Supporting Information (Nishino et al.) Text S1. 1. Detailed ... - PLOS

Supporting Information (Nishino et al.) Text S1. 1. Detailed description of PAGGGM-stored RBC model. The main body of the model is based on the published human erythrocyte metabolic model [1]. All reactions expressed in the model are shown below: 1-1. Kinetic equation and parameters used in the model Abbreviation of all reactions and reactants are corresponding to those shown in Table 1 in the main text. et denotes enzyme concentration. HK  theK catf AB theK catr PQ   et  −  K K  K K i ,Q m ,P   i ,B m ,A v= 4 I jB A B AB P Q PQ 1+ + + + + + +∑ K i ,A K i ,B K i ,B K m ,A K i ,P K i ,Q K i ,Q K m ,Q j =1 K i′,Ij K i ,B

theK catf =

theK catr =

1.662k catf  10 − pH 10 −9.55  1 + -7.02 + -pH  10  10 

(S1)

(S2)

1.662 k catr

(S3)  10 − pH 10 −9.55  1 + -7.02 +  10 - pH   10 Symbols: A, MgATP; B, GLC; P, G6P; Q, MgADP; I, Pi, 2,3-BPG and GDP Parameter et (M) Km,MgADP, Ki,MgADP (M) Km,MgATP, Ki,MgATP (M) K’i,2,3BPG (M) K’i,GSH (M) K’i,GDP (M) K’i,G6P (M) Ki,GLC (M) Km,G6P, Ki,G6P (M) kcatf (s-1) kcatr (s-1)

Value 2.50E−08 1.00E−03 1.00E−03 2.70E−03 3.00E−03 1.00E−05 1.00E−05 4.70E−05 4.70E−05 180 1.16

Parameter values were taken from [2] or adjusted by reference to observed data corrected by the literature. 1

Supporting Information (Nishino et al.) Text S1.

PGI, TPI, PGM

k A k P et  catf − catr  K m ,A K m ,P  v=  A P 1+ + K m ,A K m , P

(S4)

Symbols: (PGI) A,G6P; P, F6P (TPI) A, DHAP; P, GA3P (PGM) A, 3PG; P, 2PG Parameter PGI et (M) Km,G6P (M) Km,F6P (M) kcatf (s-1) kcatr (s-1) PGM et (M) Km,2PG (M) Km,3PG (M) kcatf (s-1) kcatr (s-1) TPI et (M) Km,DHAP (M) Km,GA3P (M) kcatf (s-1) kcatr (s-1)

Value 2.18E−07 1.81E−04 7.10E−05 1470 1760 4.10E−07 4.60E−05 1.68E−04 795 714 1.14E−06 1.62E−04 4.46E−04 1280 14560

Parameter values were taken from [2] or adjusted by reference to observed data corrected by the literature.

2

Supporting Information (Nishino et al.) Text S1. PFK

v= 1+

ρ=

A K mR ,A

1 1 + LPFK

L PFK =

 k AB kcatr PQ  − et  catf K   mR ,A K mR ,B K mR ,P K mR ,Q  ×ρ B AB P Q PQ + + + + + K mR ,B K mR ,A K mR ,B K mR ,P K mR ,Q K mR ,P K mR ,Q

(S5)

(S6)  10 -pH   Ka

  

n

2+    1 + ATP  1 + Mg  K T , ATP   K T , Mg 2 +   4

4

   

4

  1 + 2,3BPG   K T , 2,3BPG  

4

     1 + F6P + F16BP  1 + AMP  1 + Pi  K mR , F6P K mR , F16BP   K R , AMP   K R ,Pi  Symbols: A, MgATP; B, F6P; P, F1,6BP; Q, MgADP Parameter et (M) KR,AMP (M) KR,GDP (M) KR,Pi (M) KT,ATP (M) KT,2,3BPG (M) KT,Mg2+ (M) KmR,F1,6BP (M) KmR,F6P (M) KmR,MgADP (M) KmR,MgATP (M) n Ka kcatf (s-1) kcatr (s-1)

   

4

4

  1 + GDP   K R ,GDP  

4

(S7)

Value 1.10E−07 3.50E−05 1.51E−05 4.31E−04 9.80E−06 1.44E−03 4.40E−04 4.20E−04 2.70E−04 5.40E−04 6.80E−05 2 8.91E−08 822 36


3

Supporting Information (Nishino et al.) Text S1. ALD

 k catf A k catr PQ   et  −  K  K K m ,A i ,Q m ,P   v= K m,Q AP K m ,A P  I A I  Q PQ 1+ + + + 1 + + + +  K i , I K m , A K m , P K i ,Q  K i , I  K i ,Q K i , A K m , P K i ,Q K i , Q K m , P

(S8)

Symbols: A, F1,6BP; P, GA3P; Q, DHAP;I, 2,3BPG Parameter et (M) Km,F1,6BP (M) Ki,F1,6BP (M) Km,DHAP (M) Ki,DHAP (M) Km,GA3P (M) Ki,2,3BPG (M) kcatf (s-1) kcatr (s-1)

Value 3.70E−07 1.65E−05 1.98E−05 3.50E−05 1.10E−05 1.90E−04 1.50E−03 68 234

Parameter values were taken from [2] or adjusted by reference to observed data corrected by the literature. GAPDH  kcatf ABC 10 − pH kcatr PQH   et  − K m,A K i ,B K i ,C 10 −7.2 K i ,P K m,Q   v= GAPDH rd

(S9)

  10− pH K m, P Q 1 + C  + +  K i′, C  10− 7.2 K i , P K m, Q  K m, C AB 10− pH K m, P BQ AC BC  C  AP + + 1+ + + − 7.2 + K m, A K i , B K i , C K i , A K i , C K i , B K i , C  K i′, C  K i , A K i , P 10 K i , B K i , P K m, Q K m, C ABP 10− pH CQ 10− pH PQ ABC + + + + − 7.2 − 7.2 10 K i , C K i , Q 10 K i , P K m, Q K m, A K i , B K i , C K i , C K m, A K i , B K i′, P

C  C  P GAPDHrd = 1+ + K i , C  K i′, C  K i , P

10− pH K m, P BPQ 10− pH BCQ + 10− 7.2 K i , B K i , C K i , Q 10− 7.2 K i , P K m, Q K i , B K i′, P (S10) Symbols: A, NAD+; B, Pi; C, GA3P; P, 1,3BPG; Q, NADH 4

Supporting Information (Nishino et al.) Text S1. Parameter et (M) Km,NAD+ (M) Ki,NAD+ (M) Km,1,3BPG (M) Ki,GA3P (M) Ki,1,3BPG (M) Km,Pi (M) Ki,Pi (M) Km,GA3P (M) K’i,GA3P (M) Ki,NADH (M) K’i,1,3BPG (M) Km,NADH (M) kcatf (s-1) kcatr (s-1)

Value 7.66E−06 4.50E−05 4.50E−05 3.30E−06 6.50E−02 1.00E−02 3.16E−03 3.16E−03 9.50E−05 3.10E−05 1.00E−05 1.00E−06 3.30E−06 232 2765

Parameter values were taken from [2] or adjusted by reference to observed data corrected by the literature. PGK  k catf AB k PQ  et  − catr K K   m , A i , B K i ,Q K m , P  v= A B AB P Q PQ 1+ + + + + + K i , A K i , B K i , B K m , A K i , P K i ,Q K i , Q K m , P

(S11)

Symbols: A, 1,3BPG; B, MgADP; P, 3PG; Q, MgATP Parameter et (M) Ki,1,3-BPG (M) Ki,MgADP (M) Ki,MgATP (M) Ki,3PG (M) Km,1,3-BPG (M) Km,3PG (M) kcatf (s-1) kcatr (s-1)

Value 2.74E−06 1.60E−06 8.00E−05 1.30E−04 2.05E−04 2.00E−06 1.1E−03 2290 917


5

Supporting Information (Nishino et al.) Text S1. EN  k AB k PQ  et  catf − catr  K K  m ,A i , B K i ,Q K m , P  v= A B AB Q PQ 1+ + + + + K i ,A K i ,B K i ,B K m,A K i ,Q K i ,Q K m ,P

(S12)

Symbols: A, 2PG; B, Mg2+; P, Mg2+; Q, PEP Parameter et (M) Ki,Mg2+ (M) Ki,PEP (M) Ki,2PG (M) Km,Mg2+ (M) Km,2PG (M) kcatf (s-1) kcatr (s-1)

Value 2.20E−07 4.60E−04 3.10E−04 1.40E−04 4.60E−05 1.40E−04 190 50

Parameter values were taken from [2] or adjusted by reference to observed data corrected by the literature. PK

v= 1+

A K mR ,A

 k catf AB k catr PQ  et  −   K mR ,A K mR ,B K mR ,P K mR ,Q  ×ρ B AB P Q PQ + + + + + K mR ,B K mR ,A K mR ,B K mR ,P K mR ,Q K mR ,P K mR ,Q

ρ=

1 1 + LPK

LPK

 10 − 6.8  ATP   − pH 1 +    10  K T , ATP  = 4    PEP PYR 1 +  1 + F1,6BP + GDP +  K K mR , PYR   K R , F1,6BP K R ,GDP mR , PEP 

(S14) 4

Symbols: A, MgADP; B, PEP; P, PYR; Q, MgATP.

6

   

4

(S15)

(S13)


Parameter et (M) KR,F1,6BP (M) KR,GDP (M) KR,MgADP (M) KR,MgATP (M) KmR,PEP (M) KmR,PYR (M) KT,ATP (M) kcatf (s-1) kcatr (s-1)

Value 8.70E−08 5.00E−06 1.00E−04 4.74E−04 3.00E−03 2.25E−04 2.00E−03 3.39E−03 1386 3.26

Parameter values were taken from [2] or adjusted by reference to observed data corrected by the literature. LDH

 kcatf AB k PQ  et  − catr K i , A K m, B K i , Q K m, P  v=  LDH rd

(S16)

 K P  K B B  A Q AB LDH rd = 1 + m ,A + mQ 1 + + + + +  K  K K  ′ K K K K K K i , A m , B mP iQ i , B i , A iQ i , A m , B    K m,Q AP K m,A BQ PQ ABP BPQ + + + + K i ,A K m,P K i ,Q K i ,A K m ,B K i ,Q K i ,Q K m,P K i ,A K m ,B K i ,P K i ,B K m,P K i ,Q Symbols: A, NADH; B, PYR; P, NAD+; Q, LAC

7

(S17)


Parameter et (M) Km,NADH (M) Ki,NADH (M) Km,NAD+ (M) Ki,NAD+ (M) Km,PYR (M) Ki,PYR (M) K’i,PYR (M) Km,LAC (M) Ki,LAC (M) kcatf (s-1) kcatr (s-1)

Value 3.43E−06 8.44E−06 2.45E−06 1.07E−04 5.03E−04 1.37E−04 2.28E−04 1.01E−04 1.07E−03 7.33E−03 458 115

Parameter values were taken from [2] or adjusted by reference to observed data corrected by the literature. LDHP (NADPH dependent)  k catf AB k PQ et  − catr K K K m , P K m ,Q m ,A m ,B v=  B Q 1+ + K m , B K m ,Q

   

(S18)

Symbols: A, NADPH; B, PYR; P, NADP+; Q, LAC Parameter et kcatf / Km,NADPH (s-1) et kcatr / Km,NADP (s-1) Km,PYR (M) Km,LAC (M)

Value 3.46E−03 5.43E−07 4.14E−04 4.14E−04


8

Supporting Information (Nishino et al.) Text S1. DPGM, DPGase ( 2,3-BPG shunt ) DPGM: v=

et (N1AB + N 2 AC + N 3 AH) D1A + D2 B + D3C + D4 D + D5 H + D6 AB + D7 AC + D8 AH + D9 BD + D10CD + D11DH

(S19)

DPGase: v=

et (N 3 AH + N 7 DH + N 11 DH ) D1 A + D2 B + D3 C + D4 D + D5 H + D6 AB + D7 AC + D8 AH + D9 BD + D10 CD + D11 DH

(S20) N1 = k1k12 (k15 + k16 )k 3 k 4 (k10 + k 7 )k8 N 2 = k1k10 k12 (k15 + k16 )k 3 k 6 (k 5 + k8 ) N 3 = k1k14 k16 k3 (k10 (k12 (k 5 + k8 ) + k 5 k 9 ) + k 7 (k11 (k 5 + k8 ) + k12 (k 5 + k8 ) + k 5 k 9 )) N 4 = k13 k14 k16 (k 2 + k 3 )(k11k 7 (k 5 + k8 ) + k5 (k10 + k 7 )k 9 ) N 5 = k1k11 (k15 + k16 )k 3 k 4 k 7 k8 N 6 = k1k10 (k15 + k16 )k 3 k 6 (k12 (k 5 + k8 ) + k 5 k 9 ) N 7 = k11k13 k14 k16 (k 2 + k 3 )k 7 (k5 + k8 ) N 8 = k11k13 (k15 + k16 )(k 2 + k 3 )k 4 k 7 k8 N 9 = k10 k13 (k15 + k16 )(k 2 + k 3 )k5 k 6 k 9 N11 = k13 k14 k16 (k 2 + k3 )k 5 (k10 + k 7 )k9 D1 = k1 (k15 + k16 )k3 (k10 (k12 (k 5 + k8 ) + k 5 k 9 ) + k 7 (k11 (k 5 + k8 ) + k12 (k 5 + k8 ) + k 5 k 9 )) D2 = k12 (k15 + k16 )(k 2 + k 3 )k 4 (k10 k 7 )k8 D3 = k10 k12 (k15 + k16 )(k 2 k 3 )k 6 (k 5 + k8 ) D4 = k13 (k15 + k16 )(k 2 + k 3 )(k11k 7 (k 5 + k8 ) + k 5 (k10 + k 7 )k9 ) D5 = k14 k16 (k 2 + k 3 )(k10 (k12 (k 5 + k8 ) + k 5 k 9 ) + k 7 (k11 (k 5 + k8 ) + k12 (k 5 + k8 ) + k 5 k 9 )) D6 = k1 (k15 + k16 )k 4 (k11k3 (k 7 k8 ) + k10 (k12 (k3 + k8 ) + k 3 (k8 + k 9 )) + k 7 (k12 (k3 + k8 ) + k 3 (k8 + k 9 )))

(S21-S42)

D7 = k1 (k15 + k16 )k 6 (k3 (k12 k 5 + k12 k8 + k11 (k 5 + k8 ) + k 5 k 9 ) + k10 (k12 (k 5 + k8 ) + k3 (k 5 + k8 + k 9 ))) D8 = k1k14 (k16 + k 3 )(k10 (k12 (k 5 + k8 ) + k 5 k 9 ) + k 7 (k11 (k 5 + k8 ) + k12 (k 5 + k8 ) + k 5 k 9 )) D9 = k13 (k15 + k16 )( k 2 + k 3 )k 4 (k11k 3 (k 7 k8 ) + (k10 + k 7 )(k8 + k9 )) D10 = k13 (k15 + k16 )(k 2 + k3 )k 6 (k11 (k 5 + k8 ) + k 5 k 9 + k10 (k 5 + k8 + k9 )) D11 = k13 k14 (k 2 + k 3 )(k11 (k16 + k 7 )( k5 + k8 ) + k10 (k 5 k 9 + k16 (k 5 + k8 + k 9 )) + k 7 (k 5 k 9 + k16 (k5 + k8 + k 9 )))

Symbols: A, 1,3-BPG; B, 3PG; C, 2PG; D,2,3-BPG; H, 2PG or Pi

9


Parameter et (M) k2 (s-1) k3 (s-1) k4 (M-1 s-1) k5 (M-1 s-1) k6 (s-1) k7 (s-1) k8 (s-1) k9 (s-1) k10 (s-1) k11 (s-1) k12 (s-1) k13 (M-1 s-1) k14 (M-1 s-1) k15 (s-1) k16 (s-1)

Value 4.1E−07 400 9.9 1.85E+08 1.00E+08 1000 1000 10000 0.55 1979 0.01 1000 1800000 1.00E+09 610000 0.19

Parameter values were taken from [3]. PRPPsyn  PQ  Vm  AB −  K eq   v= K v K m, Q P K v K m , P Q K m, A B + K m , B A + + + AB + K v P K eq K eq

Symbols: A, R5P; B, MgATP; P, PRPP; Q, AMP Parameter Km,AMP (M) Km, ATP (M) Keq Km, PRPP (M) Km,R5P (M) Kv (M) Vm (M h-1)

Value 2.75E−04 1.70E−04 28.6 9.00E−05 6.50E−04 7.50E−04 5.54E−04

Parameter values were taken from [4].

10

(S43)

Supporting Information (Nishino et al.) Text S1. AK

v=

Vm AB K i , A K m, B + K m, A B + K m , B A + AB

(S44)

Symbols: A, ADO; B, MgATP Parameter Ki, ADO (M) Km, ADO (M) Km, MgATP (M) Vm (M s-1)

Value 5.40E−07 1.75E−06 2.70E−05 5.50E−07

Parameter values were taken from [5] and [6]. APK  AB PQ  et  k catf − k catr  K m, A K m ,B K m, P K m ,Q   v= A B AB P Q PQ + + + + + 1+ K m , A K m , B K m , A K m , B K m , P K m ,Q K m , P K m , Q Symbols: A, ADP; B, MgADP; P, AMP; Q, MgATP Parameter et (M) Km,ADP (M) Km,MgADP (M) Km,MgATP (M) Km,AMP (M) kcatf (s-1) kcatr (s-1)

Value 9.70E−07 1.00E−05 1.00E−04 1.10E−04 6.70E−05 2080 3800


11

(S45)

Supporting Information (Nishino et al.) Text S1. ATPase, AMPase, IMPase, GSHox, non-glycolytic NADH consumption v = kS

(S46)

S: substrate of the reaction Parameter AMPase a k (h-1) ATPase c k (h-1) IMPase a k (h-1) GSHox c k (s-1) NADHox b k (s-1)

Parameter values were taken from a[7],

Value 1.58 7.12E−01 9.00E−02 2.38E−05 1.63E−02 b

[2] or cadjusted to achieve the appropriate

steady-state concentration of metabolites. ADPRT, HGPRT  A  B    v = Vm   1 + K  1 + K m , A  m,B  

(S47)

Symbols: (ADPRT) A, ADE; B, PRPP (HGPRT) A, PRPP; B, HX Parameter ADPRT Km,ADE (M) Km,PRPP (M) Vm (M h-1) HGPRT Km,PRPP (M) Km,HX (M) Vm (M h-1)

Value 2.30E−06 1.95E−05 7.80E−05 5.00E−06 2.20E−04 2.01E−04


12

Supporting Information (Nishino et al.) Text S1. PRM, PNPase v = ka A − kd P

(S48)

Symbols: (PNPase) A, INO; P, HX. (PRM) A, R1P; P, R5P. Parameter PNPase ka (s-1) kd (s-1) PRM ka (s-1) kd (s-1)

Value 1.11E+03 1.00E+02 7.25 1.00E+02

Parameter values were taken from [8]. PNPase2 (guanosine phosphorylation process)

= AB

(S49) Symbols: A, GUO; B, Pi Parameter k (s-1•M-2)

Value 1.0E+08

Parameter value was determined by fitting the GUO depletion curve as measured by CE-TOFMS experiments (Figure S1). 6PGLase, ADA, AMPDA V S (S50) v= m Km + S S: substrate of the reaction

Parameter 6PGLase a Km (M) Vm (M h-1) ADA b Km (M) Vm (M h-1) AMPDA b Km (M) Vm (M h-1)

Value 7.99E−05 2.2518 5.20E−05 2.00E−02 8.00E−04 1.00E−05

Parameter values were taken from a[4], b[7]. 13

Supporting Information (Nishino et al.) Text S1. G6PDH Vm v= B 1+ K m ,B

AB K m ,A K m ,B

  1 + A  + P + ATP + 2,3 - BPG  K  K K ATP K 2,3-BPG m ,A  m ,P 

(S51)

Symbols: A, G6P; B, NADP; P, NAPDH Parameter KATP (M) K2,3BPG (M) Km,G6P (M) Km,NADP (M) Km,NADPH (M) Vm (M s-1)

Value 7.49E−04 2.29E−03 6.67E−05 3.67E−06 3.12E−06 6.40E-05

Parameter values were taken from [9]. 6PGODH v=

et ( N1AB − N 2 PQ) D1 + D2 A + D3 B + D4 P + D5 Q + D6 AB + D7 AP + D8 BQ + D9 PQ + D10 ABP + D11BPQ

N1 = k1k3k5k7 k9 N 2 = k2 k4 k6 k8k10 D1 = k2 k9 (k4 k6 + k5k6 + k5k7 ) D2 = k1k9 (k4 k6 + k5k6 + k5k7 ) D3 = k3k5 k7 k9 D4 = k2 k4 k6 k8

(S53-S65)

D5 = k2 k10 (k4 k6 + k5 k6 + k5 k7 ) D6 = k1k3 (k5k7 + k5k9 + k6 k9 + k7 k9 ) D7 = k1k4 k6 k8 D8 = k3k5 k7 k10 D9 = k8 k10 (k2 k4 + k2 k5 + k2 k6 + k4 k6 ) D10 = k1k3k8 (k5 + k6 ) D11 = k3k8k10 (k5 + k6 )

Symbols: A, NADP; B, GO6P; P, RU5P; Q, NADPH

14

(S52)


Parameter et (M) k1 (M-1 s-1) k2 (s-1) k3 (M-1 s-1) k4 (M-1 s-1) k5 (s-1) k6 (s-1) k7 (s-1) k8 (M-1 s-1) k9 (s-1) k10 (M-1 s-1) k11 (s-1) k12 (M-1 s-1)

Value 2.10E−06 2.40E+06 4.10E+02 2.00E+09 2.60E+04 48.0 30.0 6.30E+02 3.60E+04 8.00E+02 2.25E+05 3.00E+02 4.95E+06


15

Supporting Information (Nishino et al.) Text S1. GSSGR v=

et ( N1AB − N 2 P 2Q) GSSGRrd

(S66)

GSSGRrd = D1 + D2A + D3B + D4P + D5Q + D6AB + D7AP + D8BQ + D9P 2 + ( D10 + D11 )PQ + ( D12 + D13 )ABP + D14AP2 + D15BPQ + D16P Q + D17 ABP + D18BP Q 2

2

2

N1 = k1k3k5k7 k9 k11 N 2 = k2 k 4 k6 k8k10 k12 D1 = k2 k9 k11 ( k4 k6 + k4 k7 + k5k7 ) D2 = k1k9 k11 ( k4 k6 + k4 k7 + k5k7 ) D3 = k3k5k7 k9 k11 D4 = k2 k 4 k6 k8k11 D5 = k2 k9 k12 ( k4 k6 + k4 k7 + k5k7 ) D6 = k1k3 (k5 k9 k11 + k6 k9 k11 + k7 k9 k11 + k5k7 k9 + k5 k7 k11 ) D7 = k1k4 k6 k8k11 D8 = k3k5k7 k9 k12 D9 = k2 k4 k6 k8 k10 D10 = k 2 k4 k6 k8 k12 D11 = k2 k10 k12 (k4 k6 + k4 k7 + k5 k7 ) D12 = k1k3k8 k11 ( k5 + k6 ) D13 = k1k3k5k7 k9 k10 D14 = k1k 4 k6 k8k10 D15 = k3k5k7 k10 k12

(S68-S87)

D16 = k8 k10 k12 ( k2 k4 + k2 k5 + k2 k6 + k4 k6 ) D17 = k1k3k8 k10 (k5 + k6 ) D18 = k3k8k10 k12 (k5 + k6 )

Symbols: A, NADPH; B, GSSG;P, GSH; Q, NADP

16

(S67)


Parameter et (M) k1 (M-1 s-1) k2 (s-1) k3 (M-1 s-1) k4 (M-1 s-1) k5 (s-1) k6 (s-1) k7 (s-1) k8 (M-1 s-1) k9 (s-1) k10 (M-1 s-1) k11 (s-1) k12 (M-1 s-1)

Value 1.25E−07 8.50E+07 5.10E+02 1.00E+08 5.60E+05 8.10E+02 1.00E+03 1.00E+06 5.00E+07 1.00E+06 5.00E+07 7.00E+03 1.00E+08

Parameter values were taken from [4]. R5PI, X5PI  kA kP  et  3 − 2  K m ,A K m ,P  v=  A P 1+ + K m , A K m ,P K m,A =

(S88)

k 2 + k3 k + k3 , K m,P = 2 k1 k4

(S89)

Symbols: (R5PI) A, RU5P; P, R5P. (X5PI) A, RU5P; P, X5P. Parameter R5PI et (M) k1 (M-1 s-1) k2 (s-1) k3 (s-1) k4 (M-1 s-1) X5PI et (M) k1 (M-1 s-1) k2 (s-1) k3 (s-1) k4 (M-1 s-1)

Value 1.42E−05 6.09E+04 33.3 14.2 2.16E+04 4.22E−06 3.91E+06 4.38E+02 3.05E+02 1.49E+06

Parameter values were taken from [4]. 17

Supporting Information (Nishino et al.) Text S1. TA, TK1, TK2

v=

e t ( N 1 AB − N 2 PQ) D1 A + D 2 B + D3 P + D 4 Q + D5 AB + D 6 PQ + D7 BQ + D8 AP

(S90)

N1 = k1k3k5 k7 N 2 = k 2 k 4 k 6 k8 D1 = k1k3 (k6 + k7 ) D2 = k5 k7 (k2 + k3 ) D3 = k 2 k 4 (k6 + k7 )

(S91-S100)

D4 = k6 k8 (k 2 + k3 ) D5 = k1k5 (k3 + k7 ) D6 = k4 k8 (k 2 + k6 ) D7 = k5 k8 (k2 + k3 ) D8 = k1k4 (k6 + k7 )

Symbols: (TA) A, S7P; B, GA3P; P, E4P; Q, F6P (TK1) A, X5P; B, R5P; P, GA3P; Q, S7P (TK2) A, X5P; B, E4P; P, GA3P; Q, F6P

18


Parameter TA et (M) k1 (M-1 s-1) k2 (s-1) k3 (s-1) k4 (M-1 s-1) k5 (M-1 s-1) k6 (s-1) k7 (s-1) k8 (M-1 s-1) TK1 et (M) k1 (M-1 s-1) k2 (s-1) k3 (s-1) k4 (M-1 s-1) k5 (M-1 s-1) k6 (s-1) k7 (s-1) k8 (M-1 s-1) TK2 et (M) k1 (M-1 s-1) k2 (s-1) k3 (s-1) k4 (M-1 s-1) k5 (M-1 s-1) k6 (s-1) k7 (s-1) k8 (M-1 s-1)

Value 6.90E−07 2.16E+04 45.3 16.3 3.00E+04 4.90E+05 60.0 17.0 7.90E+04 3.30E−07 2.16E+05 38.0 34.0 1.56E+05 3.29E+05 1.75E+02 40.0 4.48E+04 3.30E−07 2.16E+05 38.0 34.0 1.56 E+05 2.24E+06 1.75E+02 40.0 2.13E+04


19

Supporting Information (Nishino et al.) Text S1. L_GCS v= 1+

B K mapp ,Glu

K mapp ,Glu =

Vm ABC αK m,A K mapp,Glu K m ,C BC AB ABC + app + + app K m ,Glu K m ,C K m ,A K m ,Glu αK m,A K mapp ,Glu K m ,C

K m ,Glu (1 + GSH) K i ,GSH

(S101)

(S102)

Symbols: A, MgATP; B, glutamate; C, cysteine

Parameter Ki,GSH (M) Km,MgATP (M) Km,Glu (M) Km,C (M) Vm (M h-1) α

Value 3.40E−03 4.00E−04 1.80E−03 1.00E−04 5.00E−02 0.20

Parameter values were taken from [10]. GSH_S Vm ABC αK m,A K m ,B K m,C v= A AB AC ABC + + + 1+ K m , A K m , A K m , B K m , A K m , C αK m , A K m , B K m , C

Symbols: A, L_GC; B, glycine; C, MgATP Parameter Km,L_GC (M) Km,glycine (M) Km,MgATP (M) Vm (M h-1) α

Value 9.90E−03 1.37E−03 2.30E−03 8.84E−02 2.60


20

(S103)

Supporting Information (Nishino et al.) Text S1. GSSGtransport  GSSG v = Vm   GSSG + K m ,GSSG

 MgATP   MgATP + K m , MgATP 

Parameter Km,GSSG (M) Km,MgATP (M) Vm (M h-1)

   

(S104)

Value 1.00E−04 6.30E−04 1.90E−04

Parameter values were taken from [4]. HXtr v = Pm HXin +

Vm HXin − HXin + K m

Vmin HXex  ADEex   + HXex K min 1 + Ki  

Parameter Ki (M)a Km (M) Kmin (M) Pm (h-1) Vm (M h-1) Vmin (M h-1)

(S105)

Value 1.20E−05 4.00E−04 1.80E−04 37.8 0.1516 0.1008

Parameter values were taken from [7] and [11]. LACtr, PYRtr, Pitr v = k 0X in − k1X ex where k0 = k1 Keq

K eq = 1 +

10 pHi − pKa 1 + 10 pHi − pKa r −1

(S106)

(S107)

Calculated using Donnan ratio (r) = 0.69, pKa (PYR) = 2.39, pKa (LAC) = 0.00506, pKa (Pi) = 6.75 where Hct = 0.5. X: LAC, PYR, Pi

21


Parameter LACtr k0 (s-1) k1 (s-1) PYRtr k0 (s-1) k1 (s-1) Pitr k0 (s-1) k1 (s-1)

Value 7.33E−03 5.06E−03 2.61E−02 1.80E−02 6.06E−04 5.60E−04

Parameter values were taken from [2]. INOtr, ADOtr, ADE tr

 X in X ex v = Vm  −  K m + X in K m + X ex

  

(S108)

X: INO, ADO, ADE Parameter ADEtr Km (M) Vm (M h-1) ADOtr Km (M) Vm (M h-1) INOtr Km (M) Vm (M h-1)

Value 2.60E−03 90.0E−02 1.20E−04 6.12E−02 1.20E−04 6.12E−02


22

Supporting Information (Nishino et al.) Text S1. Na+/K+ pump  ATP  ATP + K m v=

 Vm  + 2 B2 K + ex z    (K ex ) +  2 2      Pump rd 3

(S109)

 B  Pump rd = B1 B2 + 2 B2 K + ex + ( K + ex ) 2 +  3+ + 1 B1 B2 k 2 k1 + k 3 k1 ( K + ex ) 2 + B2 K + ex z Na in   Parameter B1 (M) B2 (M) B3 (M) Km (M) Vm (M h-1) k2 k1 k3 k1 z

(

Value 6.17E−05 1.33E−04 6.27E−03 7.64E−04 2.32E−03 8.20E−03 5.01E−02 0.711

Parameter values were taken from [7]. Na+, K+ leak v=

K x z log(r ) (X ex − r X in ) + r −1

Vm X ex

(K m + X ex ) − r X in (K m + r X in )

X : Na+, K+ Parameter K+Leak Km (M) Kx (M) Vm (M h-1) r z Na+Leak Km (M) Kx (M) Vm (M h-1) r z

Value 4.00E−03 6.35E−06 3.12E−03 0.620 1.00 2.10E−02 7.06E−06 2.82E−03 0.620 1.00


23

(S111)

)

(S110)

Supporting Information (Nishino et al.) Text S1. 1-2. Intracellular pH degradation profile of PAGGGM-stored RBCs The intracellular pH decline in PAGGGM-stored RBC was approximated as eq.(S112) from the estimated pH time-series under 4°C (Figure 2A).

pH t = 8.79 × 10 − 6.01 × 10 + 7.62

(S112)

1-3. Descriptions of binding processes of metabolites to Mg2+, oxyHb and deoxyHb. The binding processes between metabolites to Mg2+ and hemoglobin are also considered in the model. Kinetics and association constants for calculation of these bindings were shown below: Binding of metabolites to hemoglobin Binding substrates deoxyHb + deoxyHb + deoxyHb + fADP deoxyHb + fATP deoxyHb + deoxyHb + GDP deoxyHb + oxyHb + 1,3-BPG oxyHb + 2,3-BPG oxyHb + ADP oxyHb + ATP oxyHb + MgATP

v = K a′ AB − K d P

↔ ↔ ↔ ↔ ↔ ↔ ↔ ↔ ↔ ↔ ↔ ↔

Complex deoxyHb1,3-BPG deoxyHb2,3-BPG deoxyHbADP deoxyHbATP deoxyHbF-1,6BP deoxyHbGDP deoxyHbMgATP oxyHb1,3-BPG oxyHb2,3-BPG oxyHbADP oxyHbATP oxyHbMgATP

(S113) 2

2n  n  +  − 7 .2  − 7.2 10  10  × K K a′ = (S114) a 2 2n  n  1 + − pH +  − pH  10  10  Symbols: A and B, binding substrates; P, complex 1+

24


Parameter deoxyHb1,3-BPG Ka Kd N deoxyHb1,3-BPG Ka Kd N deoxyHbADP Ka Kd N deoxyHbATP Ka Kd N deoxyHbF-1,6BP Ka Kd N deoxyHbGDP Ka Kd N deoxyHbMgATP Ka Kd N oxyHb1,3-BPG Ka Kd N oxyHb2,3-BPG Ka Kd N oxyHbADP Ka Kd N oxyHbATP Ka

Value 1860000 1200 1.00E−06 6000000 1200 1.00E−06 1440000 1200 1.00E−06 3120000 1200 1.00E−06 1212000 1200 1.00E−06 1212000 1200 1.00E−06 168000 1200 1.00E−06 380000 1200 1.00E−06 300000 1200 1.00E−06 300000 1200 1.00E−06 432000

25

Supporting Information (Nishino et al.) Text S1. Kd N oxyHbMgATP Ka Kd N

1200 1.00E−06 46800 1200 1.00E−06

Parameter values were taken from [12]. Binding of metabolites to Mg2+ Mg1,3-BPG, Mg2,3-BPG Binding substrates Mg2+ + 1,3-BPG Mg2+ + 2,3-BPG

v = K a′ AB − K d P K a′ =

(

1 + 10

−pH

↔ ↔

Complex Mg1,3-BPG Mg2,3-BPG

(S115)

(

)

0.0032K a Kmgbpg + 10− pH × Khbpg × Kmghbpg × Khbpg + 10−2pH × Khbpg × Kh2bpg + K + × Khbpg + K + ×10−pH × Khbpg × Kkhbpg

) (

) (

) (

Symbols: A and B, binding substrates; P, complex Parameter Mg1,3-BPG Ka Kd Kh2bpg Khbpg Kkbpg Kkhbpg Kmgbpg Kmghbpg Mg2,3-BPG Ka Kd Kh2bpg Khbpg Kkbpg Kkhbpg Kmgbpg Kmghbpg

Value 228000 1200 4270000 162000000 85.1 8.9 7410 513 804000 1200 4270000 162000000 85.1 8.9 7410 513

Parameter values were taken from [12]. 26

)

(S116)

Supporting Information (Nishino et al.) Text S1. MgAMP Binding substrates Mg2+ + AMP

Complex MgAMP

↔

v = K a AB − K d P

(S117)

Symbols: A and B, binding substrates; P, complex

Parameter Ka Kd Parameter values were taken from [12].

Value 54054 1200

MgADP Binding substrates Mg2+ + ADP

↔


K a′ =

(

Complex MgADP

(S118)

)

Kmgadp + 10 − pH × Khadp × Kmgadp × Ka 1 + 10 − pH × Khadp + K + × Kkadp

(

) (

)

(S119)

Symbols: A and B, binding substrates; P, complex Parameter Ka Kd Khadp Kkadp Kmgadp Kmghadp

Value 1711.2 1200 5420000 4.8 3290 107


27

Supporting Information (Nishino et al.) Text S1. MgATP Binding substrates Mg2+ + ATP

↔


K a′ =

Complex MgATP

(S120)

(

)

Kmgadp + 10 − pH × Khadp × Kmgadp × Ka 1 + 10 − pH × Khadp + K + × Kkadp

(

) (

)

(S121)

Symbols: A and B, binding substrates; P, complex Parameter Ka Kd Khatp Kkatp Kmgatp Kmghatp Parameter values were taken from [12].

Value 2620.8 1200 9070000 14.0 43200 748.0

MgF-1,6BP, MgGDP Binding substrates Mg2+ + F-1,6-BPG Mg2+ + GDP

v = K a′ , A AB − K d , A P K a′ , A =

(

1 + 10

− pH

Complex MgF-1,6BP MgGDP

↔ ↔

) (

(S122)

(

0.0083 K a , A Kmg , A + 10 − pH × Kh , A × Kmgh , A

× Kh, A + 10

− 2 pH

) (

+

) (

)

× Kh, A × Kh 2, A + K × Kh , A + K × 10 − pH × Kh , A × Kkh , A

(S123) A, B, binding substrates; P, complex, A, f16bpg or gdp.

28

+

)


Parameter MgF-1,6-BP Ka,f16bpg Kd,f16bpg Kh2,f16bpg Kh,f16bpg Kk,f16bpg Kkh,f16bpg Kmg,f16bpg Kmgh,f16bpg MgGDP Ka,gdp Kd,gdp Kh2,gdp Kh,gdp Kk,gdp Kkh,gdp Kmg,gdp Kmgh,dgp

Value 480000 1200 1120000 7560000 10.7 3.3 363.0 89.0 480000 1200 1120000 7560000 10.7 3.3 363.0 89.0

Parameter values were taken from [12]. MgPi Binding substrates Mg2+ + Pi


K a′ =

↔

Complex MgPi

(S124)

10 −7.2 × Khpi + 0.15 Kkpi × Ka 1 + 10 −pH × Khpi + K + × Kkpi

(

) (

)

(S125)

A, B, binding substrates; P, complex Parameter Ka Kd Khpi Kkpi

Value 40800 1200 5680000 3.0


29

Supporting Information (Nishino et al.) Text S1. 1-4. Descriptions of Band3 protein mediated interactions between hemoglobin and glycolytic enzymes. Reversible binding of some glycolytic enzymes and two allosteric form of hemoglobin to Band3 protein, Kinetics and association constants for calculation of these bindings were shown below: Binding proteins Band3 + ALD Band3 + GAPDH Band3 + PFK Band3 + deoxyHb Band3 + oxyHb

v = K a AB − K d P

↔ ↔ ↔ ↔ ↔

Complex Band3-ALD Band3-GAPDH Band3-PFK Band3-deoxyHb Band3-oxyHb

(S126)

Symbols: A,B, binding proteins; P, complex Parameter Band3-ALDa Ka Kd Band3-GAPDHa Ka Kd Band3-PFKb Ka Kd Band3-deoxyHbc Ka Kd Band3-oxyHbc Ka Kd

Value 1200000000 1200 2400000000 1200 6000000000 1200 12000000 1200 120000 1200

Parameter values were taken from a[13], b[14], c[15].

30

Supporting Information (Nishino et al.) Text S1. 1-5. Initial and steady-state concentrations of all substrates in the model Abbreviation of metabolites and enzymes are corresponding to those shown in Table 1 in the main text. Substrate ADE ADO DHAP E4P F6P F1,6-BP G6P GA3P GDP GL6P GLC GO6P GSH GSSG HX IMP INO LAC L_GC NAD NADH NADP NADPH Na+ K+ PEP PRPP PYR Pi R1P R5P RU5P S7P X5P 1,3-BPG 2PG 3PG

Concentration(M) 1.53E−05 4.62E−08 1.51E−05 4.57E−07 1.94E−05 5.35E−06 5.96E−05 3.69E−06 8.77E−05 5.33E−09 4.75E−02 4.47E−05 3.27E−03 4.65E−06 1.61E−06 8.06E−06 1.45E−07 1.33E−03 4.22E−07 6.51E−05 2.40E−07 6.47E−08 6.53E−05 3.39E−02 1.33E−01 8.19E−06 1.41E−06 5.16E−05 1.01E−03 8.08E−05 5.86E−06 4.93E−06 2.10E−05 8.99E−06 2.15E−07 1.45E−05 4.77E−05

31

Supporting Information (Nishino et al.) Text S1. Continued from the preceding page

2,3-BPG (free) 2,3-BPG (total) AMP ADP ATP (free) ATP (total) glutamate glycine cycteine ADE (extracellular) GUO (extracellular) ADO (extracellular) HX (extracellular) INO (extracellular) K+ (extracellular) Na+ (extracellular) LAC (extracellular) PYR (extracellular) Pi (extracellular) Band3 binding region (free) Band3-ALD complex Band3-GAPDH complex Band3-PFK complex ALD (free) GAPDH (free) PFK (free) Band3-deoxyHb complex Band3-deoxyHb1,3-BPG complex Band3-deoxyHb2,3-BPG complex Band3-deoxyHbADP complex Band3-deoxyHbATP complex Band3-deoxyHbF1,6-BP complex Band3-deoxyHbGDP complex Band3-deoxyHbMgATP complex Band3-oxyHb Band3-oxyHb1,3-BPG complex Band3-oxyHb2,3-BPG complex Band3-oxyHbADP complex Band3-oxyHbATP complex Band3-oxyHbF1,6-BP complex Band3-oxyHbGDP complex Band3-oxyHbMgATP complex deoxyHb (free)

32

8.09E−04 3.68E−03 2.48E−05 6.28E−05 5.51E−05 1.91E−03 2.00E−04 1.80E−04 2.00E−07 1.44E−03 1.44E−03 0.00 0.00 0.00 0.00 6.40E−02 0.00 0.00 1.60E−02 2.71E−06 2.70E−07 6.47E−06 1.02E−07 9.95E−05 1.19E−03 7.54E−06 1.05E−06 3.83E−10 6.81E−06 1.13E−07 2.30E−07 6.07E−09 9.95E−08 2.07E−07 1.30E−06 9.67E−11 4.21E−07 2.93E−08 3.94E−08 0.00 0.00 7.15E−08 3.86E−05

Supporting Information (Nishino et al.) Text S1. Continued from the preceding page

deoxyHb-1,3-BPG complex deoxyHb-2,3-BPG complex deoxyHb-ADP complex deoxyHb-ATP complex deoxyHb-F1,6-BP complex deoxyHb-GDP complex deoxyHb-MgATP complex oxyHb (free) oxyHb-1,3-BPG complex oxyHb-1,3-BPG complex oxyHb-ADP complex oxyHb-ATP complex oxyHb-MgATP complex Mg2+ (free) Mg2+-1,3-BPG complex Mg2+-2,3-BPG complex Mg2+-ADP complex Mg2+-AMP complex Mg2+-ATP complex Mg2+-F1,6-BP complex Mg2+-GDP complex Mg2+-Pi complex

1.41E−08 2.51E−04 4.18E−06 8.48E−06 2.24E−06 3.67E−07 7.65E−06 4.78E−03 3.57E−07 1.55E−03 1.08E−04 1.45E−04 2.64E−04 6.03E−04 2.92E−08 5.69E−04 1.30E−04 9.11E−07 1.41E−03 1.48E−06 2.43E−05 2.14E−05

33

Supporting Information (Nishino et al.) Text S1. 2. Parameter settings In terms of the reaction activities of 3 groups (Na+/K+ pump activity, purine salvage activities, and all other reaction activities), we used the same parameter values which were estimated by using real-number genetic algorithm in our published paper [16], because those parameters are assumed to be altered only by cold temperature. In GA analysis, predicted ATP and 2,3-BPG were fit to 8 points time-series (every 7days from 0 to 49 days of storage) of ATP and 2,3-BPG in cold-stored RBCs preserved in commercially available Mannitol-Adenine-Phosphate (MAP) solution [17]. The upper and lower bounds of the three adjustable enzymatic activities were 100% and 0.1% of the original activities, respectively. The population size of each generation was 300 and parameter selection was terminated at 4,000 generations. The evaluation function by using GA analysis as follows; 1 n  [ATPexp ]i − [ ATPpred ]i EV = ∑  n i =1  [ ATPpred ]i

2

n  [ 2,3 - BPG  exp ] i − [ 2,3 - BPG pred ] i  + 1 ∑  n i =1  [ 2,3 - BPG pred ]i 

   

2

(S127)

where EV is the error rate between the predicted and the training data, n is the number of data points (n = 8), ATPexp and 2,3-BPGexp represent the reference data [17], and ATPpred and 2,3-BPGpred are the predicted values by the model. Each parameter was normalized by its initial concentration at day 0. The reaction activities of 3 groups were estimated as 0.1%, 25.0%, and 3.0% of the values in the basal model (37°C), respectively. These parameters were searched within their feasible ranges which we provided in previous study in [16]. Rate constant of guanosine phosphorylation (k = 1.0e+8 s-1·M-2) was obtained from the manually fitting to the time-series of guanosine measured by CE-TOFMS. The guanosine consumption curve calculated by the model showed good fits to the CE-TOFMS data (Figure S1). Moreover, we performed a simulation analysis to observe an influence of the rate constant of guanosine phosphorylation (k) on the dynamic behaviors of metabolic intermediates (Figure S4). In the analysis, k was varied from 1e+6 to 1e+9 and other conditions were same as PAGGGM-stored RBC model. The dynamic behaviors of some metabolic indicators, ATP and HX, were not sensitive to the guanosine phosphorylation rate. The temporal accumulation of 2,3-BPG and other metabolic intermediates were altered when the rate constant was set in lower value, but not sensitive around the value of 1e+8. Therefore, we consider that the rate constant 34

Supporting Information (Nishino et al.) Text S1. used in our model can be used to predict the effect of guanosine supply, as well as the effect of the ratio of adenine and guanosine on the metabolic dynamics of cold-stored RBC.

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