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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.