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Table 2 Robustness of the reduced model for large deviations from the nominal parameter point are presented for the glucose transport model, with a sampling frequency of 1 (starting from 1) time units.

From: A method for zooming of nonlinear models of biochemical systems

Param./Factor

10-2

10-1

100

101

102

k 1

0.079/0.091

0.079/0.10

0.081/0.091

0.083/0.10

0.084/0.11

k -1

0.085/0.23

0.084/0.093

0.081/0.091

0.078/0.10

0.078/0.089

k 2

0.16/0.93

0.080/0.55

0.081/0.091

0.063/0.083

0.054/0.062

k -2

0.054/0.10

0.062/0.074

0.081/0.091

0.097/0.10

0.10/0.10

k 3

0.081/0.091

0.082/0.091

0.081/0.091

0.079/0.089

0.075/0.082

k -3

0.070/0.080

0.079/0.089

0.081/0.091

0.082/0.091

0.081/0.091

k 4

0.23/0.32

0.21/0.30

0.081/0.091

6.36/6.93

310/336

k -4

310/336

6.36/6.93

0.081/0.091

0.21/0.30

0.23/0.32

α

0.10/0.10

0.095/0.17

0.081/0.091

0.080/0.089

0.083/0.088

β

0.076/0.088

0.091/0.096

0.081/0.091

0.075/0.15

0.074/0.19

All

0.16/0.97

0.081/0.69

0.081/0.091

0.060/0.091

0.054/0.081

  1. The nominal parameter values (k1 = 1000, k-1 = 1100, k2 = 1000, k-2 = 1200, k3 = 1000, k-3 = 7000, k4 = 1000, k-4 = 1100, α = 4.2, and β = 1) are modified by a multiplicative factor, and the maximal (for any state variable) time average/infinity norm of the relative difference between the original and the reduced model is presented. Note that due to potential numerical inaccuracies only concentrations larger than 10-6 are considered in the analysis.