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Fig. 6 | BMC Bioinformatics

Fig. 6

From: TopoFilter: a MATLAB package for mechanistic model identification in systems biology

Fig. 6

Likelihood and viable space for the theoretical example of a ligand-fluorescent reporter network with multiplicative kinetic constants k1 and k2. Bounding box for searched parameter values is given as \(\left [{k_{1}^{min},k_{1}^{max}}\right ]\times \left [{k_{2}^{min},k_{2}^{max}}\right ]\) (dashed). The ε-projection values for each of the parameters (red dashed, bottom and left) can lead to discovery of the rank 2 reduction via rank 1 reductions (first k1:=ε1, then, from viable point \(\left (\epsilon _{1},k_{2}^{min}\right), k_{2}\text {:=}\epsilon _{2}\)), whereas projection values equal to 0 cannot. With the k1 projection value greater than \(k_{1}^{max}\) (red dashed, right), the viable space, enclosed within a 0.95 quantile of the cost function, is determined only by \(k_{2}\in \left ({x_{1}^{0}-1.96\sigma _{1},x_{1}^{0}+1.96\sigma _{1}}\right)\); k1 can be projected alone to some (high enough) value. The figure was plotted with \(\left [{k_{1}^{min},k_{1}^{max}}\right ] \times \left [{k_{2}^{min},k_{2}^{max}}\right ]= \left [{0.0117,0.027}\right ] \times \left [{1.3,11.7}\right ], x_{1}^{0}=10, \sigma _{1}=0.05{\cdot }x_{1}^{0}\)

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