Optimization examples

Here we give some examples of the BioUML usage for solving the problem of parameter estimation applied to the models of biochemical pathways. For details about creation your oun optimization document in BioUML, see the chapter Optimization document. Some information about the optimization methods implemented in BioUML is done in the chapter Optimization problem.

Testing the convergence rate of the optimization methods

• Optimization document: data > Examples > Optimization > Data > Documents > test_case_1A
• Model: data > Examples > Optimization > Data > Diagrams > diagram_1A
• Experimental data: data > Examples > Optimization > Data > Experiments > exp_data_1

To analyze a convergence rate of the optimization methods implemented in BioUML [1], we considered a reaction chain extracted from the model by Neumann et al. [2] and representing activation of caspase-8 triggered by the receptor CD95 (APO-1/Fas).

The test model of caspase-8 activation

ID Reactions Reaction rates Initial values r1 CD95L + FADD:CD95R → DISC k1 ⋅ [CD95L] ⋅ [CD95R:FADD] [CD95L]0 = 113.220, [CD95R:FADD]0 = 91.266 r2 DISC + pro8 → DISC:pro8 k2 ⋅ [DISC] ⋅ [pro8] [pro8]0 = 64.477, [DISC]0 = 0.0 r3 DISC:pro8 + pro8 → 2 · p43/p41 k3 ⋅ [DISC:pro8] ⋅ [pro8] [DISC:pro8]0 = 0.0 r4 2 · p43/p41 → casp8 k4 ⋅ [p43/p41]2 [p43/p41]0 = 0.0 r5 casp8 → k5 ⋅ [casp8] [casp8]0 = 0.0

We performed estimation of parameters using the search space defined as:

where upper bounds were chosen based on the order of magnitude of parameter values proposed in [2].

Estimation was based on the experimental data obtained by Neumann et al. [2] for procaspase-8 and its cleaved products p43/p41 and caspase-8.

Time (min-1)	p43/p41 (nM)	pro-8 (nM)	casp-8 (nM)
0.0	0.058	59.963	0.000
10.0	0.268	57.565	0.041
20.0	4.760	58.590	0.316
30.0	8.252	59.422	1.397
45.0	16.144	48.190	3.520
60.0	17.021	38.950	3.947
90.0	15.269	23.502	4.871
120.0	12.530	13.127	4.878
150.0	10.335	10.703	4.228

References

1. Kutumova E., Ryabova A., Valeev T., Kolpakov F. BioUML plug-in for nonlinear parameter estimation using multiple experimental data. Virtual biology. 2013. 1:47-58.
2. Neumann L., Pforr C., Beaudouin J., Pappa A., Fricker N., Krammer P.H., Lavrik I.N., Eils R. Dynamics within the CD95 death-inducing signaling complex decide life and death of cells. Molecular Systems Biology. 2010. 6:352.