How to fit steady state data in SimBiology Desktop 5.7?

I am trying to use SimBiology to fit a simple model of receptor binding, consisting of a ligand, a receptor, and a complex. The reaction uses reversible mass action kinetics. I can fit this system to time course data, but have not been able to figure out how to use steady state data to find the forward and reverse kinetic rate constants. For example, the data I am trying to fit can be simulated by the following table:

Ligand concentration (nM) | Resulting complex concentration (normalized)

       0.01               |             0.01
       0.03               |             0.05
       0.20               |             0.15
       1.00               |             0.35
       3.00               |             0.70
       11.0               |             0.85
       110                |             1.00

I have tried to estimate parameters by having a bolus of ligand "injected" and then some (long) time later reporting the normalized complex concentration. However, this results in values which do not return the initial logistic curve. I would prefer to use SimBiology Desktop as I am new to the program, but I am willing to learn how to program a model in the workspace. Any help or tips would be appreciated. Thank you!

[Florian Augustin]

Hi Nicholas,

The estimation of rate parameters from steady state data is challenging. For example, we can look at the simple mass action L <-> C with forward and backward rate parameters kf and kb. The steady state of the concentrations for L and C is the same for [kf, kb] and any multiple thereof, e.g. [2kf, 2kb]. Therefore, the rate parameters are not estimable from steady state data in this case in this case. However, your model may include other information to define those parameters from steady state data, but it's hard to tell without knowing the model.

Lastly, I might have misunderstood your question - I assume you were able to run the fit task for steady state data, just the estimated parameters returned from the fit task do not match the transient data. Please let me know if you were actually asking about how to set up the fit task.

Best,

Florian

[Nicholas Anderson]

Florian,

Thank you for the response. I understand that steady state data alone cannot determine rates for a system. I'm sorry for the confusing. I have a mixture of kinetic and steady state data that I would like to match. So, to extend the example above, I have a few kinetic data points for the system to constrain parameter values. Is there some way that I can use both of these data in the model? I have been playing around with the system and the fit task, but I can't seem to get it to work. Thanks again!

-Nick

Answer 1

[Florian Augustin]

Hi Nick,

Here is an example of a simple model with one mass action reaction, L <-> C, with initial amounts of L and C being 1 and 0, respectively. The goal is to estimate the forward, kf, and reverse, kr, reaction rate parameters from data:

    ID         TIME        LDATA     CDATA      DOSING
    '1'               0       NaN        NaN      1   
    '1'        0.056515     1.896    0.10399    NaN   
    '1'          0.2819    1.6196    0.38043    NaN   
    '1'         0.43163    1.5161    0.48388    NaN   
    '1'          2.1167    1.3346    0.66538    NaN   
    '1'           2.666    1.3336    0.66638    NaN   
    '1'              10    1.3333    0.66667    NaN   
    '2'               0       NaN        NaN      2   
    '2'              10         2          1    NaN   
    '3'               0       NaN        NaN      3   
    '3'              10    2.6667     1.3333    NaN   
    '4'               0       NaN        NaN      4   
    '4'              10    3.3333     1.6667    NaN

This table contains data for four different experiments (ID). Each experiment corresponds to a different dose (DOSING) and has different data for L and C (LDATA/CDATA). In this example, we have steady state data (at time 10) for all experiments, but transient data is only available for the first experiment. Missing or not applicable data is indicated using NaN.

I am assuming you already have the model in the SimBiology desktop. The following steps give you a high-level overview of how to set up the fit task:

In the "Data" section, choose "Import Data from MATLAB workspace..." to add the table to the task. The "Independent Variable" should be TIME and the "Group" should be ID.

Next, click on the little + in section "Estimated Parameters" and add kf and kr to the list. Since this example is well-scaled, I suggest choosing no transformation.

Next, in section "Dosing Information", enter DOSING as "Dose Column Name" and L as "Dose Component Name".

In section "Response and Error Model Information" add "Response Column Name"s LDATA and CDATA with "Response Component Name"s L and C, respectively.

Lastly, expand section "Estimation Method" and check "Pool data". This tells the fit that all of your experiments share the same parameters, i.e. you can combine data from multiple experiments to inform the estimation of the rate parameters.

Now click the "Run" button in the tool strip on the top of the Task Editor. You should obtain rate parameters [kf, kr] close to [1, 2], which I used to create the data in the first place.

I hope this helps.

Best

-Florian

[Nicholas Anderson]

Thank you Florian. This is just the help I needed!