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. All 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] [pro8]0 = 64.477, [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

We reviewed solutions obtained by all optimization methods for 100 runs. Each run was based on the generation of 10⁷ different guesses. The best result was obtained by the particle swarm optimization (PSO) and the cellular genetic algorithm (MOCell). Methods SRES, MOCell and PSO found similar solutions. Methods ASA and glbSolve found other values for parameters k₁ and k₂ showing lower efficiency.

The objective function mean values dynamics for 100 runs. The best value obtained by PSO is marked by the red line.

The best guesses obtained by optimization methods for 100 runs Parameters SRES MOCell PSO ASA glbSolve k1 0.0004691 0.0004611 0.0004277 0.0001028 0.0020576 k2 0.0002059 0.0002046 0.0002155 0.0007875 0.0001228 k3 0.0009999 0.0010000 0.0009984 0.0009930 0.0009527 k4 0.0007915 0.0008225 0.0008419 0.0008117 0.0007790 k5 0.0325900 0.0336720 0.0334167 0.0334118 0.0313443

Values of the objective function for 100 runs Methods The best value The mean value The worst value PSO 11.787 13.164 14.703 MOCell 12.082 13.484 14.771 SRES 12.466 14.987 18.283 ASA 13.728 15.794 16.610 glbSolve 16.614 16.614 16.614

Testing the methods convergence rate for models with the different number of parameters

• Optimization documents: data > Examples > Optimization > Data > Documents
  (test cases 1A, 1B, 1C, 2, 3)
• Models: data > Examples > Optimization > Data > Diagrams

  (diagrams 1A, 1B, 1C, 2, 3 for the corresponding test cases)

• Experimental data: data > Examples > Optimization > Data > Experiments

  (exp_data_1 for the test cases 1A, 1B, 1C; exp_data_2 for the test case 2; exp_data_3 for the test case 3)

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.