(formerly known as Institute of Molecular Biotechnology - IMB)


Biocomputing Group - Sühnel Lab


CombiTool - Example Applications


In the following a few example applications of CombiTool are given. They illustrate the both basic options of the program:

The experimental data were taken from a paper on the cytotoxic effect of etoposide and cis-diamminedichloroplatinum(II) (Tsai et al., Cancer Research 49, 2390-2397 (1989) [PubMed] [Journal] [PDF]).  

The data of Table 2 were used. The original data are given in % control absorbance. We have used change of % control absorbance. This means that an original value of 100% corresponds to 0 in the Table. In a few cases the control absorbances exceed 100 %. All these values have been set to 0.



cisplatin conc. /micromol
---------
etoposide conc. / micromol
0 0.0054 0.0168 0.054 0.168 0.54 1.68 5.4 16.8
0 0 0 0 0.03 0.1 0.11 0.34 0.72 0.96
0.0043 0 0 0 0 0.05 0.12 0.34 0.72
0.0136 0 0.01 0.02 0 0.06 0.09 0.32 0.78
0.043 0.06 0.09 0.09 0.1 0.12 0.17 0.42 0.75
0.136 0.14 0.16 0.22 0.16 0.21 0.25 0.44 0.79
0.43 0.34 0.37 0.43 0.38 0.42 0.45 0.54 0.81
1.36 0.55 0.57 0.58 0.58 0.6 0.61 0.63 0.84
4.3 0.76 0.76 0.73 0.78 0.78 0.76 0.74 0.88
13.6 0.76

Determination of single-agent dose-response relations

Median-effect dose-response relation E(d) = dm/(am+ dm)

We have determined the parameters a and m by means of the nonlinear regression module of the Software package Origin (OriginLab). The parameters obtained are:

 cisplatin: a = 2.72195 +- 0.2301 ; m = 1.33533 +- 0.13342 

etoposide: a = 1.19469 +- 0.17139; m = 0.73158 +- 0.0733


Comparison of calculated and experimental single-agent data

cisplatin concentration experimental effect calculated effect
0 0 0
0.0054 0 0.0002
0.0168 0 0.0011
0.054 0.03 0.0053
0.168 0.1 0.0236
0.54 0.11 0.1034
1.68 0.34 0.3442
5.4 0.78 0.7139
16.8 0.96 0.9191


etoposide concentration experimental effect calculated effect
0 0 0
0.0043 0 0.0160
0.0136 0 0.0364
0.043 0.06 0.0807
0.136 0.14 0.1694
0.43 0.34 0.3213
1.36 0.55 0.5236
4.3 0.76 0.7184
13.6 0.76 0.8556

With these parameters the expected combination effects according to the Loewe additivity or to the Bliss independence criterion can be calculated. The following Table is a direct ouput from CombiTool.

 A: cisplatin 

B: etoposide



E(EXP) experimental combination effect

E(LA) Loewe additivity combination effect

E(BI) Bliss independence combination effect

I index of interaction


CombiTool
Median Effect Function
Agent A Agent B
a 2,72195 1,19469
m 1,33533 0,73158
Dose A Dose B E(EXP) E(LA) I E(BI) E(LA)-E(EXP) E(BI)-E(EXP) E(LA)-E(BI)
0,0054000 0,0043000 0,0000000 0,0165450 #Value 0,0162803 0,0165450 0,0162803 0,0002647
0,0054000 0,0136000 0,0100000 0,0370620 6,1450650 0,0367028 0,0270620 0,0267028 0,0003592
0,0054000 0,0430000 0,0900000 0,0814260 0,8617258 0,0809841 -0,0085740 -0,0090159 0,0004419
0,0054000 0,1360000 0,1600000 0,1700970 1,1050458 0,1696286 0,0100970 0,0096286 0,0004684
0,0054000 0,4300000 0,2700000 0,3219060 1,4058944 0,3215181 0,0519060 0,0515181 0,0003879
0,0054000 1,3600000 0,5700000 0,5240230 0,7760072 0,5238023 -0,0459770 -0,0461977 0,0002207
0,0054000 4,3000000 0,7600000 0,7186300 0,7454618 0,7185535 -0,0413700 -0,0414465 0,0000765
0,0168000 0,0043000 0,0000000 0,0176580 #Value 0,0171396 0,0176580 0,0171396 0,0005184
0,0168000 0,0136000 0,0200000 0,0383470 2,4398669 0,0375442 0,0183470 0,0175442 0,0008028
0,0168000 0,0430000 0,0900000 0,0828500 0,8854120 0,0817868 -0,0071500 -0,0082132 0,0010632
0,0168000 0,1360000 0,2200000 0,1715220 0,6580689 0,1703539 -0,0484780 -0,0496461 0,0011681
0,0168000 0,4300000 0,4300000 0,3230770 0,5367144 0,3221107 -0,1069230 -0,1078893 0,0009663
0,0168000 1,3600000 0,5800000 0,5247340 0,7371194 0,5242183 -0,0552660 -0,0557817 0,0005157
0,0168000 4,3000000 0,7300000 0,7189370 0,9271314 0,7187994 -0,0110630 -0,0112006 0,0001376
0,0540000 0,0043000 0,0000000 0,0217000 #Value 0,0212535 0,0217000 0,0212535 0,0004465
0,0540000 0,0136000 0,0000000 0,0427830 #Value 0,0415727 0,0427830 0,0415727 0,0012103
0,0540000 0,0430000 0,1000000 0,0876260 0,8282214 0,0856302 -0,0123740 -0,0143698 0,0019958
0,0540000 0,1360000 0,1600000 0,1762250 1,1668571 0,1738266 0,0162250 0,0138266 0,0023984
0,0540000 0,4300000 0,3800000 0,3269070 0,7314183 0,3249481 -0,0530930 -0,0550519 0,0019589
0,0540000 1,3600000 0,5800000 0,5270540 0,7478515 0,5262098 -0,0529460 -0,0537902 0,0008442
0,0540000 4,3000000 0,7800000 0,7199370 0,6457530 0,7199764 -0,0600630 -0,0600236 -0,0000394
0,1680000 0,0043000 0,0500000 0,0376980 0,7612760 0,0393401 -0,0123020 -0,0106599 -0,0016421
0,1680000 0,0136000 0,0600000 0,0586130 0,9739744 0,0592838 -0,0013870 -0,0007162 -0,0006708
0,1680000 0,0430000 0,1200000 0,1034430 0,8227060 0,1025271 -0,0165570 -0,0174729 0,0009159
0,1680000 0,1360000 0,2100000 0,1911000 0,8627951 0,1890937 -0,0189000 -0,0209063 0,0020063
0,1680000 0,4300000 0,4200000 0,3387260 0,6381280 0,3374227 -0,0812740 -0,0825773 0,0013033
0,1680000 1,3600000 0,6000000 0,5341350 0,6995663 0,5349651 -0,0658650 -0,0650349 -0,0008301
0,1680000 4,3000000 0,7800000 0,7229840 0,6619856 0,7251510 -0,0570160 -0,0548490 -0,0021670
0,5400000 0,0043000 0,1200000 0,1115190 0,9369304 0,1177854 -0,0084810 -0,0022146 -0,0062664
0,5400000 0,0136000 0,0900000 0,1268860 1,3909794 0,1361006 0,0368860 0,0461006 -0,0092146
0,5400000 0,0430000 0,1700000 0,1647640 0,9648642 0,1758127 -0,0052360 0,0058127 -0,0110487
0,5400000 0,1360000 0,2500000 0,2434540 0,9627176 0,2553105 -0,0065460 0,0053105 -0,0118565
0,5400000 0,4300000 0,4500000 0,3778170 0,7040781 0,3915272 -0,0721830 -0,0584728 -0,0137102
0,5400000 1,3600000 0,6100000 0,5569110 0,7595653 0,5729388 -0,0530890 -0,0370612 -0,0160278
0,5400000 4,3000000 0,7600000 0,7327350 0,8283053 0,7475946 -0,0272650 -0,0124054 -0,0148596
1,6800000 0,0043000 0,3400000 0,3468530 1,0231849 0,3547762 0,0068530 0,0147762 -0,0079232
1,6800000 0,0136000 0,3200000 0,3522970 1,1172757 0,3681714 0,0322970 0,0481714 -0,0158744
1,6800000 0,0430000 0,4200000 0,3682210 0,8419231 0,3972156 -0,0517790 -0,0227844 -0,0289946
1,6800000 0,1360000 0,4400000 0,4093880 0,8976599 0,4553577 -0,0306120 0,0153577 -0,0459697
1,6800000 0,4300000 0,5400000 0,4940840 0,8364554 0,5549823 -0,0459160 0,0149823 -0,0608983
1,6800000 1,3600000 0,6300000 0,6222820 0,9642884 0,6876610 -0,0077180 0,0576610 -0,0653790
1,6800000 4,3000000 0,7400000 0,7607480 1,1435570 0,8153987 0,0207480 0,0753987 -0,0546507
5,4000000 0,0043000 0,7200000 0,7142560 0,9789986 0,7185622 -0,0057440 -0,0014378 -0,0043062
5,4000000 0,0136000 0,7800000 0,7148600 0,7709291 0,7244050 -0,0651400 -0,0555950 -0,0095450
5,4000000 0,0430000 0,7500000 0,7167410 0,8793977 0,7370737 -0,0332590 -0,0129263 -0,0203327
5,4000000 0,1360000 0,7900000 0,7224280 0,7541449 0,7624345 -0,0675720 -0,0275655 -0,0400065
5,4000000 0,4300000 0,8100000 0,7382100 0,7193573 0,8058894 -0,0717900 -0,0041106 -0,0676794
5,4000000 1,3600000 0,8400000 0,7741400 0,6910656 0,8637620 -0,0658600 0,0237620 -0,0896220
5,4000000 4,3000000 0,8800000 0,8323840 0,6824588 0,9194794 -0,0476160 0,0394794 -0,0870954

Example graphs:

The following graph was generated within CombiTool after having calculated the Table shown above. It compares the calculated Loewe additivity surface to the experimental combination effects.

Comparison of the Loewe additivity surface and experimental data

                         enlarge image (GIF, PDF)


In this graph a direct relationship between the index of interaction I and the deviation from the Loewe additivity surface is shown. The graph was generated within Origin.

Correlation between the index of interaction I and the effect difference between the Loewe additivity and experimental effects for the data set shown above

                     enlarge image (GIF, PDF)

The following graphs illustrate the capability of CombiTool to analyze three agents. The single-agent relations are of the power function type:

     E(d) = (d/a)m

Parameters:

 agent A:    a=15,      m =1.5; 

agent B: a=1, m =0.9;

agent C: a=0.00025, m =0.4.

All fixed doses have the values 400. The plot with the single-agent relations was generated with Origin, the surface plots with CombiTool.

Loewe additivity surfaces for the combination of three agents keeping the dose of one agent fixed

             enlarge image (GIF, PDF)

Here difference response surfaces are shown for Weibull single agent relations:

       E(d) = 1 - exp[-(a d)m]

Parameters:

 left plot:    aA=aB=0.02,  mA=mB=2.6 

middle plot: aA=aB=0.02, mA=mB=0.6

right plot: aA=aB=0.02, mA=1.8, mB=0.4

Difference response surfaces (Loewe additivity - Bliss independence)

             enlarge image (GIF, PDF)


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