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Table 1 Kinetic rate equations

From: Modeling and simulation of the main metabolism in Escherichia coli and its several single-gene knockout mutants with experimental verification

Reactions Model equations   References
Cell growth μ = { μ m ( 1 [ X ] X m ) ( [ G l c e x ] K s + [ G l c e x ] ) k A T P v A T P ( . ) , ( [ G l c e x ] > 0 ) μ m A [ A c e e x ] K s A + [ A c e e x ] k A T P v A T P ( . ) , ( [ G l c e x ] 1 a n d [ A c e e x ] > 0 ) (1a)
(1b)
 
Phosphotransferasesystem v P T S = v P T S max [ G l c e x ] [ P E P ] [ P Y R ] ( K a 1 + K a 2 [ P E P ] [ P Y R ] + K a 3 [ G l c e x ] + [ G l c e x ] [ P E P ] [ P Y R ] ) ( 1 + [ G 6 P ] n G 6 P K G 6 P ) (2a) [8, 33]
Non-PTS glucokinase v G l k = v G l k max [ G l c ] [ A T P ] ( K m G l c + [ G l c ] ) ( K m A T P + [ A T P ] ) (2b) [49]
Phosphoglucoseisomerase v P g i = v P g i max ( [ G 6 P ] [ F 6 P ] K e q ) K G 6 P ( 1 + F 6 P K F 6 P ( 1 + [ F 6 P ] K 6 p g i n h F 6 P ) + [ 6 P G ] K 6 p g i n h G 6 P ) + G 6 P (3) [8]
Phospho-fructokinase v P f k = v P f k max K A T P [ F 6 P ] K ( A T P , A D P ) ( [ F 6 P ] + K S F 6 P K b ( A D P , A M P ) + [ P E P ] K P E P K a ( A D P , A M P ) ) × ( 1 + L P f k ( 1 + [ F 6 P ] ( K a ( A D P , A M P ) K s F 6 P ( K b ( A D P , A M P ) + [ P E P ] K P E P ) ) ) n P f k ) (4) [8]
Adolase v A l d o = v A l d o max ( [ F D P ] [ G A P ] [ G A P ] K e q ) ( K F D P + [ F D P ] + K G A P [ G A P ] [ K e q V b l f ] + K D H A P [ G A P ] [ K e q V b l f ] + [ F D P ] [ G A P ] K i n h P E P + [ G A P ] [ G A P ] K e q V b l f ) (5) [8]
G3P dehydrogenase v G A P D H = v G A P D H max ( [ G A P ] [ P E P ] [ N A D H ] K e q [ N A D ] ) ( K G A P ( 1 + [ P E P ] K P G P ) + [ G A P ] ) ( K N A D N A D ( 1 + [ N A D H ] | K N A D H ) + 1 ) (6) [8]
Pyruvate kinase v P y k = v P y k max [ P E P ] ( [ P E P ] K P E P + 1 ) n P y k 1 [ A D P ] K P E P ( L P y k ( 1 + [ A T P ] K A T P [ F D P ] K F D P + [ A M P ] K A M P + 1 ) n P y k + ( [ P E P ] K P E P + 1 ) n P y k ) ( [ A D P ] + K A D P ) (7) [8]
PEP carboxylase v P p c = K 1 + K 2 [ A c C o A ] + K 3 [ F D P ] + K 4 [ A c C o A ] [ F D P ] 1 + K 5 [ A c C o A ] + K 6 [ F D P ] ( [ P E P ] K m + [ P E P ] ) (8) [38]
PEP carboxykinase v P c k = v P c k max ( [ O A A ] [ A T P ] [ A D P ] K m O A A [ A T P ] [ A D P ] + [ O A A ] | [ A T P ] [ A D P ] + K i A T P K m O A A K i A D P + K i A T P K m O A A K m P E P K i A D P [ P E P ] + K i A T P K m O A A K i P E P K I A T P [ A T P ] [ P E P ] [ A D P ] + K i A T P K m O A A K i A D P K I O A A [ O A A ] ) (9) [15]
Pyruvate dehydrogenasecomplex v P D H = v P D H max [ N A D ] ( 1 1 + K i [ N A D H ] [ N A D ] ) ( [ P Y R ] K m P Y R ) ( 1 K m N A D ) ( [ C O A ] K m C O A ) ( 1 + [ P Y R ] K m P Y R ) ( 1 N A D + 1 K m N A D + [ N A D H ] K m N A D H [ N A D ] ) ( 1 + [ C O A ] K m C O A + [ A c C o A ] K m A c C o A ) (10) [40]
Pta v P t a = v P t a max ( 1 K i A c C o A K m P ) ( [ A c C o A ] [ P ] [ A c P ] [ C o A ] K e q ) ( 1 + [ A c C o A ] K i A c C o A + [ P ] K i P + A C P K i A C P + [ C o A ] K i C o A + ( [ A c C o A ] [ P ] K i A c C o A K m P ) + ( [ A c P ] [ C o A ] K m A C P K i C o A ) ) (11) [40, 41]
Ack v A c k = v A c k max ( 1 K m A D P K m A C P ) ( [ A c P ] [ A D P ] [ A C E ] [ A T P ] K e q ) ( 1 + [ A c P ] K m A C P + A C E K m A C E ) ( 1 + [ A D P ] K m A D P + [ A T P ] K m A T P ) (12) [40]
Acs v A c s = v A c s max [ A C E ] [ N A D P ] ( K m + [ A C E ] ) ( K e q + [ N A D P ] ) (13) [42]
Citrate Synthase v C S = v C S max [ A c C o A ] [ O A A ] ( K d A c C o A K m O A A + K m A c C o A [ O A A ] ) + ( [ A c C o A ] K m O A A ( 1 + [ N A D H ] K i 1 N A D H ) ) + ( [ A c C o A ] [ O A A ] ( 1 + [ N A D H ] K i 2 N A D H ) ) (14) [43]
ICDH v I C D H = [ I C D H ] K f K m i C i T K d N A D P ( [ I C I T ] [ N A D P H ] [ 2 K G ] K e q I C D H [ N A D P ] ) ( 1 [ N A D P ] + [ I C I T ] K m N A D P K m i C i T K d N A D P [ N A D P ] + 1 K d N A D P + [ I C I T ] K m i C i T K d N A D P + [ I C I T ] K d i C i T [ N A D P ] [ N A D P H ] K m N A D P K m i C i T K d N A D P K e i n h N A D P H + [ N A D P H ] K e k n h 2 K G K m 2 K G K e n h e N A D P H [ N A D P ] + [ 2 K G ] K m N A D P H K m 2 K G K e n h e N A D P H [ N A D P ] + [ 2 K G ] K m 2 K G [ N A D P H ] K e n h e N A D P H [ N A D P ] + [ 2 K G ] K m N A D P H K m 2 K G K e n h e N A D P H [ N A D P H ] K e k n N A D P [ N A D P ] ) (15) [44]
Isocitrate lyase v I c l = v I c l _ f max [ I C I T ] K m i C i T ( 1 + [ I C I T ] K m i C i T + [ S U C ] K m S U C + [ G O X ] K m G O X + [ I C I T ] K m i C i T [ S U C ] K m S U C + [ S U C ] K m S U C [ G O X ] K m G O X + I K I ) (16) [46]
Malate synthase v M S = v M S _ f max [ G O X ] K m G O X [ A c C o A ] K m A c C o A v M S _ r max [ M A L ] K m M A L ( 1 + [ G O X ] K m G O X + [ M A L ] K m M A L + ( 1 + [ A c C o A ] K m A c C o A ) ) (17) [46]
αKG dehydrogenase v α K G D H = v 2 K G D H max [ α K G ] [ C o A ] { K m N A D [ α K G ] [ C o A ] [ N A D ] + K m C o A [ α K G ] + K m 2 K G [ C o A ] + [ α K G ] [ C o A ] + K m 2 K G K z [ S U C ] [ N A D H ] K I S U C [ N A D ] + K m N A D [ α K G ] [ C o A ] [ N A D H ] K I N A D H [ N A D ] + K m C o A [ α K G ] [ S U C ] K I S U C + K m 2 K G K Z [ α K G ] [ S U C ] [ N A D H ] K I 2 K G K I S U C [ N A D ] } (18) [45]
Succinate dehydrogenase v S D H = v S D H 1 v S D H 2 ( [ S U C ] [ F U M ] K e q ) K m S U C v S D H 2 + v S D H 2 [ S U C ] + V S D H 1 [ F U M ] K e q (19) [45]
Fumarase v F u m = v F u m 1 v F u m 2 ( [ F U M ] [ M A L ] K F u m e q ) K m F u m v F u m 1 + v F u m 2 [ F U M ] + V F u m 1 [ M A L ] K e q (20) [45]
Malate dehydrogenase v M D H = v M D H 1 v M D H 2 ( [ M A L ] [ O A A ] K e q ) ( K I N A D K m M A L v M D H 2 [ N A D ] + K m M A L v M D H 2 + K m N A D V M D H 2 [ M A L ] [ N A D ] + v M D H 2 [ M A L ] + K m O A A v M D H 1 [ N A D H ] K e q [ N A D ] + K m N A D H v M D H 1 [ O A A ] K e q [ N A D ] + v M D H 1 [ N A D H ] [ O A A ] K e q [ N A D ] + v M D H 1 K m O A A [ N A D H ] K e q K I N A D + v M D H 2 K m N A D [ M A L ] [ O A A ] K I O A A [ N A D ] + v M D H 2 [ M A L ] [ N A D H ] K I N A D H + v M D H 1 [ M A L ] [ N A D H ] [ O A A ] K e q K I M A L [ N A D ] + v M D H 2 [ M A L ] [ O A A ] K I I O A A + v M D H 1 [ N A D H ] [ O A A ] K I I N A D K e q + K I N A D v M D H 2 [ M A L ] [ N A D H ] [ O A A ] K I I N A D K m O A A K I N A D H ) (21) [45]
Malic enzyme v M e z = v M e z max [ M A L ] [ N A D P ] ( K M A L + [ M A L ] ) ( K e q + [ N A D P ] ) (22) [45]
G6PDH v G 6 P D H = v G 6 P D H max [ G 6 P ] ( [ G 6 P ] + K G 6 P ) ( 1 + [ N A D P H ] K N A D P H G 6 P ) ( K N A D P [ N A D P ] ( 1 + N A D P H K N A D P H N A D P ) + 1 ) (23) [8]
PGDH v G 6 P D H = v G 6 P D H max [ G 6 P ] ( [ 6 P G ] + K 6 P G ) ( 1 + K N A D P N A D P ( 1 + [ N A D P H ] K N A D P H i n h ) ( 1+ [ A T P ] K A T P i n h ) ) (24) [8]
Rpe v R p e = v R p e max ( [ R u 5 P ] [ X u 5 P ] K e q R p e ) (25) [8]
Rpi v R p i = v R p i max ( [ R u 5 P ] [ R 5 P ] K e q R p i ) (26) [8]
TktA v T k t A = v T k t A max ( [ R 5 P ] [ X u 5 P ] [ S 7 P ] [ G A P ] K e q T k t A ) (27) [8]
TktB v T k t B = v T k t B max ( [ X u 5 P ] [ E 4 P ] [ F 6 P ] [ G A P ] K e q T k t B ) (28) [8]
Tal v T a l = v T a l max ( [ G A P ] [ S 7 P ] [ E 4 P ] [ F 6 P ] K e q T k t B ) (29) [8]