Estimating chain length for time delays in dynamical systems using profile likelihood

Bioinformatics.              online article

Apparent time delays in partly observed, biochemical reaction networks can be modelled by lumping amore complex reaction into a series of linear reactions often referred to as the linear chain trick. Since most delaysin biochemical reactions are no true, hard delays but a consequence of complex unobserved processes, this ap-proach often more closely represents the true system compared with delay differential equations. In this paper, weaddress the question of how to select the optimal number of additional equations, i.e. the chain length (CL).We derive a criterion based on parameter identifiability to infer CLs and compare this method to choosingthe model with a CL that leads to the best fit in a maximum likelihood sense, which corresponds to optimizing theBayesian information criterion. We evaluate performance with simulated data as well as with measured biologicaldata for a model of JAK2/STAT5 signalling and access the influence of different model structures and data character-istics. Our analysis revealed that the proposed method features a superior performance when applied to biologicalmodels and data compared with choosing the model that maximizes the likelihood.