In other words, the QSS values, upon which the back-translation formulas are based, is zero.
We now turn to the problem B above: deriving back-translation formulas.
We then calculate the back-translation formulas (Step B) using Eqs.
(19 - 21 19 - 21k-trasslation formulae to compute the trajectories of the original state variables A, B, and C.
(11) and (13) can in principle be used to calculate back-translation formulae, as is demonstrated with the small example model in the next section.
The method is based on lumping of states, and includes a general and formal algorithm for both determining appropriate lumps, and for calculating the analytical back-translation formulas.
All in all, we believe that the main contribution of this paper is the introduction of the concept of back-translation, and the demonstration that it is possible to derive back-translation formulas in an automatic manner.
In particular, the method should A Automatically identify lumps in a model B Deliver analytical formulas for back-translation In this section we focus on step A, which we will sub-divide in several sub-steps, and in the next section we turn to the calculation of back-translation formulas.
To sum up the comparison between our new lumping approach and balanced truncation: the two methods perform similarly from an input-output perspective, but our novel method is much more useful in a systems biology context, since then an increased interpretability, through the lumping and the back-translation formulas, is highly advantageous.
We will now illustrate how one can use nonlinear analogues to the methodological steps introduced in this paper to derive fraction parameters, η, which again gives back-translation formulas; interestingly, the fraction parameters may also be used to easily calculate the in [ 41] obtained rate expression.
