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arnold11

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Reactions

AGPase

HeP + ATP > ∅

ATP_S

ATP synthetase

ADP + Pi = ATP

F26BPc_P

F26BPc phosphatase

F26BPc > HePc + Pic

F6P_TK

F6P transketolase

HeP + TP = E4P + PeP

F6Pc_K

F6Pc kinase

HePc + ATPc = F26BPc + ADPc

FBP_A

FBP aldolase

{2.0}TP = FBP

FBPase

FBP = HeP + Pi

FBPc_A

FBPc aldolase

{2.0}TPc = FBPc

FBPcase

FBPc = HePc + Pic

GAP_DH

GAP dehydrogenase

DPGA + NADPH > TP + NADP

GCAc_Ox

GCAc oxidase

GCAc > GOAc

GCEA_DH

GCEA dehydrogenase

HPRc + NADH = GCEAc + NAD

GCEA_K

GCEA kinase

ATP + GCEA = PGA + ADP

GLUcGOAc_AT

GLUc:GOAc aminotransferase

GLUc + GOAc = KGc + GLYc

GLYc_DC

GLYc decarboxylase

{2.0}GLYc > SERc

GPT_GCA

GPT - GCA

GCA > GCAc

GPT_GCAc

GPT - GCAc

GCAc > GCA

GPT_GCEA

GPT - GCEA

GCEA > GCEAc

GPT_GCEAc

GPT - GCEAc

GCEAc > GCEA

PGA_K

PGA kinase

PGA + ATP > DPGA + ADP

PGAc_Deg

PGAc degradation

PGAc > ∅

PGCA_P

PGCA phosphatase

PGCA > GCA

Ru5P_K

Ru5P kinase

PeP + ATP = RuBP + ADP

RuBisCO_CO2

RuBisCO - CO2

RuBP > {2.0}PGA

RuBisCO_O2

RuBisC0 - O2

RuBP > PGA + PGCA

S7P_TK

S7P transketolase

TP + S7P = {2.0}PeP

SBP_A

SBP aldolase

TP + E4P = SBP

SBPase

SBP = S7P + Pi

SERcGOAc_AT

SERc:GOAc aminotransferase

SERc + GOAc = HPRc + GLYc

SucPc_P

SucPc phosphatase

SucPc = Succ + Pic

SucPc_S

SucPc synthase

HePc + UDPGc = SucPc + UDPc

Succ_Deg

Succ degradation

Succ > ∅

TPT_DHAP

TPT - DHAP

TP > TPc

TPT_GAP

TPT - GAP

TP > TPc

TPT_PGA

TPT - PGA

PGA > PGAc

UGPase

HePc + UTPc = UDPGc + PiPic

Parameters

Global parameters

cA*

cAc*

cNc*

cP*

cPc*

cUc*

chloroplast*

cytosol*

AGPase

K2*

KA1*

KA2*

KA3*

Vm*

K1*

KR1*

ATP_S

Ks1*

Ks2*

Vm*

Kp1*

F26BPc_P

Ks1*

Vm*

Kr1*

Kr2*

F6P_TK

Vm*

Ks1*

Ks2*

Kr1*

Kr2*

F6Pc_K

Kr3*

Vm*

Ks2*

Kr2*

Kr1*

Ks1*

FBP_A

Kp1*

Vm*

Ks2*

Ks1*

FBPase

Ks1*

Vm*

Kr2*

Kr1*

FBPc_A

Ks1*

Vm*

Ks2*

Kp1*

FBPcase

Kp1*

Kp2*

Vm*

GAP_DH

K1*

K2*

Vm*

GCAc_Ox

Km*

GCEA_DH

Ks1*

Kr1*

Vm*

GCEA_K

Ks1*

Vm*

Kr1*

Ks2*

GLUcGOAc_AT

Vm*

Ks1*

Kr1*

Ks2*

GLYc_DC

Kr1*

Vm*

Ks1*

GPT_GCA

Ki*

Km*

GPT_GCAc

Ki*

Km*

GPT_GCEA

Ki*

Km*

GPT_GCEAc

Km*

Ki*

PGA_K

Kr1*

Ks2*

Ks1*

Vm*

PGAc_Deg

Km*

PGCA_P

Kr1*

Kr2*

Vm*

Ks1*

Ru5P_K

Kr2*

Vm*

Kr42*

Ks2*

Kr41*

Ks1*

Kr1*

Kr3*

RuBisCO_CO2

KR1*

KR2*

KR3*

KR4*

KR5*

RuBisCO_O2

KR5*

KR1*

KR2*

KR3*

KR4*

S7P_TK

Ks1*

Kr2*

Kr1*

Ks2*

Vm*

SBP_A

Ks1*

Vm*

Ks2*

SBPase

Ks1*

Vm*

Kr1*

SERcGOAc_AT

Ks2*

Kr1*

Ks1*

Vm*

SucPc_P

Ks1*

Vm*

Kr1*

SucPc_S

Ks2*

Kr5*

Kr4*

Kr3*

Kr2*

Kr1*

Ks1*

Vm*

Succ_Deg

Km*

TPT_DHAP

KR2*

KR1*

Vm*

KA*

KR3*

TPT_GAP

Vm*

KA*

KR1*

KR2*

KR3*

TPT_PGA

KR1*

KA*

KR2*

KR3*

Vm*

UGPase

Vm*

Ks1*

Ks2*

Kp1*

Kp2*

Initial values

ATP*

DPGA*

E4P*

F26BPc*

FBP*

FBPc*

GCA*

GCAc*

GCEA*

GCEAc*

GLYc*

GOAc*

HPRc*

HeP*

HePc*

PGA*

PGAc*

PGCA*

PeP*

RuBP*

S7P*

SBP*

SERc*

SucPc*

Succ*

TP*

TPc*

UDPGc*

Functions and Rules

Assignment rules

Ru5P = PeP / (1.0 + 1.0 / 0.4 + 1.0 / 0.67)

Pi = cP - 2.0 * (RuBP + DPGA + FBP + SBP) - (PGA + TP + HeP + E4P + S7P + PeP + ATP + PGCA)

X5P = PeP / 0.67 / (1.0 + 1.0 / 0.4 + 1.0 / 0.67)

G1P = HeP * 0.058 / (1.0 + 1.0 / 2.3 + 0.058)

GAP = 0.05 * TP / (1.0 + 0.05)

DHAP = TP / (1.0 + 0.05)

G6P = HeP / (1.0 + 1.0 / 2.3 + 0.058)

R5P = PeP / 0.4 / (1.0 + 1.0 / 0.4 + 1.0 / 0.67)

K52a = 0.0025 * (1.0 + F26BPc / 7.000000e-05)

ADPc = cAc - ATPc

Wo_min = 0.24 * 2.913930914 * O2 / (O2 + 0.222 * (1.0 + CO2 / 0.0115)) * ((1.0 + RuBP / E - abs(1.0 - RuBP / E)) / 2.0)

UDPc = cUc - UTPc - UDPGc

DHAPc = TPc / (1.0 + 0.05)

G1Pc = HePc * 0.0584 / (1.0 + 1.0 / 2.3 + 0.0584)

Wc_min = 2.913930914 * CO2 / (CO2 + 0.0115 * (1.0 + O2 / 0.222)) * ((1.0 + RuBP / E - abs(1.0 - RuBP / E)) / 2.0)

PiPic = PiTc - Pic

Pic = 12000000.0 / 2.0 * (sqrt(1.0 + 4.0 * PiTc / 12000000.0) - 1.0)

F6Pc = HePc / 2.3 / (1.0 + 1.0 / 2.3 + 0.0584)

PiTc = cPc - 2.0 * (FBPc + F26BPc) - (PGAc + TPc + HePc + SucPc + ATPc + UTPc)

GAPc = 0.05 * TPc / (1.0 + 0.05)

G6Pc = HePc / (1.0 + 1.0 / 2.3 + 0.0584)

ADP = cA - ATP

F6P = HeP / 2.3 / (1.0 + 1.0 / 2.3 + 0.058)

Function definitions

function_4(s1, s2, p1, q, Ks1, Ks2, Kp1, Vm) = Vm * (s1 * s2 - p1 / q) / (Ks1 * Ks2 * ((1 + s1 / Ks1) * (1 + s2 / Ks2) + p1 / Kp1))

function_6(Vm, s1, s2, p1, p2, Ks1, Ks2, r1, Kr1, r2, Kr2, q) = Vm * (s1 * s2 - p1 * p2 / q) / ((s1 + Ks1 * (1 + r1 / Kr1 + r2 / Kr2)) * (s2 + Ks2))

function_16(Vm, s1, r1, Kr1, r2, Kr2, Ks1) = Vm * s1 / ((s1 + Ks1) * (1 + r1 / Kr1) * (1 + r2 / Kr2))

function_5(Vm, s1, p1, p2, q, Ks1, r1, Kr1, r2, Kr2) = Vm * (s1 - p1 * p2 / q) / (s1 + Ks1 * (1 + r1 / Kr1 + r2 / Kr2))

function_17(substrate, Km, V) = V * substrate / (Km + substrate)

function_18(substrate, Inhibitor, Km, V, Ki) = V * substrate / (Km + substrate + Km * Inhibitor / Ki)

function_9(Vm, s1, s2, p1, p2, q, Ks1, r1, Kr1, r2, Kr2, r3, Kr3, r4, Kr41, Ks2, Kr42) = Vm * (s1 * s2 - p1 * p2 / q) / ((s1 + Ks1 * (1 + r1 / Kr1 + r2 / Kr2 + r3 / Kr3)) * (s2 * (1 + r4 / Kr41) + Ks2 * (1 + r4 / Kr42)))

function_12(s1, p1, p2, q, Ks1, Kp1, Kp2, Vm) = Vm * (s1 - p1 * p2 / q) / (Ks1 * (s1 / Ks1 + (1 + p1 / Kp1) * (1 + p2 / Kp2)))

function_8(Vm, s1, p1, p2, q, Ks1, r1, Kr1) = Vm * (s1 - p1 * p2 / q) / (s1 + Ks1 * (1 + r1 / Kr1))

function_15(Vm, s1, s2, p1, p2, q, Ks1, r1, Kr1, r2, Kr2, Ks2, r3, Kr3) = Vm * (s1 * s2 - p1 * p2 / q) / ((s1 + Ks1 * (1 + r1 / Kr1) * (1 + r2 / Kr2)) * (s2 + Ks2 * (1 + r3 / Kr3)))

function_21(Vm, s1, s2, p1, p2, q, Ks1, r1, Kr1) = Vm * (s1 * s2 - p1 * p2 / q) / (s1 + Ks1 * (1 + r1 / Kr1))

function_14(Vm, s1, s2, p1, p2, q, Ks1, r1, Kr1, Ks2, r2, Kr2, r3, Kr3, r4, Kr4, r5, Kr5) = Vm * (s1 * s2 - p1 * p2 / q) / ((s1 + Ks1 * (1 + r1 / Kr1)) * (s2 + Ks2 * (1 + r2 / Kr2) * (1 + r3 / Kr3) * (1 + r4 / Kr4) * (1 + r5 / Kr5)))

function_22(Vm, s1, Ks1, r1, Kr1) = Vm * s1 / (s1 + Ks1 * (1 + r1 / Kr1))

function_3(Vm, s1, s2, K1, K2) = Vm * s1 * s2 / ((s1 + K1) * (s2 + K2))

function_1(Vm, S, K, R1, KR1, R2, KR2, R3, KR3, R4, KR4, R5, KR5) = Vm * S / (S + K * (1 + R1 / KR1 + R2 / KR2 + R3 / KR3 + R4 / KR4 + R5 / KR5))

function_20(Vm, s1, s2, p1, p2, q, Ks1, r1, Kr1, Ks2) = Vm * (s1 * s2 - p1 * p2 / q) / ((s1 + Ks1 * (1 + r1 / Kr1)) * (s2 + Ks2))

function_11(Vm, S, KA, A, K, R1, KR1, R2, KR2, R3, KR3) = Vm * S / (S * (1 + KA / A) + K * (1 + (1 + KA / A) * (R1 / KR1 + R2 / KR2 + R3 / KR3)))

function_7(Vm, s1, s2, p1, q, Ks1, Ks2) = Vm * (s1 * s2 - p1 / q) / ((s1 + Ks1) * (s2 + Ks2))

function_19(Vm, s1, Ks1, r1, Kr1, r2, Kr2) = Vm * s1 / (s1 + Ks1 * (1 + r1 / Kr1) * (1 + r2 / Kr2))

function_10(Vm, S1, S2, K1, K2, R1, KR1, R2, KA1, A1, KA2, A2, KA3, A3) = Vm * S1 * S2 / ((S1 + K1) * (1 + R1 / KR1) * (S2 + K2 * (1 + K2 * R2 / (KA1 * A1 + KA2 * A2 + KA3 * A3))))

function_2(Vm, s1, s2, Ks1, Ks2, r1, Kr1) = Vm * s1 * s2 / ((s1 + Ks1) * (s2 + Ks2 * (1 + r1 / Kr1)))

function_13(s1, s2, p1, p2, q, Ks1, Ks2, Kp1, Kp2, Vm) = Vm * (s1 * s2 - p1 * p2 / q) / (Ks1 * Ks2 * ((1 + s1 / Ks1) * (1 + s2 / Ks2) + (1 + p1 / Kp1) * (1 + p2 / Kp2) - 1))

Events

Constraints

Note that constraints are not enforced in simulations. It remains the responsibility of the user to verify that simulation results satisfy these constraints.

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A quantitative comparison of Calvin-Benson cycle models.

Anne Arnold
Zoran Nikoloski

Trends Plant Sci. 2011; 16 (12): 676-683

PubMed: 22001849
DOI: 10.1016/j.tplants.2011.09.004
ISSN: 1878-4372
URL: https://ncbi.nlm.nih.gov/pubmed/22001849

Abstract

The Calvin-Benson cycle (CBC) provides the precursors for biomass synthesis necessary for plant growth. The dynamic behavior and yield of the CBC depend on the environmental conditions and regulation of the cellular state. Accurate quantitative models hold the promise of identifying the key determinants of the tightly regulated CBC function and their effects on the responses in future climates. We provide an integrative analysis of the largest compendium of existing models for photosynthetic processes. Based on the proposed ranking, our framework facilitates the discovery of best-performing models with regard to metabolomics data and of candidates for metabolic engineering.

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000393) Biomodels notes: The steady state concentration of the metabolites involved are reproduced here. This is the reproduction of the Table S7 (referring Zhu 2007) of the reference (supp. material) publication. The simulation was done using Copasi v4.7 (Build 34). JWS Online curation: This model was curated by reproducing the figures as described in the BioModels Notes. No additional changes were made.

JWS Online documentation

ATP (ATP)
DPGA (DPGA)
E4P (E4P)
F26BPc (F26BPc)
FBP (FBP)
FBPc (FBPc)
GCA (GCA)
GCAc (GCAc)
GCEA (GCEA)
GCEAc (GCEAc)
GLYc (GLYc)
GOAc (GOAc)
HPRc (HPRc)
HeP (HeP)
HePc (HePc)
PGA (PGA)
PGAc (PGAc)
PGCA (PGCA)
PeP (PeP)
RuBP (RuBP)
S7P (S7P)
SBP (SBP)
SERc (SERc)
SucPc (SucPc)
Succ (Succ)
TP (TP)
TPc (TPc)
UDPGc (UDPGc)

AGPase (AGPase)
ATP_S (ATP synthetase)
F26BPc_P (F26BPc phosphatase)
F6P_TK (F6P transketolase)
F6Pc_K (F6Pc kinase)
FBP_A (FBP aldolase)
FBPase (FBPase)
FBPc_A (FBPc aldolase)
FBPcase (FBPcase)
GAP_DH (GAP dehydrogenase)
GCAc_Ox (GCAc oxidase)
GCEA_DH (GCEA dehydrogenase)
GCEA_K (GCEA kinase)
GLUcGOAc_AT (GLUc:GOAc aminotransferase)
GLYc_DC (GLYc decarboxylase)
GPT_GCA (GPT - GCA)
GPT_GCAc (GPT - GCAc)
GPT_GCEA (GPT - GCEA)
GPT_GCEAc (GPT - GCEAc)
PGA_K (PGA kinase)
PGAc_Deg (PGAc degradation)
PGCA_P (PGCA phosphatase)
Ru5P_K (Ru5P kinase)
RuBisCO_CO2 (RuBisCO - CO2)
RuBisCO_O2 (RuBisC0 - O2)
S7P_TK (S7P transketolase)
SBP_A (SBP aldolase)
SBPase (SBPase)
SERcGOAc_AT (SERc:GOAc aminotransferase)
SucPc_P (SucPc phosphatase)
SucPc_S (SucPc synthase)
Succ_Deg (Succ degradation)
TPT_DHAP (TPT - DHAP)
TPT_GAP (TPT - GAP)
TPT_PGA (TPT - PGA)
UGPase (UGPase)