Difference between revisions of "Optimization examples"

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A brief description of the optimization methods implemented in BioUML as well as their application to non-linear models of biochemical processes can be found in the section [[Optimization problem]].
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<font size=3>
  
−
Here we give some examples of how to use the BioUML software for parameter estimation.
+
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]].
  
−
==Creation of an optimization document==
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==Testing the convergence rate of the optimization methods==
  
−
[[File:optimization_examples_figure_1.png|thumb|Step to create a new optimization]]
+
<ul>
 +
<li>'''Optimization document''': ''data'' > ''Examples'' > ''Optimization'' > ''Data'' > ''Documents'' > ''test_case_1A''</li>
 +
<li>'''Model''': ''data'' > ''Examples'' > ''Optimization'' > ''Data'' > ''Diagrams'' > ''diagram_1A''</li>
 +
<li>'''Experimental data''': ''data'' > ''Examples'' > ''Optimization'' > ''Data'' > ''Experiments'' > ''exp_data_1''</li>
 +
</ul>
  
−
BioUML allows performing parameter estimation of biochemical models represented as [[Diagram document]] via creation of a special optimization document.
 
  
−
You can start creating this document in two ways.
+
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
−
<ol>
+
CD95 (APO-1/Fas).
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<li>Go to the '''Data''' tab of the repository pane and select the appropriate directory to store your data in.
+
−
For our example, we will use '''data''' > '''Examples''' > '''Optimization''' > '''Data''' > '''Documents'''.
+
−
Click the left mouse button on the selected directory and choose the item '''New optimization''' in the pop-up menu.
+
−
</li>
+
−
<li>
+
−
Go to the '''Analyses''' tab of the repository pane. Find the list of available optimization methods in the tree under '''analyses''' > '''Methods''' > '''Optimization'''.
+
−
Click the left mouse button on a method by which you want to perform parameter estimation and select '''New optimization''' in the pop-up menu.
+
−
</li>
+
−
</ol>
+
  
−
After following one of these instructions, the input dialog opens. Сlick to the field '''Create optimization document''' and type a name for your optimization document.
+
<table border="0" cellspacing="0" cellpadding="4">
−
Then click to the field '''Diagram''' and indicate the diagram wchich parameters you want to estimate. In our example, we will use '''data/Examples/Optimization/Data/Diagrams/diagram_1A'''.
+
  <tr>
−
When you click '''OK''', a new optimization document appeares in the selected directory of the repository pane and the corresponding tab opens in the document pane to start the optimization execution.
+
    <td>[[File:optimization_examples_model_1.png|thumb|The test model of caspase-8 activation]]</td>
 +
    <td>&nbsp;&nbsp;&nbsp;&nbsp;</td>
 +
    <td>
 +
      <table  border="1" align="center" cellspacing="0" cellpadding="4">
 +
        <tr>
 +
          <td>'''ID'''</td>
 +
          <td>'''Reactions'''</td>
 +
          <td>'''Reaction rates'''</td>
 +
          <td>'''Initial values'''</td>
 +
        </tr>
 +
        <tr>
 +
          <td>r1</td>
 +
          <td>CD95L + FADD:CD95R → DISC</td>
 +
          <td>''k''<sub>1</sub> ⋅ [CD95L] ⋅ [CD95R:FADD]</td>
 +
          <td>[CD95L]<sub>0</sub> = 113.220, [CD95R:FADD]<sub>0</sub> = 91.266</td>
 +
        </tr>
 +
        <tr>
 +
          <td>r2</td>
 +
          <td>DISC + pro8 → DISC:pro8</td>
 +
          <td>''k''<sub>2</sub> ⋅ [DISC] ⋅ [pro8]</td>
 +
          <td>[pro8]<sub>0</sub> = 64.477, [DISC]<sub>0</sub> = 0.0</td>
 +
        </tr>
 +
        <tr>
 +
          <td>r3</td>
 +
          <td>DISC:pro8 + pro8 → 2 · p43/p41</td>
 +
          <td>''k''<sub>3</sub> ⋅ [DISC:pro8] ⋅ [pro8]</td>
 +
          <td>[pro8]<sub>0</sub> = 64.477, [DISC:pro8]<sub>0</sub> = 0.0</td>
 +
        </tr>
 +
        <tr>
 +
          <td>r4</td>
 +
          <td>2 · p43/p41 → casp8</td>
 +
          <td>''k''<sub>4</sub> ⋅ [p43/p41]<sup>2</sup></td>
 +
          <td>[p43/p41]<sub>0</sub> = 0.0</td>
 +
        </tr>
 +
        <tr>
 +
          <td>r5</td>
 +
          <td>casp8 →</td>
 +
          <td>''k''<sub>5</sub> ⋅ [casp8]</td>
 +
          <td>[casp8]<sub>0</sub> = 0.0</td>
 +
        </tr>
 +
      </table>
 +
    </td>
 +
  </tr>
 +
</table>
  
−
The existing document can be opened by the double-click. If you want to remove a document, click the left mouse button on it and select the item "Remove".
+
We performed estimation of parameters using the search space defined as:
−
To save any changes in the document, press the button [[File:optimization_examples_save-icon.png]] in the top panel of the framework.
+
 
 +
[[File:optimization_examples_formula_1.png]]
 +
 
 +
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.
 +
 
 +
<table  border="1" cellspacing="0" cellpadding="4">
 +
  <tr>
 +
    <td>'''Time (min<sup>-1</sup>)'''</td>
 +
    <td>'''p43/p41 (nM)'''</td>
 +
    <td>'''pro-8 (nM)'''</td>
 +
    <td>'''casp-8 (nM)'''</td>
 +
  </tr>
 +
  <tr>
 +
    <td>0.0</td>
 +
    <td>0.058</td>
 +
    <td>59.963</td>
 +
    <td>0.000</td>
 +
  </tr>
 +
  <tr>
 +
    <td>10.0</td>
 +
    <td>0.268</td>
 +
    <td>57.565</td>
 +
    <td>0.041</td>
 +
  </tr>
 +
  <tr>
 +
    <td>20.0</td>
 +
    <td>4.760</td>
 +
    <td>58.590</td>
 +
    <td>0.316</td>
 +
  </tr>
 +
  <tr>
 +
    <td>30.0</td>
 +
    <td>8.252</td>
 +
    <td>59.422</td>
 +
    <td>1.397</td>
 +
  </tr>
 +
  <tr>
 +
    <td>45.0</td>
 +
    <td>16.144</td>
 +
    <td>48.190</td>
 +
    <td>3.520</td>
 +
  </tr>
 +
  <tr>
 +
    <td>60.0</td>
 +
    <td>17.021</td>
 +
    <td>38.950</td>
 +
    <td>3.947</td>
 +
  </tr>
 +
  <tr>
 +
    <td>90.0</td>
 +
    <td>15.269</td>
 +
    <td>23.502</td>
 +
    <td>4.871</td>
 +
  </tr>
 +
  <tr>
 +
    <td>120.0</td>
 +
    <td>12.530</td>
 +
    <td>13.127</td>
 +
    <td>4.878</td>
 +
  </tr>
 +
  <tr>
 +
    <td>150.0</td>
 +
    <td>10.335</td>
 +
    <td>10.703</td>
 +
    <td>4.228</td>
 +
  </tr>
 +
</table>
 +
 
 +
We  reviewed solutions obtained by all optimization methods for 100 runs. Each run was based on the generation of 10<sup>7</sup> 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 ''k''<sub>1</sub> and ''k''<sub>2</sub> showing lower efficiency.
 +
 
 +
<table border="0" cellspacing="0" cellpadding="4">
 +
  <tr>
 +
    <td>[[File:optimization_examples_figure_2.png|thumb|The objective function mean values dynamics for 100 runs. The best value obtained by PSO is marked by the red line.]]</td>
 +
    <td>&nbsp;&nbsp;&nbsp;&nbsp;</td>
 +
    <td>
 +
'''The best guesses obtained by optimization methods for 100 runs'''
 +
      <table  border="1" cellspacing="0" cellpadding="4">
 +
        <tr>
 +
          <td>'''Parameters'''</td>
 +
          <td>'''SRES'''</td>
 +
          <td>'''MOCell'''</td>
 +
          <td>'''PSO'''</td>
 +
          <td>'''ASA'''</td>
 +
          <td>'''glbSolve'''</td>
 +
        </tr>
 +
        <tr>
 +
          <td>''k''<sub>1</sub></td>
 +
          <td>0.0004691</td>
 +
          <td>0.0004611</td>
 +
          <td>0.0004277</td>
 +
          <td>0.0001028</td>
 +
          <td>0.0020576</td>
 +
        </tr>
 +
        <tr>
 +
          <td>''k''<sub>2</sub></td>
 +
          <td>0.0002059</td>
 +
          <td>0.0002046</td>
 +
          <td>0.0002155</td>
 +
          <td>0.0007875</td>
 +
          <td>0.0001228</td>
 +
        </tr>
 +
        <tr>
 +
          <td>''k''<sub>3</sub></td>
 +
          <td>0.0009999</td>
 +
          <td>0.0010000</td>
 +
          <td>0.0009984</td>
 +
          <td>0.0009930</td>
 +
          <td>0.0009527</td>
 +
        </tr>
 +
        <tr>
 +
          <td>''k''<sub>4</sub></td>
 +
          <td>0.0007915</td>
 +
          <td>0.0008225</td>
 +
          <td>0.0008419</td>
 +
          <td>0.0008117</td>
 +
          <td>0.0007790</td>
 +
        </tr>
 +
        <tr>
 +
          <td>''k''<sub>5</sub></td>
 +
          <td>0.0325900</td>
 +
          <td>0.0336720</td>
 +
          <td>0.0334167</td>
 +
          <td>0.0334118</td>
 +
          <td>0.0313443</td>
 +
        </tr>
 +
      </table>
 +
    </td>
 +
    <td>&nbsp;&nbsp;&nbsp;&nbsp;</td>
 +
    <td>
 +
'''Values of the objective function for 100 runs'''
 +
      <table  border="1" cellspacing="0" cellpadding="4">
 +
        <tr>
 +
          <td>'''Methods'''</td>
 +
          <td nowrap>'''The best value'''</td>
 +
          <td nowrap>'''The mean value'''</td>
 +
          <td nowrap>'''The worst value'''</td>
 +
        </tr>
 +
        <tr>
 +
          <td>'''PSO'''<sub> </sub></td>
 +
          <td>11.787</td>
 +
          <td>13.164</td>
 +
          <td>14.703</td>
 +
        </tr>
 +
        <tr>
 +
          <td>'''MOCell'''<sub> </sub></td>
 +
          <td>12.082</td>
 +
          <td>13.484</td>
 +
          <td>14.771</td>
 +
        </tr>
 +
        <tr>
 +
          <td>'''SRES'''<sub> </sub></td>
 +
          <td>12.466</td>
 +
          <td>14.987</td>
 +
          <td>18.283</td>
 +
        </tr>
 +
        <tr>
 +
          <td>'''ASA'''<sub> </sub></td>
 +
          <td>13.728</td>
 +
          <td>15.794</td>
 +
          <td>16.610</td>
 +
        </tr>
 +
        <tr>
 +
          <td>'''glbSolve'''<sub> </sub></td>
 +
          <td>16.614</td>
 +
          <td>16.614</td>
 +
          <td>16.614</td>
 +
        </tr>
 +
      </table>
 +
    </td>
 +
  </tr>
 +
</table>
 +
 
 +
==Testing the computational speed of the optimization methods==
  
−
The working area of the optimization document includes a window located in the lower right corner of the framework. It is designed to select the optimization options given into several tabs:
 
−
<ul>
 
−
<li>
 
−
'''Parameters''' - contains all parameters of the diagram. Select the parameters which you want to fit, and click the up arrow [[File:optimization_examples_up_arrow-icon.png]]. The list of the selected items appears in the table located above. In order to remove unnecessary items from this table, select them and click the down arrow [[File:optimization_examples_down_arrow-icon.png]].
 
−
If you want to change the start values of some parameters, enter them in the column '''Initial value''' of the parameters tab and press the button [[File:optimization_examples_save-icon.png]] in this tab.
 
−
The relevant values are automatically changed in the column '''Value''' of the fitting table. You can define the search space by setting lower and upper bounds for each fitting parameter.
 
−
You can also specify each parameter as local or global using tick in the column '''Local'''. It is assumed, that the global parameters take the same value for all experiments, while the local parameters have different values for different experimental groups. For more detailes, see description of the '''Experiments''' tab below.
 
−
</li>
 
−
<li>
 
−
'''Variables''' - contains all species of the diagram with the same options as the '''Parameters''' tab.
 
−
</li>
 
−
<li>
 
−
'''Experiments''' - contains information about experimental data used for the parameter estimation.
 
−
Before creation of new experiment in the optimization document, you need to import experimental data file from your computer to the repository tree.
 
−
For this perpose, you can, for example, use directory '''data/Examples/Optimization/Data/Experiments'''.
 
−
Click the left mouse button on this directory and choose the item '''Import''' in the pop-up menu.
 
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Then click the button '''Computer''' in the opened dialog and find the required file in the file system of your computer.
 
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Note, that data in the file must represent time course or steady-state values of several species or parameters used in your diagram.
 
−
To create new experiment in your optimization document, click the button [[File:optimization_examples_add_experiment-icon.png]] and fill the following fields in the opened dialog:
 
 
<ul>
 
<ul>
−
<li>
+
<li>'''Optimization documents''': ''data'' > ''Examples'' > ''Optimization'' > ''Data'' > ''Documents'' <div></div> (test cases 1A, 1B, 1C, 2, 3) </li>
−
''Name'' -
+
<li>'''Models''': ''data'' > ''Examples'' > ''Optimization'' > ''Data'' > ''Diagrams'' <div></div> (diagrams 1A, 1B, 1C, 2, 3 for the corresponding test cases) </li>
−
</li>
+
<li>'''Experimental data''': ''data'' > ''Examples'' > ''Optimization'' > ''Data'' > ''Experiments'' <div></div> (''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) </li>
−
<li>
+
−
''Diagram state'' -
+
−
</li>
+
−
<li>
+
−
''Experiment data'' -
+
−
</li>
+
 
</ul>
 
</ul>
  
−
To save any changes in the optimization experiment, press the button [[File:optimization_examples_save-icon.png]] in the '''Experiments''' tab.
 
−
To remove any unnecessary experiment, select it and press the button [[File:optimization_examples_remove_experiment-icon.png]].
 
−
</li>
 
−
<li>
 
−
'''Constraints'''
 
−
</li>
 
−
<li>
 
−
'''Simulation'''
 
−
</li>
 
−
<li>
 
−
'''Optimization''' - contains the buttons to start [[File:optimization_examples_start-icon.png]] and stop [[File:optimization_examples_stop-icon.png]] parameter estimation,
 
−
draw the plots for visual presentation of results [[File:optimization_examples_plot-icon.png]],
 
−
and open a diagram showing the schematic structure of the optimization document [[File:optimization_examples_diagram-icon.png]].
 
−
In this tab, you can choose one of the optimization methods and specify its options.
 
−
Before start parameter estimation, click to the field '''Optimization result''' and specify an appropriate directory (e.g. '''data/Examples/Optimization/Data/Simulations/my_results''').
 
−
When you click to the '''start''' button, information about the calculation progress and the best (smallest) values found for the objective and penalty functions up to this time appears below the optimization method options.
 
−
</li>
 
−
</ul>
 
  
 +
We tested a computational speed of such optimization methods in BioUML as particle swarm optimization, adaptive simulated annealing, stochastic ranking evolution strategy (SRES), and cellular genetic algorithm.
 +
For this purpose, we used biochemical models with the different number of parameters and species introduced in the following test cases.
 +
Firstly, we derived three models of CD95-induced activation of caspase-8 from the model by Neumann et al. [2] with varying degrees of detail (the test cases 1A, 1B and 1C).
 +
Secondly, we took the test case proposed by Mendes et al. [3] for the MAP kinase cascade model developed by Kholodenko et al. [4] (the test case 2).
 +
Finally, we tested the model by Bagci et al. [5] representing the mitochondria-depended apoptosis (the test case 3).
 +
 +
As expected, the computational speed for all test cases directly depended on the number of parameters and species in the model.
 +
The greatest computational speed was shown by the method of particle swarm optimization.
 +
The other methods showed about the same speed for running in one core, wherease, for running in several cores, the computational speed of PSO, SRES and MOCell was evidently higher compared to the simulated annealing.
 +
 +
<font size=2>
 
<gallery>
 
<gallery>
−
File:optimization_examples_parameters_tab.png|Preparation the set of parameters to fit
+
File:optimization_examples_model_1.png|'''Test case 1A''': 7 species and 5 reaction rate parameters.
−
File:optimization_examples_experimental_data_import.png|Experimental data import
+
File:optimization_examples_model_2.png|'''Test case 1B''': 13 species and 10 reaction rate parameters.
−
File:optimization_examples_experiments_tab.png|Experiments tab
+
File:optimization_examples_model_3.png|'''Test case 1C''': 18 species and 12 reaction rate parameters.
−
File:optimization_examples_constraints_tab.png|Constraints tab
+
File:optimization_examples_model_4.png|'''Test case 2''': 8 species and 22 reaction rate parameters.
−
File:optimization_examples_simulation_tab.png|Simulation tab
+
File:optimization_examples_model_5.png|'''Test case 3''': 32 species and 57 reaction rate parameters.
−
File:optimization_examples_optimization_tab.png|Optimization tab
+
File:optimization_examples_figure_3.png|The number of objective function evaluations per second for the different test cases in BioUML.
 
</gallery>
 
</gallery>
 +
</font>
 +
 +
==References==
 +
# 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.
 +
# 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.
 +
# Mendes P., Hoops S., Sahle S., Gauges R., Dada J., Kummer U. Computational modeling of biochemical networks using COPASI. ''Methods in Molecular Biology''. 2009. 500:17–59.
 +
# Kholodenko B.N. Negative feedback and ultrasensitivity can bring about oscillations in the mitogenactivated protein kinase cascades. ''European Journal of Biochemistry''. 2000. 267(6):1583–1588.
 +
# Bagci E.Z., Vodovotz Y., Billiar T.R., Ermentrout G.B., Bahar I. Bistability in apoptosis: roles of bax, bcl-2, and mitochondrial permeability transition pores. ''Biophysical Journal''. 2006. 90(5):1546–1559.
 +
 +
</font>

Latest revision as of 12:07, 16 March 2022

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.

[edit] 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:

Optimization examples formula 1.png

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

[edit] Testing the computational speed of the optimization methods

  • 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)


We tested a computational speed of such optimization methods in BioUML as particle swarm optimization, adaptive simulated annealing, stochastic ranking evolution strategy (SRES), and cellular genetic algorithm. For this purpose, we used biochemical models with the different number of parameters and species introduced in the following test cases. Firstly, we derived three models of CD95-induced activation of caspase-8 from the model by Neumann et al. [2] with varying degrees of detail (the test cases 1A, 1B and 1C). Secondly, we took the test case proposed by Mendes et al. [3] for the MAP kinase cascade model developed by Kholodenko et al. [4] (the test case 2). Finally, we tested the model by Bagci et al. [5] representing the mitochondria-depended apoptosis (the test case 3).

As expected, the computational speed for all test cases directly depended on the number of parameters and species in the model. The greatest computational speed was shown by the method of particle swarm optimization. The other methods showed about the same speed for running in one core, wherease, for running in several cores, the computational speed of PSO, SRES and MOCell was evidently higher compared to the simulated annealing.

  • Test case 1A: 7 species and 5 reaction rate parameters.

  • Test case 1B: 13 species and 10 reaction rate parameters.

  • Test case 1C: 18 species and 12 reaction rate parameters.

  • Test case 2: 8 species and 22 reaction rate parameters.

  • Test case 3: 32 species and 57 reaction rate parameters.

  • The number of objective function evaluations per second for the different test cases in BioUML.

[edit] 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.
  3. Mendes P., Hoops S., Sahle S., Gauges R., Dada J., Kummer U. Computational modeling of biochemical networks using COPASI. Methods in Molecular Biology. 2009. 500:17–59.
  4. Kholodenko B.N. Negative feedback and ultrasensitivity can bring about oscillations in the mitogenactivated protein kinase cascades. European Journal of Biochemistry. 2000. 267(6):1583–1588.
  5. Bagci E.Z., Vodovotz Y., Billiar T.R., Ermentrout G.B., Bahar I. Bistability in apoptosis: roles of bax, bcl-2, and mitochondrial permeability transition pores. Biophysical Journal. 2006. 90(5):1546–1559.

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