Table 1.

Error results for the nonlinear methods of model reduction applied to the E. coli chemotaxis model

Number of	Empirical balanced	Lumping	Combined method
dimensions	truncation
6	1.396%	0.15%	-
5	1.655%	0.51%	-
4	#	0.54%	0.51%
3	#	4.77%	2.00%
2	#	12.88%	2.84%
1	#	75.56%	21.86%

Note: ‘ #’ implies Matlab could not numerically simulate this reduction using ode15s due to stiffness. ‘-’ implies the reduction error at this point was equal to the lumping error. The errors stated represent the maximal relative error between the original and reduced systems when simulated to steady-state under the introduction of 10μ M concentration of attractant ligand at t=0