Table 3.

Comparison of maximal relative error under differing lumping inverses for the reduction of the E coli model via lumping in isolation

Dimensions	Moore-Penrose	Steady-state	Average
6	6.67%	0.15%	0.18%
5	10.58%	0.55%	0.51%
4	13.99%	0.54%	1.26%
3	26.93%	4.78%	4.77%
2	78.36%	13.45%	12.88%
1	70.92%	75.56%	82.34%

Each row represents a further level of dimensional reduction for the model, whilst the columns represent the different methods of lumping inverse. The ‘Moore-Penrose’ column contains values where the lumping inverse $\stackrel{\circledR }{L}$ is the Moore-Penrose or pseudoinverse of the lumping matrix L. The ‘steady-state’ column contains values where the lumping inverse $\stackrel{\circledR }{L}$ is selected to reconstruct the unperturbed steady-state values of the original system such that ${\mathit{x}}_{{\mathit{u}}_0}^{\ast }=\stackrel{\circledR }{L}{\tilde{\mathit{x}}}_{{\mathit{u}}_0}^{\ast }$. 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