deficiency. PNAS 92, 268–271.
I, C., B, Y., C U. & D, H. (1993). Selective
inhibition of Plasmodium falciparum aldolase by a tubulin
derived peptide and identification of the binding site. Mol.
Biochem. Parasitol. 58, 135–143.
J, J. D., K, F. J. & S, T. L. (1985). Mode of
interactions of phosphofructokinasae with the erythrocyte
membrane. J. Biol. Chem. 260, 10426–10433.
K, H. & B, J. A. (1973). The control of flux. In: Rate
Control of Biological Processes (Davies, D. D. ed), pp. 65–104.
Cambridge: Cambridge University Press.
K, N. S. & U, K. (1977). Changes in allosteric
properties of phosphofructokinase bound to erythrocyte
membranes. J. Biol. Chem. 252, 7418–7420.
K, T. & O, J. (1988). Control mechanism by dynamic
macromolecular interactions. Curr. Top. Cell. Regul. 29, 1–33.
K, H. R. & W, J. L. (1992). Association of Glycolytic
Enzymes with the Cytoskeleton. Curr. Top. Cell. Regul. 33,
15–30.
L, E. & P, G. A. (1990). Crystallographic analysis of the
complex between triophosphate isomerase and 2- phosphoglycolate at 2.5 A resolution: implications for catalysis. Biochemistry.
29, 6619–6625.
L, P. S., R, P. & H, M. L. (1993). Regulation
of glycolysis via reversible enzyme binding to the membrane
protein, Band 3. J. Biol. Chem. 268, 14627–14631.
M́-H, E., S, J. M. & P́, J. A. (1984). Studies
on glycolysis in vitro: role of glucose phosphorylation and
phosphofructokinase activity on total velocity. Int. J. Biochem.
16, 476–496.
N, E. B. & K, J. R. (1988). Triosephosphate
isomerase: energetics of the reaction catalysed by the yeast
enzyme expressed in Escherichia coli. Biochemistry. 27,
5939–5947.
O́, J. (1995). Cell architecture and Metabolic Channeling.
Heidelberg: Springer-Verlag.
P, S. & S, C. (1993). Mechanism of red blood cell
aging: Relationship of cell density and cell age. Am. J. Hematol.
42, 46–52.
R, T. A., H, R., J, G. & R, S.
(1974). A linear steady-state treatment of enzymatic chains.
A mathematical model of glycolysis of human erythrocytes.
Eur. J. Biochem. 42, 107–120.
R, A. A., S, T. L. & W, A. (1989). Association
of glyceraldehyde-3-phosphate dehydrogenase with the plasma
membrane of the intact human red blood cell. J. Biol. Chem. 264,
6438–6446.
R, R., P, M-O. & B, Y. (1978). The first case of a
complete deficiency of diphosphoglycerate mutase in human
erythrocytes. J. Clin. Invest. 62, 907–915.
R, I. A., F, W. J. & W, J. V. B. (1990). Proton diffusion
in the active site of triosephosphate isomerase. Biochemistry. 29,
4312–4317.
S, M., H, R. & R, S. M. (1981). Mathematische Modellierung der Glykolyse und des Adeninnukleotidstoffwechsels menschlicher Erythrozyten II. Acta Biol. Med.
Germ. 40, 1683–1697.
S, R. & H̈, H.-G. (1995). Use of mathematical
models for predicting the metabolic effect of large-scale enzyme
     
activity alterations. Application to enzyme deficiences of red
blood cells. Eur. J. Biochem. 229, 403–418.
S, J. R. & K, H. (1993). Responses of metabolic
systems to large changes in enzyme activities and effectors. 1. The
linear treatment of unbranched chains. Eur. J. Biochem. 213,
613–624.
T, K. R. & Z, C. R. (1990). Red cell enzymopathies of
glycolytic pathway. Sem. Hematol. 27, 165–185.
T, I., M, S. N. P. & S, T. L. (1982). Effect of red cell
membrane binding on the catalytic activity of glyceraldehyde3-phosphate dehydrogenase. J. Biol. Chem. 257, 1438–1442.
U, T. (1978). The role of isozymes in metabolism: A model
of metabolic pathways as the basis for the biological role of
isozymes. Curr. Top. Cell. Reg. 13, 233–251.
U, T. (1991). The role of isoenzymes in metabolite channeling.
J. theor. Biol. 152, 81–84.
447
V, W. N. & P, D. E. (1984). Erythrocyte enzymopathies, hemolytic anemia, and multisystem disease: an
annotated review. Blood. 64, 583–591.
V́, B. G., K́, J. & O́, J. (1996). Specific
characteristics of phosphofructokinase-microtubule interaction.
FEBS Lett. 379, 191–195.
V́, B. G. & S, T. L. (1989). Elasticity of the human red
cell membrane skeleton. Effects of temperature and denaturants.
Biophys. J. 55, 255–262.
V, K. W. & K, H. R. (1993). Glycolytic enzyme-tubulin
interactions: role of tubulin carboxy terminals. J. Mol. Recognit.
6, 167–177.
Y, M. & M, K. (1985). AMP deaminase reaction
as a control system of glycolysis in yeast. J. Biol. Chem. 260,
4729–4732.