Basic Parameter Estimation and Singular Fisher Information Matrix

[cw00137]

Hi, 

I am attempting to model an experiment (mainly for practice in quantitatively modelling a small system before attempting to model a larger one). The experiment is simple in vitro treatment of cells with a ligand and (relative) measurement by western blot. 

My system is:

1) Fibroblast -> Collagen_I     #basal secretion of collagen by fibroblasts (i.e. [LA] = 0). Parameter = k1

2) Fibroblast + LA -> Fibroblast + LA + Collagen_I         #effect of LA on collagen secretion by fibroblasts. Parameter =k2

I'm using mass action kinetics, a fibroblast density of 1e5, an initial collagen concentration of 0 and varying the concentration of LA (0, 10, 50 and 100 uM) over 24 hours. 

My current strategy for estimating these parameters is to put the data into a tab separated text file of the form:

Time (s) Collagen_I LA

86400 1 0

86400 1.1 10

86400 1.4 50

86400 1.4 100

 

...and run the parameter estimation using time course, and collagen and LA as dependent variables to find both the basal and LA induced rate of collagen_I synthesis. The problem is that I am getting a singular fisher information matrix error. I think I understand that I need more data but I'm not clear on the matter. Could you perhaps tell me what my mistake is and possibly how to fix it?

Thanks

[Felix Winter]

Hi Ciaran (?),

If I understand your setup correctly you are trying to estimate the two
parameter values k1 and k2 based on data gathered in several independent
experiments. To do this in Copasi, you have to split the data into several files
which contain each the data from one experiment. For the example data you
provided this would look like this:

File 1:
Time Collagen_I LA
86400 1 0

File 2:
Time Collagen_I LA
86400 1.4 50

etc. ...

Then each of these files have to be added independently as experimental data.
Another thing you need to change in your current setup is the value of the
"Type" column for LA. As this seems to be the initial concentration the type is
not dependent, but independent.

These two changes should be enough to get rid of the error and start the
estimation. At least for me this does work.

Best regards, Felix

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Felix Winter
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18057 Rostock, Germany


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[Ciaran Welsh]

Yes this has worked, thank you. 

Ciaran 

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[Ciaran Welsh]

Hi Felix, 

I'm having another problem similar to the one a few days ago (i.e. singular fisher information matrix). I'd really appreciate it if you could point out what I'm doing wrong this time (I'm hoping eventually I'll be able to identify on my own when my data/model will produce a singular fisher information matrix but I'm as yet a bit inexperienced). 

I am modellling another experiment similar to the last. They treated cells with bFGF (or without) and measured PA  at various times. I have set up two reactions:

1) basal PA synthesis from BAE cells;

2) bFGF induced synthesis from BAE cells

I'm trying to estimate both parameters using time course data. I have attached a zip containing all the data and the copasi file that I am working from. Of note, the solution to the problem last time was to separate the data points into separate files. I tried that again and I still got a singular fisher matrix error. Do you know how to fix this problem. 

With thanks

Ciaran 

[Felix Winter]

Hi Ciaran,

I'm glad to hear that my previous answer was useful. The problem with the
current model seems to be the initial concentration of the BAE cells. In the
file you attached they have a very small initial concentration (1.660538783e-15)
compared to the expected concentration of the species you expect to be produced
by the two reactions (up to 3.35). If I understand your email and the data
correctly, the measurements are from species which are produced by the cells.
This would imply that the number of cells remains constant. This is something
currently not represented in your model. To keep the concentration of BAE_cells
constant, you need to the "simulation type" setting for this species to "fixed".
Right now, for each 'particle' of PA to be produced, one 'particle' of BAE_Cells
is consumed. The maximum concentration for PA which can be achieved is therefor
identical to the initial concentration of BAE_Cells.

I hope this helps.

Best regards, Felix.

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[Ciaran Welsh]

Hi Felix, 

Yes you are correct, the parameter estimation function is working correctly now (despite the model being drastically wrong apparently and not fitting the data). I naively thought setting the partical number to 1e6 would be adequate and it would have taken a long time for me to see the real problem, so thank you. 

Happy holidays. 

Ciaran 

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