How to encode observable which is a change from baseline?

[matthiaskoenig]

Hi all,

I have a lot of fold change data relative to baseline, i.e. time 0.
How can I encode an observable for such data?

I.e. I have a parameter p in the model and want an observable p_change = p/p[t=0]?
There is no way I could put this in an SBML model (or is there?)
The value p[t=0] is determined by pre-equilibration, i.e. not a constant p0 that I could put in the model to calculate p/p0.

These fold changes against baseline are very common in data. What is the best way to work with this in PeTab?

Best Matthias

[dweindl]

Hi Matthias,

I think in PEtab v1 this will be a bit of a hack - in PEtab v2 this will be easier.

What I could imagine could work:

Adding some pre-equilibration indicator parameter preeq_indicator.

Conditions table:

conditionId	preeq_indicator
preequilibration	1
main	0

And then have an event in the model, that triggers if preeq_indicator == 0 and has an event assignment, assigning the current value of p to some constant parameter p_0. Then you define some observable with observableFormula p / p_0.

Best
Daniel

[matthiaskoenig]

Good point. So this should work with something along the lines of:

experiments table:

experimentId	time	conditionId
timecourse_ss	-inf
timecourse_pr	-10	condition_p0
timecourse_1	0	condition_sim

conditions table:

conditionId	targetId	targetValue
condition_p0	p0	p
condition_sim	Dose	100

I.e. I would run a pre-equilibration and then assign the steady state value to the constant parameter p0. I then add a pre-simulation so I can plot my fold change (as 1.0) and compare against values in the time [-10, 0). Then I apply the changes.
I would then use the observable p_change = p/p0.

[dweindl]

If I understood your problem correctly, you can just drop timecourse_pr from the experiment table and change condition_p0 to condition_sim in the conditions table (i.e. include the assignment of p0 to condition_sim; this will be applied before the observable is evaluated at t=0).

[matthiaskoenig]

I also have data at t=-10, .... t=0 which is ~1.0 for the fold change (these are baseline measurements). I just added the additional period to test if I can handle these values also.

Perfect. This seems to work really nicely with the new timecourses.
In a similar manner I can do things such as percental change: p_pchange = (p0 - p)/p * 100 %

[JanHasenauer]

The general issue with fold change data is that even if the measurement noise distribution for p[t=0] and and p[t] is simple, the noise distribution for the ratio is rather complicated, see e.g. https://doi.org/10.1049/syb2.12055.

I would suggest to consider the use of the alternative observables y[t=0] = sp[t=0] and y[t] = sp[t] with a scaling factor s which needs to be estimated. That circumvents issue with the noise model. The scaling factor s can for many noise distributions be calculated analytically (https://doi.org/10.1093/bioinformatics/bty514). A support for this is provided in pyPESTO and we are currently considering this also for NLME models.