How to fit kinetic law parameters to a multiple data set?

Dear Support,

I'm working with Matlab 2012a and Simbiology Desktop. Realising some experiments i got a multiple data set containing one column with the experiment ID, one logging the time and a further column displaying one substate concentration. I have realised five experiments in total verying the initial substate concentration. Due to the measurement the logged time status in each experiment is not the same for all experiments, so diplaying all substrate columns over one time column is not possible.

Now i like to fit kinetic parameters of the prebuild Ordered Bi-Bi- Kinetic Law in Simbiology (v = (Vmax*cA*cB)/(kiA*kB+cA*kB+cB*kA*cA*cB)) to my data. I chose "individual fit" Estimation Method, put the estimated parameters and selected the response column and component.

The question is, how could i fit the parameters to the whole set of data? The problem i got with this task is, that the experiments data is related to certain initial amount of the substrate component. How is it possible to use the whole data set for parameter estimation without running one fit task for each initial amount?

Selecting one initial amount i tried to fit the parameters to the corresponding experimental data. The problem here is that the fitted curve does not fit the experiental data, in other words, in the simulation result you see that the curve must be a lot steeper. Varying the inital estimate of that parameter does not have any influence. Do you have any idea what could be the problem here? Is it possible to estimate the initial component amount as well? I mean i know inital amount but for minimizing error puposes it could be helpful.

Next thing is that it looks like that is not possible to fit more than one parameter at the same time (e.g. Vmax and kA or kB and kA) because the result is utopistic and the errors much larger than estimated value. In my level of awareness it must be possible from the mathematical site. So whats wrong here?

I would be glad if you could give me some helpful advices or solutions.

Thanks!!

Answer 1

[Arthur Goldsipe]

Hi,

It is possible to estimate a single set of parameter using multiple experiments using the "individual fit" estimation method in a Parameter fit of the SimBiology Desktop. You will need to update a couple of things:

First, you need to enable the "Pool data" checkbox in the Algorithm Settings section of the task. This estimates a single set of parameters for all experiments.

Second, you need to specify how each experiment differs. In the model, set the initial concentration of substrate to 0, since the substrate will be added during estimation. Then, add a column to the experimental data to represent the amount of substrate added. For each experiment, add/edit the row for the initial time to include the amount of substrate added. If you did not collect a measurement at this time, set the measurement column to NaN. For times other than 0, set the added substrate column to NaN.

Finally, you need to configure the task to use this new information. If you haven't already done so, select the appropriate column of the data as the Group variable in the toolstrip at the top of the desktop. Then, edit the "Dosing Information" section of the task, selecting the name of the column that contains the amount of added substrate and the appropriate species of the model. The dose type should be "bolus" since the amount is added all at once.

If you use this task, you cannot directly estimate the amount of substrate used in each experiment. If you have some parameters that are the same for certain experiments but different for others, you need to use a different estimation method, such as the one labelled "population fit (NLMEFIT)."

Finally, even with these changes, you may find that the estimated parameters do not match the data well. I usually see this when the initial values for the estimated parameters are not very close to the optimal values. I would try a different set of initial values. This is basically a limitation of the gradient-based optimization methods used with such estimation problems.

To get a good guess for the initial parameter values, you may find it useful to play with the model using the Simulation Viewer. This lets you quickly adjust parameter values and see how that affects simulation results. Here's a quick overview of how to use it. View the model and click the "Simulation Viewer" button in the toolstrip. In the Simulation Viewer, click the little button to the right of "Adjust Quantity Values" and select the "Properties" menu item. Enable the checkbox next to the substrate initial concentration and the parameters you wish to estimate. Right-click the figure under "View Live Results" and make sure the substrate concentration gets plotted. Right-click the figure and select "Define external Data To Plot" if you want to overlay the experimental data. Then, adjust the parameter values to update the simulation. Keep adjusting until you find a set of parameters that approximate your experimental results.

I'm afraid that's all the detail I can go into here. But I hope that's enough to help you with your problem.

-Arthur

[Martin]

Hi Arthur,

your Answer helped me a lot analysing my data set. Going more into detailed understanding of the posibilities working with simbiology some more questions are coming up. So, do you have any advise how i could get more information about what fitting method wether individual or population could be the best for my purpose? Using population fit i will be able to get a lot more information about the fitting procedure and the goodness of fit. But in that method there are a lot of things to consider such as choosing the right error model or the right method for approximate the NLME Model Liklihood and optimization function. The data i got comes from measunring an substrate decay and the datapoints show a linear developing for the observed time course. The function describing the decay must be the one mentioned in my question above. The only thing i varied is the initial concentration of certain substrate. What i like to know is, what is the best set of methods for accomplish the parameter estimation for KiA, KA, KB, Vmax in that particular case? Do you have any recomendation or a good hint for literature?

That would be great!

Thanks a lot!