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Table 4 Balance equations and time-scale constraints for each species and for each collective species chosen

From: A multiscale approximation in a heat shock response model of E. coli

 

Balance equations

Time-scale constraints

S 1

ρ13=ρ14

γ α 1 max( ρ 13 , ρ 14 )

S 2

max( ρ 3 , ρ 4 , ρ 5 , ρ 6 , ρ 7 , ρ 8 )=max( ρ 2 , ρ 9 )

γ α 2 max( ρ 2 , ρ 3 , ρ 4 , ρ 5 , ρ 6 , ρ 7 , ρ 8 , ρ 9 )

S 3

ρ 2 =max( ρ 3 , ρ 5 , ρ 6 , ρ 7 )

γ α 3 max( ρ 2 , ρ 3 , ρ 5 , ρ 6 , ρ 7 )

S 4

ρ6=ρ18

γ α 4 max( ρ 6 , ρ 18 )

S 5

ρ5=ρ16

γ α 5 max( ρ 5 , ρ 16 )

S 6

max( ρ 7 , ρ 8 , ρ 12 , ρ 15 )=max( ρ 9 , ρ 10 , ρ 17 )

γ α 6 max( ρ 7 , ρ 8 , ρ 9 , ρ 10 , ρ 12 , ρ 15 , ρ 17 )

S 7

ρ 9 =max( ρ 8 , ρ 15 )

γ α 7 max( ρ 8 , ρ 9 , ρ 15 )

S 8

max( ρ 1 , ρ 12 )=max( ρ 10 , ρ 11 )

γ α 8 max( ρ 1 , ρ 10 , ρ 11 , ρ 12 )

S 9

ρ10=ρ12

γ α 9 max( ρ 10 , ρ 12 )

S2 + S3 + S7

ρ4=ρ15

γmax( α 2 , α 3 , α 7 )max( ρ 4 , ρ 15 )

S2 + S3

max( ρ 4 , ρ 8 )= ρ 9

γmax( α 2 , α 3 )max( ρ 4 , ρ 8 , ρ 9 )

S2 + S7

max( ρ 3 , ρ 4 , ρ 5 , ρ 6 , ρ 7 )=max( ρ 2 , ρ 15 )

γmax( α 2 , α 7 )max( ρ 2 , ρ 3 , ρ 4 , ρ 5 , ρ 6 , ρ 7 , ρ 15 )

S6 + S7 + S9

ρ7=ρ17

γmax( α 6 , α 7 , α 9 )max( ρ 7 , ρ 17 )

S6 + S7

max( ρ 7 , ρ 12 )=max( ρ 10 , ρ 17 )

γmax( α 6 , α 7 )max( ρ 7 , ρ 10 , ρ 12 , ρ 17 )

S6 + S9

max( ρ 7 , ρ 8 , ρ 15 )=max( ρ 9 , ρ 17 )

γmax( α 6 , α 9 )max( ρ 7 , ρ 8 , ρ 9 , ρ 15 , ρ 17 )

S8 + S9

ρ1=ρ11

γmax( α 8 , α 9 )max( ρ 1 , ρ 11 )

  1. In each case, either the balance equation or the time-scale constraint must hold.