How to use sensitivity analysis and parameter scan to contrast species

[Krutik Patel]

Dear Copasi members,

I have a fairly complex model so I will provide a simple toy model with four species which should suffice: A up-regulates D, A is down-regulated by B and C. B and C have differing levels if modulations on A. I wish to use some of COPASI's functions e.g. sensitivity analysis and parameter scans to contrast the effects of B and C on A and D.  

A -> D

B -| A

C -| A

For simplicity all initial conditions are 1, most reactions are mass action/ constant flux and all parameters are set to 0.1, except B -| A which has been set to 0.2. So in theory, B will have twice the effect than C. A->D function is M . k1, where M = A. 

Firstly, I can perform sensitivity analysis with the following specifications: Subtask - Time Series, Effect - All Variables of the model, Cause - All Parameter Values, Secondary Cause - Not Set. The unscaled B -| A and C -| A reactions were both -0.70872. The scales reactions were -0.188304 and -0.0941566 for B and C respectively. So B is clearly having a bigger effect on A. However, I cannot figure out how the scaling works, and this would be tricky for publication. Is there a formula I can use to try and calculate this? Furthermore, what do these numbers represent, i.e. are they transient values over a certain time course, or a percentage change?

Next, I want to use parameter scans to visualise the effects of modulating B and C, to show that B is the stronger down-regulator of A and D. When I try to create a new scan of [B]_0 I can see B changing but no effect on A or D. Is it possible to use COPASI's parameter scan function to see what I wish to see? 

Also, any other thoughts on how to visualise differering effects of B and C using COPASI would be welcome. 

I have added the toy .cps model to this question. 

Thanks in advance for any help. 

Krutik

[Frank Bergmann]

Hello Krutik, 

the scaled sensitivities simply multiply with the actual values of the parameters and concentrations, so the value of -0.18 is calculated by: 

      scaled_value = unscaled_value * parameter_value / concentration

what would make it perhaps clearer would be to use the steady state task, rather than to just perform a short time course. You would get the same result, if you ran a metabolic control analysis, and looked at the flux control coefficients. 

as for the visualization, maybe you can  use a scan of the reaction parameter vs the steady state concentration of A. 

Cheers

Frnak

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