Supplementary material
Rate equations
PGAM; ENO; HPI; TPI:
Michaelis-Menten (Uni Uni) reversible
S
P
 Vr
Kms
Kmp

S
P
1

Kms Kmp
Vf
vnet
Vf
Vr
KmS
KmP
maximal rate of the forward reaction
maximal rate of the reverse reaction
Michaelis constant for substrate S (3PG for PGAM; 2PG for ENO; G6P for HPI;
DHAP for TPI)
Michaelis constant for product P (2PG for PGAM; PEP for ENO; F6P for HPI; G3P
for TPI)
PGAM:
Michaelis-Menten (Uni Uni) reversible with competitive inhibition
S
P
 Vr
Kms
Kmp

S
P
I
1


Kms Kmp Ki
Vf
vnet
Ki
inhibition (dissociation) constant for inhibitor I (PPi)
ENO:
Michaelis-Menten (Uni Uni) reversible with two competitive inhibitors
S
P
 Vr
Kms
Kmp


I
I2
P 
  S
Kms1 
 
 Ki Kj Kmp 
Vf
vnet
I is PPi; I2 is 3PG
Ki
Inhibition (dissociation) constant for inhibitor I
Kj
inhibition (dissociation) constant for inhibitor I2
PPDK:
Bi Bi Ping Pong reversible
vnet

PQ 

Vf  AB 
Keq 




Q 
Vf
A 


AB  KmBA  KmAB1 
KmQP 1 

  QKmp  P 

 KiQ  Vr  Keq 
 KiA 

where
Keq equilibrium constant
KiA
product inhibition constant of A acting on the reverse reaction
KiQ
product inhibition constant of Q acting on the forward reaction
A
is PEP
B
is PPi
or Ter-reactant reversible
vnet

PQR 

Vf  ABC 
Keq 


Vf  KmQ  P Vf  KmP  Q Vf  KmQ  R Vf  KmR  Q
Vf  PQR
KmAB  KmBA  KmCB  KmBC 



 ABC 
Vr  Keq
Vr  Keq
Vr  Keq
Vr  Keq
Vr  Keq
KmA
KmP
KmB
KmQ
KmC
KmR
Michaelis constant for the first bound substrate A (PEP)
Michaelis constant for the first released product P (Pyr)
Michaelis constant for the second bound substrate B (AMP)
Michaelis constant for the second released product Q (ATP)
Michaelis constant for the third bound substrate C (PPi)
Michaelis constant for the third released product R (Pi)
PYK:
Bi Bi Ordered reversible
vnet

PQ 
Vf  AB 
Keq 



P 
Vf
A 
KmAB 
B 




AB1 
KmQP 1 
  KmB A  KiA   KmAB 
  QKmP 1 
  PQ1 


Vr  Keq 
 Kip 
 KiA 
 KiAKmB 
 KiB 
HK:
Bi Bi Random reversible with both mixed-type inhibition and activation
Vmf 
AB  Act PQ 
 AB 


KaKb 
Kact
Keq 
vnet 
A
B
AB
I
AI
BI
ABI
Act
A  Act
B  Act
AB  Act
P
Q
PQ
1













Ka Kb KaKb Ki KaKi KbKi KaKbKi Kact KaKact KbKact KaKbKact Kp Kq KpKq
Kact activation constant for activator Act (PPi).
PPi-PFK:
Bi Bi Random reversible
vnet
 VfAB   VrPQ 


  
 KaKb   KpKq 

A
B
AB
P
Q
PQ
1





Ka Kb KaKb Kp Kq KpKq
ALDO:
Uni Bi Random reversible
 Vf  S   Vr  PQ 


  
 Ks   KpKq 
vnet 
S
P
Q
PQ
1



Ks Kp Kq KpKq
The equation with simple competitive inhibition by PPi includes an additional I/Ki term in the
denominator.
For each rate-equation where inhibition or activation parameters are included,
it was chosen the type of equation (competitive, non-competitive or mixed-type
inhibition; competitive, non-competitive or mixed-type activation) that best fitted the
experimental points.
Table S1. Kinetic parameters of the enzymes in the final E. histolytica glycolytic segment
pH 6.0
Enzyme
Vf
Vr
PGAM
50*
44.8*
ENO
KmA
44.4*
KmC
830** (3PG)
473  212
219*
KmB
KmQ
KmR
Others
106** (2PG)
KiPPi 173#
102** (PEP)
KiPPi 137#
(6)#
60** (2PG)
86.4  33
KmP
(5) #
Kj3PG 610#
PPDK
131*
8.2*
30** (PEP)
2**(AMP)
91** (PPi)
305** (Pyr)
284** (ATP)
(Pi)
Keq 0.73***
221#
597 (2) #
1342 (2) #
KiA 1000 †
KiQ 1000 †
mass action
irreversible
k= 2000 †
LDH
PYK
13.1*
0.8*
22.6§
210§
1000 †
1000 †
Ordered bi bi
Keq 100 †
Kia 1000 †
Kib 1000 †
Kip 1000 †
Table S1 continuation
pH 7.0
PGAM
50*
21.3*
ENO
292*
47*
500**
55**
66*
KiPPi 660#
63*
KiPPi 280#
95  60 (5) #
Kj3PG 460#
PPDK
148*
2*
24** (PEP)
20**
(AMP)
470**
(PPi)
68**(Pyr)
(ATP)
(Pi)
Keq 0.73***
85#
940#
340#
Kia 1000 †
Kiq 1000 †
mass action
irreversible
k= 10000 †
LDH
PYK
14.8*
0.9*
22.6§
210§
1000 †
1000 †
Ordered bi bi
Keq 100 †
Kia 1000 †
Kib 1000 †
Kip 1000 †
Vf and Vr in mU; Km in M. *Data on enzyme proportion and Vr were calculated from Saavedra et al 2007 [10]. ** Kinetic
data taken from Saavedra et al 2005 [16]. *** Keq PPDK at pH 6.3 and 37C [17]. # Data determined in the present paper.
Data from Saavedra et al, 2004 [12]. † Data taken arbitrarily.
§
Table S2. Control analysis in the modeled final segment of Entamoeba histolytica
glycolysis
The enzyme activity proportions were PGAM 1 (50 mU), ENO 4.75, PPDK 2.64 at pH 6.0;
PGAM 1 (50 mU), ENO 6.4, PPDK 2.8 at pH 7.0. The rate equation used for both PGAM
and ENO in the modeling was Michaelis-Menten reversible, whereas that for PPDK was BiBi Ping-Pong with KmPi of 2 mM and KiPEP and Kipyr of 1 mM.
pH 6.0
pH 7.0
Flux rate,
nmol min-1
34.4
20.5
[2PG], M
47
312
[PEP], M
142
1420
J
CPGAM
0.76
0.46
J
CENO
0.10
0.13
J
CPPDK
0.14
0.41
Table S3. Kinetic parameters of the enzymes in the first E. histolytica glycolytic segment
pH 7.0
Enzyme
Vf
Vr
KmA
KmB
KmP
KmQ
Others
Keq 656 **
 1.38 #
HK
50*
40** (Gluc)
77* (ATP)
89  11 (4)#
1000† (G6P)
120** (ADP)
 1.59 #
 2.5 #
KactPPi 67.5 #
KiAMP 24** 5.5 (2) #
HPI
PPi-PFK
ALDO (+ Co2+)
TPI
GPDH
130** (F6P)
122.2*
112.7*
73.3 §
67.6 §
120*
153*
90 §
114.8 §
148*
201*
4** (FBP)
88.8 §
120.6 §
27  9 (3) #
1809*
5445*
740** (G3P)
170 #
660** (G6P)
455** (F6P)
50**(PPi)
76  32 (3) #
1.2†
124** (FBP)
1440** (Pi)
0.5 †
Ki PPi 435 # (2); 43 †
105** (DHAP)
108** (G3P)
 1.0 †
1400** (DHAP)
mass action
irreversible k= 5000 †
Table S3 continuation
pH 6.0
Keq 656 *
 1.2 #
HK
50*
25** (Gluc)
121** (ATP)
1000† (G6P)
235** (ADP)
 1.45 #
1.3 #
Kact PPi 150 #
KiAMP 36**
HPI
PPi-PFK
ALDO (+ Co2+)
TPI
GPDH
122.6*
108.4*
73.5 ***
65 ***
121.6*
197.5*
103.3 ***
167.9 ***
84*
149.5*
28** (FBP)
67.2 ***
119.6 ***
75 (2) #
2298*
3209*
320** (G3P)
610** (G6P)
14 #
460** (F6P)
 1.0 †
695** (F6P)
380 **(PPi)
109** (FBP)
2300** (Pi)
 1.0 †
Ki PPi 211 #
264** (DHAP)
210** (G3P)
 1.0 †
445** (DHAP)
mass action
irreversible k=1000 †
Vf and Vr in mU; Km in M. *Data on enzyme proportion and Vr were calculated from Saavedra et al 2007 [10]. ** Kinetic
data taken from Saavedra et al 2005 [16]. *** Vm values adjusted (see main text). # Data determined in the present paper.
† Data arbitrarily taken.
Table S4. Effect of PPi on the HK activity from different sources
Biological source
Protein added in
the assay (g)
Activity
mU (mg protein)-1
PPi activation,
% Control
E. histolytica recombinant
0.085
440, 000
178
E. histolytica native
30-219
73-360
157  29 (6)
yeast commercial
0.05-0.066
106,000-351,000
169 (2)
rat AS-30D hepatoma
54-77
80-320
96.5  20 (3)
human HeLa cells
229-725
17-19
102 (2)
The HK activity was assayed in the absence and in the presence of 1 mM PP i at pH 7.0
and 37C. For the enzymes from E. histolytica native, hepatoma and HeLa cells, cytosolic
cell extracts were used, whereas for E. histolytica recombinant and yeast, the purified
enzymes were diluted 1:200 and 1:1000, respectively. The assay was initiated by adding
the enzyme.
400
250
-1
Flux, nmol min ; Metabolite, M
[2PG]
200
300
[2PG]
150
200
100
100
50
[PEP]
50
40
15
30
Flux
Flux
20
10
10
[PEP]
5
0
0
200
400
600
800
1000
1200
1400
25
50
75
100
125
150
175
200
150
175
200
0.9
0.9
PGAM
PGAM
0.8
Flux Control Coefficient
0.8
0.7
0.3
0.2
ENO
ENO
0.2
0.1
0.1
0
200
400
600
800
1000
1200
1400
PGAM Km3PG (M)
25
50
75
100
125
ENO Km2PG, M
Figure S1. Effect of varying the Km values on flux control coefficient and, rate and metabolite
concentrations at pH 6.0
The dotted lines indicate the experimentally determined Km values
3
Relative flux
pH 6.0
pH 7.0
2
1
0
0
1
2
3
R factor
4
Figure S2A. Flux rate- Enzyme proportion relationship for the first
glycolytic segment
The r factor represents the simultaneous fold-variation in the five enzyme activities; with r =
1, the HK activity was 50 mU at both pH values, whereas the HPI, PP i-PFK,ALDO and TPI
activities added were, respectively, 122.6, 121.6, 84 and 2298 mU at pH 6.0; and 122.2,
120, 148 and 1809 mU at pH 7.0.
-1
flux (nmoles min )
10
8
6
4
2
0
0
100
200
300
400
500
EhALDO (mU)
Figure S2B. Flux control by ALDO in the absence of added Co2+ in the
reconstituted upper segment.